Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
370 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 112 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 | #120 |
| commutator | C2×C4 | C22×C4×C41 |
| Frattini, cosocle | C22×C4 | C23×C41 |
| prime radical | C2×AGL(1,ℤ/8)×C41 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C22×C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#520 | C2 | semidirect |
| 3. C2×#104×C41 | C2 | semidirect |
| 4. C41×#418 | C2 | semidirect |
| 5. C41×#390 | C2 | semidirect |
| 6. C41×#343 | C2 | semidirect |
| 7. C41×#339 | C2 | semidirect |
| 11. AGL(1,ℤ/8)×C41 | C4 | semidirect |
| 40. C2×D4×C41 | C2×C4 | semidirect |
| 52. M16×C41 | C2×C4 | semidirect |
| 75. Q8×C41 | C22⋊C4 | semidirect |
| 83. D4×C41 | C22⋊C4 | semidirect |
| 125. #1883 | C41 | direct (N × H) |
| 134. #520 | C2×C41 | semidirect |
| 135. C2×#104 | C2×C41 | semidirect |
| 136. #418 | C2×C41 | semidirect |
| 137. #390 | C2×C41 | semidirect |
| 138. #343 | C2×C41 | semidirect |
| 139. #339 | C2×C41 | semidirect |
| 140. C41 | #1883 | direct (N × H) |
| 144. AGL(1,ℤ/8) | C4×C41 | semidirect |
| 173. C2×D4 | C2×C4×C41 | semidirect |
| 185. M16 | C2×C4×C41 | semidirect |
| 208. Q8 | C22⋊C4×C41 | semidirect |
| 216. D4 | C22⋊C4×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×AGL(1,ℤ/8)×C41 | 2 |
| C41×#520 | 2 |
| C2×#104×C41 | 2 |
| C41×#418 | 2 |
| C41×#390 | 2 |
| C41×#343 | 2 |
| C41×#339 | 2 |
| #1883 | 41 |