Subgroup Embeddings in the Symmetric Group of Degree Nine

This paper is devoted to the determination of embedding properties of all nonprimary subgroups of the symmetric group on nine letters and continues previous investigations of the authors. The above-mentioned subgroups were tested for the following properties: abnormality, pronormality, paranormality, their weak analogs, weak normality, and the subnormalizer condition. The technique of Burnside marks, as well as respective information on the table of marks of from the TOM library of the computer algebra package GAP (Groups, Algorithms and Programming), were used. The subgroups of prime-power orders were not considered, because many of the above-mentioned concepts coincide for such subgroups. The total number of subgroups considered turned out to be 432. Bibliography: 18 titles.