Radical subgroups of the finite exceptional groups of Lie type E6

We consider the finite exceptional groups of Lie type E-6(+1) (q) = E-6(q) and E-6(-1) (q) = E-2(6)(q), both the universal versions. We classify, up to conjugacy, the maximal p-local subgroups and radical p-subgroups of G = E-6(epsilon)(q) for p >= 5 with p inverted iota q and q = epsilon mod p, and for p = 3 with 3 inverted iota q and q = -epsilon mod 3. As an application, the essential p-rank of the Frobenius category. F-D (G) is determined, where D is a Sylow p-subgroup of G. Moreover, if p = 3, then we show that there is a subgroup H = F-4 (q) of G containing D such that F-D (G) = F-D (H), that is, H controls 3-fusion in G. (C) 2014 Elsevier Inc. All rights reserved.