There are few formal denominations of Satanism outside of the USA, and instead, a gradual series of local groups rise and fade, lasting only a few years each, and based on individual personalities. The central Church of Satan was the first and is by far the largest and most stable. There is also the Temple of Set, First Satanic Church and in more modern times, The Satanic Temple, who are a political lobbying group simply using Satanic imagery to further their aim, often intentionally entertainingly. Most denominations collapse within a few years. There are a few tiny denominations that promote indefensibly extremist far-right ideology. Most Satanists don't follow any particular organisation, and so, aside from a small number who (normally temporarily) attach to one of the more difficult groups, denominations are not of much significance to those who are valuating individual Satanists.
Some theologies and theories place Satan as a saviour and a defender of righteousness, and the white light God as an evil oppressor. Most common is the acceptance of Satan as a "true" correct symbol used to represent crisp reality, with God as the negative symbol of delusion. Satanic religions hold to this idea even if they lack the actual belief in a real god or Satan. These are common themes in Satanic music, and are also present in nearly all schools of thought that are labelled as Devil Worship. Some ancient Gnostic religions also hold that the good-seeming god is evil, whereas there are other more obscure good forces in life.
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Founded in USA in 1966CE by Anton Szandor LaVey. A philosophy of elitism, self-development and self-interest with few set ethics. The COS was the first organised representation of Satanism; indeed, before then, there was no such thing as Satanism except for Christian devil worshippers. It is criticized for its contradictory nature: how can an individualistic religion of dissenters have a representative organisation? The answer is that the COS grants its members full freedom and autonomy and members join for personal reasons, to feel good1. Most Satanists are LaVeyan but do not join the COS. Of all the multiple denominations of Satanism that have arisen since the COS was founded, the COS is the only organisation to stand the test of time, and it remains an enigmatic but slow-moving source of inspiration for 'those who carry the red card'.
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Founded in USA in 1975CE by Michael A. Aquino2,3. Theistic Satanism. Policy is that it is undecided whether or not Set is a real supernatural entity or not. Aquino argues that Anton LaVey's The Satanic Bible was supernaturally inspired4, but he didn't like the way the COS came to handle new members and promotions, and he left in 1975 to found his own church, the TOS3, and wrote The Book of Coming Forth by Night which was "structured as a statement by the Egyptian god Set... to continue the work started in the Church of Satan"3. The Egyptian element has become the primary element of the TOS and academics question why it is still called 'Satanism'5.
The ToS has been registered as a tax-exempt church in the USA since its founding. A 1995 survey of membership in the UK by researcher Graham Harvey, which Michael Aquino personally encouraged members to fill out, revealed that members had a similar life profile to national averages in terms of employment, sexuality and voting habits, with no signs of extremism, although most were male. However, there were only 11 responses to base the analysis on2.
“[It looks like] there are less than one hundred such Satanists in the UK [although] we should not imagine a gathering of fifty ToS Satanists for whatever purposes. Jean La Fountaine reports that "according to one former member I spoke to who attended several meetings, they never assembled more than about twelve members". As with [the] CoS, the ToS encourages individualism, not congregationalism. Members... rarely meet.”
"Satanism: Performing Alterity and Othering"
Graham Harvey (2009)2
Founded in UK in the 1980s. Theistic Satanism, secretive. There was a period of prolific activity around the year 2000, but, it appears that the bulk it was all a single person, writing under multiple pseudonyms. Associated with some very problematic ideas and far-right extremism.
“[Some] Satanist groups... are small even when they seem to have a larger presence. The Order of the Nine Angels (ONA) is a good example. A prolific author who uses several different pen-names (e.g. Anton Long, Stephen Brow and Christos Beest) has developed a form of Satanism that is distinguishable by the complexity of its cosmology and by its assertion of the need to be sinister. The former, however, elaborates ideas that are common ground to many esotericists and to sci-fi films and books (e.g. that the everyday world is not the only dimension of reality), while the latter is almost certainly the presentation of a face designed to shock.”
"Satanism: Performing Alterity and Othering" by Graham Harvey (2009)6
Founded in USA in 1999CE by Karla LaVey. Created by Lavey's daughter as a protest against Barton's leadership and the moving of the Church of Satan headquarters to New York. The First Satanic Church are centered solely in San Francisco, USA, and have little activity aside from running an annual black mass plus Karla LaVey's radio shows where she plays music from her father's era, plus some other stereotyped iconoclasts who also feature on the Black Masses.
Local Satanism each has its own shades of cultural understandings of theological, philosophical and societal concepts. For example, Satanists in Scandinavia have wilder (more colourful) and more subdued (inconspicuous) appearances than the goths of the USA and the UK. As Satanism was versed in the social and political language of the USA which often means it applies poorly elsewhere, the social and political elements appropriate to Satanism elsewhere is often different in terms of suitable theory, nuance and style.
“For example throughout Scandinavia Satanists are much more likely to call LaVeyan Satanism a 'philosophy', but in the USA where religiosity is much higher overall, Satanists proclaim a religion of Satanism.”
Didrik Søderlind and Asbjørn Dyrendal (2009)7
But despite a few specific differences, American and Scandinavian Satanism still mostly look the same7.
As a movement of individualists and counter-cultural mavericks, it is fair to assume that most Satanists ponder forming their own movement, with their own horde of enthusiastic acolytes ready to listen to their thoughts. So, the first denominations sprung from the Church of Satan very early in its life.
“The Church of Satanic Brotherhood was formed [in 1973] by group leaders in Michigan, Ohio and Florida. This Church lasted only until 1974, when one of the founders announced his conversion to Christianity in a dramatic incident staged for the press in St. Petersburg. Other members of the Church of Satan in Kentucky and Indiana left to form the Ordo Templi Satanis, also short lived.”
"Infernal Legitimacy" by James R. Lewis (2009)8
The vast majority of sects and spinoffs only make a local stir, and very few last more than a few years. Local groups are dominated by a single personality who pulls it together and (possibly) arranges some real-life meetings, and online ones tend to form around debates, nearly always, these are debates about the Church of Satan.