Maximal $ extrm {PSL}_2$ Subgroups of Exceptional Groups of Lie Type

With a few possible exceptions, the authots prove that any almost simple group with socle PSL2(pa), that is maximal inside an almost simple exceptional group of Lie type F4, E6, 2E6 and E7, is the fixed points under the Frobenius map of a corresponding maximal closed subgroup of type A1 inside the algebraic group.