Finite Group DatabasebetaFinite Group DatabasebetaOrder 3520.
624 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 624 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 | C2×C11×#41 | C2×C5 |
| hypercenter | C2×#41 | AGL(1,𝔽11) |
| hypocenter | C11 | C5×#550 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#41×C11⋊C5 | C2 | semidirect |
| 2. C2×#4343⋊C5 | C2 | semidirect |
| 3. Q8×Dic11⋊C5 | C2 | semidirect |
| 4. #66991⋊C5 | C2 | semidirect |
| 5. #66993⋊C5 | C2 | semidirect |
| 6. #66983⋊C5 | C2 | semidirect |
| 7. C4×C22⋊AGL(1,𝔽11) | C2 | semidirect |
| 22. #10623365 | C5 | semidirect |
| 25. Q8×C11⋊C5 | D4 | semidirect |
| 37. C2×C11×#41 | C2×C5 | semidirect |
| 38. C2×#4343 | C2×C5 | semidirect |
| 39. Q8×Dic11 | C2×C5 | semidirect |
| 40. #66993 | C2×C5 | semidirect |
| 41. #66991 | C2×C5 | semidirect |
| 42. #66983 | C2×C5 | semidirect |
| 43. C4×C22⋊D11 | C2×C5 | semidirect |
| 56. Dic11⋊C5 | #41 | semidirect |
| 85. Q8×C11 | C5×D4 | semidirect |
| 112. C11⋊C5 | #550 | semidirect |
| 124. Dic11 | C5×#41 | semidirect |
| 140. C2×#41 | AGL(1,𝔽11) | semidirect |
| 177. C11 | C5×#550 | semidirect |
| 185. Q8 | C22⋊AGL(1,𝔽11) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×C11⋊C5 | 2 |
| C2×#4343⋊C5 | 2 |
| Q8×Dic11⋊C5 | 2 |
| #66991⋊C5 | 2 |
| #66993⋊C5 | 2 |
| #66983⋊C5 | 2 |
| C4×C22⋊AGL(1,𝔽11) | 2 |
| #10623365 | 5 |
| C5×#550 | 11 |