Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
662 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 131 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×D41 |
| commutator, socle, cosocle | C22×C41 | C24 |
| Fitting | #120×C41 | C2 |
| hypercenter | #120 | D41 |
| hypocenter | C41 | C2×#120 |
| LCS | G ▷ C22×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×D41 | C2 | semidirect |
| 2. C2×D4×D41 | C2 | semidirect |
| 3. #13050134 | C2 | semidirect |
| 4. #13050133 | C2 | semidirect |
| 5. #13050132 | C2 | semidirect |
| 6. C22⋊C4×D41 | C2 | semidirect |
| 7. #120×C41 | C2 | semidirect |
| 8. C24×C41 | C22 | semidirect |
| 11. C23×D41 | C22 | semidirect |
| 12. C23×D41 | C22 | semidirect |
| 13. C2×D4×C41 | C22 | semidirect |
| 14. C2×C22⋊D41 | C22 | semidirect |
| 15. C2×C22⋊D41 | C22 | semidirect |
| 17. C2×D164 | C22 | semidirect |
| 18. C2×C4×D41 | C22 | semidirect |
| 19. C22⋊C4×C41 | C22 | semidirect |
| 20. C22⋊Dic41 | C22 | semidirect |
| 21. #10620281 | C22 | semidirect |
| 24. C23×C41 | C23 | semidirect |
| 30. C22×D41 | D4 | semidirect |
| 33. C22×D41 | C23 | semidirect |
| 35. C2×C4×C41 | C23 | semidirect |
| 38. C2×Dic41 | C23 | semidirect |
| 44. C22×C41 | C2×D4 | semidirect |
| 52. C2×D41 | C2×D4 | semidirect |
| 60. D41 | #120 | direct (N × H) |
| 62. C41 | C2×#120 | semidirect |
| 68. #120 | D41 | direct (N × H) |
| 74. C24 | C2×D41 | semidirect |
| 79. C2×D4 | C2×D41 | semidirect |
| 83. C22⋊C4 | C2×D41 | semidirect |
| 95. C23 | C22×D41 | semidirect |
| 102. C2×C4 | C22×D41 | semidirect |
| 113. C22 | D4×D41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D41 | 2 |
| C2×D4×D41 | 2 |
| #13050134 | 2 |
| #13050133 | 2 |
| #13050132 | 2 |
| C22⋊C4×D41 | 2 |
| #120×C41 | 2 |
| C2×#120 | 41 |