Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
261 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×C22⋊C4 |
| commutator | C2×C4 | C2×C42 |
| Frattini, cosocle | C23×C4 | C23 |
| socle | C22 | C4×C22⋊C4 |
| prime radical | #525 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C8 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1752 | C2 | semidirect |
| 3. C8×C22⋊C4 | C2 | semidirect |
| 6. #1298 | C2 | semidirect |
| 7. #1297 | C2 | semidirect |
| 8. C2×#131 | C4 | semidirect |
| 15. #424 | C4 | semidirect |
| 16. #408 | C4 | semidirect |
| 20. #405 | C4 | semidirect |
| 27. #328 | C4 | semidirect |
| 28. #328 | C4 | semidirect |
| 29. #327 | C4 | semidirect |
| 30. #327 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2929 | 2 |
| #1752 | 2 |
| C8×C22⋊C4 | 2 |
| #1501 | 2 |
| #1298 | 2 |
| #1297 | 2 |