Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
698 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 212 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 | C2×#120 |
| commutator, Frattini, cosocle | C2×C4 | C24×C41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ C22×C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×2−1+4×C41 | C2 | semidirect |
| 2. C41×#575 | C2 | semidirect |
| 3. C41×#536 | C2 | semidirect |
| 4. C41×#456 | C2 | semidirect |
| 5. C41×#454 | C2 | semidirect |
| 6. C41×#421 | C2 | semidirect |
| 7. C2×#101×C41 | C2 | semidirect |
| 18. #137×C41 | C22 | semidirect |
| 20. AGL(1,ℤ/8)×C41 | C22 | semidirect |
| 23. C4⋊Q8×C41 | C22 | semidirect |
| 24. #124×C41 | C22 | semidirect |
| 28. #104×C41 | C22 | semidirect |
| 29. #101×C41 | C22 | semidirect |
| 117. #3020 | C41 | direct (N × H) |
| 124. C2×2−1+4 | C2×C41 | semidirect |
| 125. #575 | C2×C41 | semidirect |
| 126. #536 | C2×C41 | semidirect |
| 127. #456 | C2×C41 | semidirect |
| 128. #454 | C2×C41 | semidirect |
| 129. #421 | C2×C41 | semidirect |
| 130. C2×#101 | C2×C41 | semidirect |
| 131. C41 | #3020 | direct (N × H) |
| 142. #137 | C22×C41 | semidirect |
| 144. AGL(1,ℤ/8) | C22×C41 | semidirect |
| 147. C4⋊Q8 | C22×C41 | semidirect |
| 148. #124 | C22×C41 | semidirect |
| 152. #104 | C22×C41 | semidirect |
| 153. #101 | C22×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×2−1+4×C41 | 2 |
| C41×#575 | 2 |
| C41×#536 | 2 |
| C41×#456 | 2 |
| C41×#454 | 2 |
| C41×#421 | 2 |
| C2×#101×C41 | 2 |
| #3020 | 41 |