Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
414 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #140751 |
| commutator | C2×C16 | C22×C8 |
| Frattini, cosocle | C2×#346 | C23 |
| prime radical | C2×#2263 | C4 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ C2×C4×C8 ◁ #11405 ◁ G | |
| LECS | G ▷ C2×#346 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #151024 | C2 | semidirect |
| 3. C2×#7390 | C2 | semidirect |
| 4. #150071 | C2 | semidirect |
| 5. #149504 | C2 | semidirect |
| 6. #140752 | C2 | semidirect |
| 7. #140747 | C2 | semidirect |
| 35. C2×SD64 | C8 | semidirect |
| 36. C2×D32 | C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#13658 | 2 |
| #151024 | 2 |
| C2×#7390 | 2 |
| #150071 | 2 |
| #149504 | 2 |
| #140752 | 2 |
| #140747 | 2 |