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Note: Search results may be incomplete due to uncomputed quantities: Subgroup label (103813812 objects)

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Subgroup label Subgroup order Cyclic Abelian Solvable
Normal Characteristic Perfect Maximal Central
Ambient label Ambient order Direct product Semidirect product
Quotient label Subgroup index Cyclic quotient Abelian quotient Solvable quotient
Maximal quotient Non-trivial proper Hall subgroup Sylow subgroup
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Results (24 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
568.2.1.a1.a1 $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ ✓ ✓ $C_{568}$ $2^{3} \cdot 71$ $C_1$ $1$ ✓
1136.1.2.a1.a1 $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ ✓ ✓ ✓ $C_{1136}$ $2^{4} \cdot 71$ $C_2$ $2$ ✓
1136.5.2.b1.a1 $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ ✓ ✓ $C_2\times C_{568}$ $2^{4} \cdot 71$ $C_2$ $2$ ✓
1136.5.2.b1.b1 $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ ✓ ✓ $C_2\times C_{568}$ $2^{4} \cdot 71$ $C_2$ $2$ ✓
1136.6.2.b1.a1 $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ ✓ $\OD_{16}\times C_{71}$ $2^{4} \cdot 71$ $C_2$ $2$ ✓
1136.6.2.b1.b1 $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ ✓ $\OD_{16}\times C_{71}$ $2^{4} \cdot 71$ $C_2$ $2$ ✓
1136.7.2.b1.a1 $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ ✓ ✓ $D_8\times C_{71}$ $2^{4} \cdot 71$ $C_2$ $2$ ✓
1136.8.2.c1.a1 $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ ✓ ✓ $\SD_{16}\times C_{71}$ $2^{4} \cdot 71$ $C_2$ $2$ ✓
1136.9.2.b1.a1 $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ ✓ ✓ $Q_{16}\times C_{71}$ $2^{4} \cdot 71$ $C_2$ $2$ ✓
1136.15.2.a1.a1 $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ ✓ ✓ $C_{71}:C_{16}$ $2^{4} \cdot 71$ $C_2$ $2$ ✓
1136.21.2.b1.a1 $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ ✓ ✓ $C_8\times D_{71}$ $2^{4} \cdot 71$ $C_2$ $2$ ✓
1136.23.2.b1.a1 $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ ✓ ✓ $C_{568}:C_2$ $2^{4} \cdot 71$ $C_2$ $2$ ✓
1136.26.2.b1.a1 $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ ✓ ✓ $D_{568}$ $2^{4} \cdot 71$ $C_2$ $2$ ✓
1136.29.2.c1.a1 $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ ✓ ✓ $C_{568}:C_2$ $2^{4} \cdot 71$ $C_2$ $2$ ✓
1136.31.2.b1.a1 $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ ✓ ✓ $C_{71}:Q_{16}$ $2^{4} \cdot 71$ $C_2$ $2$ ✓
1704.1.3.a1.a1 $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ $C_3:C_{568}$ $2^{3} \cdot 3 \cdot 71$ $3$ $-$
1704.4.3.a1.a1 $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ ✓ ✓ ✓ $C_{1704}$ $2^{3} \cdot 3 \cdot 71$ $C_3$ $3$ ✓
3408.a.6.c1.a1 $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ ✓ $C_{1704}:C_2$ $2^{4} \cdot 3 \cdot 71$ $C_6$ $2 \cdot 3$ ✓
26696.a.47.a1.a1 $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ ✓ ✓ ✓ $C_{26696}$ $2^{3} \cdot 47 \cdot 71$ $C_{47}$ $47$ ✓
53392.a.94._.A $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ $C_{26696}.C_2$ $2^{4} \cdot 47 \cdot 71$ $C_{94}$ $2 \cdot 47$ ✓
80088.b.141.a1.a1 $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ ✓ ✓ $C_{80088}$ $2^{3} \cdot 3 \cdot 47 \cdot 71$ $C_{141}$ $3 \cdot 47$ ✓
160176.a.282._.A $C_{568}$ $2^{3} \cdot 71$ ✓ ✓ $C_{10011}:\SD_{16}$ $2^{4} \cdot 3 \cdot 47 \cdot 71$ $C_{282}$ $2 \cdot 3 \cdot 47$ ✓
184219440.b.324330._.A $C_{568}$ $2^{3} \cdot 71$ ✓ $\PGL(2,569)$ $2^{4} \cdot 3 \cdot 5 \cdot 19 \cdot 71 \cdot 569$ $2 \cdot 3 \cdot 5 \cdot 19 \cdot 569$ $-$
5871759072.a.10337604._.A $C_{568}$ $2^{3} \cdot 71$ ✓ $\PSL(2,2273)$ $2^{5} \cdot 3 \cdot 71 \cdot 379 \cdot 2273$ $2^{2} \cdot 3 \cdot 379 \cdot 2273$ $-$
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