Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
334 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 96 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 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C4×C41 |
| Frattini, cosocle | C22×C4 | C23×C41 |
| prime radical | C41×#525 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#407 | C2 | semidirect |
| 3. C2×#95×C41 | C2 | semidirect |
| 4. C41×#328 | C2 | semidirect |
| 5. C41×#327 | C2 | semidirect |
| 6. C2×#41×C41 | C4 | semidirect |
| 11. C22⋊Q8×C41 | C4 | semidirect |
| 13. #121×C41 | C4 | semidirect |
| 18. #117×C41 | C4 | semidirect |
| 25. C2×Q8×C41 | C2×C4 | semidirect |
| 29. C2×D4×C41 | C2×C4 | semidirect |
| 46. C4⋊C4×C41 | C2×C4 | semidirect |
| 47. C4⋊C4×C41 | C2×C4 | semidirect |
| 111. #1504 | C41 | direct (N × H) |
| 121. #407 | C2×C41 | semidirect |
| 122. C2×#95 | C2×C41 | semidirect |
| 123. #328 | C2×C41 | semidirect |
| 124. #327 | C2×C41 | semidirect |
| 125. C41 | #1504 | direct (N × H) |
| 126. C2×#41 | C4×C41 | semidirect |
| 131. C22⋊Q8 | C4×C41 | semidirect |
| 133. #121 | C4×C41 | semidirect |
| 138. #117 | C4×C41 | semidirect |
| 145. C2×Q8 | C2×C4×C41 | semidirect |
| 149. C2×D4 | C2×C4×C41 | semidirect |
| 166. C4⋊C4 | C2×C4×C41 | semidirect |
| 167. C4⋊C4 | C2×C4×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#525 | 2 |
| C41×#407 | 2 |
| C2×#95×C41 | 2 |
| C41×#328 | 2 |
| C41×#327 | 2 |
| #1504 | 41 |