On families of hopf algebras without the dual Chevalley property

Let k[double-struck] be an algebraically closed field of characteristic zero. We construct several families of finite-dimensional Hopf algebras over k[double-struck] without the dual Chevalley property via the generalized lifting method. In particular, we obtain 14 families of new Hopf algebras of dimension 128 with non-pointed duals which cover the eight families obtained in our unpublished version, arXiv:1701.01991 [math.QA].