Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
529 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 529 conjugacy classes of subgroups — too many to draw. Only its 183 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 | C22×C22⋊C4 |
| prime radical | #3455 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#117 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2921 | C2 | semidirect |
| 3. #2296 | C2 | semidirect |
| 4. #1986 | C2 | semidirect |
| 5. #1980 | C2 | semidirect |
| 6. #1897 | C2 | semidirect |
| 7. #1896 | C2 | semidirect |
| 8. #1806 | C2 | semidirect |
| 9. #542 | C4 | semidirect |
| 10. #541 | C4 | semidirect |
| 11. #540 | C4 | semidirect |
| 38. C4⋊Q8 | C2×C4 | semidirect |
| 39. C4⋊Q8 | C2×C4 | semidirect |
| 40. #127 | C2×C4 | semidirect |
| 44. #125 | C2×C4 | semidirect |
| 46. #124 | C2×C4 | semidirect |
| 58. C4×Q8 | C2×C4 | semidirect |
| 62. C4×D4 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3455 | 2 |
| #2921 | 2 |
| #2296 | 2 |
| #1986 | 2 |
| #1980 | 2 |
| #1897 | 2 |
| #1896 | 2 |
| #1806 | 2 |