Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
330 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D241 |
| commutator, socle, cosocle | C22×C241 | C24 |
| Frattini | C22 | C23×D241 |
| Fitting | #117×C241 | C2 |
| hypercenter | #117 | D241 |
| hypocenter | C241 | #525 |
| LCS | G ▷ C22×C241 ▷ C241 | |
| UCS | C1 ◁ C2×C4 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16838770 | C2 | semidirect |
| 2. C22×C4×D241 | C2 | semidirect |
| 3. #21440626 | C2 | semidirect |
| 4. #21440622 | C2 | semidirect |
| 5. #21440617 | C2 | semidirect |
| 6. #21440612 | C2 | semidirect |
| 7. C4×D964 | C2 | semidirect |
| 8. #117×C241 | C2 | semidirect |
| 11. C2×Dic482 | C22 | semidirect |
| 13. C2×D964 | C22 | semidirect |
| 19. C2×C4×D241 | C22 | semidirect |
| 20. C4⋊Dic241 | C22 | semidirect |
| 22. #16838747 | C22 | semidirect |
| 24. C4⋊C4×C241 | C22 | semidirect |
| 26. C42×C241 | C22 | semidirect |
| 42. C2×C4×C241 | D4 | semidirect |
| 54. C2×D241 | #41 | semidirect |
| 65. C241 | #525 | semidirect |
| 74. #117 | D241 | semidirect |
| 88. C4⋊C4 | C2×D241 | semidirect |
| 92. C42 | C2×D241 | semidirect |
| 108. C2×C4 | D964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838770 | 2 |
| C22×C4×D241 | 2 |
| #21440626 | 2 |
| #21440622 | 2 |
| #21440617 | 2 |
| #21440612 | 2 |
| C4×D964 | 2 |
| #117×C241 | 2 |
| #525 | 241 |