Finite Group DatabasebetaFinite Group DatabasebetaOrder 31713.
36 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C11×C312 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | #15668333 | C11 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 3 | C11×C31⋊C3 | — | 31 | 2 | no | maximal |
| 4 | C312 | C3×C11 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 5 | C11×C31 | — | 3 | 10 | no | — |
| 6 | C11×C31 | C31⋊C3 | 1 | 2 | yes | complemented |
| 7 | C31⋊C3 | — | 31 | 2 | no | — |
| 8 | C3×C11 | — | 961 | 1 | no | Hall |
| 9 | C31 | — | 3 | 10 | no | — |
| 10 | C31 | C11×C31⋊C3 | 1 | 2 | yes | complemented |
| 11 | C11 | #15668333 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 12 | C3 | — | 961 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #15668333 |
| commutator, cosocle, hypocenter | C312 | C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C312 | C3 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C11 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×C312 | C3 | semidirect |
| 2. #15668333 | C11 | direct (N × H) |
| 4. C312 | C3×C11 | semidirect |
| 6. C11×C31 | C31⋊C3 | semidirect |
| 10. C31 | C11×C31⋊C3 | semidirect |
| 11. C11 | #15668333 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×C312 | 3 |
| #15668333 | 11 |
| C11×C31⋊C3 | 31 |