Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
337 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 337 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #12836 |
| commutator | C22×C16 | C22×C4 |
| Frattini, cosocle | C2×C4×C16 | C23 |
| socle | C2 | #134695 |
| prime radical | C2×#41 | #107 |
| LCS | G ▷ C22×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C22×C8 ◁ C4×#131 ◁ C4×#504 ◁ G | |
| LECS | G ▷ C2×C4×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #151040 | C2 | semidirect |
| 3. #151035 | C2 | semidirect |
| 5. #94028 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #512731 | 2 |
| #151040 | 2 |
| #151035 | 2 |
| #134683 | 2 |
| #94028 | 2 |