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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 344 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1296.3432.1.a1 $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_1$ $1$ ✓
1296.3432.2.a1 $C_3^4:D_4$ $2^{3} \cdot 3^{4}$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_2$ $2$ ✓
1296.3432.2.b1 $C_3^4:D_4$ $2^{3} \cdot 3^{4}$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_2$ $2$ ✓
1296.3432.2.c1 $C_2\times C_3^3:C_{12}$ $2^{3} \cdot 3^{4}$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_2$ $2$ ✓
1296.3432.2.d1 $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_2$ $2$ ✓
1296.3432.2.e1 $C_3^3:(C_4\times S_3)$ $2^{3} \cdot 3^{4}$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_2$ $2$ ✓
1296.3432.2.f1 $C_3^3:(C_4\times S_3)$ $2^{3} \cdot 3^{4}$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_2$ $2$ ✓
1296.3432.2.g1 $C_3^4:Q_8$ $2^{3} \cdot 3^{4}$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_2$ $2$ ✓
1296.3432.3.a1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $3$ $-$
1296.3432.3.b1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $3$ $-$
1296.3432.3.c1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $3$ $-$
1296.3432.4.a1 $C_3^2\times C_6^2$ $2^{2} \cdot 3^{4}$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1296.3432.4.b1 $C_3^2:C_6^2$ $2^{2} \cdot 3^{4}$ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1296.3432.4.c1 $C_3^3:D_6$ $2^{2} \cdot 3^{4}$ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1296.3432.4.d1 $C_3^3:C_{12}$ $2^{2} \cdot 3^{4}$ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1296.3432.4.e1 $C_3^3:C_{12}$ $2^{2} \cdot 3^{4}$ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1296.3432.4.f1 $C_3^3:C_{12}$ $2^{2} \cdot 3^{4}$ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1296.3432.4.g1 $C_3^3:C_{12}$ $2^{2} \cdot 3^{4}$ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1296.3432.6.a1 $C_6^2:C_6$ $2^{3} \cdot 3^{3}$ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
1296.3432.6.b1 $C_6^2:S_3$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
1296.3432.6.c1 $C_6^2.S_3$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
1296.3432.6.d1 $C_6^2:C_6$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.6.e1 $C_6^2:C_6$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.6.f1 $C_6^2:C_6$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.6.g1 $C_6^2:C_6$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.6.h1 $C_6^2:C_6$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.6.i1 $C_6^2:C_6$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.6.j1 $C_6^2.C_6$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.6.k1 $C_6^2.C_6$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.6.l1 $C_6^2.C_6$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.6.m1 $C_3^3:D_4$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.6.n1 $C_3^2:D_{12}$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.6.o1 $C_6.S_3^2$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.6.p1 $C_6.S_3^2$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.6.q1 $C_3^2:D_{12}$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.6.r1 $C_6.S_3^2$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.6.s1 $C_6.S_3^2$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.6.t1 $C_6.S_3^2$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.6.u1 $C_6.S_3^2$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.6.v1 $C_3^3:Q_8$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.6.w1 $C_3^3:Q_8$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.6.x1 $C_3^3:Q_8$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.3432.8.a1 $C_3^3\times C_6$ $2 \cdot 3^{4}$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
1296.3432.8.b1 $C_3^3\times C_6$ $2 \cdot 3^{4}$ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{3}$ $-$
1296.3432.8.c1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{3}$ $-$
1296.3432.8.d1 $C_3^3:C_6$ $2 \cdot 3^{4}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{3}$ $-$
1296.3432.9.a1 $C_{12}.D_6$ $2^{4} \cdot 3^{2}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $3^{2}$ $-$
1296.3432.9.b1 $D_6.D_6$ $2^{4} \cdot 3^{2}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $3^{2}$ $-$
1296.3432.9.c1 $D_6.D_6$ $2^{4} \cdot 3^{2}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $3^{2}$ $-$
1296.3432.9.d1 $D_6.D_6$ $2^{4} \cdot 3^{2}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $3^{2}$ $-$
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