Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
356 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 356 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 | C22×C41 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C41 |
| prime radical | C41×#3283 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C42×C41 ◁ C8×D4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#2241 | C2 | semidirect |
| 3. C41×#2224 | C2 | semidirect |
| 4. C41×#1673 | C2 | semidirect |
| 5. C41×#1362 | C2 | semidirect |
| 6. C41×#1331 | C2 | semidirect |
| 7. C41×D4⋊C16 | C2 | semidirect |
| 70. D8×C41 | SD16 | semidirect |
| 118. #12371 | C41 | direct (N × H) |
| 136. #2241 | C2×C41 | semidirect |
| 137. #2224 | C2×C41 | semidirect |
| 138. #1673 | C2×C41 | semidirect |
| 139. #1362 | C2×C41 | semidirect |
| 140. #1331 | C2×C41 | semidirect |
| 141. D4⋊C16 | C2×C41 | semidirect |
| 164. C41 | #12371 | direct (N × H) |
| 210. D8 | SD16×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3283 | 2 |
| C41×#2241 | 2 |
| C41×#2224 | 2 |
| C41×#1673 | 2 |
| C41×#1362 | 2 |
| C41×#1331 | 2 |
| C41×D4⋊C16 | 2 |
| #12371 | 41 |