Ultrasolvable covering of the group $Z_2$ by the groups $Z_8$, $Z_{16}$ and $Q_8$

We construct infinite series of non-trivial ultrasolvable embedding problems with cyclic kernel of order $8,16$ and quaternion kernel of order $8$. Moreover, we discover $2$-local non-split universally solvable embedding problems of a quadratic extension into a Galois algebra whose kernel is generalized quaternion or cyclic.