Simple non abelian group with $D_\pi$ Schmidt subgroups

Let $G$ be a finite simple group, $S$ be its Hall Schmidt $\pi$-subgroup. If $2\in\pi$ then $G$ is not a $D_\pi$-group. If $2\notin\pi$ and $G\notin\{A_n(q),^2 A_n(q)\}$ then $G$ is a $D_\pi$-group.