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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 638 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1944.3566.1.a1.a1 $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_1$ $1$ ✓
1944.3566.2.a1.a1 $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_2$ $2$ ✓
1944.3566.2.a1.b1 $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_2$ $2$ ✓
1944.3566.2.b1.a1 $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_2$ $2$ ✓
1944.3566.2.b1.b1 $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_2$ $2$ ✓
1944.3566.2.c1.a1 $C_3^3.C_6^2$ $2^{2} \cdot 3^{5}$ ✓ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_2$ $2$ ✓
1944.3566.2.d1.a1 $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$ ✓ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_2$ $2$ ✓
1944.3566.2.e1.a1 $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$ ✓ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_2$ $2$ ✓
1944.3566.3.a1.a1 $D_9\times S_3^2$ $2^{3} \cdot 3^{4}$ ✓ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_3$ $3$ ✓
1944.3566.3.b1.a1 $C_{18}:C_6\times S_3$ $2^{3} \cdot 3^{4}$ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $3$ $-$
1944.3566.3.b1.b1 $C_{18}:C_6\times S_3$ $2^{3} \cdot 3^{4}$ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $3$ $-$
1944.3566.3.c1.a1 $C_3\times S_3^3$ $2^{3} \cdot 3^{4}$ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $3$ $-$
1944.3566.4.a1.a1 $C_3^4.C_6$ $2 \cdot 3^{5}$ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_2^2$ $2^{2}$ ✓
1944.3566.4.a1.b1 $C_3^4.C_6$ $2 \cdot 3^{5}$ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_2^2$ $2^{2}$ ✓
1944.3566.4.b1.a1 $D_9:C_3^3$ $2 \cdot 3^{5}$ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_2^2$ $2^{2}$ ✓
1944.3566.4.c1.a1 $C_3^4.C_6$ $2 \cdot 3^{5}$ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_2^2$ $2^{2}$ ✓
1944.3566.4.d1.a1 $C_3^4.S_3$ $2 \cdot 3^{5}$ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_2^2$ $2^{2}$ ✓
1944.3566.4.d1.b1 $C_3^4.S_3$ $2 \cdot 3^{5}$ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_2^2$ $2^{2}$ ✓
1944.3566.4.e1.a1 $C_3^4.S_3$ $2 \cdot 3^{5}$ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_2^2$ $2^{2}$ ✓
1944.3566.6.a1.a1 $C_3^2.S_3^2$ $2^{2} \cdot 3^{4}$ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $S_3$ $2 \cdot 3$
1944.3566.6.a1.b1 $C_3^2.S_3^2$ $2^{2} \cdot 3^{4}$ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $S_3$ $2 \cdot 3$
1944.3566.6.b1.a1 $C_3^2:D_{18}$ $2^{2} \cdot 3^{4}$ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_6$ $2 \cdot 3$ ✓
1944.3566.6.b1.b1 $C_3^2:D_{18}$ $2^{2} \cdot 3^{4}$ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_6$ $2 \cdot 3$ ✓
1944.3566.6.c1.a1 $C_9:S_3^2$ $2^{2} \cdot 3^{4}$ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_6$ $2 \cdot 3$ ✓
1944.3566.6.c1.b1 $C_9:S_3^2$ $2^{2} \cdot 3^{4}$ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_6$ $2 \cdot 3$ ✓
1944.3566.6.d1.a1 $C_3^2\times S_3^2$ $2^{2} \cdot 3^{4}$ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $S_3$ $2 \cdot 3$
1944.3566.6.e1.a1 $C_9\times S_3^2$ $2^{2} \cdot 3^{4}$ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_6$ $2 \cdot 3$ ✓
1944.3566.6.f1.a1 $C_3^2:D_{18}$ $2^{2} \cdot 3^{4}$ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_6$ $2 \cdot 3$ ✓
1944.3566.6.g1.a1 $C_9:S_3^2$ $2^{2} \cdot 3^{4}$ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_6$ $2 \cdot 3$ ✓
1944.3566.6.h1.a1 $C_9:C_6^2$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3566.6.h1.b1 $C_9:C_6^2$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3566.6.i1.a1 $C_3^3.D_6$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3566.6.i1.b1 $C_3^3.D_6$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3566.6.j1.a1 $C_3^2\times S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3566.6.j1.b1 $C_3^2\times S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3566.6.k1.a1 $C_3^2.S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3566.6.k1.b1 $C_3^2.S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3566.6.l1.a1 $C_3^2.S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3566.6.l1.b1 $C_3^2.S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3566.6.m1.a1 $C_3^2.S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3566.6.m1.b1 $C_3^2.S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3566.6.n1.a1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3566.6.n1.b1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3566.6.o1.a1 $C_3^2.C_6^2$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3566.6.o1.b1 $C_3^2.C_6^2$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3566.6.p1.a1 $C_9\times S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3566.6.q1.a1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3566.6.r1.a1 $C_3^2.S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3566.6.r1.b1 $C_3^2.S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
1944.3566.6.s1.a1 $C_3^2.S_3^2$ $2^{2} \cdot 3^{4}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $2 \cdot 3$ $-$
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