Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
540 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 193 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C22×C4 | C24 |
| commutator | C22 | C23×C8 |
| socle | C23 | C23×C4 |
| prime radical | C2×#120 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1954 | C2 | semidirect |
| 3. #1923 | C2 | semidirect |
| 4. #1869 | C2 | semidirect |
| 5. #1779 | C2 | semidirect |
| 7. C23×C8 | C22 | semidirect |
| 10. C2×C4⋊C8 | C22 | semidirect |
| 13. C2×C22⋊C8 | C22 | semidirect |
| 14. C2×C4×C8 | C22 | semidirect |
| 19. #336 | C22 | semidirect |
| 30. #120 | C8 | semidirect |
| 47. C24 | C2×C8 | semidirect |
| 77. C22⋊C4 | C2×C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#120 | 2 |
| #1954 | 2 |
| #1923 | 2 |
| #1869 | 2 |
| #1779 | 2 |