Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
252 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 252 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 | #466 |
| commutator, Frattini, cosocle | C4×C8 | C23×C41 |
| prime radical | C41×#1667 | 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 |
|---|---|---|
| 1. C41×#2248 | C2 | semidirect |
| 2. D4×C16×C41 | C2 | semidirect |
| 3. C41×#1669 | C2 | semidirect |
| 5. C41×#1372 | C2 | semidirect |
| 6. C41×#1362 | C2 | semidirect |
| 7. C41×#1361 | C2 | semidirect |
| 73. C16×C41 | D8 | semidirect |
| 84. D4×C41 | SD32 | semidirect |
| 98. #12432 | C41 | direct (N × H) |
| 113. #2248 | C2×C41 | semidirect |
| 114. D4×C16 | C2×C41 | semidirect |
| 115. #1669 | C2×C41 | semidirect |
| 117. #1372 | C2×C41 | semidirect |
| 118. #1362 | C2×C41 | semidirect |
| 119. #1361 | C2×C41 | semidirect |
| 140. C41 | #12432 | direct (N × H) |
| 191. C16 | D8×C41 | semidirect |
| 202. D4 | SD32×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#2248 | 2 |
| D4×C16×C41 | 2 |
| C41×#1669 | 2 |
| C41×#1667 | 2 |
| C41×#1372 | 2 |
| C41×#1362 | 2 |
| C41×#1361 | 2 |
| #12432 | 41 |