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×C4⋊Q8 | C2×C5 |
| hypercenter | C4⋊Q8 | AGL(1,𝔽11) |
| hypocenter | C11 | C5×#532 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#4343⋊C5 | C2 | semidirect |
| 2. C4⋊Q8×C11⋊C5 | C2 | semidirect |
| 3. #67000⋊C5 | C2 | semidirect |
| 4. #66948⋊C5 | C2 | semidirect |
| 5. #66946⋊C5 | C2 | semidirect |
| 6. #66927⋊C5 | C2 | semidirect |
| 7. C42×AGL(1,𝔽11) | C2 | semidirect |
| 21. #10623256 | C5 | semidirect |
| 35. C4×AGL(1,𝔽11) | D4 | semidirect |
| 36. C2×#4343 | C2×C5 | semidirect |
| 37. C11×C4⋊Q8 | C2×C5 | semidirect |
| 38. #67000 | C2×C5 | semidirect |
| 39. #66948 | C2×C5 | semidirect |
| 40. #66946 | C2×C5 | semidirect |
| 41. #66927 | C2×C5 | semidirect |
| 42. C42×D11 | C2×C5 | semidirect |
| 51. C4×C11⋊C5 | #41 | semidirect |
| 91. C4×D11 | C5×D4 | semidirect |
| 106. C11⋊C5 | #532 | semidirect |
| 114. C4×C11 | C5×#41 | semidirect |
| 132. C4⋊Q8 | AGL(1,𝔽11) | semidirect |
| 165. C11 | C5×#532 | semidirect |
| 194. C4 | #4343⋊C5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4343⋊C5 | 2 |
| C4⋊Q8×C11⋊C5 | 2 |
| #67000⋊C5 | 2 |
| #66948⋊C5 | 2 |
| #66946⋊C5 | 2 |
| #66927⋊C5 | 2 |
| C42×AGL(1,𝔽11) | 2 |
| #10623256 | 5 |
| C5×#532 | 11 |