First and foremost, there is no such thing as "LaVeyan Satanism", despite what wikipedia says. There is only Satanism, as in the religion and philosophy codified by Anton LaVey. Before that nobody used the terms "Satanist" or "Satanism". "and lord knows, I looked!". - Dr. LaVey
Second, Satanism doesn't need to be broken down. Satanism is what it is. Its tenets and structure are simple, straightforward and to the point. No need for complexity.
Wish me luck...