Finite Group DatabasebetaFinite Group DatabasebetaOrder 31218.
32 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 | C112×D43 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | C112×C43 | C2×C3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C11×D43 | — | 3 | 4 | no | — |
| 5 | C2×C112⋊C3 | — | 43 | 1 | no | maximal, Hall |
| 6 | C11×C43 | — | 3 | 4 | no | — |
| 7 | C112⋊C3 | D43 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 8 | C3×D43 | — | 121 | 1 | no | maximal, Hall |
| 9 | C2×C112 | — | 43 | 1 | no | Hall |
| 10 | C3×C43 | — | 121 | 1 | no | Hall |
| 11 | C112 | C3×D43 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | D43 | C112⋊C3 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 13 | C43 | C2×C112⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C2×C11 | — | 129 | 4 | no | — |
| 15 | C11 | — | 3 | 4 | no | — |
| 16 | C2×C3 | — | 5203 | 1 | no | Hall |
| 17 | C3 | — | 121 | 1 | no | Sylow |
| 18 | C2 | — | 43 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C43 | C2×C3 |
| LCS | G ▷ C112×C43 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C43×C112⋊C3 | C2 | semidirect |
| 2. C112×D43 | C3 | semidirect |
| 3. C112×C43 | C2×C3 | semidirect |
| 7. C112⋊C3 | D43 | direct (N × H) |
| 11. C112 | C3×D43 | semidirect |
| 12. D43 | C112⋊C3 | direct (N × H) |
| 13. C43 | C2×C112⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×C112⋊C3 | 2 |
| C112×D43 | 3 |
| C2×C112⋊C3 | 43 |
| C3×D43 | 121 |