Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
398 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | #3633 |
| commutator, hypocenter | C17 | C2×C8×C16 |
| Frattini | C2×C4 | C22×#3633 |
| Fitting | C22×C8×C17 | C8 |
| socle, prime radical | C23×C17 | C4×C8 |
| cosocle | C4×#3624 | C23 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C22×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C8×#63241 | C2 | direct (N × H) |
| 14. C2×#63241 | C8 | direct (N × H) |
| 29. C2×#3624 | C16 | semidirect |
| 34. #63241 | C2×C8 | direct (N × H) |
| 35. C2×C8×C17 | C16 | semidirect |
| 41. C2×#3622 | C16 | semidirect |
| 56. #3624 | C2×C16 | semidirect |
| 58. C8×C17 | C2×C16 | semidirect |
| 59. #3622 | C2×C16 | semidirect |
| 82. C2×C17 | C8×C16 | semidirect |
| 100. C17 | C2×C8×C16 | semidirect |
| 111. C2×C8 | #63241 | direct (N × H) |
| 133. C8 | C2×#63241 | direct (N × H) |
| 145. C2 | C8×#63241 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#63241 | 2 |
| C8×#63241 | 2 |
| C2×C8×#3624 | 2 |
| C2×C8×C16 | 17 |