Finite Group DatabasebetaFinite Group DatabasebetaOrder 8692.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C53×D41 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C41×C53 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | Dic53 | — | 41 | 1 | no | maximal, Hall |
| 4 | #4223 | — | 53 | 1 | no | maximal, Hall |
| 5 | C2×C53 | — | 41 | 1 | no | — |
| 6 | D41 | D53 | 1 | 1 | yes | characteristic |
| 7 | C53 | #4223 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 8 | C41 | Dic53 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C4 | — | 2173 | 1 | no | Sylow |
| 10 | C2 | — | 41 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C41×C53 | C4 |
| LCS | G ▷ C41×C53 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×C53 | C4 | semidirect |
| 7. C53 | #4223 | semidirect |
| 8. C41 | Dic53 | semidirect |