Finite Group DatabasebetaFinite Group DatabasebetaOrder 24242.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C17×C23×C31 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D713 | — | 17 | 1 | no | maximal, Hall |
| 3 | D527 | — | 23 | 1 | no | maximal, Hall |
| 4 | D391 | — | 31 | 1 | no | maximal, Hall |
| 5 | C23×C31 | D17 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | C17×C31 | D23 | 1 | 1 | yes | characteristic, complemented, Hall |
| 7 | C17×C23 | D31 | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | D31 | — | 391 | 1 | no | Hall |
| 9 | D23 | — | 527 | 1 | no | Hall |
| 10 | D17 | — | 713 | 1 | no | Hall |
| 11 | C31 | D391 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | C23 | D527 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 13 | C17 | D713 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C2 | — | 12121 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C23×C31 | C2 |
| LCS | G ▷ C17×C23×C31 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17×C23×C31 | C2 | semidirect |
| 5. C23×C31 | D17 | semidirect |
| 6. C17×C31 | D23 | semidirect |
| 7. C17×C23 | D31 | semidirect |
| 11. C31 | D391 | semidirect |
| 12. C23 | D527 | semidirect |
| 13. C17 | D713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×C23×C31 | 2 |
| D713 | 17 |
| D527 | 23 |
| D391 | 31 |