Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
188 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 59 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 | C22×AGL(1,𝔽11) |
| commutator, socle, cosocle | C22×C11 | C23×C5 |
| Fitting | C2×D4×C11 | C2×C5 |
| hypercenter | C2×D4 | AGL(1,𝔽11) |
| hypocenter | C11 | C5×#121 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D4×C11⋊C5 | C2 | semidirect |
| 2. C2×C22⋊AGL(1,𝔽11) | C2 | semidirect |
| 3. C2×C22⋊AGL(1,𝔽11) | C2 | semidirect |
| 4. C22×Dic11⋊C5 | C2 | semidirect |
| 5. C22⋊(Dic11⋊C5) | C2 | semidirect |
| 6. ((C2×D11)⋊C4)⋊C5 | C2 | semidirect |
| 7. (Dic11⋊C4)⋊C5 | C2 | semidirect |
| 19. #66992 | C5 | semidirect |
| 25. C22×C11⋊C5 | D4 | semidirect |
| 33. Dic11⋊C5 | D4 | semidirect |
| 34. C2×D4×C11 | C2×C5 | semidirect |
| 35. C2×C22⋊D11 | C2×C5 | semidirect |
| 36. C2×C22⋊D11 | C2×C5 | semidirect |
| 37. C22×Dic11 | C2×C5 | semidirect |
| 38. C22⋊Dic11 | C2×C5 | semidirect |
| 39. (C2×D11)⋊C4 | C2×C5 | semidirect |
| 40. Dic11⋊C4 | C2×C5 | semidirect |
| 66. C11⋊C5 | #121 | semidirect |
| 72. C22×C11 | C5×D4 | semidirect |
| 80. Dic11 | C5×D4 | semidirect |
| 115. C2×D4 | AGL(1,𝔽11) | semidirect |
| 120. C11 | C5×#121 | semidirect |
| 147. C22 | 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×D4×C11⋊C5 | 2 |
| C2×C22⋊AGL(1,𝔽11) | 2 |
| C22×Dic11⋊C5 | 2 |
| C22⋊(Dic11⋊C5) | 2 |
| ((C2×D11)⋊C4)⋊C5 | 2 |
| (Dic11⋊C4)⋊C5 | 2 |
| #66992 | 5 |
| C5×#121 | 11 |