I'm searching for (a class of) examples of Hopf algebras , which have the following properties:

they should be finite dimensional

they should not be semisimple

they should be local

they should not be symmetric (or if this is not possible, weaken the condition to:

they should not be Morita equivalent to local blocks of group algebras)

Note that a finite dimensional Hopf algebra is always selfinjective and a class of examples of local selfinjective nonsemisimple finite dimensional Hopf algebras are the group algebras of p-groups over a field of characteristic p ( but they are symmetric).