Finite Group DatabasebetaFinite Group DatabasebetaOrder 31772.
96 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C47×C13⋊D13 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C132×C47 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | C47⋊#261 | — | 13 | 14 | no | maximal |
| 4 | D13×C47 | — | 13 | 14 | no | — |
| 5 | #10621728 | — | 47 | 1 | no | maximal, Hall |
| 6 | C13×C47 | #261 | 1 | 14 | yes | complemented |
| 7 | C13⋊D13 | D47 | 1 | 1 | yes | characteristic |
| 8 | Dic47 | — | 169 | 1 | no | Hall |
| 9 | C132 | Dic47 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | C2×C47 | — | 169 | 1 | no | — |
| 11 | #261 | — | 611 | 14 | no | — |
| 12 | C47 | #10621728 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 13 | D13 | — | 13 | 14 | no | — |
| 14 | C13 | C47⋊#261 | 1 | 14 | yes | complemented |
| 15 | C4 | — | 7943 | 1 | no | Sylow |
| 16 | C2 | — | 169 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C132×C47 | C4 |
| prime radical, cosocle | C47×C13⋊D13 | C2 |
| LCS | G ▷ C132×C47 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C132×C47 | C4 | semidirect |
| 6. C13×C47 | #261 | semidirect |
| 9. C132 | Dic47 | semidirect |
| 12. C47 | #10621728 | semidirect |
| 14. C13 | C47⋊#261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×C13⋊D13 | 2 |
| C47⋊#261 | 13 |
| #10621728 | 47 |