Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
371 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 371 conjugacy classes of subgroups — too many to draw. Only its 95 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 | C22×C4 | C22×C4 |
| Frattini, cosocle | C23×C4 | C23 |
| prime radical | C2×#121 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1797 | C2 | semidirect |
| 4. C4⋊#95 | C2 | semidirect |
| 5. #1294 | C2 | semidirect |
| 8. C2×C4×D4 | C4 | semidirect |
| 13. #390 | C4 | semidirect |
| 14. #389 | C4 | semidirect |
| 18. C4×C4⋊C4 | C4 | semidirect |
| 77. C2×D4 | C4⋊C4 | semidirect |
| 119. C4⋊C4 | C4⋊C4 | semidirect |
| 243. C4 | #327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#121 | 2 |
| #1797 | 2 |
| C2×#327 | 2 |
| C4⋊#95 | 2 |
| #1294 | 2 |