Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
2046 conjugacy classes of subgroups; only the 1659 normal subgroups are shown.
This group has 2046 conjugacy classes of subgroups — too many to draw. Only its 1659 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C43 | D61 |
| commutator, hypocenter | C61 | C2×C42×C8 |
| Frattini | C22×C4 | C23×D61 |
| Fitting | C2×C43×C61 | C2 |
| socle, prime radical | C24×C61 | C22×C4 |
| cosocle | C22×C4×C61 | C24 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C42×#92418 | C2 | direct (N × H) |
| 5. C2×C4×#92418 | C4 | direct (N × H) |
| 13. C4×#92418 | C2×C4 | direct (N × H) |
| 16. C2×C42×C61 | C8 | semidirect |
| 29. C42×C61 | C2×C8 | semidirect |
| 31. C2×#92418 | C42 | direct (N × H) |
| 36. C2×C4×C61 | C4×C8 | semidirect |
| 42. #92418 | C2×C42 | direct (N × H) |
| 49. C4×C61 | C2×C4×C8 | semidirect |
| 54. C2×C61 | C42×C8 | semidirect |
| 64. C61 | C2×C42×C8 | semidirect |
| 69. C2×C42 | #92418 | direct (N × H) |
| 84. C42 | C2×#92418 | direct (N × H) |
| 90. C2×C4 | C4×#92418 | direct (N × H) |
| 102. C4 | C2×C4×#92418 | direct (N × H) |
| 104. C2 | C42×#92418 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#92418 | 2 |
| C42×#92418 | 2 |
| C2×C43×C61 | 2 |
| C2×C42×C8 | 61 |