Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
512 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 512 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 | C24×C41 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C23×C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q16×C41 | C2 | semidirect |
| 4. C41×#467 | C2 | direct (N × H) |
| 5. C2×#107×C41 | C2 | semidirect |
| 6. C2×#103×C41 | C2 | semidirect |
| 10. C2×Q16×C41 | C22 | semidirect |
| 20. #107×C41 | C22 | semidirect |
| 21. #103×C41 | C22 | semidirect |
| 47. C23×C41 | Q16 | semidirect |
| 73. C22×C41 | C2×Q16 | semidirect |
| 82. C2×#467 | C41 | direct (N × H) |
| 84. C2×C41 | #467 | direct (N × H) |
| 88. C22×Q16 | C2×C41 | semidirect |
| 91. #467 | C2×C41 | direct (N × H) |
| 92. C2×#107 | C2×C41 | semidirect |
| 93. C2×#103 | C2×C41 | semidirect |
| 94. C41 | C2×#467 | direct (N × H) |
| 98. C2×Q16 | C22×C41 | semidirect |
| 108. #107 | C22×C41 | semidirect |
| 109. #103 | C22×C41 | semidirect |
| 135. C23 | Q16×C41 | semidirect |
| 161. C22 | C2×Q16×C41 | semidirect |
| 171. C2 | C41×#467 | 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 |
| C23×C8×C41 | 2 |
| C2×C22⋊Q8×C41 | 2 |
| C41×#467 | 2 |
| C2×#107×C41 | 2 |
| C2×#103×C41 | 2 |
| C2×#467 | 41 |