Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
3422 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 3422 conjugacy classes of subgroups — too many to draw. Only its 245 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D11 |
| commutator, socle, cosocle | C23×C11 | C24 |
| Fitting | C2×C11×#120 | C2 |
| hypercenter | C2×#120 | D11 |
| hypocenter | C11 | #2846 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×D11 | C2 | semidirect |
| 2. C2×C11×#120 | C2 | semidirect |
| 3. C2×#66990 | C2 | semidirect |
| 4. #10622860 | C2 | semidirect |
| 5. #10622568 | C2 | semidirect |
| 10. C22×D4×C11 | C22 | semidirect |
| 11. C22×C22⋊D11 | C22 | semidirect |
| 13. C2×C11×C22⋊C4 | C22 | semidirect |
| 14. C2×C22⋊Dic11 | C22 | semidirect |
| 16. C2×(C2×D11)⋊C4 | C22 | semidirect |
| 18. C24×C11 | D4 | semidirect |
| 20. C24×C11 | C23 | semidirect |
| 26. C23×D11 | D4 | semidirect |
| 30. C22×C4×C11 | C23 | semidirect |
| 32. C22×Dic11 | C23 | semidirect |
| 60. C2×#120 | D11 | semidirect |
| 68. C22×C11 | #120 | semidirect |
| 74. C2×D11 | #120 | semidirect |
| 82. C22×D4 | C2×D11 | semidirect |
| 87. C2×C22⋊C4 | C2×D11 | semidirect |
| 101. C24 | C22⋊D11 | semidirect |
| 103. C24 | C22×D11 | semidirect |
| 108. C22×C4 | C22×D11 | semidirect |
| 112. C11 | #2846 | semidirect |
| 143. C22 | #66990 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D11 | 2 |
| C2×C11×#120 | 2 |
| C2×#66990 | 2 |
| #10622860 | 2 |
| #10622568 | 2 |
| #2846 | 11 |