Finite Group DatabasebetaFinite Group DatabasebetaOrder 31712.
28 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D7928 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C991⋊C16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | D8×C991 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D3964 | — | 2 | 1 | no | — |
| 5 | D4×C991 | — | 2 | 1 | no | — |
| 6 | C8×C991 | C22 | 1 | 1 | yes | characteristic |
| 7 | C22×C991 | — | 4 | 1 | no | — |
| 8 | C2×D991 | — | 4 | 1 | no | — |
| 9 | C4×C991 | D4 | 1 | 1 | yes | characteristic |
| 10 | C2×C991 | — | 8 | 1 | no | — |
| 11 | C2×C991 | D8 | 1 | 1 | yes | characteristic |
| 12 | D991 | — | 8 | 1 | no | — |
| 13 | C991 | D16 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | D16 | — | 991 | 1 | no | maximal, Sylow |
| 15 | D8 | — | 991 | 1 | no | — |
| 16 | D8 | D991 | 1 | 1 | yes | characteristic, complemented |
| 17 | C16 | — | 991 | 1 | no | — |
| 18 | D4 | — | 2 | 1 | no | — |
| 19 | D4 | — | 1982 | 1 | no | — |
| 20 | C8 | C2×D991 | 1 | 1 | yes | characteristic |
| 21 | C22 | — | 4 | 1 | no | — |
| 22 | C22 | — | 3964 | 1 | no | — |
| 23 | C4 | C22⋊D991 | 1 | 1 | yes | characteristic |
| 24 | C2 | — | 8 | 1 | no | — |
| 25 | C2 | — | 7928 | 1 | no | — |
| 26 | C2 | #30629377 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D7928 | C2 | semidirect |
| 2. C991⋊C16 | C2 | semidirect |
| 3. D8×C991 | C2 | semidirect |
| 13. C991 | D16 | semidirect |
| 16. D8 | D991 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7928 | 2 |
| C991⋊C16 | 2 |
| D8×C991 | 2 |
| D16 | 991 |