Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1061 conjugacy classes of subgroups; only the 447 normal subgroups are shown.
This group has 1061 conjugacy classes of subgroups — too many to draw. Only its 447 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 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25 |
| prime radical | C22×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C22×#41 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #3202 | C2 | direct (N × H) |
| 3. C2×#485 | C2 | semidirect |
| 4. C2×#470 | C2 | semidirect |
| 5. C2×#467 | C2 | semidirect |
| 6. C2×#451 | C2 | semidirect |
| 23. #485 | C22 | semidirect |
| 24. #470 | C22 | semidirect |
| 25. #467 | C22 | semidirect |
| 26. #451 | C22 | semidirect |
| 185. C2 | #3202 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#536 | 2 |
| #3202 | 2 |
| C2×#485 | 2 |
| C2×#470 | 2 |
| C2×#467 | 2 |
| C2×#451 | 2 |
| C2×#408 | 2 |