MAXIMAL SUBGROUPS OF LARGE RANK IN EXCEPTIONAL GROUPS OF LIE TYPE

Let G = G(q) be a finite almost simple exceptional group of Lie type over the field of q elements, where q = pa and p is prime. The main result of the paper determines all maximal subgroups M of G(q) such that M is an almost simple group which is also of Lie type in characteristic p, under the condition that rank(M) > 1 2 rank(G). The conclusion is that either M is a subgroup of maximal rank, or it is of the same type as G over a subfield of Fq, or (G,M) is one of (E 6(q), F4(q)), (E 6 (q), C4(q)), (E7(q), 3D4(q)). This completes work of the first author with Saxl and Testerman, in which the same conclusion was obtained under some extra assumptions.