Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
785 conjugacy classes of subgroups; only the 239 normal subgroups are shown.
This group has 785 conjugacy classes of subgroups — too many to draw. Only its 239 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 | #3449 | 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. #2905 | C2 | semidirect |
| 3. C2×#421 | C2 | semidirect |
| 4. C22×#104 | C2 | semidirect |
| 5. C4×#117 | C2 | semidirect |
| 6. #1963 | C2 | semidirect |
| 7. #1962 | C2 | semidirect |
| 11. #536 | C4 | semidirect |
| 12. #535 | C4 | semidirect |
| 20. #423 | C22 | semidirect |
| 23. C2×#104 | C22 | semidirect |
| 24. C2×#104 | C22 | semidirect |
| 25. C2×#104 | C22 | semidirect |
| 28. #376 | C22 | semidirect |
| 29. C43 | C22 | semidirect |
| 49. C4⋊Q8 | C2×C4 | semidirect |
| 50. #127 | C2×C4 | semidirect |
| 51. #124 | C2×C4 | semidirect |
| 61. #117 | D4 | semidirect |
| 69. C2×C42 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3449 | 2 |
| #2905 | 2 |
| C2×#421 | 2 |
| C22×#104 | 2 |
| C4×#117 | 2 |
| #1963 | 2 |
| #1962 | 2 |