Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1857 conjugacy classes of subgroups; only the 575 normal subgroups are shown.
This group has 1857 conjugacy classes of subgroups — too many to draw. Only its 575 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C23 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#537 | C2 | semidirect |
| 2. C2×#532 | C2 | semidirect |
| 3. #2856 | C2 | semidirect |
| 4. #2656 | C2 | semidirect |
| 5. #2542 | C2 | semidirect |
| 6. #2541 | C2 | semidirect |
| 7. #2540 | C2 | semidirect |
| 8. C2×C4×C4⋊C4 | C2 | semidirect |
| 58. C2×C4⋊C4 | D4 | semidirect |
| 67. C2×C42 | D4 | semidirect |
| 147. C2×C4 | #127 | semidirect |
| 176. C4 | #537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#537 | 2 |
| C2×#532 | 2 |
| #2856 | 2 |
| #2656 | 2 |
| #2542 | 2 |
| #2541 | 2 |
| #2540 | 2 |
| C2×C4×C4⋊C4 | 2 |