Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
709 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 709 conjugacy classes of subgroups — too many to draw. Only its 263 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×C22⋊C4 |
| commutator | C22 | C23×C8 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | C23×D4 | C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C4×D4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2972 | C2 | semidirect |
| 3. #1460 | C2 | semidirect |
| 4. #1459 | C2 | semidirect |
| 5. #1458 | C2 | semidirect |
| 6. C2×#323 | C2 | semidirect |
| 20. #431 | C22 | semidirect |
| 21. C2×C22⋊C8 | C22 | semidirect |
| 22. #324 | C22 | semidirect |
| 24. #323 | C22 | semidirect |
| 28. C22×D4 | C8 | semidirect |
| 70. C24 | C2×C8 | semidirect |
| 81. C2×D4 | C2×C8 | semidirect |
| 82. C2×D4 | C2×C8 | semidirect |
| 93. C22×C4 | C2×C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#518 | 2 |
| #2972 | 2 |
| #1460 | 2 |
| #1459 | 2 |
| #1458 | 2 |
| C2×#323 | 2 |