The fixed group is distributed one to each element, like the other two. Taurus is earth, Leo fire, Scorpio water and Aquarius air, and the polarity alternates as it does everywhere else in the zodiac, so Taurus and Scorpio carry the receptive charge and Leo and Aquarius the active one.
What that distribution means in practice is that fixity is not a single flavour. Fixed earth holds a possession, fixed fire holds a position, fixed water holds a feeling and fixed air holds an opinion, and the four are not interchangeable in a reading. The tradition's descriptions of the individual signs carry that distinction and the modal summary does not, which is a general reason to treat the three qualities as one axis of a sign's definition rather than as its character.
The four also stand opposite one another in two pairs, Taurus against Scorpio and Leo against Aquarius, and every sign of a given quality is either opposite or square to every other sign of that quality. That geometry is why the qualities matter structurally: a chart with several planets in fixed signs will usually have them in hard aspect to one another, so the mode is a shorthand for a pattern of tension as well as a description of temperament.
Modern astrology adds the fixed grand cross and reads it for stalemate and endurance, which is a twentieth century elaboration of the same geometry rather than a doctrine drawn from the older sources.