Finite Group DatabasebetaFinite Group DatabasebetaOrder 31218.
26 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C43×C112⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C11×D473 | — | 3 | 1 | no | maximal, Hall |
| 3 | C112×C43 | D3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | D473 | — | 3 | 1 | no | — |
| 5 | C11×D43 | — | 33 | 1 | no | — |
| 6 | #10624391 | — | 43 | 1 | no | maximal, Hall |
| 7 | C11×C43 | — | 3 | 1 | no | — |
| 8 | C11×C43 | — | 3 | 1 | no | — |
| 9 | C11×C43 | — | 6 | 1 | no | — |
| 10 | C112⋊C3 | D43 | 1 | 1 | yes | characteristic, complemented, Hall |
| 11 | D129 | — | 121 | 1 | no | maximal, Hall |
| 12 | C11×D11 | — | 129 | 1 | no | Hall |
| 13 | C3×C43 | — | 121 | 1 | no | Hall |
| 14 | C112 | D129 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 15 | D43 | — | 33 | 1 | no | Hall |
| 16 | C43 | #10624391 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 17 | C2×C11 | — | 1419 | 1 | no | — |
| 18 | D11 | — | 129 | 1 | no | — |
| 19 | C11 | — | 3 | 1 | no | — |
| 20 | C11 | — | 3 | 1 | no | — |
| 21 | C11 | — | 6 | 1 | no | — |
| 22 | D3 | — | 5203 | 1 | no | Hall |
| 23 | C3 | — | 121 | 1 | no | Sylow |
| 24 | C2 | — | 1419 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C43×C112⋊C3 | C2 |
| Fitting, socle | C112×C43 | D3 |
| LCS | G ▷ C43×C112⋊C3 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C43×C112⋊C3 | C2 | semidirect |
| 3. C112×C43 | D3 | semidirect |
| 10. C112⋊C3 | D43 | semidirect |
| 14. C112 | D129 | semidirect |
| 16. C43 | #10624391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×C112⋊C3 | 2 |
| C11×D473 | 3 |
| #10624391 | 43 |
| D129 | 121 |