Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
3951 conjugacy classes of subgroups; only the 1039 normal subgroups are shown.
This group has 3951 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, socle | C24 | C22⋊C4 |
| commutator | C22 | C24×C4 |
| Frattini, cosocle | C23 | C25 |
| prime radical | C24×D4 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C26 ◁ G | |
| LECS | G ▷ C23 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×C22⋊C4 | C2 | semidirect |
| 3. C22×#99 | C2 | direct (N × H) |
| 4. C26 | C4 | semidirect |
| 8. C23×D4 | C4 | semidirect |
| 11. C24×C4 | C4 | semidirect |
| 13. C22×C22⋊C4 | C22 | semidirect |
| 14. C2×#99 | C22 | direct (N × H) |
| 21. C25 | C2×C4 | semidirect |
| 29. C22×D4 | C2×C4 | semidirect |
| 35. C23×C4 | C2×C4 | semidirect |
| 37. C2×C22⋊C4 | C23 | semidirect |
| 38. #99 | C23 | direct (N × H) |
| 55. C24 | C22×C4 | semidirect |
| 63. C2×D4 | C22×C4 | semidirect |
| 69. C22×C4 | C22×C4 | semidirect |
| 71. C22⋊C4 | C24 | semidirect |
| 85. C23 | #99 | direct (N × H) |
| 92. C23 | C23×C4 | semidirect |
| 102. C2×C4 | C23×C4 | semidirect |
| 115. C22 | C2×#99 | direct (N × H) |
| 128. C2 | C22×#99 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D4 | 2 |
| C23×C22⋊C4 | 2 |
| C22×#99 | 2 |