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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 (1-50 of 235 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
224.104.224.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$
448.236.224.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{56}:Q_8$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.237.224.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2.D_{14}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.237.224.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2.D_{14}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.244.224.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_{14}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.248.224.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_{14}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.249.224.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_8.D_{28}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.249.224.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_8.D_{28}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.250.224.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2.D_{14}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.250.224.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2.D_{14}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.255.224.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^3.D_{28}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.257.224.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^3.D_{28}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.267.224.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{28}.D_4$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.270.224.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^2.D_{56}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.272.224.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^3.D_{28}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.273.224.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^3.D_{28}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.363.224.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_{14}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.375.224.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{28}:\SD_{16}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.379.224.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_{14}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.380.224.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{28}:Q_8$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.383.224.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{28}:Q_{16}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.385.224.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_{14}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.654.224.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_2^3.D_{28}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.654.224.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_2^3.D_{28}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.655.224.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^3.D_{28}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.667.224.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^3.D_{28}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.668.224.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{56}:D_4$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.671.224.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_{56}.D_4$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.671.224.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_{56}.D_4$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
448.1200.224.a1 $C_2$ $2$ ✓ ✓ ✓ $\OD_{16}:D_{14}$ $2^{6} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
672.407.224.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_{24}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
672.418.224.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_{24}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
672.457.224.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_{12}.D_{28}$ $2^{5} \cdot 3 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
672.459.224.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_{12}.D_{28}$ $2^{5} \cdot 3 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
672.802.224.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ ✓ $C_{12}.D_{28}$ $2^{5} \cdot 3 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
672.974.224.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
1120.317.224.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{40}.D_{14}$ $2^{5} \cdot 5 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
1120.327.224.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{40}.D_{14}$ $2^{5} \cdot 5 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
1120.418.224.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{20}.D_{28}$ $2^{5} \cdot 5 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
1120.420.224.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{20}.D_{28}$ $2^{5} \cdot 5 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
1120.673.224.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ ✓ $C_{20}.D_{28}$ $2^{5} \cdot 5 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
1120.845.224.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_4.D_{140}$ $2^{5} \cdot 5 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ ✓
1344.1547.224.c1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{12}.D_{56}$ $2^{6} \cdot 3 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$
1344.1551.224.c1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_2\times C_{12}).D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$
1344.1576.224.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{84}.\SD_{16}$ $2^{6} \cdot 3 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$
1344.1577.224.c1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_2\times C_{12}).D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$
1344.1580.224.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ $(C_2\times C_{12}).D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$
1344.1580.224.b1.b1 $C_6$ $2 \cdot 3$ ✓ ✓ $(C_2\times C_{12}).D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$
1344.1588.224.c1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_2\times C_{12}).D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$
1344.1589.224.c1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_2\times C_{12}).D_{28}$ $2^{6} \cdot 3 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$
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