Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
609 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 609 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 | C23×D4 | C22 |
| 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. #2344 | C2 | semidirect |
| 4. #1934 | C2 | semidirect |
| 5. #1925 | C2 | semidirect |
| 6. #1862 | C2 | semidirect |
| 7. #1823 | C2 | semidirect |
| 8. #1808 | C2 | semidirect |
| 10. C4×#102 | C2 | semidirect |
| 11. C8×C22⋊C4 | C2 | semidirect |
| 18. C2×#107 | C22 | semidirect |
| 19. C2×#102 | C4 | semidirect |
| 27. C2×C4×C8 | C22 | semidirect |
| 29. #389 | C22 | semidirect |
| 36. C4×C4⋊C4 | C22 | semidirect |
| 38. #340 | C22 | semidirect |
| 39. #340 | C22 | semidirect |
| 40. #340 | C22 | semidirect |
| 41. #336 | C22 | semidirect |
| 54. C22×C8 | C2×C4 | semidirect |
| 64. C2×C4⋊C4 | C2×C4 | semidirect |
| 84. #102 | C2×C4 | semidirect |
| 85. #102 | C2×C4 | semidirect |
| 187. D4 | #117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#102 | 2 |
| #2344 | 2 |
| D4×C22⋊C4 | 2 |
| #1934 | 2 |
| #1925 | 2 |
| #1862 | 2 |
| #1823 | 2 |
| #1808 | 2 |
| #1786 | 2 |
| C4×#102 | 2 |
| C8×C22⋊C4 | 2 |