Embeddings of nonprimary subgroups in the symmetic group $S_9$

This paper contains investigation of all nonprimary subgroups of the symmetric group $S_9$. Embedding properties of these subgroups are listed in a table. Such properties as abnormality, pronormality, paranormality, weak normality, etc. were checked with the help of a computer. Algorithms and codes of the first author were used for this purpose. The research exploits the technique of Burnside marks as well as the respective information on the table of marks of $S_9$ from the computer algebra package GAP. The subgroups were investigated up to conjugacy, the total number of conjugacy classes of nonprimary subgroups of $S_9$ is 432. Certain subgroups were additionally checked by other programs based on the double coset method.