Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
549 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 549 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24 |
| prime radical | C2×#459 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C43 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#474 | C2 | semidirect |
| 3. #2858 | C2 | semidirect |
| 4. C42×D4 | C2 | semidirect |
| 5. #1988 | C2 | semidirect |
| 6. #1982 | C2 | semidirect |
| 7. #1925 | C2 | semidirect |
| 8. #1879 | C2 | semidirect |
| 9. #1831 | C2 | semidirect |
| 134. C42 | D8 | semidirect |
| 156. D4 | #124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#474 | 2 |
| C2×#459 | 2 |
| #2858 | 2 |
| C42×D4 | 2 |
| #1988 | 2 |
| #1982 | 2 |
| #1925 | 2 |
| #1879 | 2 |
| #1831 | 2 |