There has been a lot of systematic study in recent decades of the maximal subgroups of
finite simple groups, especially groups of Lie type. This goes far beyond the
special case here, but is written down in modern language. One standard
reference (though no longer readily accessible outside libraries) is a monograph: MR1057341 (91g:20001)
Kleidman, Peter(1-PRIN); Liebeck, Martin(4-LNDIC),
The subgroup structure of the finite classical groups.
London Mathematical Society Lecture Note Series, 129. Cambridge University Press, Cambridge, 1990. x+303 pp. ISBN: 0-521-35949-X
20-02 (20D06 20G40). This builds on earlier work by M. Aschbacher and others.
(Kleidman left a position at Caltech to enter the financial world, but Liebeck
has remained active at Imperial College, London). John Cullinan (now at Bard College), a recent Ph.D. student here
in number theory, found Kleidman-Liebeck especially helpful for
the special cases in his thesis.
There may be some overlap between that work and what you are studying: MR2314732 (2008b:14077) 14K15 (11G10)
Cullinan, John (1-BARD)
Local-global properties of torsion points on three-dimensional abelian varieties. J. Algebra 311 (2007), no. 2, 736–774.

For a useful survey as of
1987: MR933365 (89c:20029) 20D05 (20E28)
Seitz, Gary M. (1-OR),
Representations and maximal subgroups.
The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986), 275–287,
Proc. Sympos. Pure Math., 47, Part 1, Amer. Math. Soc., Providence, RI, 1987.