TL;DR: In this paper, the subgroup embedding properties for 110 subgroups of the symmetric group of degree 8 were studied and the results were obtained by using of the computer algebra system GAP.
Abstract: The paper is devoted to studying some subgroup embedding properties for 110 subgroups of the symmetric group of degree 8. We deal with those nonprimary subgroups whose degree is exactly eight. The results were obtained by using of the computer algebra system GAP. They are summarized in a table. It was found that every polynormal subgroup is also paranormal. Bibliography: 12titles.