Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
590 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 214 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 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C41 |
| prime radical | C24×C41 | D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C23×C4×C41 ◁ C23×C8×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#2236 | C2 | semidirect |
| 3. C41×#2216 | C2 | semidirect |
| 4. C41×#2188 | C2 | semidirect |
| 9. C2×Q32×C41 | C22 | semidirect |
| 17. C41×#366 | C22 | semidirect |
| 18. C41×#358 | C22 | semidirect |
| 75. C23×C41 | Q32 | semidirect |
| 97. #33755 | C41 | direct (N × H) |
| 113. #2236 | C2×C41 | semidirect |
| 114. #2216 | C2×C41 | semidirect |
| 115. #2188 | C2×C41 | semidirect |
| 125. C2×Q32 | C22×C41 | semidirect |
| 133. #366 | C22×C41 | semidirect |
| 134. #358 | C22×C41 | semidirect |
| 136. C41 | #33755 | direct (N × H) |
| 192. C23 | Q32×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C41×#467 | 2 |
| C41×#2236 | 2 |
| C41×#2216 | 2 |
| C41×#2188 | 2 |
| C2×C41×C22⋊C16 | 2 |
| #33755 | 41 |