Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
332 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 86 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 | #2127 |
| commutator | C42 | C22×C4×C41 |
| Frattini, cosocle | #124 | C23×C41 |
| prime radical | C41×#535 | C22 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ C22×C41 ◁ C22×C4×C41 ◁ C41×#535 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C41×#1414 | C2 | semidirect |
| 5. C41×#1407 | C2 | semidirect |
| 6. C41×#541 | C4 | semidirect |
| 9. C41×#492 | C4 | semidirect |
| 10. C41×#490 | C4 | semidirect |
| 16. C41×#433 | C4 | semidirect |
| 30. C4⋊Q8×C41 | C2×C4 | semidirect |
| 35. #125×C41 | C2×C4 | semidirect |
| 54. #97×C41 | C2×C4 | semidirect |
| 55. C4×C8×C41 | C2×C4 | semidirect |
| 127. #13607 | C41 | direct (N × H) |
| 150. #1414 | C2×C41 | semidirect |
| 151. #1407 | C2×C41 | semidirect |
| 158. #541 | C4×C41 | semidirect |
| 161. #492 | C4×C41 | semidirect |
| 162. #490 | C4×C41 | semidirect |
| 168. #433 | C4×C41 | semidirect |
| 175. C41 | #13607 | direct (N × H) |
| 183. C4⋊Q8 | C2×C4×C41 | semidirect |
| 188. #125 | C2×C4×C41 | semidirect |
| 207. #97 | C2×C4×C41 | semidirect |
| 208. C4×C8 | C2×C4×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3222 | 2 |
| C41×#2134 | 2 |
| C41×#2127 | 2 |
| C41×#1414 | 2 |
| C41×#1407 | 2 |
| #13607 | 41 |