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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 225 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
224.137.224.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_{28}.D_4$ $2^{5} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$
448.498.224.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4.(C_4\times D_{14})$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.500.224.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{28}:(C_2\times C_4)$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.501.224.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{14}.(C_2\times D_8)$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.505.224.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times C_{28}).D_4$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.556.224.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_{14}$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.560.224.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_{14}$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.562.224.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $Q_8.D_{28}$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.564.224.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_{14}$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.579.224.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times C_{28}).D_4$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.581.224.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{28}.D_4$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.583.224.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times C_{28}).D_4$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.586.224.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times C_{28}).D_4$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.614.224.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_{14}$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.616.224.b1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2.D_{14}$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.616.224.b1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2.D_{14}$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.617.224.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{28}:\SD_{16}$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.620.224.b1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2.D_{14}$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.620.224.b1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_4^2.D_{14}$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.621.224.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{28}:Q_8$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.623.224.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_{14}$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.624.224.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{28}:Q_{16}$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.628.224.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4^2.D_{14}$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.759.224.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $(Q_8\times C_{14}):C_4$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.759.224.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $(Q_8\times C_{14}):C_4$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.761.224.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_7\times Q_8):D_4$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.762.224.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times C_{14}):Q_{16}$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
448.1261.224.a1 $C_2$ $2$ ✓ ✓ ✓ $C_{28}.C_2^4$ $2^{6} \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
672.451.224.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_{84}.D_4$ $2^{5} \cdot 3 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
672.465.224.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_{28}.D_{12}$ $2^{5} \cdot 3 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
672.662.224.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $D_{28}.D_6$ $2^{5} \cdot 3 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
672.664.224.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_{84}.C_2^3$ $2^{5} \cdot 3 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
672.835.224.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ ✓ $C_{84}.D_4$ $2^{5} \cdot 3 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
672.1007.224.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_{84}.D_4$ $2^{5} \cdot 3 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
1120.412.224.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
1120.426.224.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{28}.D_{20}$ $2^{5} \cdot 5 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
1120.572.224.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $D_{28}.D_{10}$ $2^{5} \cdot 5 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
1120.574.224.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{140}.C_2^3$ $2^{5} \cdot 5 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
1120.708.224.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
1120.880.224.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{140}.D_4$ $2^{5} \cdot 5 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$ ✓
1344.1554.224.c1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_2\times C_{84}).D_4$ $2^{6} \cdot 3 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$
1344.1556.224.c1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{84}.D_8$ $2^{6} \cdot 3 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$
1344.1574.224.c1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_2\times C_{28}).D_{12}$ $2^{6} \cdot 3 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$
1344.1584.224.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ $(C_2\times C_{84}).D_4$ $2^{6} \cdot 3 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$
1344.1584.224.b1.b1 $C_6$ $2 \cdot 3$ ✓ ✓ $(C_2\times C_{84}).D_4$ $2^{6} \cdot 3 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$
1344.1586.224.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ $(C_2\times C_{28}).D_{12}$ $2^{6} \cdot 3 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$
1344.1586.224.b1.b1 $C_6$ $2 \cdot 3$ ✓ ✓ $(C_2\times C_{28}).D_{12}$ $2^{6} \cdot 3 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$
1344.1604.224.c1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{84}.\SD_{16}$ $2^{6} \cdot 3 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$
1344.1607.224.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{84}.\SD_{16}$ $2^{6} \cdot 3 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$
1344.1617.224.c1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_2\times C_{28}).D_{12}$ $2^{6} \cdot 3 \cdot 7$ $C_{28}.D_4$ $2^{5} \cdot 7$
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