Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
800 conjugacy classes of subgroups; only the 340 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 340 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C101 | C22×C22⋊C4 |
| commutator | C22 | C23×C4×C101 |
| Frattini, cosocle | C23 | C24×C101 |
| prime radical | C2×H(5,𝔽2)×C101 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C101 ◁ C22×D4×C101 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #518×C101 | C2 | semidirect |
| 3. #410×C101 | C2 | semidirect |
| 4. C2×#99×C101 | C2 | semidirect |
| 6. C2×#41×C101 | C4 | semidirect |
| 8. C22×D4×C101 | C4 | semidirect |
| 12. #117×C101 | C22 | semidirect |
| 13. C2×C22⋊C4×C101 | C22 | semidirect |
| 14. #99×C101 | C22 | semidirect |
| 15. C24×C101 | C2×C4 | semidirect |
| 19. C2×Q8×C101 | C2×C4 | semidirect |
| 23. C2×D4×C101 | C2×C4 | semidirect |
| 24. C2×D4×C101 | C2×C4 | semidirect |
| 28. C22×C4×C101 | C2×C4 | semidirect |
| 29. C22×C4×C101 | C2×C4 | semidirect |
| 71. #2883 | C101 | direct (N × H) |
| 72. C101 | #2883 | direct (N × H) |
| 74. #518 | C2×C101 | semidirect |
| 75. #410 | C2×C101 | semidirect |
| 76. C2×#99 | C2×C101 | semidirect |
| 78. C2×#41 | C4×C101 | semidirect |
| 80. C22×D4 | C4×C101 | semidirect |
| 84. #117 | C22×C101 | semidirect |
| 85. C2×C22⋊C4 | C22×C101 | semidirect |
| 86. #99 | C22×C101 | semidirect |
| 87. C24 | C2×C4×C101 | semidirect |
| 91. C2×Q8 | C2×C4×C101 | semidirect |
| 95. C2×D4 | C2×C4×C101 | semidirect |
| 96. C2×D4 | C2×C4×C101 | semidirect |
| 100. C22×C4 | C2×C4×C101 | semidirect |
| 101. C22×C4 | C2×C4×C101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×H(5,𝔽2)×C101 | 2 |
| #518×C101 | 2 |
| #410×C101 | 2 |
| C2×#99×C101 | 2 |
| #2883 | 101 |