Finite Group DatabasebetaFinite Group DatabasebetaOrder 2640.
132 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C11×A4 | C22×C5 |
| Fitting, socle | C22×C11 | C2×C5×D3 |
| LCS | G ▷ C11×A4 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. A4×AGL(1,𝔽11) | C2 | semidirect |
| 2. A4⋊AGL(1,𝔽11) | C2 | semidirect |
| 3. S4×C11⋊C5 | C2 | semidirect |
| 5. A4×C11⋊C5 | C22 | semidirect |
| 7. D11×S4 | C5 | semidirect |
| 9. C22×AGL(1,𝔽11) | D3 | semidirect |
| 18. A4×D11 | C2×C5 | semidirect |
| 19. C11⋊S4 | C2×C5 | semidirect |
| 20. C11×S4 | C2×C5 | semidirect |
| 23. C22×C11⋊C5 | C2×D3 | semidirect |
| 33. C11×A4 | C22×C5 | semidirect |
| 42. AGL(1,𝔽11) | S4 | direct (N × H) |
| 44. C22×D11 | C5×D3 | semidirect |
| 56. C11⋊C5 | C2×S4 | semidirect |
| 59. C22×C11 | C2×C5×D3 | semidirect |
| 80. S4 | AGL(1,𝔽11) | direct (N × H) |
| 85. D11 | C5×S4 | semidirect |
| 98. A4 | C2×AGL(1,𝔽11) | semidirect |
| 99. C11 | C2×C5×S4 | semidirect |
| 122. C22 | D3×AGL(1,𝔽11) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×AGL(1,𝔽11) | 2 |
| A4⋊AGL(1,𝔽11) | 2 |
| S4×C11⋊C5 | 2 |
| D4×AGL(1,𝔽11) | 3 |
| D3×AGL(1,𝔽11) | 4 |
| D11×S4 | 5 |
| C2×C5×S4 | 11 |