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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 60 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
224.104.1.a1.a1 $C_4.D_{28}$ $2^{5} \cdot 7$ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $C_1$ $1$ ✓
224.104.2.a1.a1 $D_{28}:C_2$ $2^{4} \cdot 7$ ✓ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $C_2$ $2$ ✓
224.104.2.b1.a1 $C_{14}:Q_8$ $2^{4} \cdot 7$ ✓ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $C_2$ $2$ ✓
224.104.2.c1.a1 $C_7\times \OD_{16}$ $2^{4} \cdot 7$ ✓ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $C_2$ $2$ ✓
224.104.2.d1.a1 $C_{56}:C_2$ $2^{4} \cdot 7$ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $C_2$ $2$ ✓
224.104.2.d1.b1 $C_{56}:C_2$ $2^{4} \cdot 7$ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $C_2$ $2$ ✓
224.104.2.e1.a1 $C_7:Q_{16}$ $2^{4} \cdot 7$ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $C_2$ $2$ ✓
224.104.2.e1.b1 $C_7:Q_{16}$ $2^{4} \cdot 7$ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $C_2$ $2$ ✓
224.104.4.a1.a1 $C_2\times C_{28}$ $2^{3} \cdot 7$ ✓ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $C_2^2$ $2^{2}$ ✓
224.104.4.b1.a1 $D_{28}$ $2^{3} \cdot 7$ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $C_2^2$ $2^{2}$ ✓
224.104.4.c1.a1 $C_7:Q_8$ $2^{3} \cdot 7$ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $C_2^2$ $2^{2}$ ✓
224.104.4.c1.b1 $C_7:Q_8$ $2^{3} \cdot 7$ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $C_2^2$ $2^{2}$ ✓
224.104.4.d1.a1 $C_7:Q_8$ $2^{3} \cdot 7$ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $C_2^2$ $2^{2}$ ✓
224.104.4.e1.a1 $C_{56}$ $2^{3} \cdot 7$ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $C_2^2$ $2^{2}$ ✓
224.104.4.e1.b1 $C_{56}$ $2^{3} \cdot 7$ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $C_2^2$ $2^{2}$ ✓
224.104.4.f1.a1 $C_7:D_4$ $2^{3} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2^{2}$ $-$
224.104.4.g1.a1 $C_{14}:C_4$ $2^{3} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2^{2}$ $-$
224.104.4.h1.a1 $C_4\times D_7$ $2^{3} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2^{2}$ $-$
224.104.4.i1.a1 $C_7:Q_8$ $2^{3} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2^{2}$ $-$
224.104.7.a1.a1 $Q_{16}:C_2$ $2^{5}$ $2$ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $7$ $-$
224.104.8.a1.a1 $C_2\times C_{14}$ $2^{2} \cdot 7$ ✓ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $D_4$ $2^{3}$
224.104.8.b1.a1 $C_{28}$ $2^{2} \cdot 7$ ✓ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $D_4$ $2^{3}$
224.104.8.c1.a1 $C_{28}$ $2^{2} \cdot 7$ ✓ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $C_2^3$ $2^{3}$ ✓
224.104.8.d1.a1 $D_{14}$ $2^{2} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2^{3}$ $-$
224.104.8.e1.a1 $C_7:C_4$ $2^{2} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2^{3}$ $-$
224.104.8.e1.b1 $C_7:C_4$ $2^{2} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2^{3}$ $-$
224.104.8.f1.a1 $C_7:C_4$ $2^{2} \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2^{3}$ $-$
224.104.14.a1.a1 $\OD_{16}$ $2^{4}$ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $D_7$ $2 \cdot 7$
224.104.14.b1.a1 $D_4:C_2$ $2^{4}$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2 \cdot 7$ $-$
224.104.14.c1.a1 $C_2\times Q_8$ $2^{4}$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2 \cdot 7$ $-$
224.104.14.d1.a1 $\SD_{16}$ $2^{4}$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2 \cdot 7$ $-$
224.104.14.d1.b1 $\SD_{16}$ $2^{4}$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2 \cdot 7$ $-$
224.104.14.e1.a1 $Q_{16}$ $2^{4}$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2 \cdot 7$ $-$
224.104.14.e1.b1 $Q_{16}$ $2^{4}$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2 \cdot 7$ $-$
224.104.16.a1.a1 $C_{14}$ $2 \cdot 7$ ✓ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $C_2\times D_4$ $2^{4}$
224.104.16.b1.a1 $C_{14}$ $2 \cdot 7$ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $2^{4}$ $-$
224.104.16.c1.a1 $D_7$ $2 \cdot 7$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2^{4}$ $-$
224.104.28.a1.a1 $C_2\times C_4$ $2^{3}$ ✓ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $D_{14}$ $2^{2} \cdot 7$
224.104.28.b1.a1 $C_8$ $2^{3}$ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $D_{14}$ $2^{2} \cdot 7$
224.104.28.b1.b1 $C_8$ $2^{3}$ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $D_{14}$ $2^{2} \cdot 7$
224.104.28.c1.a1 $D_4$ $2^{3}$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2^{2} \cdot 7$ $-$
224.104.28.d1.a1 $C_2\times C_4$ $2^{3}$ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $2^{2} \cdot 7$ $-$
224.104.28.e1.a1 $C_2\times C_4$ $2^{3}$ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $2^{2} \cdot 7$ $-$
224.104.28.f1.a1 $D_4$ $2^{3}$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2^{2} \cdot 7$ $-$
224.104.28.g1.a1 $Q_8$ $2^{3}$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2^{2} \cdot 7$ $-$
224.104.28.h1.a1 $Q_8$ $2^{3}$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2^{2} \cdot 7$ $-$
224.104.28.h1.b1 $Q_8$ $2^{3}$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2^{2} \cdot 7$ $-$
224.104.28.i1.a1 $Q_8$ $2^{3}$ $C_4.D_{28}$ $2^{5} \cdot 7$ $2^{2} \cdot 7$ $-$
224.104.32.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $Q_{16}:C_2$ $2^{5}$ ✓
224.104.56.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_4.D_{28}$ $2^{5} \cdot 7$ $D_{28}$ $2^{3} \cdot 7$
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