Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
389 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 389 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 | #152629 |
| commutator | C2×C32 | C22×C4 |
| Frattini, cosocle | C22×C32 | C23 |
| prime radical | #512941 | C2 |
| 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 |
|---|---|---|
| 1. #513308 | C2 | semidirect |
| 3. C2×#7541 | C2 | semidirect |
| 4. #152295 | C2 | semidirect |
| 5. #94770 | C2 | semidirect |
| 41. M128 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #513308 | 2 |
| #512941 | 2 |
| C2×#7541 | 2 |
| #152295 | 2 |
| #94770 | 2 |