Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
529 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 529 conjugacy classes of subgroups — too many to draw. Only its 179 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C22×C4 | C24 |
| commutator, socle | C23 | C23×C4 |
| prime radical | C2×#127 | C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#436 | C2 | semidirect |
| 2. C2×C8×D4 | C2 | semidirect |
| 4. #1954 | C2 | semidirect |
| 5. #1954 | C2 | semidirect |
| 6. #1870 | C2 | semidirect |
| 7. #1869 | C2 | semidirect |
| 8. #1831 | C2 | semidirect |
| 9. #1744 | C2 | semidirect |
| 74. C4×C8 | D4 | semidirect |
| 85. C2×D4 | M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#436 | 2 |
| C2×C8×D4 | 2 |
| C4×#127 | 2 |
| #1954 | 2 |
| #1870 | 2 |
| #1869 | 2 |
| #1831 | 2 |
| #1744 | 2 |