Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1342 conjugacy classes of subgroups; only the 811 normal subgroups are shown.
This group has 1342 conjugacy classes of subgroups — too many to draw. Only its 811 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×C82 | D61 |
| commutator, hypocenter | C61 | C22×C82 |
| Frattini | C42 | C23×D61 |
| Fitting | C2×C82×C61 | C2 |
| socle | C23×C61 | C2×C42 |
| prime radical | C23×D61 | C42 |
| cosocle | C42×C61 | C24 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C82 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C8×#92418 | C2 | semidirect |
| 3. C82×D61 | C2 | direct (N × H) |
| 4. C2×C82×C61 | C2 | semidirect |
| 11. C8×#92418 | C22 | semidirect |
| 13. C82×C61 | C22 | semidirect |
| 16. C2×C8×D61 | C8 | direct (N × H) |
| 34. C2×C8×C61 | C2×C8 | semidirect |
| 40. C2×#92418 | C2×C8 | semidirect |
| 42. C8×D61 | C2×C8 | direct (N × H) |
| 53. C8×C61 | C22×C8 | semidirect |
| 54. #92418 | C22×C8 | semidirect |
| 58. C2×D61 | C82 | direct (N × H) |
| 66. C2×C82 | D61 | direct (N × H) |
| 67. C2×C61 | C2×C82 | semidirect |
| 69. D61 | C2×C82 | direct (N × H) |
| 78. C82 | C2×D61 | direct (N × H) |
| 79. C61 | C22×C82 | semidirect |
| 103. C2×C8 | C8×D61 | direct (N × H) |
| 120. C8 | C2×C8×D61 | direct (N × H) |
| 129. C2 | C82×D61 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C8×D61 | 2 |
| C2×C8×#92418 | 2 |
| C82×D61 | 2 |
| C2×C82×C61 | 2 |
| C22×C82 | 61 |