Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
40 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D6112 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C191⋊C64 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | D32×C191 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D3056 | — | 2 | 1 | no | — |
| 5 | D16×C191 | — | 2 | 1 | no | — |
| 6 | C32×C191 | C22 | 1 | 1 | yes | characteristic |
| 7 | D1528 | — | 4 | 1 | no | — |
| 8 | D8×C191 | — | 4 | 1 | no | — |
| 9 | C16×C191 | D4 | 1 | 1 | yes | characteristic |
| 10 | D764 | — | 8 | 1 | no | — |
| 11 | D4×C191 | — | 8 | 1 | no | — |
| 12 | C8×C191 | D8 | 1 | 1 | yes | characteristic |
| 13 | C22×C191 | — | 16 | 1 | no | — |
| 14 | C2×D191 | — | 16 | 1 | no | — |
| 15 | C4×C191 | D16 | 1 | 1 | yes | characteristic |
| 16 | C2×C191 | — | 32 | 1 | no | — |
| 17 | C2×C191 | D32 | 1 | 1 | yes | characteristic |
| 18 | D191 | — | 32 | 1 | no | — |
| 19 | C191 | D64 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 20 | D64 | — | 191 | 1 | no | maximal, Sylow |
| 21 | D32 | — | 191 | 1 | no | — |
| 22 | D32 | D191 | 1 | 1 | yes | characteristic, complemented |
| 23 | C64 | — | 191 | 1 | no | — |
| 24 | D16 | — | 2 | 1 | no | — |
| 25 | D16 | — | 382 | 1 | no | — |
| 26 | C32 | C2×D191 | 1 | 1 | yes | characteristic |
| 27 | D8 | — | 4 | 1 | no | — |
| 28 | D8 | — | 764 | 1 | no | — |
| 29 | C16 | C22⋊D191 | 1 | 1 | yes | characteristic |
| 30 | D4 | — | 8 | 1 | no | — |
| 31 | D4 | — | 1528 | 1 | no | — |
| 32 | C8 | #15690272 | 1 | 1 | yes | characteristic |
| 33 | C22 | — | 16 | 1 | no | — |
| 34 | C22 | — | 3056 | 1 | no | — |
| 35 | C4 | #20259263 | 1 | 1 | yes | characteristic |
| 36 | C2 | — | 32 | 1 | no | — |
| 37 | C2 | — | 6112 | 1 | no | — |
| 38 | C2 | #27132498 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #27132498 |
| commutator, cosocle | C32×C191 | C22 |
| Frattini | C32 | C2×D191 |
| Fitting | D32×C191 | C2 |
| socle | C2×C191 | D32 |
| hypercenter | D32 | D191 |
| hypocenter | C191 | D64 |
| LCS | G ▷ C32×C191 ▷ C16×C191 ▷ C8×C191 ▷ C4×C191 ▷ C2×C191 ▷ C191 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 ◁ D32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D6112 | C2 | semidirect |
| 2. C191⋊C64 | C2 | semidirect |
| 3. D32×C191 | C2 | semidirect |
| 19. C191 | D64 | semidirect |
| 22. D32 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D6112 | 2 |
| C191⋊C64 | 2 |
| D32×C191 | 2 |
| D64 | 191 |