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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 240 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1344.8525.1.a1 $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_1$ $1$ ✓
1344.8525.2.a1 $D_{28}.D_6$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8525.2.b1 $C_{84}.D_4$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8525.2.c1 $D_{56}:C_6$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8525.2.d1 $C_8.D_{42}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8525.2.e1 $C_{42}:Q_{16}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8525.2.f1 $C_{24}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8525.2.g1 $D_{56}:S_3$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8525.2.h1 $D_{21}:Q_{16}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8525.3.a1 $Q_{16}.D_{14}$ $2^{6} \cdot 7$ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $3$ $-$
1344.8525.4.a1 $D_{28}:C_6$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8525.4.b1 $D_{84}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8525.4.c1 $C_{42}:Q_8$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8525.4.d1 $C_2\times C_{168}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8525.4.e1 $C_{21}:\OD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8525.4.f1 $D_{28}:S_3$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8525.4.g1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8525.4.h1 $C_{168}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8525.4.i1 $C_3\times D_{56}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8525.4.j1 $D_{21}:Q_8$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8525.4.k1 $C_8\times D_{21}$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8525.4.l1 $C_{168}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8525.4.m1 $C_{21}:Q_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8525.4.n1 $C_{21}:Q_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8525.4.o1 $C_{21}:Q_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8525.4.p1 $C_{21}:Q_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8525.4.q1 $D_{14}.D_6$ $2^{4} \cdot 3 \cdot 7$ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $2^{2}$ $-$
1344.8525.4.r1 $D_{84}:C_2$ $2^{4} \cdot 3 \cdot 7$ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $2^{2}$ $-$
1344.8525.4.s1 $C_{12}.D_{14}$ $2^{4} \cdot 3 \cdot 7$ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $2^{2}$ $-$
1344.8525.6.a1 $D_{56}:C_2$ $2^{5} \cdot 7$ ✓ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $S_3$ $2 \cdot 3$
1344.8525.6.b1 $Q_8.D_{14}$ $2^{5} \cdot 7$ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
1344.8525.6.c1 $C_{28}.D_4$ $2^{5} \cdot 7$ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
1344.8525.6.d1 $C_8.D_{14}$ $2^{5} \cdot 7$ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
1344.8525.6.e1 $C_{14}\times Q_{16}$ $2^{5} \cdot 7$ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
1344.8525.6.f1 $Q_{16}:D_7$ $2^{5} \cdot 7$ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
1344.8525.6.g1 $D_{56}:C_2$ $2^{5} \cdot 7$ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
1344.8525.6.h1 $D_7\times Q_{16}$ $2^{5} \cdot 7$ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
1344.8525.7.a1 $D_8.D_6$ $2^{6} \cdot 3$ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $7$ $-$
1344.8525.8.a1 $C_{21}:D_4$ $2^{3} \cdot 3 \cdot 7$ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $D_4$ $2^{3}$
1344.8525.8.b1 $C_2\times C_{84}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.8525.8.c1 $C_3\times D_{28}$ $2^{3} \cdot 3 \cdot 7$ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.8525.8.d1 $C_4\times D_{21}$ $2^{3} \cdot 3 \cdot 7$ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.8525.8.e1 $D_{84}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $D_4$ $2^{3}$
1344.8525.8.f1 $C_{21}:Q_8$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $D_4$ $2^{3}$
1344.8525.8.g1 $C_{21}:Q_8$ $2^{3} \cdot 3 \cdot 7$ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.8525.8.h1 $C_{21}:Q_8$ $2^{3} \cdot 3 \cdot 7$ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.8525.8.i1 $C_{168}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.8525.8.j1 $C_{168}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.8525.8.k1 $C_{21}:C_8$ $2^{3} \cdot 3 \cdot 7$ ✓ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
1344.8525.8.l1 $C_{21}:D_4$ $2^{3} \cdot 3 \cdot 7$ $D_{56}.D_6$ $2^{6} \cdot 3 \cdot 7$ $2^{3}$ $-$
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