Maximal von Neumann subalgebras arising from maximal subgroups

Ge asked the question whether $LF_{\infty}$ can be embedded into $LF_2$ as a maximal subfactor. We answer it affirmatively by three different approaches, all containing same key ingredient: existence of subgroups with infinite index. also show that point stabilizer for every faithful, 4-transitive action on an set give rise to von Neumann subalgebras. Combining this known results constructing highly transitive actions, we get many subalgebras arising from