Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
2590 conjugacy classes of subgroups; only the 1464 normal subgroups are shown.
This group has 2590 conjugacy classes of subgroups — too many to draw. Only its 1464 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | #595 |
| commutator, hypocenter | C17 | C24×C16 |
| Frattini | C4 | C24×#595 |
| Fitting | C23×C8×C17 | C4 |
| socle | C24×C17 | C2×C8 |
| prime radical | C24×D17 | C8 |
| cosocle | #3622 | C25 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C23×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#10587529 | C2 | direct (N × H) |
| 2. C23×#63216 | C2 | semidirect |
| 4. C2×#10587529 | C22 | direct (N × H) |
| 5. C22×#63216 | C22 | semidirect |
| 21. C2×#63216 | C23 | semidirect |
| 22. #10587529 | C23 | direct (N × H) |
| 24. C23×D17 | C16 | semidirect |
| 36. #63216 | C24 | semidirect |
| 38. C23×C17 | C2×C16 | semidirect |
| 40. C22×D17 | C2×C16 | semidirect |
| 53. C22×C17 | C22×C16 | semidirect |
| 55. C2×D17 | C22×C16 | semidirect |
| 67. C2×C17 | C23×C16 | semidirect |
| 69. D17 | C23×C16 | semidirect |
| 82. C17 | C24×C16 | semidirect |
| 99. C23 | #10587529 | direct (N × H) |
| 111. C22 | C2×#10587529 | direct (N × H) |
| 117. C2 | C22×#10587529 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587529 | 2 |
| C23×#63216 | 2 |
| C23×C8×D17 | 2 |
| C24×C16 | 17 |