Aschbacher's Component Theorem

Suppose that $E(G)$ (the commuting product of all components of $G$) is Simple and $G$ contains a Semisimple Involution. Then there is some Semisimple Involution $x$ such that $C_G(x)$ has a Normal Subgroup $K$ which is either Quasisimple or Isomorphic to $O^+(4,q)'$ and such that $Q=C_G(K)$ is Tightly Embedded.

See also Involution (Group), Isomorphic Groups, Normal Subgroup, Quasisimple Group, Simple Group, Tightly Embedded