Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
569 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 569 conjugacy classes of subgroups — too many to draw. Only its 183 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. C2×#442 | C2 | semidirect |
| 3. C22×#106 | C2 | semidirect |
| 4. #2361 | C2 | semidirect |
| 5. #1972 | C2 | semidirect |
| 6. #1943 | C2 | semidirect |
| 7. #1926 | C2 | semidirect |
| 8. #1874 | C2 | semidirect |
| 9. #1864 | C2 | semidirect |
| 10. #1776 | C2 | semidirect |
| 11. #1752 | C2 | semidirect |
| 18. #466 | C4 | semidirect |
| 49. C2×D8 | C2×C4 | semidirect |
| 52. C22×C8 | C2×C4 | semidirect |
| 58. #121 | C2×C4 | semidirect |
| 77. #107 | C2×C4 | semidirect |
| 80. #106 | D4 | semidirect |
| 83. #102 | C2×C4 | semidirect |
| 203. C8 | C4×D4 | semidirect |
| 215. C22 | #442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#466 | 2 |
| C2×#442 | 2 |
| C22×#106 | 2 |
| #2361 | 2 |
| #1972 | 2 |
| #1943 | 2 |
| #1926 | 2 |
| #1874 | 2 |
| #1864 | 2 |
| #1776 | 2 |
| #1752 | 2 |