Let F denote a saturated formation. In this paper we study some properties of F-hypercentrally embedded subgroups, i.e., those subgroups T of a finite group G such that every chief factor of G between its core and its normal closure is F-central in G. We prove that these subgroups form a sublattice of the lattice of all subgroups of G, if F is subgroup-closed. The main result of the paper is the following: if F contains the class of nilpotent groups and G is a soluble group, a subgroup T which permutes with all Sylow subgroups of G is F-hypercentrally embedded in G if and only if T permutes with some F-normalizer of G.