Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1062 conjugacy classes of subgroups.
The subgroup lattice has 246 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C2×C4 | C25 |
| commutator, socle | C22 | C24×C4 |
| prime radical | C22×#41 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2925 | C2 | semidirect |
| 3. #2924 | C2 | semidirect |
| 4. #2923 | C2 | semidirect |
| 5. #2920 | C2 | semidirect |
| 6. C2×#432 | C2 | semidirect |
| 7. #2906 | C2 | semidirect |
| 9. #2875 | C2 | semidirect |
| 26. #433 | C22 | semidirect |
| 30. #432 | C22 | semidirect |
| 31. #432 | C22 | semidirect |
| 32. #432 | C22 | semidirect |
| 34. #431 | C22 | semidirect |
| 35. #424 | C22 | semidirect |
| 36. #423 | C22 | semidirect |
| 37. C2×C4⋊C8 | C22 | semidirect |
| 41. #405 | C22 | semidirect |
| 42. C4×M16 | C22 | semidirect |
| 43. C2×#97 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#41 | 2 |
| #2925 | 2 |
| #2924 | 2 |
| #2923 | 2 |
| #2920 | 2 |
| C2×#432 | 2 |
| #2906 | 2 |
| #2880 | 2 |
| #2875 | 2 |