Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
16033 conjugacy classes of subgroups.
The subgroup lattice has 681 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C42 | C25 |
| commutator | C22 | C24×C42 |
| Frattini, cosocle | C42 | C26 |
| socle | C23 | C23×C42 |
| prime radical | C26 | C42 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #6342473 | C2 | direct (N × H) |
| 3. C2×#17338 | C2 | semidirect |
| 4. C2×#17327 | C2 | semidirect |
| 5. C2×#17324 | C2 | semidirect |
| 24. #17338 | C22 | semidirect |
| 25. #17327 | C22 | semidirect |
| 26. #17324 | C22 | semidirect |
| 27. C2×#1454 | C22 | semidirect |
| 28. C2×#1453 | C22 | semidirect |
| 29. C2×#1451 | C22 | semidirect |
| 30. C2×C8×M16 | C22 | semidirect |
| 101. #1454 | C23 | semidirect |
| 102. #1453 | C23 | semidirect |
| 103. #1451 | C23 | semidirect |
| 104. C8×M16 | C23 | semidirect |
| 105. C2×#322 | C23 | semidirect |
| 106. C2×C82 | C23 | semidirect |
| 247. #322 | C24 | semidirect |
| 248. C82 | C24 | semidirect |
| 678. C2 | #6342473 | 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 |
| #6342473 | 2 |
| C2×#17338 | 2 |
| C2×#17327 | 2 |
| C2×#17324 | 2 |