A survey of maximal subgroups of exceptional groups of Lie type

Let G be a simple algebraic group of exceptional type G2, F4, E6, E7 or E8 over an algebraically closed field K of characteristic p. The analysis of maximal subgroups of exceptional groups has a history stretching back to the fundamental work of Dynkin [3], who determined the maximal connected subgroups of G in the case where K has characteristic zero. The flavour of his result is that apart from parabolic subgroups and reductive subgroups of maximal rank, there are just a few further conjugacy classes of maximal connected subgroups, mostly of rather small dimension compared to dimG. In particular, G has only finitely many conjugacy classes of maximal connected subgroups.

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