Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
308 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C41 |
| prime radical | C41×#2206 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C42×C41 ◁ C41×#446 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×#3389 | C2 | semidirect |
| 2. C41×#2244 | C2 | semidirect |
| 4. C41×#1688 | C2 | semidirect |
| 5. C41×#1363 | C2 | semidirect |
| 6. C41×#1338 | C2 | semidirect |
| 7. C41×#1333 | C2 | semidirect |
| 75. D8×C41 | SD16 | semidirect |
| 124. #12360 | C41 | direct (N × H) |
| 141. #3389 | C2×C41 | semidirect |
| 142. #2244 | C2×C41 | semidirect |
| 144. #1688 | C2×C41 | semidirect |
| 145. #1363 | C2×C41 | semidirect |
| 146. #1338 | C2×C41 | semidirect |
| 147. #1333 | C2×C41 | semidirect |
| 172. C41 | #12360 | direct (N × H) |
| 221. D8 | SD16×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3389 | 2 |
| C41×#2244 | 2 |
| C41×#2206 | 2 |
| C41×#1688 | 2 |
| C41×#1363 | 2 |
| C41×#1338 | 2 |
| C41×#1333 | 2 |
| #12360 | 41 |