Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
10945 conjugacy classes of subgroups.
The subgroup lattice has 574 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C42 | #95 |
| commutator | C23 | C23×C42 |
| Frattini, cosocle | C2×C42 | C25 |
| socle | C23 | C22×#95 |
| prime radical | C26 | C42 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C42 ◁ C24×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #181415 | C2 | direct (N × H) |
| 3. C2×#8128 | C2 | semidirect |
| 17. #8128 | C22 | semidirect |
| 18. C2×#1309 | C22 | semidirect |
| 74. #1309 | C23 | semidirect |
| 571. C2 | #181415 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#2920 | 2 |
| #181415 | 2 |
| C2×#8128 | 2 |