Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
2409 conjugacy classes of subgroups; only the 991 normal subgroups are shown.
This group has 2409 conjugacy classes of subgroups — too many to draw. Only its 991 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 | C22×C22⋊C4 |
| commutator | C22 | C24×C4 |
| Frattini, cosocle | C23 | C25 |
| prime radical | C22×2−1+4 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×Q8 ◁ G | |
| LECS | G ▷ C23 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#519 | C2 | semidirect |
| 3. #2884 | C2 | direct (N × H) |
| 4. C2×#410 | C2 | semidirect |
| 7. C2×2−1+4 | C4 | semidirect |
| 9. C22×#41 | C4 | semidirect |
| 11. C23×Q8 | C4 | semidirect |
| 14. #519 | C22 | semidirect |
| 17. #410 | C22 | semidirect |
| 26. C2×#41 | C2×C4 | semidirect |
| 33. C22×Q8 | C2×C4 | semidirect |
| 131. C2 | #2884 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×2−1+4 | 2 |
| C2×#519 | 2 |
| #2884 | 2 |
| C2×#410 | 2 |