  In this paper, we determine the finite groups with a Sylow $r$-subgroup
contained in a unique maximal subgroup. The proof involves a reduction to
almost simple groups, and our main theorem extends earlier work of Aschbacher
in the special case $r=2$. Several applications are presented. This includes
some new results on weakly subnormal subgroups of finite groups, which can be
used to study variations of the Baer-Suzuki theorem.
