Since magick is subjective and everybody has their own assho…OPINION, i’m going to leave my hierarchy here, for the world to argue over and/or ignore entirely.
The 4 Elemental Kings (the Royal Stars)
West: Bayemon aka Paimon (Antares aka alpha Scorpii).
South: Egym, or Belzebuth? (Fomalhaut aka alpha Piscis Austrinis).
East: Magoa aka Magot (Aldebaran aka alpha Tauri).
North: Amaymon (Regulus aka alpha Leonis).
The 7 Planetary Rulers (Kings of the Days Of The Week), with their Servitors given under political units. The Kings aren’t named in Goetia, but you can find their names listed in a variety of other grammars, such as the Grimoirium Verum, Grimoire of Pope Honorius, and others.
Lucifer rules Monday. Monday represents the astrological element of Water (Cancer). Under Lucifer are the Marquises (Samigina, Amon, Leraje, Naberius, Ronove, Forneus, Marchosias, Phenex, Sabnock, Shax, Orias, Andras, Andrealphus, Cimeies, and Decarabia).
Frimost rules Tuesday. (From what i gather, Frimost may either be Belzebuth and/or Egyn, or in some traditions is replaced by them.) Tuesday represents the planet Mars, and also the astrological elements of Fire (Aries) and Water (Scorpio). Under Frimost are the Earls, or Counts (Botis, Marax, Glasya-Labolas, Ronove, Furfur, Halphas, Raum, Vine, Bifrons, and Andromalius).
Astaroth rules Wednesday. Wednesday represents the planet Mercury, and also the astrological elements of Air (Gemini) and Earth (Virgo). Under Astaroth are the Presidents (Marbas, Buer, Botis, Marax, Glasya-Labolas, Foras, Gaap, Malphas, Haagenti, Caim, Ose, Amy, Zagan, and Valac).
Silcharde rules Thursday. Thursday represents the planet Jupiter, and also the astrological elements of Water (Pisces) and Fire (Sagittarius). Under Silcharde are the Princes aka Prelates (Vassago, Sitri, Ipos, Gaap, Stolas, Orobas, Seere).
Bechard rules Friday. Friday represents the planet Venus, and also the astrological elements of Earth (Taurus) and Air (Libra). Under Bechard are the Dukes (Agares, Valefor, Barbatos, Gusion, Eligos, Zepar, Bathim, Sallos, Aim, Bune, Berith, Astaroth, Focalor, Vepar, Vual, Crocell, Alloces, Murmur, Gremory, Vapula, Haures, Amdusias, and Dantalion).
Guland rules Saturday. Saturday represents the planet Saturn, and also the astrological elements of Air (Aquarius) and Earth (Capricorn). Under Guland is the Knight Furcas.
Surgat rules Sunday. Sunday represents the Sun, and also the astrological element of Fire (Leo). Under Surgat are the Kings (Bael, Paimon, Beleth, Corson, Asmoday, Vine, Balam, Zagan, and Belial).
The Ars Goetia division makes perfect sense when the Kings of the Day are given in order. Lucifer rules over the other 6 kings, who split into two columns of 3: Wednesday, Friday, and Sunday (days of Mercury, Venus, and the Sun), and Tuesday, Thursday, and Saturday (days of Mars, Jupiter, and Saturn).
It would only mke sense to conjure the proper elemental king, then Lucifer, then the King of the Day you want, and finally the spirit of Ars Goetia you want to contact.
This puts the entire conjuration under a strict chain of command. This i feel would be the proper way of conjuring a spirit without resorting to the Spirits’ Chain or other such foolery put in the grammars that would only end up getting you fucked up if you were stupid enough to try that shit.
The idea of spirit rulers over spirit armies and hierarchies also extends to Afro-Caribbean traditions such as Haitian Vodou, Cuban Palo, and Brazilian Quimbanda, so it’s a legit way of doing the work.
Finally, the spirit layout given in Ars Goetia has no seeming link to the idea of putting Goetia spirits under the decans opposite the spirits of Shemhamphorash. I don’t see the connection in any way, sorry.