Embedding properties of non-primary subgroups of the symmetric group of degree eight

The paper is devoted to investigation of some subgroup embedding properties for 110 subgroups of the symmetric group on eight letters. We deal with those non-primary subgroups whose degree is exactly eight. The results were obtained by using of the computer algebra system GAP. They are summarized in a form of the table. We found out that every polynormal subgroup is at the same time also paranormal.