Thompson subgroups and large abelian unipotent subgroups of Lie-type groups

Let $U$ be a unipotent radical of a Borel subgroup of a Lie-type group over a finite field. For the classical types the Thompson subgroups and large abelian subgroups of the group $U$ were found to the middle 1980's. We complete a solution of well-known problem of their description for the exceptional Lie-types.