Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
297 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 297 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24 |
| prime radical | #3050 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#467 | C2 | semidirect |
| 3. #2237 | C2 | semidirect |
| 4. #2235 | C2 | semidirect |
| 5. #2232 | C2 | semidirect |
| 6. #2217 | C2 | semidirect |
| 7. #2216 | C2 | semidirect |
| 8. #2189 | C2 | semidirect |
| 9. #2188 | C2 | semidirect |
| 10. #2185 | C2 | semidirect |
| 11. C2×C22⋊C16 | C2 | semidirect |
| 17. C2×Q32 | C22 | semidirect |
| 18. C2×SD32 | C22 | semidirect |
| 34. #367 | C22 | semidirect |
| 35. #366 | C22 | semidirect |
| 36. #358 | C22 | semidirect |
| 37. #358 | C22 | semidirect |
| 38. #358 | C22 | semidirect |
| 39. #357 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3050 | 2 |
| C2×#467 | 2 |
| #2237 | 2 |
| #2235 | 2 |
| #2232 | 2 |
| #2217 | 2 |
| #2216 | 2 |
| #2189 | 2 |
| #2188 | 2 |
| #2185 | 2 |
| C2×C22⋊C16 | 2 |