Geodesic
Ultrasolvable covering of the group $Z_2$ by the groups $Z_8$, $Z_{16}$ and~$Q_8$
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 28, Tome 435 (2015), pp. 47-72

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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. 
@article{ZNSL_2015_435_a3,
     author = {D. D. Kiselev},
     title = {Ultrasolvable covering of the group $Z_2$ by the groups $Z_8$, $Z_{16}$ and~$Q_8$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {47--72},
     publisher = {mathdoc},
     volume = {435},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_435_a3/}
}
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D. D. Kiselev. Ultrasolvable covering of the group $Z_2$ by the groups $Z_8$, $Z_{16}$ and~$Q_8$. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 28, Tome 435 (2015), pp. 47-72. http://geodesic.mathdoc.fr/item/ZNSL_2015_435_a3/