Maximal 2-local subgroups of E7(q)

Abstract Let G = E 7 ( q ) be the finite exceptional group of Lie type (universal version). We classify, up to conjugacy, all maximal-proper 2-local subgroups of G , that is, all 2-local M G which are maximal with respect to inclusion among all proper subgroups of G which are 2-local. For this purpose, we first determine, up to conjugacy, all elementary-abelian 2-subgroups of G containing the center Z ( G ) . These classifications are an important first step towards a classification of the 2-radical subgroups of G .