Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
65470 conjugacy classes of subgroups; only the 32651 normal subgroups are shown.
This group has 65470 conjugacy classes of subgroups — too many to draw. Only its 32651 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24×C4 | C2×D61 |
| commutator, cosocle | C2×C61 | C27 |
| Frattini | C2 | C26×D61 |
| Fitting | C25×C4×C61 | C2 |
| socle | C25×C61 | C23 |
| hypercenter | C25×C4 | D61 |
| hypocenter | C61 | C24×#41 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C24×C4 ◁ C25×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#11758222 | C2 | direct (N × H) |
| 2. C24×Dic122 | C2 | semidirect |
| 3. C24×D244 | C2 | semidirect |
| 4. C24×C22⋊D61 | C2 | semidirect |
| 5. C24×C4×D61 | C2 | semidirect |
| 6. C25×C4×C61 | C2 | semidirect |
| 8. C22×#11758222 | C22 | direct (N × H) |
| 9. C23×Dic122 | C22 | semidirect |
| 10. C23×D244 | C22 | semidirect |
| 11. C23×C22⋊D61 | C22 | semidirect |
| 13. C23×C4×D61 | C22 | semidirect |
| 17. C24×C4×C61 | C22 | semidirect |
| 20. C2×#11758222 | C23 | direct (N × H) |
| 21. C22×Dic122 | C23 | semidirect |
| 22. C22×D244 | C23 | semidirect |
| 23. C22×C22⋊D61 | C23 | semidirect |
| 25. C22×C4×D61 | C23 | semidirect |
| 31. C23×C4×C61 | C23 | semidirect |
| 33. C24×C61 | #41 | semidirect |
| 40. C22×C4×C61 | C24 | semidirect |
| 41. C2×C22⋊D61 | C24 | semidirect |
| 43. #11758222 | C24 | direct (N × H) |
| 44. C2×D244 | C24 | semidirect |
| 45. C2×C4×D61 | C24 | semidirect |
| 46. C2×Dic122 | C24 | semidirect |
| 48. C23×C61 | C2×#41 | semidirect |
| 55. C2×C4×C61 | C25 | semidirect |
| 56. C22⋊D61 | C25 | semidirect |
| 58. D244 | C25 | semidirect |
| 59. C4×D61 | C25 | semidirect |
| 60. Dic122 | C25 | semidirect |
| 63. C22×C61 | C22×#41 | semidirect |
| 76. C25×C4 | D61 | semidirect |
| 78. C2×C61 | C23×#41 | semidirect |
| 91. C24×C4 | C2×D61 | semidirect |
| 92. C61 | C24×#41 | semidirect |
| 106. C23×C4 | C22×D61 | semidirect |
| 110. C24 | #11758222 | direct (N × H) |
| 121. C22×C4 | C23×D61 | semidirect |
| 125. C23 | C2×#11758222 | direct (N × H) |
| 135. C2×C4 | C24×D61 | semidirect |
| 139. C22 | C22×#11758222 | direct (N × H) |
| 147. C2 | C23×#11758222 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11758222 | 2 |
| C24×Dic122 | 2 |
| C24×D244 | 2 |
| C24×C22⋊D61 | 2 |
| C24×C4×D61 | 2 |
| C25×C4×C61 | 2 |
| C24×#41 | 61 |