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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 524 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1344.8546.1.a1.a1 $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_1$ $1$ ✓
1344.8546.2.a1.a1 $D_{28}:D_6$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8546.2.b1.a1 $D_{28}:D_6$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8546.2.c1.a1 $C_{56}:D_6$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8546.2.d1.a1 $C_{24}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8546.2.e1.a1 $C_{12}.D_{28}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8546.2.f1.a1 $D_{84}:C_2^2$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8546.2.g1.a1 $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8546.2.h1.a1 $D_{56}:S_3$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8546.2.h1.b1 $D_{56}:S_3$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8546.2.i1.a1 $C_{24}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8546.2.i1.b1 $C_{24}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8546.2.j1.a1 $C_{24}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8546.2.j1.b1 $C_{24}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8546.2.k1.a1 $C_{24}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8546.2.k1.b1 $C_{24}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8546.3.a1.a1 $D_{56}:C_2^2$ $2^{6} \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $3$ $-$
1344.8546.4.a1.a1 $D_6\times C_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.b1.a1 $D_{28}:C_6$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.c1.a1 $C_6\times D_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.d1.a1 $D_{84}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.e1.a1 $C_{42}:Q_8$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.f1.a1 $\OD_{16}\times C_{21}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.g1.a1 $C_{12}.C_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.h1.a1 $D_{28}:S_3$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.i1.a1 $D_{28}:S_3$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.i1.b1 $D_{28}:S_3$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.j1.a1 $D_{84}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.k1.a1 $S_3\times C_{56}$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.k1.b1 $S_3\times C_{56}$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.l1.a1 $S_3\times D_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.m1.a1 $D_{28}:S_3$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.m1.b1 $D_{28}:S_3$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.n1.a1 $C_{12}.D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.o1.a1 $C_{168}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.o1.b1 $C_{168}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.p1.a1 $C_3\times D_{56}$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.p1.b1 $C_3\times D_{56}$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.q1.a1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.q1.b1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.r1.a1 $C_3:D_{56}$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.r1.b1 $C_3:D_{56}$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.s1.a1 $C_{168}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.s1.b1 $C_{168}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.t1.a1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.t1.b1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.u1.a1 $C_{168}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.u1.b1 $C_{168}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.v1.a1 $C_{21}:Q_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8546.4.v1.b1 $C_{21}:Q_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
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