Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
619 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 619 conjugacy classes of subgroups — too many to draw. Only its 191 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×#493 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×D8 | C2 | semidirect |
| 3. #2366 | C2 | semidirect |
| 4. #1982 | C2 | semidirect |
| 5. #1970 | C2 | semidirect |
| 6. #1879 | C2 | semidirect |
| 7. C4×#107 | C2 | semidirect |
| 8. C8×C4⋊C4 | C2 | semidirect |
| 14. #493 | C4 | semidirect |
| 38. C2×D8 | C2×C4 | semidirect |
| 39. C2×D8 | C2×C4 | semidirect |
| 44. #127 | C2×C4 | semidirect |
| 59. #107 | D4 | semidirect |
| 64. C4×C8 | C2×C4 | semidirect |
| 105. C4⋊C4 | D8 | semidirect |
| 156. C8 | C4×D4 | semidirect |
| 176. C4 | C4×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#493 | 2 |
| C2×C4×D8 | 2 |
| #2366 | 2 |
| #1982 | 2 |
| #1970 | 2 |
| #1879 | 2 |
| C4×#107 | 2 |
| C8×C4⋊C4 | 2 |