Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1253 conjugacy classes of subgroups; only the 487 normal subgroups are shown.
This group has 1253 conjugacy classes of subgroups — too many to draw. Only its 487 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C23 | C25 |
| prime radical | C23×D4 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#543 | C2 | semidirect |
| 3. #2561 | C2 | semidirect |
| 4. #2503 | C2 | semidirect |
| 5. #2488 | C2 | semidirect |
| 7. C2×#381 | C2 | semidirect |
| 8. #2273 | C2 | semidirect |
| 15. C2×C22⋊Q8 | C22 | semidirect |
| 21. #400 | C22 | semidirect |
| 22. #397 | C22 | semidirect |
| 23. #393 | C22 | semidirect |
| 24. #391 | C22 | semidirect |
| 25. #388 | C22 | semidirect |
| 28. #382 | C22 | semidirect |
| 31. #381 | C22 | semidirect |
| 34. C4×C22⋊C4 | C22 | semidirect |
| 35. C2×#95 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#543 | 2 |
| C22×#123 | 2 |
| #2561 | 2 |
| #2503 | 2 |
| #2488 | 2 |
| #2308 | 2 |
| C2×#381 | 2 |
| #2273 | 2 |