Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
544 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 232 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C41 |
| prime radical | C22×D4×C41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C2×C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4⋊Q8×C41 | C2 | semidirect |
| 4. C41×#461 | C2 | direct (N × H) |
| 5. C2×C4⋊C8×C41 | C2 | semidirect |
| 6. C2×#103×C41 | C2 | semidirect |
| 14. C4⋊Q8×C41 | C22 | semidirect |
| 22. C4⋊C8×C41 | C22 | semidirect |
| 23. #103×C41 | C22 | semidirect |
| 67. C2×C4×C41 | SD16 | semidirect |
| 87. C4×C41 | C2×SD16 | semidirect |
| 90. C2×#461 | C41 | direct (N × H) |
| 92. C2×C41 | #461 | direct (N × H) |
| 97. C2×C4⋊Q8 | C2×C41 | semidirect |
| 99. #461 | C2×C41 | direct (N × H) |
| 100. C2×C4⋊C8 | C2×C41 | semidirect |
| 101. C2×#103 | C2×C41 | semidirect |
| 102. C41 | C2×#461 | direct (N × H) |
| 110. C4⋊Q8 | C22×C41 | semidirect |
| 118. C4⋊C8 | C22×C41 | semidirect |
| 119. #103 | C22×C41 | semidirect |
| 163. C2×C4 | SD16×C41 | semidirect |
| 183. C4 | C2×SD16×C41 | semidirect |
| 187. C2 | C41×#461 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×SD16×C41 | 2 |
| C2×C4⋊Q8×C41 | 2 |
| C2×C4×D4×C41 | 2 |
| C41×#461 | 2 |
| C2×C4⋊C8×C41 | 2 |
| C2×#103×C41 | 2 |
| C2×#461 | 41 |