Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
856 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C41 | #1790 |
| commutator | C2×D4 | C22×C4×C41 |
| Frattini, cosocle | C2×#41 | C23×C41 |
| prime radical | C41×#3549 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ C2×C4×C41 ◁ C2×#41×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#2132 | C2 | semidirect |
| 3. C41×#2122 | C2 | semidirect |
| 4. C41×#1914 | C2 | semidirect |
| 5. C41×#1884 | C2 | semidirect |
| 6. C41×#568 | C22 | semidirect |
| 8. C41×H(3,𝔽4) | C4 | semidirect |
| 12. D42×C41 | C4 | semidirect |
| 19. C41×#413 | C22 | semidirect |
| 21. C41×#410 | C22 | semidirect |
| 179. #12769 | C41 | direct (N × H) |
| 202. #2132 | C2×C41 | semidirect |
| 203. #2122 | C2×C41 | semidirect |
| 204. #1914 | C2×C41 | semidirect |
| 205. #1884 | C2×C41 | semidirect |
| 212. #568 | C22×C41 | semidirect |
| 214. H(3,𝔽4) | C4×C41 | semidirect |
| 218. D42 | C4×C41 | semidirect |
| 225. #413 | C22×C41 | semidirect |
| 227. #410 | C22×C41 | semidirect |
| 233. C41 | #12769 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3549 | 2 |
| C41×#2132 | 2 |
| C41×#2122 | 2 |
| C41×#1914 | 2 |
| C41×#1884 | 2 |
| #12769 | 41 |