The Ars Goetia is a group comprised of seventy two demons with exemplary strength. Their great amount of power and leadership status among the lesser demons also grants each Goetia the authority to exert command over Lucifer's other forces within Hell. Lucifer himself is confident enough of the Goetia's abilities to send them out on potentially hazardous missions, such as gathering information in the Human World, fighting strong angels such as Seraphim by themselves and searching for items that would benefit the Emperor of Hell or even destroying certain things that may be an obstacle.
The Ars Goetia are not actually pure demons, but they were in actuality fallen angels that rebelled alongside Lucifer during the War in Heaven. Lucifer's respect and even care for the Ars Goetia is reflected in his manner of addressing them, often referring to them as "my dear brothers" or "my beloved fallen". While many of them are completely loyal to Lucifer, some of them are discreetly so fearful of him that they almost desire to refuse following him. Lucifer himself is known to be harsh and cruel to them should they fail in a certain task, but he is not completely without mercy as he chooses to spare them from a cruel punishment unlike Satan.
There seems to be a sort of hierarchy among the Goetia; a higher-ranked member apparently can give orders to lower-ranked members. This is evidenced with the demon Satanachia holding Aamon, Pruflas, and Barbatos as his own subordinates. When a demon of the Goetia is either summoned or tasked by Lucifer, it usually involves one or more Goetia demons operating together, with the strongest members exercising command over the others, being less powerful then they. And even then, it is also due to the status that they hold such as a Count or an Earl being under the command of a Marquis.
While the Ars Goetia appear to constantly gather in Hell's council to discuss certain events alongside their lord Lucifer, they can have their own quarters within Hell, which ranges from castles, underground fortresses, or even a seperate dimension that is teathered to Hell. These palaces are modified to suit the specific Goetia demon's taste.