Subroups normalized by the commutator subgroup of the Levi subgroup

We describe subgroups of the unipotent radical of a maximal parabolic subgroup of a Chevalley group over a field normalized by the commutator subgroup of the Levi subgroup over a field $K$. It is shown that in the typical case such subgroups are in one-to-one correspondence with the closed subsets of $\{1,2,\dots,n\}$ for a natural $n$. In the exceptional cases the classification also involves additive subgroups of $K$. See the table in the paper for a detailed list of the possibilities.