Finite Group DatabasebetaFinite Group DatabasebetaOrder 484.
22 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C112 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C112 | C4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 3 | C4×C11 | — | 11 | 1 | no | maximal |
| 4 | Dic11 | C11 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 5 | C2×C11 | — | 2 | 5 | no | — |
| 6 | C2×C11 | D11 | 1 | 1 | yes | characteristic |
| 7 | C2×C11 | C2×C11 | 1 | 1 | yes | characteristic |
| 8 | C11 | — | 2 | 5 | no | — |
| 9 | C11 | Dic11 | 1 | 1 | yes | characteristic, direct product factor |
| 10 | C11 | C4×C11 | 1 | 1 | yes | characteristic, complemented |
| 11 | C4 | — | 11 | 1 | no | Sylow |
| 12 | C2 | C11×D11 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D11 |
| commutator, hypocenter | C11 | C4×C11 |
| Frattini | C2 | C11×D11 |
| Fitting, socle, prime radical | C2×C112 | C2 |
| cosocle | C2×C11 | C2×C11 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C11 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C112 | C4 | semidirect |
| 4. Dic11 | C11 | direct (N × H) |
| 9. C11 | Dic11 | direct (N × H) |
| 10. C11 | C4×C11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C112 | 2 |
| C4×C11 | 11 |
| Dic11 | 11 |