Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
564 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 564 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 |
|---|---|---|
| 1. C22×Q16×C41 | C2 | semidirect |
| 3. C2×C4⋊Q8×C41 | C2 | semidirect |
| 5. C41×#497 | C2 | direct (N × H) |
| 6. C2×#97×C41 | C2 | semidirect |
| 11. C2×Q16×C41 | C22 | semidirect |
| 16. C4⋊Q8×C41 | C22 | semidirect |
| 22. #97×C41 | C22 | semidirect |
| 78. C2×#497 | C41 | direct (N × H) |
| 80. C2×C41 | #497 | direct (N × H) |
| 83. C22×Q16 | C2×C41 | semidirect |
| 85. C2×C4⋊Q8 | C2×C41 | semidirect |
| 87. #497 | C2×C41 | direct (N × H) |
| 88. C2×#97 | C2×C41 | semidirect |
| 89. C41 | C2×#497 | direct (N × H) |
| 94. C2×Q16 | C22×C41 | semidirect |
| 99. C4⋊Q8 | C22×C41 | semidirect |
| 105. #97 | C22×C41 | semidirect |
| 162. C2 | C41×#497 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q16×C41 | 2 |
| C22×SD16×C41 | 2 |
| C2×C4⋊Q8×C41 | 2 |
| C2×#124×C41 | 2 |
| C41×#497 | 2 |
| C2×#97×C41 | 2 |
| C2×#497 | 41 |