The Labyrinth's constitution says "Through their ichor each god is allowed to leave a living legacy in the realm.", and Nemesis herself says 17 gods were involved in the constitution's creation: The 12 Olympians, Hestia, Hades, Nemesis and her sisters.
Presumably the 6 of the 7 beasts are the legacies of Zeus/Athena/Demeter/Ares/Artemis/Apollo (Hermes said The Effigy was a weird one, and Nikos describes it as being forged by the gods rather than just one, so I'm not sure where this one falls) , while the wine/basin/mirror/parting gift/Asphodel meadow are the legacies of Dionysus/Hermes/Hestia/Poseidon/Hades.
Which leaves Hera/Hephaestus/Aphrodite/Nemesis&co unaccounted for.
Hephaestus would make sense for the Effigy I suppose Aphrodite would as well but eh , although we don't have his opinion on the labyrinth's creation so it's hard to say if he actually would, or why.
I'm inclined to think Nemesis' fragment (probably along w/ her sisters) serve(s) as the Labyrinths mind(s)
(Sidenote, but I'm betting the mystery tab in the files is for the godly fragments)