Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
537 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 537 conjugacy classes of subgroups — too many to draw. Only its 163 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×D4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | C2×#496 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C43 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#127 | C2 | semidirect |
| 3. C4×#124 | C2 | semidirect |
| 4. #1961 | C2 | semidirect |
| 5. #1959 | C2 | semidirect |
| 6. #1880 | C2 | semidirect |
| 7. #1879 | C2 | semidirect |
| 8. #1879 | C2 | semidirect |
| 9. #1877 | C2 | semidirect |
| 10. #1836 | C2 | semidirect |
| 11. #1745 | C2 | semidirect |
| 21. #496 | C4 | semidirect |
| 53. C2×SD16 | C2×C4 | semidirect |
| 56. C2×D8 | C2×C4 | semidirect |
| 60. #127 | C2×C4 | semidirect |
| 62. #124 | C2×C4 | semidirect |
| 96. #97 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#496 | 2 |
| C4×#127 | 2 |
| C4×#124 | 2 |
| #1961 | 2 |
| #1959 | 2 |
| #1880 | 2 |
| #1879 | 2 |
| #1877 | 2 |
| #1836 | 2 |
| #1745 | 2 |