Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
981 conjugacy classes of subgroups; only the 519 normal subgroups are shown.
This group has 981 conjugacy classes of subgroups — too many to draw. Only its 519 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. #3082 | C2 | semidirect |
| 4. #3078 | C2 | semidirect |
| 23. #479 | C22 | semidirect |
| 24. #477 | C22 | semidirect |
| 25. #475 | C22 | semidirect |
| 37. C22×Q8 | Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3458 | 2 |
| C2×#519 | 2 |
| #3082 | 2 |
| #3078 | 2 |
| #2911 | 2 |
| #2905 | 2 |
| C2×#419 | 2 |