  Classifying Hopf algebras of a given dimension is a hard and open question.
Using the generalized lifting method, we determine all finite-dimensional Hopf
algebras over an algebraically closed field of characteristic zero whose
coradical generates a Hopf algebra $H$ of dimension $16$ without the Chevalley
property and the corresponding infinitesimal braidings are simple objects in
$\HYD$. In particular, we figure out $8$ classes of new Hopf algebras of
dimension $128$ without the Chevalley property.
