Finite Group DatabasebetaFinite Group DatabasebetaOrder 10769.
28 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C11×C89 | C11 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C89⋊C11 | C11 | 1 | 11 | yes | maximal, direct product factor |
| 3 | C112 | — | 89 | 1 | no | maximal, Sylow |
| 4 | C89 | C112 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 5 | C11 | — | 89 | 11 | no | — |
| 6 | C11 | C89⋊C11 | 1 | 1 | yes | characteristic, direct product factor |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C89⋊C11 |
| commutator, cosocle, hypocenter | C89 | C112 |
| Frattini | C1 | G |
| Fitting, socle | C11×C89 | C11 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C11 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×C89 | C11 | semidirect |
| 2. C89⋊C11 | C11 | direct (N × H) |
| 4. C89 | C112 | semidirect |
| 6. C11 | C89⋊C11 | direct (N × H) |