Finite Group DatabasebetaFinite Group DatabasebetaOrder 2662.
17 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | 11−1+2 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Sylow |
| 2 | C11×D11 | — | 11 | 1 | no | maximal |
| 3 | D121 | C11 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C112 | D11 | 1 | 1 | yes | characteristic |
| 5 | C121 | — | 2 | 5 | no | — |
| 6 | C121 | C2×C11 | 1 | 1 | yes | characteristic, complemented |
| 7 | C2×C11 | — | 121 | 1 | no | — |
| 8 | D11 | — | 11 | 1 | no | — |
| 9 | C11 | — | 22 | 1 | no | — |
| 10 | C11 | C11×D11 | 1 | 1 | yes | characteristic |
| 11 | C2 | — | 121 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C121 | C2×C11 |
| Frattini, socle | C11 | C11×D11 |
| Fitting | 11−1+2 | C2 |
| LCS | G ▷ C121 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. 11−1+2 | C2 | semidirect |
| 3. D121 | C11 | semidirect |
| 6. C121 | C2×C11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 11−1+2 | 2 |
| C11×D11 | 11 |
| D121 | 11 |