Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
575 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 575 conjugacy classes of subgroups — too many to draw. Only its 197 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 | #3480 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×Q8 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×M16 | C2 | semidirect |
| 3. C42×Q8 | C2 | semidirect |
| 4. #1980 | C2 | semidirect |
| 5. #1962 | C2 | semidirect |
| 6. #1806 | C2 | semidirect |
| 7. C4×#104 | C2 | semidirect |
| 8. #559 | C4 | semidirect |
| 9. #557 | C4 | semidirect |
| 10. #556 | C4 | semidirect |
| 12. #550 | C4 | semidirect |
| 106. M16 | #41 | semidirect |
| 136. C42 | #41 | semidirect |
| 142. Q8 | #104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3480 | 2 |
| Q8×M16 | 2 |
| C42×Q8 | 2 |
| #1980 | 2 |
| #1962 | 2 |
| #1806 | 2 |
| C4×#104 | 2 |