Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1359 conjugacy classes of subgroups; only the 999 normal subgroups are shown.
This group has 1359 conjugacy classes of subgroups — too many to draw. Only its 999 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D4 |
| commutator | C4 | C24×C4 |
| Frattini, cosocle | C2×C4 | C25 |
| socle | C23 | C2×C4⋊C4 |
| prime radical | C25 | Q8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#430 | C2 | direct (N × H) |
| 4. C22×#108 | C2 | semidirect |
| 15. #430 | C22 | direct (N × H) |
| 16. C2×#108 | C22 | semidirect |
| 39. #108 | C23 | semidirect |
| 105. C22 | #430 | direct (N × H) |
| 118. C2 | C2×#430 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×M16 | 2 |
| C2×#430 | 2 |
| C22×#108 | 2 |