Finite Group DatabasebetaFinite Group DatabasebetaOrder 30532.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D7633 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C17×C449 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | #14267798 | — | 17 | 1 | no | maximal, Hall |
| 4 | D449 | — | 17 | 1 | no | — |
| 5 | C449 | #595 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 6 | #595 | — | 449 | 1 | no | maximal, Hall |
| 7 | D17 | — | 449 | 1 | no | — |
| 8 | C17 | #14267798 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C4 | — | 7633 | 1 | no | Sylow |
| 10 | C2 | — | 7633 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C449 | C4 |
| prime radical, cosocle | D7633 | C2 |
| LCS | G ▷ C17×C449 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C17×C449 | C4 | semidirect |
| 5. C449 | #595 | semidirect |
| 8. C17 | #14267798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7633 | 2 |
| #14267798 | 17 |
| #595 | 449 |