Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1059 conjugacy classes of subgroups; only the 391 normal subgroups are shown.
This group has 1059 conjugacy classes of subgroups — too many to draw. Only its 391 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C2×D4 |
| commutator | C4 | C22×C42 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | C23×D4 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C22×#97 | C2 | semidirect |
| 4. C2×C4×C4⋊C4 | C2 | semidirect |
| 5. #1762 | C2 | direct (N × H) |
| 6. C2×#340 | C2 | semidirect |
| 12. C2×C4×D4 | C4 | semidirect |
| 19. C2×#102 | C4 | semidirect |
| 22. C2×#97 | C22 | semidirect |
| 24. C4×C4⋊C4 | C22 | semidirect |
| 26. #340 | C22 | semidirect |
| 44. C22×C8 | C2×C4 | semidirect |
| 48. C4×D4 | C2×C4 | semidirect |
| 54. C2×C4⋊C4 | C2×C4 | semidirect |
| 65. #102 | C2×C4 | semidirect |
| 81. C2×D4 | C42 | semidirect |
| 110. C2×C8 | C22×C4 | semidirect |
| 116. C4⋊C4 | C22×C4 | semidirect |
| 141. D4 | C2×C42 | semidirect |
| 192. C2 | #1762 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D4 | 2 |
| C22×#102 | 2 |
| C22×#97 | 2 |
| C2×C4×C4⋊C4 | 2 |
| #1762 | 2 |
| C2×#340 | 2 |