Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
3302 conjugacy classes of subgroups.
The subgroup lattice has 534 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×C42 |
| commutator | C2×C4 | C23×C42 |
| Frattini, cosocle | C22×C8 | C25 |
| socle | C22 | C23×#97 |
| prime radical | C22×#41 | M16 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C42 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. Q8×#347 | C2 | semidirect |
| 4. D4×#347 | C2 | semidirect |
| 5. #493201 | C2 | semidirect |
| 6. #493177 | C2 | semidirect |
| 7. C2×C4×#347 | C2 | semidirect |
| 11. #33485 | C4 | semidirect |
| 12. #33484 | C4 | semidirect |
| 13. #33479 | C4 | semidirect |
| 14. C16×#41 | C4 | semidirect |
| 67. #2183 | C2×C4 | semidirect |
| 68. Q8×C16 | C2×C4 | semidirect |
| 69. #2169 | C2×C4 | semidirect |
| 70. #2168 | C2×C4 | semidirect |
| 71. D4×C16 | C2×C4 | semidirect |
| 72. #2163 | C2×C4 | semidirect |
| 73. #2163 | C2×C4 | semidirect |
| 74. #2162 | C2×C4 | semidirect |
| 75. #2162 | C2×C4 | semidirect |
| 82. C4×M32 | C2×C4 | semidirect |
| 83. C4×M32 | C2×C4 | semidirect |
| 87. C2×#346 | C2×C4 | semidirect |
| 88. C2×C4×C16 | C2×C4 | semidirect |
| 209. #347 | #41 | direct (N × H) |
| 348. #41 | #347 | direct (N × H) |
| 443. C16 | C4×#41 | semidirect |
| 451. Q8 | C2×#347 | semidirect |
| 454. D4 | C2×#347 | semidirect |
| 480. C2×C4 | C2×#347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×M32 | 2 |
| #41×#97 | 2 |
| Q8×#347 | 2 |
| D4×#347 | 2 |
| #493201 | 2 |
| #493177 | 2 |
| C2×C4×#347 | 2 |