Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
323 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 323 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 | #152418 |
| commutator | C2×C32 | C22×C4 |
| Frattini, cosocle | C22×C32 | C23 |
| prime radical | C2×#41 | D16 |
| LCS | G ▷ C2×C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ C2×#504 ◁ C2×#2258 ◁ G | |
| LECS | G ▷ C22×C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #153578 | C2 | semidirect |
| 3. C2×#7548 | C2 | semidirect |
| 6. #94767 | C2 | semidirect |
| 7. #94765 | C2 | semidirect |
| 24. #7514 | C4 | semidirect |
| 48. M128 | C2×C4 | semidirect |
| 50. C2×C64 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #512720 | 2 |
| #153578 | 2 |
| C2×#7548 | 2 |
| #153432 | 2 |
| #152296 | 2 |
| #94767 | 2 |
| #94765 | 2 |