Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
5815 conjugacy classes of subgroups; only the 1375 normal subgroups are shown.
This group has 5815 conjugacy classes of subgroups — too many to draw. Only its 1375 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C25 | C23 |
| commutator | C22 | C24×C4 |
| Frattini, cosocle | C23 | C25 |
| prime radical | C24×D4 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C25 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C25×C4 | C2 | semidirect |
| 3. C23×C22⋊C4 | C2 | semidirect |
| 4. C23×C22⋊C4 | C2 | semidirect |
| 5. C2×#386 | C2 | direct (N × H) |
| 6. C22×#95 | C2 | semidirect |
| 11. C23×D4 | C4 | semidirect |
| 18. C24×C4 | C22 | semidirect |
| 21. C22×C22⋊C4 | C22 | semidirect |
| 22. C22×C22⋊C4 | C22 | semidirect |
| 23. #386 | C22 | direct (N × H) |
| 24. C2×#95 | C22 | semidirect |
| 32. C25 | C2×C4 | semidirect |
| 41. C22×D4 | C2×C4 | semidirect |
| 53. C23×C4 | C2×C4 | semidirect |
| 54. C23×C4 | D4 | semidirect |
| 58. C23×C4 | C23 | semidirect |
| 61. C2×C22⋊C4 | C23 | semidirect |
| 62. C2×C22⋊C4 | C23 | semidirect |
| 63. #95 | C23 | semidirect |
| 79. C24 | C22⋊C4 | semidirect |
| 82. C24 | C22×C4 | semidirect |
| 95. C2×D4 | C22×C4 | semidirect |
| 109. C22×C4 | C22×C4 | semidirect |
| 110. C22×C4 | C2×D4 | semidirect |
| 134. C23 | C2×C22⋊C4 | semidirect |
| 141. C23 | C23×C4 | semidirect |
| 161. C2×C4 | C23×C4 | semidirect |
| 162. C2×C4 | C22×D4 | semidirect |
| 174. C22 | #386 | direct (N × H) |
| 176. C22 | C22×C22⋊C4 | semidirect |
| 191. C2 | C2×#386 | 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 |
| C25×C4 | 2 |
| C23×C22⋊C4 | 2 |
| C2×#386 | 2 |
| C22×#95 | 2 |