Geodesic
Examples of Nonpronormal Relatively Maximal Subgroups of Finite Simple Groups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 4, pp. 140-145

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Using R. Wilson's recent results, we prove the existence of triples $(\mathfrak{X},G,H)$ such that $\mathfrak{X}$ is a complete (i.e., closed under taking subgroups, homomorphic images, and extensions) class of finite groups, $G$ is a finite simple group, and $H$ is its $\mathfrak{X}$-maximal subgroup nonpronormal in $G$. This disproves a conjecture stated earlier by the second author and W. Guo.
Keywords: complete class of groups, relatively maximal subgroup, pronormal subgroup, finite simple group. 
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B. Li; D. O. Revin. Examples of Nonpronormal Relatively Maximal Subgroups of Finite Simple Groups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 4, pp. 140-145. http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a11/