Finite groups with local covering p-subgroups

A subgroup [Formula: see text] of a finite group [Formula: see text] is called a local covering subgroup of [Formula: see text] if [Formula: see text] for all maximal [Formula: see text]-invariant subgroups [Formula: see text] of [Formula: see text]. In this note, we characterize the finite groups [Formula: see text] in which all subgroups of order [Formula: see text] enjoy the local covering property, where [Formula: see text] is a prime power with [Formula: see text].