Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
982 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 982 conjugacy classes of subgroups — too many to draw. Only its 230 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 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C41 |
| prime radical | C2×C41×#555 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#3139 | C2 | semidirect |
| 3. C41×#3110 | C2 | semidirect |
| 4. C41×#1646 | C2 | semidirect |
| 5. C41×#1558 | C2 | semidirect |
| 6. C41×#1490 | C2 | semidirect |
| 17. C41×#487 | C22 | semidirect |
| 19. C41×#474 | C22 | semidirect |
| 20. C41×#461 | C22 | semidirect |
| 26. C41×#333 | C22 | semidirect |
| 27. C41×D4⋊C8 | C22 | semidirect |
| 131. #18552 | C41 | direct (N × H) |
| 147. #3139 | C2×C41 | semidirect |
| 148. #3110 | C2×C41 | semidirect |
| 149. #1646 | C2×C41 | semidirect |
| 150. #1558 | C2×C41 | semidirect |
| 151. #1490 | C2×C41 | semidirect |
| 166. #487 | C22×C41 | semidirect |
| 168. #474 | C22×C41 | semidirect |
| 169. #461 | C22×C41 | semidirect |
| 175. #333 | C22×C41 | semidirect |
| 176. D4⋊C8 | C22×C41 | semidirect |
| 177. C41 | #18552 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C41×#555 | 2 |
| C41×#3139 | 2 |
| C41×#3110 | 2 |
| C41×#1646 | 2 |
| C41×#1558 | 2 |
| C41×#1490 | 2 |
| #18552 | 41 |