Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
138 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C107⋊#95 | C2 | 1 | 6 | yes | maximal |
| 2 | C2×C42×C107 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C22×Dic107 | C22 | 1 | 4 | yes | — |
| 4 | C22×C4×C107 | C22 | 1 | 3 | yes | — |
| 5 | C42×C107 | C4 | 1 | 4 | yes | complemented |
| 6 | C23×C107 | C23 | 1 | 1 | yes | characteristic |
| 7 | C2×C4×C107 | — | 2 | 6 | no | — |
| 8 | C2×C4×C107 | C2×C4 | 1 | 6 | yes | — |
| 9 | C2×Dic107 | — | 2 | 12 | no | — |
| 10 | C22×C107 | C22×C4 | 1 | 1 | yes | characteristic |
| 11 | C22×C107 | #41 | 1 | 6 | yes | — |
| 12 | C4×C107 | — | 2 | 6 | no | — |
| 13 | Dic107 | — | 4 | 4 | no | — |
| 14 | C2×C107 | #117 | 1 | 3 | yes | — |
| 15 | C2×C107 | #126 | 1 | 4 | yes | — |
| 16 | C107 | #383 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 17 | #383 | — | 107 | 1 | no | maximal, Sylow |
| 18 | C2×C42 | D107 | 1 | 1 | yes | characteristic |
| 19 | #95 | — | 107 | 6 | no | — |
| 20 | C22×C4 | — | 107 | 4 | no | — |
| 21 | C22×C4 | C2×D107 | 1 | 3 | yes | — |
| 22 | C42 | Dic107 | 1 | 4 | yes | complemented |
| 23 | C23 | C22×D107 | 1 | 1 | yes | characteristic |
| 24 | C2×C4 | — | 2 | 6 | no | — |
| 25 | C2×C4 | — | 214 | 12 | no | — |
| 26 | C2×C4 | C2×Dic107 | 1 | 6 | yes | — |
| 27 | C22 | C22×Dic107 | 1 | 1 | yes | characteristic |
| 28 | C22 | #13133818 | 1 | 6 | yes | — |
| 29 | C4 | — | 2 | 6 | no | — |
| 30 | C4 | — | 428 | 4 | no | — |
| 31 | C2 | #16812068 | 1 | 3 | yes | — |
| 32 | C2 | #16812103 | 1 | 4 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D107 |
| commutator | C22×C107 | C22×C4 |
| Fitting | C2×C42×C107 | C2 |
| socle | C23×C107 | C23 |
| hypercenter | C2×C42 | D107 |
| hypocenter | C107 | #383 |
| LCS | G ▷ C22×C107 ▷ C107 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C42×C107 | C4 | semidirect |
| 16. C107 | #383 | semidirect |
| 22. C42 | Dic107 | semidirect |