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) > ½ 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 (E6ε(q), F4(q)), (E6ε(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.