On the heritability of the Sylow π-theorem by subgroups

Let π be a set of primes. We say that the Sylow π-theorem holds for a finite group G, or G is a Dπ-group, if the maximal π-subgroups of G are conjugate. Obviously, the Sylow π-theorem implies the existence of π-Hall subgroups. In this paper, we give an affirmative answer to Problem 17.44, (b), in the Kourovka notebook: namely, we prove that in a Dπ-group an overgroup of a π-Hall subgroup is always a Dπ-group.