Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
102 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 102 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C251 | #102 |
| commutator | C2×C8 | C2×C4×C251 |
| Frattini, cosocle | C4×C8 | C22×C251 |
| prime radical | C2×D8×C251 | C4 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C251 ◁ C42×C251 ◁ C4×C8×C251 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4⋊C16×C251 | C2 | semidirect |
| 3. #334×C251 | C2 | semidirect |
| 50. C251 | #1360 | direct (N × H) |
| 51. #1360 | C251 | direct (N × H) |
| 53. C4⋊C16 | C2×C251 | semidirect |
| 54. #334 | C2×C251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #495×C251 | 2 |
| C4⋊C16×C251 | 2 |
| #334×C251 | 2 |
| #1360 | 251 |