Seven Great Satans

The Seven Great Satans also known as the Seven Princes of Hell make up the new rulers of the Underworld and leaders of the Devils. Originally there was only four but after the sealing of Trihexa, Sirzechs Lucifer and the other three Great Satans transformed the four Satan system into a seven Satan system in order to increase the power of the Great Satans and hopefully remove more bias from the corrupt system of the past that favored pure blooded devils. Due to one of the requirements being to remove yourself from your family, those from the new Lucifer family are not allowed to take on the Satan title Lucifer.

History
After Sirzechs, Falbium, and Serafall sealed themselves with Trihexa, Ajuka worked on creating the Seven Satan System after the completion of the first Azazel Cup, with the help of the Belial Clan, Ajuka was able to accomplish this task. Even though the system wasn't perfect, due to some devils still seeing the Bael family as the head, the new system is much better at controlling bias in the Underworld.

After the death of the last Seven Great Satans (including Issei, Sairaorg, Diehauser, and the other four) during the Second Great war and the unsealing of Trihexa, the seven strongest young devils were chosen due to their accomplishments and strength demonstrated during the Second Great War. It was revealed that five of the Great Satans were friends as teenagers and made up their own team called the "Alpha Annihilators" during the war.

Despite the changes in the number of Satans, the rule still applies that the Satans must give up their family name and status in order to become one in order to eliminate bias that they might hold told their family, because of this Lucifer clan members aren't allowed to take on the name Lucifer. Another rule was put into place that only two of the descendants of Great Satans are allowed to be the descendants of Issei Hyoudou, this is to eliminate the possibility that his descendants could dominate and take control of the current system, the two current Satans of Issei Hyoudou are the children of Rias Gremory and Akeno Himejima.