Subgroups of the unipotent radical of a maximal parabolic subgroup of a Chevalley group over a field K, which are normalized by the commutator subgroup of the Levi subgroup, are described. It is shown that in the typical case, such subgroups are in one-to-one correspondence with the closed subsets of {1, 2, ..., 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 possibilities. Bibliography: 7 titles.