Finite Group DatabasebetaFinite Group DatabasebetaOrder 8864.
28 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D2216 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C16×C277 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | D1108 | — | 2 | 2 | no | — |
| 4 | C8×C277 | C22 | 1 | 1 | yes | characteristic |
| 5 | C2×D277 | — | 4 | 2 | no | — |
| 6 | C4×C277 | D4 | 1 | 1 | yes | characteristic |
| 7 | C2×C277 | D8 | 1 | 1 | yes | characteristic |
| 8 | D277 | — | 8 | 2 | no | — |
| 9 | C277 | D16 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | D16 | — | 277 | 1 | no | maximal, Sylow |
| 11 | D8 | — | 277 | 2 | no | — |
| 12 | C16 | D277 | 1 | 1 | yes | characteristic, complemented |
| 13 | D4 | — | 554 | 2 | no | — |
| 14 | C8 | C2×D277 | 1 | 1 | yes | characteristic |
| 15 | C22 | — | 1108 | 2 | no | — |
| 16 | C4 | D1108 | 1 | 1 | yes | characteristic |
| 17 | C2 | — | 2216 | 2 | no | — |
| 18 | C2 | D2216 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D2216 |
| commutator | C8×C277 | C22 |
| Frattini | C8 | C2×D277 |
| Fitting | C16×C277 | C2 |
| socle | C2×C277 | D8 |
| hypercenter | C16 | D277 |
| hypocenter | C277 | D16 |
| LCS | G ▷ C8×C277 ▷ C4×C277 ▷ C2×C277 ▷ C277 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D2216 | C2 | semidirect |
| 2. C16×C277 | C2 | semidirect |
| 9. C277 | D16 | semidirect |
| 12. C16 | D277 | semidirect |