One of history's most famous exorcists, Father Sebastien Michaelis, described the ranking of devils in his Admirable History (1612).
He also noted the sins of which each is in charge:

Fallen angels of the first sphere - namely the Seraphim, Cherubim and Thrones.

Seraphim:
The Devil: Lucifer
Beelzebub was Prince of the Seraphim, and next after Lucifer. And the chief of the nine choirs of angels are fallen. Of the choir of Seraphim there fell at first Lucifer, Beelzebub and Leviathan, who did all revolt. Michael was the first that resisted Lucifer, and the rest of the "good" angels followed him and so he is now the chief among them.
Leviathan is the prince of the same order, and is the ringleader of the heretics, tempting men with sins that are directly repugnant unto faith.
Asmodeus is of the same order. He continues as a Seraphim to this day, that is, he burns with the desire to tempt men with his wine of luxuriousness, and is the prince of the wantons.
Abaddon
Samael
Semyazza was a Grigori (meaning "Watchers" in Greek), a group of fallen "sons of God" who descended upon the earth to mate with human females. The Grigori were bound to the earth during the Great Flood as punishment for their fall.

Balberith is Prince of the Cherubim. He tempts men to commit homicides, and to be quarrelsome, contentious, and blasphemous.
Azazel
Lauviah
Marou
Salikotal

Astaroth, Prince of the Thrones, is always desirous to sit idle and be at ease. He tempts men with idleness and sloth.
Verrine is also one of the Thrones and is next in place after Astaroth. He tempts men with impatience.
Gressil is the third in the order of Thrones. He tempts men with impurity and uncleanness.
Sonneillon is the fourth in the order of Thrones. He tempts men with hatred against their enemies.
Focalor
Forneas
Murmur
Nelchael
Pruflas
Raum

Carreau, Prince of Powers. He tempts men with hardness of heart.
Carnivean is also a Prince of Powers. He tempts men to obscenity and shamelessness.
Oeillet is a Prince of Dominions. He tempts men to break the vow of poverty.
Rosier is the second in the order of Dominions. He tempts men to fall in love.
Verrier is Prince of Principalities. He tempts men against the vow of obedience.