Finite Group DatabasebetaFinite Group DatabasebetaOrder 6304.
30 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #15691342 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#13096802 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | M16×C197 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #13096802 | — | 2 | 1 | no | — |
| 5 | #13096802 | C4 | 1 | 2 | yes | — |
| 6 | C2×C4×C197 | C22 | 1 | 1 | yes | characteristic |
| 7 | C8×C197 | — | 2 | 1 | no | — |
| 8 | C22×C197 | Q8 | 1 | 1 | yes | characteristic |
| 9 | C4×C197 | C2×C4 | 1 | 1 | yes | characteristic |
| 10 | C4×C197 | D4 | 1 | 1 | yes | characteristic |
| 11 | C2×C197 | — | 2 | 1 | no | — |
| 12 | C2×C197 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 13 | C197 | #108 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | #108 | — | 197 | 1 | no | maximal, Sylow |
| 15 | M16 | — | 197 | 1 | no | — |
| 16 | M16 | D197 | 1 | 1 | yes | characteristic |
| 17 | C2×C8 | — | 197 | 1 | no | — |
| 18 | C2×C4 | C2×D197 | 1 | 1 | yes | characteristic |
| 19 | C8 | — | 2 | 1 | no | — |
| 20 | C8 | — | 394 | 1 | no | — |
| 21 | C8 | — | 197 | 2 | no | — |
| 22 | C22 | Dic394 | 1 | 1 | yes | characteristic |
| 23 | C4 | C4×D197 | 1 | 1 | yes | characteristic |
| 24 | C4 | C22⋊D197 | 1 | 1 | yes | characteristic |
| 25 | C2 | — | 2 | 1 | no | — |
| 26 | C2 | #15691337 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22⋊D197 |
| commutator | C4×C197 | C2×C4 |
| Frattini | C2×C4 | C2×D197 |
| Fitting | M16×C197 | C2 |
| socle | C2×C197 | C4⋊C4 |
| hypercenter | M16 | D197 |
| hypocenter | C197 | #108 |
| LCS | G ▷ C4×C197 ▷ C2×C197 ▷ C197 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 13. C197 | #108 | semidirect |