Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
278 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C41 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C41 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×#550 | C2 | semidirect |
| 2. C41×#493 | C2 | semidirect |
| 3. C41×#460 | C2 | semidirect |
| 4. C41×#459 | C2 | semidirect |
| 5. C41×#331 | C2 | semidirect |
| 6. C41×Q8⋊C8 | C2 | semidirect |
| 7. C41×D4⋊C8 | C2 | semidirect |
| 56. Q8×C41 | D8 | semidirect |
| 101. #1621 | C41 | direct (N × H) |
| 108. #550 | C2×C41 | semidirect |
| 109. #493 | C2×C41 | semidirect |
| 110. #460 | C2×C41 | semidirect |
| 111. #459 | C2×C41 | semidirect |
| 112. #331 | C2×C41 | semidirect |
| 113. Q8⋊C8 | C2×C41 | semidirect |
| 114. D4⋊C8 | C2×C41 | semidirect |
| 115. C41 | #1621 | direct (N × H) |
| 164. Q8 | D8×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#550 | 2 |
| C41×#493 | 2 |
| C41×#460 | 2 |
| C41×#459 | 2 |
| C41×#331 | 2 |
| C41×Q8⋊C8 | 2 |
| C41×D4⋊C8 | 2 |
| #1621 | 41 |