Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
32 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D1552 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #15690716 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | Q32×C97 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D776 | — | 2 | 1 | no | — |
| 5 | Q16×C97 | — | 2 | 1 | no | — |
| 6 | C16×C97 | C22 | 1 | 1 | yes | characteristic |
| 7 | Q8×C97 | — | 4 | 1 | no | — |
| 8 | D388 | — | 4 | 1 | no | — |
| 9 | C8×C97 | D4 | 1 | 1 | yes | characteristic |
| 10 | C2×D97 | — | 8 | 1 | no | — |
| 11 | C4×C97 | — | 8 | 1 | no | — |
| 12 | C4×C97 | D8 | 1 | 1 | yes | characteristic |
| 13 | C2×C97 | D16 | 1 | 1 | yes | characteristic |
| 14 | D97 | — | 16 | 1 | no | — |
| 15 | C97 | SD64 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 16 | SD64 | — | 97 | 1 | no | maximal, Sylow |
| 17 | Q32 | D97 | 1 | 1 | yes | characteristic, complemented |
| 18 | D16 | — | 97 | 1 | no | — |
| 19 | C32 | — | 97 | 1 | no | — |
| 20 | Q16 | — | 2 | 1 | no | — |
| 21 | D8 | — | 194 | 1 | no | — |
| 22 | C16 | C2×D97 | 1 | 1 | yes | characteristic |
| 23 | Q8 | — | 4 | 1 | no | — |
| 24 | D4 | — | 388 | 1 | no | — |
| 25 | C8 | C22⋊D97 | 1 | 1 | yes | characteristic |
| 26 | C22 | — | 776 | 1 | no | — |
| 27 | C4 | — | 8 | 1 | no | — |
| 28 | C4 | #13095496 | 1 | 1 | yes | characteristic |
| 29 | C2 | — | 1552 | 1 | no | — |
| 30 | C2 | #15690751 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #15690751 |
| commutator | C16×C97 | C22 |
| Frattini | C16 | C2×D97 |
| Fitting | Q32×C97 | C2 |
| socle | C2×C97 | D16 |
| hypercenter | Q32 | D97 |
| hypocenter | C97 | SD64 |
| LCS | G ▷ C16×C97 ▷ C8×C97 ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15690716 | C2 | semidirect |
| 3. Q32×C97 | C2 | semidirect |
| 15. C97 | SD64 | semidirect |
| 17. Q32 | D97 | semidirect |