Finite Group DatabasebetaFinite Group DatabasebetaOrder 6176.
50 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#13095400 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C22×Dic193 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13095400 | — | 2 | 2 | no | — |
| 4 | C2×Dic193 | — | 2 | 2 | no | — |
| 5 | C2×Dic193 | C4 | 1 | 1 | yes | characteristic |
| 6 | C2×Dic193 | C22 | 1 | 1 | yes | characteristic |
| 7 | C23×C193 | C4 | 1 | 1 | yes | characteristic |
| 8 | C22×C193 | — | 2 | 1 | no | — |
| 9 | C22×C193 | — | 2 | 1 | no | — |
| 10 | C22×C193 | C8 | 1 | 2 | yes | complemented |
| 11 | C22×C193 | C2×C4 | 1 | 1 | yes | characteristic |
| 12 | Dic193 | — | 2 | 1 | no | — |
| 13 | Dic193 | D4 | 1 | 2 | yes | — |
| 14 | C2×C193 | — | 2 | 2 | no | — |
| 15 | C2×C193 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 16 | C2×C193 | C2×C8 | 1 | 1 | yes | characteristic |
| 17 | C2×C193 | M16 | 1 | 1 | yes | characteristic |
| 18 | C193 | C22⋊C8 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 19 | C22⋊C8 | — | 193 | 1 | no | maximal, Sylow |
| 20 | C22×C4 | — | 193 | 1 | no | — |
| 21 | C2×C8 | — | 193 | 2 | no | — |
| 22 | C23 | #11715871 | 1 | 1 | yes | characteristic |
| 23 | C2×C4 | — | 386 | 2 | no | — |
| 24 | C2×C4 | — | 193 | 1 | no | — |
| 25 | C2×C4 | — | 193 | 1 | no | — |
| 26 | C8 | — | 386 | 2 | no | — |
| 27 | C22 | — | 2 | 1 | no | — |
| 28 | C22 | — | 2 | 1 | no | — |
| 29 | C22 | #13095400 | 1 | 2 | yes | complemented |
| 30 | C22 | C2×#11715871 | 1 | 1 | yes | characteristic |
| 31 | C4 | — | 386 | 1 | no | — |
| 32 | C4 | — | 193 | 2 | no | — |
| 33 | C2 | — | 2 | 2 | no | — |
| 34 | C2 | C22⋊#11715871 | 1 | 1 | yes | characteristic |
| 35 | C2 | C2×#13095400 | 1 | 1 | yes | characteristic |
| 36 | C2 | #15690564 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×#11715871 |
| commutator | C2×C193 | C2×C8 |
| Fitting | C23×C193 | C4 |
| socle | C22×C193 | C2×C4 |
| hypercenter | C23 | #11715871 |
| hypocenter | C193 | C22⋊C8 |
| LCS | G ▷ C2×C193 ▷ C193 | |
| UCS | C1 ◁ C22 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13095400 | C2 | semidirect |
| 10. C22×C193 | C8 | semidirect |
| 18. C193 | C22⋊C8 | semidirect |
| 29. C22 | #13095400 | semidirect |