Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
24030 conjugacy classes of subgroups; only the 4939 normal subgroups are shown.
This group has 24030 conjugacy classes of subgroups — too many to draw. Only its 4939 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C25 | C22×D61 |
| commutator, cosocle | C22×C61 | C26 |
| Frattini | C22 | C25×D61 |
| Fitting | C24×D4×C61 | C2 |
| socle | C25×C61 | C23 |
| hypercenter | C24×D4 | D61 |
| hypocenter | C61 | C23×#127 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C25 ◁ C24×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×D244 | C2 | semidirect |
| 2. C24×C22⋊D61 | C2 | semidirect |
| 3. C22×#14519773 | C2 | direct (N × H) |
| 4. C23×C4×Dic61 | C2 | semidirect |
| 5. C24×D4×C61 | C2 | semidirect |
| 8. C23×D244 | C22 | semidirect |
| 10. C23×C22⋊D61 | C22 | semidirect |
| 12. C2×#14519773 | C22 | direct (N × H) |
| 13. C22×C4×Dic61 | C22 | semidirect |
| 16. C23×D4×C61 | C22 | semidirect |
| 22. C22×D244 | C23 | semidirect |
| 24. C22×C22⋊D61 | C23 | semidirect |
| 25. C23×Dic61 | D4 | semidirect |
| 27. #14519773 | C23 | direct (N × H) |
| 28. C2×C4×Dic61 | C23 | semidirect |
| 34. C22×D4×C61 | C23 | semidirect |
| 35. C23×C4×C61 | D4 | semidirect |
| 49. C2×D4×C61 | C24 | semidirect |
| 50. C22×C4×C61 | C2×D4 | semidirect |
| 53. C2×C22⋊D61 | C24 | semidirect |
| 54. C22×Dic61 | C2×D4 | semidirect |
| 57. C2×D244 | C24 | semidirect |
| 58. C4×Dic61 | C24 | semidirect |
| 62. C23×C61 | #127 | semidirect |
| 72. C2×C4×C61 | C22×D4 | semidirect |
| 75. C2×Dic61 | C22×D4 | semidirect |
| 82. C22×C61 | C2×#127 | semidirect |
| 89. C4×C61 | C23×D4 | semidirect |
| 90. Dic61 | C23×D4 | semidirect |
| 93. C24×D4 | D61 | semidirect |
| 97. C2×C61 | C22×#127 | semidirect |
| 108. C23×D4 | C2×D61 | semidirect |
| 113. C61 | C23×#127 | semidirect |
| 126. C22×D4 | C22×D61 | semidirect |
| 129. C23×C4 | C22⋊D61 | semidirect |
| 149. C2×D4 | C23×D61 | semidirect |
| 152. C22×C4 | C2×C22⋊D61 | semidirect |
| 162. C23 | #14519773 | direct (N × H) |
| 172. C2×C4 | C22×C22⋊D61 | semidirect |
| 180. C22 | C2×#14519773 | direct (N × H) |
| 185. C4 | C23×C22⋊D61 | semidirect |
| 188. C2 | C22×#14519773 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D244 | 2 |
| C24×C22⋊D61 | 2 |
| C22×#14519773 | 2 |
| C23×C4×Dic61 | 2 |
| C24×D4×C61 | 2 |
| C23×#127 | 61 |