Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
539 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 539 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, socle | C23 | C22×D4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | C2×#466 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2361 | C2 | semidirect |
| 3. #1934 | C2 | semidirect |
| 4. #1918 | C2 | semidirect |
| 5. #1879 | C2 | semidirect |
| 6. #1874 | C2 | semidirect |
| 7. C4×#102 | C2 | semidirect |
| 8. C8×C22⋊C4 | C2 | semidirect |
| 9. C2×#340 | C2 | semidirect |
| 16. #466 | C4 | semidirect |
| 42. C2×D8 | C2×C4 | semidirect |
| 44. C22×C8 | C2×C4 | semidirect |
| 49. #121 | C2×C4 | semidirect |
| 68. #107 | C2×C4 | semidirect |
| 71. #102 | C2×C4 | semidirect |
| 127. C22⋊C4 | D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#466 | 2 |
| #2361 | 2 |
| #1934 | 2 |
| #1918 | 2 |
| #1879 | 2 |
| #1874 | 2 |
| C4×#102 | 2 |
| C8×C22⋊C4 | 2 |
| C2×#340 | 2 |