Finite groups with only 𝔉 {\mathfrak{F}} -normal and 𝔉 {\mathfrak{F}} -abnormal subgroups

Let G be a finite group, and let {\mathfrak{F}} be a class of groups. A chief factor {H/K} of G is said to be {\mathfrak{F}} -central (in G) if the semidirect product {(H/K)\rtimes(G/C_{G}(H/K))\in\mathfrak{F}} . We say that a subgroup A of G is {\mathfrak{F}} -normal in G if every chief factor {H/K} of G between {A_{G}} and {A^{G}} is {\mathfrak{F}} -central in G and {\mathfrak{F}} -abnormal in G if V is not {\mathfrak{F}} -normal in W for every two subgroups {V<W} of G such that {A\leq V} . We give a description of finite groups in which every subgroup is either {\mathfrak{F}} -normal or {\mathfrak{F}} -abnormal.