  We provide a parameterization of all fusion subcategories of the
equivariantization by a group action on a fusion category. As applications, we
classify the Hopf subalgebras of a family of semisimple Hopf algebras of
Kac-Paljutkin type and recover Naidu-Nikshych-Witherspoon classification of the
fusion subcategories of the representation category of a twisted quantum double
of a finite group.
