In early Judeo-Christian writings, there are generally a group of seven known archangels:
In the earliest Christian writings, the seven are noted as: Michael, Gabriel, Raphael, Uriel, Chamuel, Jophiel, and Zadkiel.
As said earlier, Michael, Gabriel, Raphael, and Lucifer are effectively out of the picture. Uriel is dead. The Angel Joshua, who his the caretaker of The Garden, seems to have powers associated with that of Chamuel.
Jophiel is believed to be the archangel who drove Adam and Eve from the garden and responsible for guarding the Tree of Life, but the name has not surfaced in the show. Both Jophiel and Zadkiel appear to be subservient to Michael, but are still considered to be archangels.
In slightly later Christian writings, a slightly different set of archangels are named: Gabriel, Michael, Raphael, Uriel, Simiel (aka Satan), Oriphiel and Zachariel
In early Jewish writings (which aren't officially recognized by Jewish or Christian traditions), seven also appear: Gabriel, Michael, Raphael, Uriel, Raguel, Remiel and Saraqael.
Roman Catholic tradition recognizes only three archangels: Gabriel, Michael and Raphael. (All other named angels were officially invalidated in 2002, because the book that named them was not officially included in The Bible)
Eastern Orthodox tradition recognizes seven archangels: Gabriel, Michael, Raphael, Uriel, Selaphiel, Jegudiel, and Barachiel. (Eastern Orthodox tradition officially recognizes the book that the Roman Catholic tradition does not).
In Anglican and Episcopal tradition, there are four archangels recognized: Gabriel, Michael Raphael, and Uriel.
Depending on which religious traditions or writings the writers of the show chose to run with, there could potentially be up to seven archangels (or more if the writers chose to recognize all the named archangels that show up in the various religious traditions)