Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
2639 conjugacy classes of subgroups; only the 999 normal subgroups are shown.
This group has 2639 conjugacy classes of subgroups — too many to draw. Only its 999 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22⋊C4 |
| commutator | C22 | C24×C4 |
| Frattini, cosocle | C23 | C25 |
| socle | C23 | C2×C22⋊C4 |
| prime radical | C23×#41 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C23 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#117 | C2 | semidirect |
| 3. C2×#410 | C2 | direct (N × H) |
| 4. C22×#99 | C2 | semidirect |
| 8. C22×#41 | C4 | semidirect |
| 10. C23×Q8 | C4 | semidirect |
| 11. C23×D4 | C4 | semidirect |
| 13. C24×C4 | C4 | semidirect |
| 16. C2×#117 | C22 | semidirect |
| 20. #410 | C22 | direct (N × H) |
| 21. C2×#99 | C22 | semidirect |
| 30. C2×#41 | C2×C4 | semidirect |
| 34. C22×Q8 | C2×C4 | semidirect |
| 40. C22×D4 | C2×C4 | semidirect |
| 50. C23×C4 | C2×C4 | semidirect |
| 56. #117 | C23 | semidirect |
| 61. #99 | C23 | semidirect |
| 78. C2×Q8 | C22×C4 | semidirect |
| 86. C2×D4 | C22×C4 | semidirect |
| 107. C22×C4 | C22×C4 | semidirect |
| 170. C22 | #410 | direct (N × H) |
| 186. C2 | C2×#410 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#41 | 2 |
| C22×#117 | 2 |
| C2×#410 | 2 |
| C22×#99 | 2 |