Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
510 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C41 | AΣL(1,𝔽16) |
| commutator | C2×Q8 | C22×C4×C41 |
| Frattini, cosocle | #124 | C23×C41 |
| prime radical | C2×C41×#454 | C2 |
| LCS | G ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C23×C41 ◁ C22×C4×C41 ◁ C2×#124×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C41×#354 | C2 | semidirect |
| 3. C2×C41×#329 | C2 | semidirect |
| 4. C41×#1404 | C2 | direct (N × H) |
| 5. C2×2−1+4×C41 | C4 | semidirect |
| 10. C41×#454 | C4 | semidirect |
| 13. C2×#101×C41 | C4 | semidirect |
| 17. C41×#354 | C22 | semidirect |
| 19. C41×#329 | C22 | semidirect |
| 23. 2−1+4×C41 | C2×C4 | semidirect |
| 48. #101×C41 | C2×C4 | semidirect |
| 150. C2×#1404 | C41 | direct (N × H) |
| 172. C2×#354 | C2×C41 | semidirect |
| 173. C2×#329 | C2×C41 | semidirect |
| 174. #1404 | C2×C41 | direct (N × H) |
| 180. C2×C41 | #1404 | direct (N × H) |
| 182. C2×2−1+4 | C4×C41 | semidirect |
| 187. #454 | C4×C41 | semidirect |
| 190. C2×#101 | C4×C41 | semidirect |
| 194. #354 | C22×C41 | semidirect |
| 196. #329 | C22×C41 | semidirect |
| 197. C41 | C2×#1404 | direct (N × H) |
| 201. 2−1+4 | C2×C4×C41 | semidirect |
| 226. #101 | C2×C4×C41 | semidirect |
| 353. C2 | C41×#1404 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C41×#454 | 2 |
| C2×C41×#354 | 2 |
| C2×C41×#329 | 2 |
| C41×#1404 | 2 |
| C2×#1404 | 41 |