Finite Group DatabasebetaFinite Group DatabasebetaOrder 10682.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C49×C109 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D763 | — | 7 | 1 | no | maximal |
| 3 | C7×C109 | D7 | 1 | 1 | yes | characteristic |
| 4 | D109 | — | 49 | 1 | no | Hall |
| 5 | C109 | D49 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 6 | D49 | — | 109 | 1 | no | maximal, Hall |
| 7 | C49 | D109 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 8 | D7 | — | 763 | 1 | no | — |
| 9 | C7 | D763 | 1 | 1 | yes | characteristic |
| 10 | C2 | — | 5341 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C49×C109 | C2 |
| Frattini | C7 | D763 |
| socle | C7×C109 | D7 |
| LCS | G ▷ C49×C109 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C49×C109 | C2 | semidirect |
| 5. C109 | D49 | semidirect |
| 7. C49 | D109 | semidirect |