Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
519 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 519 conjugacy classes of subgroups — too many to draw. Only its 179 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×D4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | C22×D8 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×SD16 | C2 | semidirect |
| 3. #2367 | C2 | semidirect |
| 4. #1983 | C2 | semidirect |
| 5. #1968 | C2 | semidirect |
| 7. #1878 | C2 | semidirect |
| 8. C4×#106 | C2 | semidirect |
| 9. C8×C4⋊C4 | C2 | semidirect |
| 16. #495 | C4 | semidirect |
| 42. C2×Q16 | C2×C4 | semidirect |
| 45. C2×SD16 | C2×C4 | semidirect |
| 53. #124 | C2×C4 | semidirect |
| 79. C4×C8 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#495 | 2 |
| C2×C4×SD16 | 2 |
| #2367 | 2 |
| #1983 | 2 |
| #1968 | 2 |
| #1879 | 2 |
| #1878 | 2 |
| C4×#106 | 2 |
| C8×C4⋊C4 | 2 |