Finite Group DatabasebetaFinite Group DatabasebetaOrder 3520.
620 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 196 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×AGL(1,𝔽11) |
| commutator, socle, cosocle | C22×C11 | C24×C5 |
| Fitting | C11×#127 | C2×C5 |
| hypercenter | #127 | AGL(1,𝔽11) |
| hypocenter | C11 | C5×#532 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#4341⋊C5 | C2 | semidirect |
| 2. #127×C11⋊C5 | C2 | semidirect |
| 3. #66991⋊C5 | C2 | semidirect |
| 4. #66989⋊C5 | C2 | semidirect |
| 5. D4×Dic11⋊C5 | C2 | semidirect |
| 6. C42×AGL(1,𝔽11) | C2 | semidirect |
| 7. #66922⋊C5 | C2 | semidirect |
| 21. #10623247 | C5 | semidirect |
| 34. C4×AGL(1,𝔽11) | D4 | semidirect |
| 36. C2×#4341 | C2×C5 | semidirect |
| 37. C11×#127 | C2×C5 | semidirect |
| 38. #66991 | C2×C5 | semidirect |
| 39. #66989 | C2×C5 | semidirect |
| 40. D4×Dic11 | C2×C5 | semidirect |
| 41. C42×D11 | C2×C5 | semidirect |
| 42. #66922 | C2×C5 | semidirect |
| 50. C4×C11⋊C5 | #41 | semidirect |
| 90. C4×D11 | C5×D4 | semidirect |
| 106. C11⋊C5 | #532 | semidirect |
| 113. C4×C11 | C5×#41 | semidirect |
| 133. #127 | AGL(1,𝔽11) | semidirect |
| 165. C11 | C5×#532 | semidirect |
| 194. C4 | #4341⋊C5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4341⋊C5 | 2 |
| #127×C11⋊C5 | 2 |
| #66991⋊C5 | 2 |
| #66989⋊C5 | 2 |
| D4×Dic11⋊C5 | 2 |
| C42×AGL(1,𝔽11) | 2 |
| #66922⋊C5 | 2 |
| #10623247 | 5 |
| C5×#532 | 11 |