Finite Group DatabasebetaFinite Group DatabasebetaOrder 352.
26 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Dic44 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D88 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C11×C16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D44 | — | 2 | 1 | no | — |
| 5 | Dic22 | — | 2 | 1 | no | — |
| 6 | C8×C11 | C22 | 1 | 1 | yes | characteristic |
| 7 | C2×D11 | — | 4 | 1 | no | — |
| 8 | C4×C11 | D4 | 1 | 1 | yes | characteristic |
| 9 | Dic11 | — | 4 | 1 | no | — |
| 10 | SD32 | — | 11 | 1 | no | maximal, Sylow |
| 11 | C2×C11 | D8 | 1 | 1 | yes | characteristic |
| 12 | D11 | — | 8 | 1 | no | — |
| 13 | Q16 | — | 11 | 1 | no | — |
| 14 | D8 | — | 11 | 1 | no | — |
| 15 | C16 | D11 | 1 | 1 | yes | characteristic, complemented |
| 16 | C11 | SD32 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 17 | Q8 | — | 22 | 1 | no | — |
| 18 | D4 | — | 22 | 1 | no | — |
| 19 | C8 | C2×D11 | 1 | 1 | yes | characteristic |
| 20 | C22 | — | 44 | 1 | no | — |
| 21 | C4 | — | 44 | 1 | no | — |
| 22 | C4 | D44 | 1 | 1 | yes | characteristic |
| 23 | C2 | — | 88 | 1 | no | — |
| 24 | C2 | D88 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Dic44 | C2 | semidirect |
| 3. C11×C16 | C2 | semidirect |
| 15. C16 | D11 | semidirect |
| 16. C11 | SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic44 | 2 |
| D88 | 2 |
| C11×C16 | 2 |
| SD32 | 11 |