Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
40 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D2272 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C71⋊C64 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | D32×C71 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D1136 | — | 2 | 1 | no | — |
| 5 | D16×C71 | — | 2 | 1 | no | — |
| 6 | C32×C71 | C22 | 1 | 1 | yes | characteristic |
| 7 | D568 | — | 4 | 1 | no | — |
| 8 | D8×C71 | — | 4 | 1 | no | — |
| 9 | C16×C71 | D4 | 1 | 1 | yes | characteristic |
| 10 | D4×C71 | — | 8 | 1 | no | — |
| 11 | D284 | — | 8 | 1 | no | — |
| 12 | C8×C71 | D8 | 1 | 1 | yes | characteristic |
| 13 | C22×C71 | — | 16 | 1 | no | — |
| 14 | C2×D71 | — | 16 | 1 | no | — |
| 15 | C4×C71 | D16 | 1 | 1 | yes | characteristic |
| 16 | C2×C71 | — | 32 | 1 | no | — |
| 17 | C2×C71 | D32 | 1 | 1 | yes | characteristic |
| 18 | D71 | — | 32 | 1 | no | — |
| 19 | D64 | — | 71 | 1 | no | maximal, Sylow |
| 20 | C71 | D64 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 21 | D32 | — | 71 | 1 | no | — |
| 22 | D32 | D71 | 1 | 1 | yes | characteristic, complemented |
| 23 | C64 | — | 71 | 1 | no | — |
| 24 | D16 | — | 2 | 1 | no | — |
| 25 | D16 | — | 142 | 1 | no | — |
| 26 | C32 | C2×D71 | 1 | 1 | yes | characteristic |
| 27 | D8 | — | 4 | 1 | no | — |
| 28 | D8 | — | 284 | 1 | no | — |
| 29 | C16 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 30 | D4 | — | 8 | 1 | no | — |
| 31 | D4 | — | 568 | 1 | no | — |
| 32 | C8 | #11765850 | 1 | 1 | yes | characteristic |
| 33 | C22 | — | 16 | 1 | no | — |
| 34 | C22 | — | 1136 | 1 | no | — |
| 35 | C4 | #14556069 | 1 | 1 | yes | characteristic |
| 36 | C2 | — | 32 | 1 | no | — |
| 37 | C2 | — | 2272 | 1 | no | — |
| 38 | C2 | #17985834 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #17985834 |
| commutator | C32×C71 | C22 |
| Frattini | C32 | C2×D71 |
| Fitting | D32×C71 | C2 |
| socle | C2×C71 | D32 |
| hypercenter | D32 | D71 |
| hypocenter | C71 | D64 |
| LCS | G ▷ C32×C71 ▷ C16×C71 ▷ C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 ◁ D32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D2272 | C2 | semidirect |
| 2. C71⋊C64 | C2 | semidirect |
| 3. D32×C71 | C2 | semidirect |
| 20. C71 | D64 | semidirect |
| 22. D32 | D71 | semidirect |