Finite Group DatabasebetaFinite Group DatabasebetaOrder 31712.
26 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D7928 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C991⋊C16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | Q16×C991 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D3964 | — | 2 | 1 | no | — |
| 5 | Q8×C991 | — | 2 | 1 | no | — |
| 6 | C8×C991 | C22 | 1 | 1 | yes | characteristic |
| 7 | C2×D991 | — | 4 | 1 | no | — |
| 8 | C4×C991 | — | 4 | 1 | no | — |
| 9 | C4×C991 | D4 | 1 | 1 | yes | characteristic |
| 10 | C2×C991 | D8 | 1 | 1 | yes | characteristic |
| 11 | D991 | — | 8 | 1 | no | — |
| 12 | C991 | SD32 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 13 | SD32 | — | 991 | 1 | no | maximal, Sylow |
| 14 | Q16 | D991 | 1 | 1 | yes | characteristic, complemented |
| 15 | D8 | — | 991 | 1 | no | — |
| 16 | C16 | — | 991 | 1 | no | — |
| 17 | Q8 | — | 2 | 1 | no | — |
| 18 | D4 | — | 1982 | 1 | no | — |
| 19 | C8 | C2×D991 | 1 | 1 | yes | characteristic |
| 20 | C22 | — | 3964 | 1 | no | — |
| 21 | C4 | — | 4 | 1 | no | — |
| 22 | C4 | C22⋊D991 | 1 | 1 | yes | characteristic |
| 23 | C2 | — | 7928 | 1 | no | — |
| 24 | C2 | #30629377 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C991⋊C16 | C2 | semidirect |
| 3. Q16×C991 | C2 | semidirect |
| 12. C991 | SD32 | semidirect |
| 14. Q16 | 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 |
| Q16×C991 | 2 |
| SD32 | 991 |