Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
2046 conjugacy classes of subgroups; only the 1152 normal subgroups are shown.
This group has 2046 conjugacy classes of subgroups — too many to draw. Only its 1152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | #595 |
| commutator, hypocenter | C17 | C2×C42×C8 |
| Frattini | C23 | C23×#595 |
| Fitting | C43×C17 | C4 |
| socle | C23×C17 | C23×C4 |
| prime radical | C23×D17 | C22×C4 |
| cosocle | C22×Dic17 | C24 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C42×#3624 | C2 | semidirect |
| 5. C4×#63242 | C4 | direct (N × H) |
| 21. C42×D17 | C8 | semidirect |
| 23. C4×#3624 | C2×C4 | semidirect |
| 33. #63242 | C42 | direct (N × H) |
| 35. C42×C17 | C2×C8 | semidirect |
| 37. C4×Dic17 | C2×C8 | semidirect |
| 49. C4×D17 | C4×C8 | semidirect |
| 51. #3624 | C2×C42 | semidirect |
| 60. C4×C17 | C2×C4×C8 | semidirect |
| 61. Dic17 | C2×C4×C8 | semidirect |
| 73. D17 | C42×C8 | semidirect |
| 86. C17 | C2×C42×C8 | semidirect |
| 100. C42 | #63242 | direct (N × H) |
| 121. C4 | C4×#63242 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#63242 | 2 |
| C42×#3624 | 2 |
| C43×D17 | 2 |
| C2×C42×C8 | 17 |