Semipermutable subgroup

In mathematics, in algebra, in the realm of group theory, a subgroup formula_1 of a finite group formula_2 is said to be semipermutable if formula_1 commutes with every subgroup formula_4 whose order is relatively prime to that of formula_1.
Clearly, every permutable subgroup of a finite group is semipermutable. The converse, however, is not necessarily true.