Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
552 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 233 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D127 |
| commutator | C22×C127 | C23×C4 |
| Fitting | #382×C127 | C2 |
| socle, prime radical, cosocle | C23×C127 | C24 |
| hypercenter | #382 | D127 |
| hypocenter | C127 | #2351 |
| LCS | G ▷ C22×C127 ▷ C127 | |
| UCS | C1 ◁ C23 ◁ #382 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. C4×Dic254 | C4 | semidirect |
| 48. Dic254 | C4⋊C4 | semidirect |
| 90. C127 | #2351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic254 | 2 |
| C2×#16861174 | 2 |
| #22549773 | 2 |
| #22549772 | 2 |
| #22549740 | 2 |
| C4×C4⋊Dic127 | 2 |
| #22549727 | 2 |
| #382×C127 | 2 |
| #2351 | 127 |