Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1195 conjugacy classes of subgroups; only the 487 normal subgroups are shown.
This group has 1195 conjugacy classes of subgroups — too many to draw. Only its 487 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 | C2×#532 | C2 |
| 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. C2×#533 | C2 | semidirect |
| 3. #2642 | C2 | semidirect |
| 4. #2641 | C2 | semidirect |
| 5. #2640 | C2 | semidirect |
| 6. #2639 | C2 | semidirect |
| 7. #2398 | C2 | semidirect |
| 8. #2297 | C2 | semidirect |
| 9. C2×#376 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#533 | 2 |
| C2×#532 | 2 |
| #2642 | 2 |
| #2641 | 2 |
| #2640 | 2 |
| #2639 | 2 |
| #2398 | 2 |
| #2297 | 2 |
| C2×#376 | 2 |