Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
813 conjugacy classes of subgroups; only the 439 normal subgroups are shown.
This group has 813 conjugacy classes of subgroups — too many to draw. Only its 439 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 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25 |
| prime radical | C24 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×#117 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #3242 | C2 | semidirect |
| 4. #3166 | C2 | semidirect |
| 5. #3139 | C2 | semidirect |
| 7. #3078 | C2 | semidirect |
| 25. #501 | C22 | semidirect |
| 26. #499 | C22 | semidirect |
| 27. #491 | C22 | semidirect |
| 28. #487 | C22 | semidirect |
| 32. #479 | C22 | semidirect |
| 33. #477 | C22 | semidirect |
| 34. #475 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3458 | 2 |
| C2×#541 | 2 |
| #3242 | 2 |
| #3166 | 2 |
| #3139 | 2 |
| #3095 | 2 |
| #3078 | 2 |
| #2921 | 2 |