The Four Satanic Crown Princes of Hell

While all of the infernal names are said to reside in the Royal Palace of Hell, four are set apart as being particularly powerful. These are known to LaVeyan Satanists as the crown princes of Hell.

Each prince is associated with a cardinal direction: north, south, east and west. This is in line with other Western magical practices that commonly associate supernatural beings with the cardinal points. Specifically, ceremonial magic has commonly ascribed the four Biblical archangels—Michael, Raphael, Uriel, and Gabriel—to the four directions for several hundred years.

In the Satanic Bible, Anton LaVey also associates each prince with one of the four physical elements: fire, earth, air, and water. This is again a common practice in Western magical traditions.

Satan

Satan is a Hebrew term meaning "adversary." Unlike the common Christian view of Satan as opposing the will of God, in his original context, Satan was a servant of God. He tested the faith of God's followers by being adversarial toward them, tempting them to stray from God's path or denounce him in their moments of misery.

For Satanists, he is:

"The adversary of: mundanity, mediocrity, right hand path, stupidity, conformity for the sake of conformity, self destruction, religion, gods."
—The Aspect of Satan, Vexen Crabtree

He is associated in the Satanic Bible with the element of fire and the south.

Lucifer

The Book of Isaiah addresses the Babylonian king by a phrase that translates roughly to "Day Star, Son of the Dawn." When Christians translated the passage into Latin, the term was rendered as Lucifer. This literally means "morning star," and it came to erroneously be considered a proper name.

There is nothing in Isaiah that associates Lucifer with Satan, but the imagery of Lucifer as a fallen angel struck a chord with Christians. The association of Lucifer with Satan was further cemented in the Christian mind by works such as Dante's Divine Comedy and Milton's Paradise Lost.

The Satanic Bible celebrates the original meaning of the name, describing Lucifer as the "bringer of light, enlightenment," (p. 57) and associating him with air and the east. He is a person's inner light, which society attempts to drag into the darkness of conformity.

It is important to note that Luciferians have a slightly different view of Lucifer.

Belial

The Hebrew term Belial is generally translated to mean "without worth," although the "Satanic Bible" uses a less often used translation "without a master." In the New Testament, the term is used as a synonym for Satan. He is also frequently associated with sex, lust, confusion, and darkness.

The "Satanic Bible" also associates Belial with independence, the earth, and the north, the direction of darkness.

Earth is the element of grounding and realism. It keeps people's feet on the ground rather than having their head in the clouds, confused by self-deceit and external influence. Earth is also commonly associated with fertility and thus with sex and lust, referring back to the common Christian understanding of Belial. 

Leviathan

The Books of Psalms, Job, and Isaiah all mention a great sea creature called Leviathan. In these texts, Leviathan is monstrous but not demonic, as Christians often understand the beast to be. Leviathan may also have its origins in Tiamat and Lotan, both monstrous Mesopotamian creatures that sow chaos and are eventually slain by hero-gods.

For Satanists, Leviathan is:

"A great sea monster, sexual desire, from out of the unknown and feared depths. The hidden truth; the hidden and horrible nature of existence and struggle. A great, powerful creature that continually gathers strength to attack all the world's religions. An unstoppable force from within man." —Leviathan Aspects, Vexen Crabtree

Unsurprisingly, Leviathan is associated with water and the west.