Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
2879 conjugacy classes of subgroups; only the 1039 normal subgroups are shown.
This group has 2879 conjugacy classes of subgroups — too many to draw. Only its 1039 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | D4 |
| commutator | C4 | C24×C4 |
| Frattini, cosocle | C2×C4 | C25 |
| socle | C24 | C22⋊C4 |
| prime radical | C23×#41 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×M16 | C2 | semidirect |
| 3. C23×C42 | C2 | semidirect |
| 4. C22×#104 | C2 | direct (N × H) |
| 7. C22×#41 | C4 | semidirect |
| 9. C23×Q8 | C4 | semidirect |
| 11. C23×D4 | C4 | semidirect |
| 16. C22×M16 | C22 | semidirect |
| 19. C22×C42 | C22 | semidirect |
| 20. C2×#104 | C22 | direct (N × H) |
| 26. C2×#41 | C2×C4 | semidirect |
| 29. C22×Q8 | C2×C4 | semidirect |
| 33. C22×D4 | C2×C4 | semidirect |
| 46. C2×M16 | C23 | semidirect |
| 49. C2×C42 | C23 | semidirect |
| 50. #104 | C23 | direct (N × H) |
| 60. #41 | C22×C4 | semidirect |
| 63. C2×Q8 | C22×C4 | semidirect |
| 67. C2×D4 | C22×C4 | semidirect |
| 83. M16 | C24 | semidirect |
| 86. C42 | C24 | semidirect |
| 91. C23 | #104 | direct (N × H) |
| 96. Q8 | C23×C4 | semidirect |
| 100. D4 | C23×C4 | semidirect |
| 120. C22 | C2×#104 | direct (N × H) |
| 133. C2 | C22×#104 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#41 | 2 |
| C23×M16 | 2 |
| C23×C42 | 2 |
| C22×#104 | 2 |