Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
949 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 949 conjugacy classes of subgroups — too many to draw. Only its 207 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 | C2×C22⋊C4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | C22×#121 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#407 | C2 | semidirect |
| 3. C2×C4×C22⋊C4 | C2 | semidirect |
| 4. #1507 | C2 | direct (N × H) |
| 5. C2×#327 | C2 | semidirect |
| 7. C23×D4 | C4 | semidirect |
| 14. C2×#121 | C4 | semidirect |
| 15. C2×#121 | C4 | semidirect |
| 18. C22×C4⋊C4 | C4 | semidirect |
| 23. #407 | C22 | semidirect |
| 25. C2×C22⋊C8 | C22 | semidirect |
| 27. C4×C22⋊C4 | C22 | semidirect |
| 28. C2×#95 | C22 | semidirect |
| 29. #327 | C22 | semidirect |
| 41. C22×D4 | C2×C4 | semidirect |
| 66. #121 | C2×C4 | semidirect |
| 71. C2×C4⋊C4 | C2×C4 | semidirect |
| 82. C22⋊C8 | C23 | semidirect |
| 84. #95 | C23 | semidirect |
| 264. C2 | #1507 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#121 | 2 |
| C2×#407 | 2 |
| C2×C4×C22⋊C4 | 2 |
| #1507 | 2 |
| C2×#327 | 2 |