Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
584 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 584 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 | C2×#127×C41 | C2 |
| 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 |
|---|---|---|
| 1. C22×SD16×C41 | C2 | semidirect |
| 3. C2×C4×Q8×C41 | C2 | semidirect |
| 4. C41×#460 | C2 | direct (N × H) |
| 5. C2×C4⋊C8×C41 | C2 | semidirect |
| 6. C2×#102×C41 | C2 | semidirect |
| 12. C2×SD16×C41 | C22 | semidirect |
| 17. C4×Q8×C41 | C22 | semidirect |
| 22. C4⋊C8×C41 | C22 | semidirect |
| 23. #102×C41 | C22 | semidirect |
| 27. C2×Q8×C41 | D4 | semidirect |
| 58. Q8×C41 | C2×D4 | semidirect |
| 69. C2×C4×C41 | SD16 | semidirect |
| 89. C4×C41 | C2×SD16 | semidirect |
| 92. C2×#460 | C41 | direct (N × H) |
| 94. C2×C41 | #460 | direct (N × H) |
| 98. C22×SD16 | C2×C41 | semidirect |
| 100. C2×C4×Q8 | C2×C41 | semidirect |
| 101. #460 | C2×C41 | direct (N × H) |
| 102. C2×C4⋊C8 | C2×C41 | semidirect |
| 103. C2×#102 | C2×C41 | semidirect |
| 104. C41 | C2×#460 | direct (N × H) |
| 110. C2×SD16 | C22×C41 | semidirect |
| 115. C4×Q8 | C22×C41 | semidirect |
| 120. C4⋊C8 | C22×C41 | semidirect |
| 121. #102 | C22×C41 | semidirect |
| 125. C2×Q8 | D4×C41 | semidirect |
| 156. Q8 | C2×D4×C41 | semidirect |
| 167. C2×C4 | SD16×C41 | semidirect |
| 187. C4 | C2×SD16×C41 | semidirect |
| 191. C2 | C41×#460 | 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×#127×C41 | 2 |
| C2×C4×Q8×C41 | 2 |
| C41×#460 | 2 |
| C2×C4⋊C8×C41 | 2 |
| C2×#102×C41 | 2 |
| C2×#460 | 41 |