Finite Group DatabasebetaFinite Group DatabasebetaOrder 7533.
100 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | (C31⋊C9)⋊C9 | C3 | 1 | 8 | yes | maximal, complemented |
| 2 | (C3×C31⋊C3)⋊C9 | C3 | 1 | 4 | yes | maximal |
| 3 | C92×C31 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C32×C31⋊C3 | C32 | 1 | 1 | yes | characteristic |
| 5 | C3×C9×C31 | C32 | 1 | 4 | yes | — |
| 6 | C3×C31⋊C9 | C32 | 1 | 8 | yes | — |
| 7 | C32×C31 | C33 | 1 | 1 | yes | characteristic |
| 8 | C3×C31⋊C3 | — | 3 | 4 | no | — |
| 9 | C9×C31 | — | 3 | 4 | no | — |
| 10 | C31⋊C9 | — | 3 | 8 | no | — |
| 11 | #6898 | — | 31 | 1 | no | maximal, Sylow |
| 12 | C3×C31 | #737 | 1 | 4 | yes | — |
| 13 | C31⋊C3 | — | 9 | 1 | no | — |
| 14 | C9⋊C9 | — | 31 | 8 | no | — |
| 15 | C32⋊C9 | — | 31 | 4 | no | — |
| 16 | C92 | C31⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 17 | C31 | #6898 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 18 | C33 | — | 31 | 1 | no | — |
| 19 | C3×C9 | — | 31 | 8 | no | — |
| 20 | C3×C9 | C3×C31⋊C3 | 1 | 4 | yes | — |
| 21 | C32 | — | 93 | 4 | no | — |
| 22 | C32 | C32×C31⋊C3 | 1 | 1 | yes | characteristic |
| 23 | C9 | — | 3 | 4 | no | — |
| 24 | C9 | — | 93 | 8 | no | — |
| 25 | C3 | — | 279 | 1 | no | — |
| 26 | C3 | #14578912 | 1 | 4 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×C31⋊C3 |
| commutator, socle | C32×C31 | C33 |
| Fitting | C92×C31 | C3 |
| hypercenter | C92 | C31⋊C3 |
| hypocenter | C31 | #6898 |
| LCS | G ▷ C32×C31 ▷ C31 | |
| UCS | C1 ◁ C32 ◁ C92 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. (C31⋊C9)⋊C9 | C3 | semidirect |
| 3. C92×C31 | C3 | semidirect |
| 16. C92 | C31⋊C3 | semidirect |
| 17. C31 | #6898 | semidirect |