Finite Group DatabasebetaFinite Group DatabasebetaOrder 23622.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×C31×C127 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D3937 | — | 3 | 1 | no | maximal, Hall |
| 3 | C31×C127 | D3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | D381 | — | 31 | 1 | no | maximal, Hall |
| 5 | C3×C127 | D31 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | D127 | — | 93 | 1 | no | Hall |
| 7 | D93 | — | 127 | 1 | no | maximal, Hall |
| 8 | C127 | D93 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C3×C31 | D127 | 1 | 1 | yes | characteristic, complemented, Hall |
| 10 | D31 | — | 381 | 1 | no | Hall |
| 11 | C31 | D381 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | D3 | — | 3937 | 1 | no | Hall |
| 13 | C3 | D3937 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C2 | — | 11811 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C31×C127 | C2 |
| LCS | G ▷ C3×C31×C127 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C31×C127 | C2 | semidirect |
| 3. C31×C127 | D3 | semidirect |
| 5. C3×C127 | D31 | semidirect |
| 8. C127 | D93 | semidirect |
| 9. C3×C31 | D127 | semidirect |
| 11. C31 | D381 | semidirect |
| 13. C3 | D3937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C31×C127 | 2 |
| D3937 | 3 |
| D381 | 31 |
| D93 | 127 |