Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
996 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 996 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 | C41×#3151 | 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 |
|---|---|---|
| 1. C41×#3550 | C2 | semidirect |
| 3. C41×#3138 | C2 | semidirect |
| 4. C41×#1657 | C2 | semidirect |
| 5. C41×#1526 | C2 | semidirect |
| 6. C41×#1525 | C2 | semidirect |
| 8. C41×#563 | C22 | semidirect |
| 27. C41×#330 | C22 | semidirect |
| 28. C41×#329 | C22 | semidirect |
| 145. #19077 | C41 | direct (N × H) |
| 161. #3550 | C2×C41 | semidirect |
| 163. #3138 | C2×C41 | semidirect |
| 164. #1657 | C2×C41 | semidirect |
| 165. #1526 | C2×C41 | semidirect |
| 166. #1525 | C2×C41 | semidirect |
| 173. #563 | C22×C41 | semidirect |
| 192. #330 | C22×C41 | semidirect |
| 193. #329 | C22×C41 | semidirect |
| 194. C41 | #19077 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3550 | 2 |
| C41×#3151 | 2 |
| C41×#3138 | 2 |
| C41×#1657 | 2 |
| C41×#1526 | 2 |
| C41×#1525 | 2 |
| #19077 | 41 |