Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
959 conjugacy classes of subgroups; only the 467 normal subgroups are shown.
This group has 959 conjugacy classes of subgroups — too many to draw. Only its 467 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C24 |
| commutator, Frattini, socle, cosocle | C23 | C25 |
| prime radical | C22×#41 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2811 | C2 | semidirect |
| 2. #2809 | C2 | semidirect |
| 3. #2784 | C2 | semidirect |
| 4. #2732 | C2 | semidirect |
| 5. #2396 | C2 | semidirect |
| 6. C4×C22⋊Q8 | C2 | semidirect |
| 35. C2×#41 | Q8 | semidirect |
| 75. C2×Q8 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2811 | 2 |
| #2809 | 2 |
| #2784 | 2 |
| #2732 | 2 |
| #2396 | 2 |
| C4×C22⋊Q8 | 2 |
| #2297 | 2 |