An Example of a Relatively Maximal Nonpronormal Subgroup of Odd Order in a Finite Simple Group

We prove the existence of a triple (X,G,H) , where X is a class of finite groups consisting of groups of odd order which is complete (i.e., closed under subgroups, homomorphic images, and extensions), G is a finite simple group, H is an X -maximal subgroup in G , and H is not pronormal in G .