Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
457 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 457 conjugacy classes of subgroups — too many to draw. Only its 169 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 | C22×D4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| socle | C22 | C2×C4×D4 |
| prime radical | #3147 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#444 | C2 | semidirect |
| 3. #2935 | C2 | semidirect |
| 4. #1980 | C2 | semidirect |
| 5. #1975 | C2 | semidirect |
| 6. #1876 | C2 | semidirect |
| 7. C4×#108 | C2 | semidirect |
| 8. #1770 | C2 | semidirect |
| 13. #495 | C4 | semidirect |
| 14. #495 | C4 | semidirect |
| 15. #494 | C4 | semidirect |
| 16. #493 | C4 | semidirect |
| 17. #492 | C4 | semidirect |
| 65. #108 | D4 | semidirect |
| 178. C4 | #444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3147 | 2 |
| C2×#444 | 2 |
| #2935 | 2 |
| #1980 | 2 |
| #1975 | 2 |
| #1876 | 2 |
| C4×#108 | 2 |
| #1770 | 2 |