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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 96 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
324.162.1.a1.a1 $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ ✓ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $C_1$ $1$ ✓
324.162.2.a1.a1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ ✓ ✓ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $C_2$ $2$ ✓
324.162.3.a1.a1 $C_3^3:C_4$ $2^{2} \cdot 3^{3}$ ✓ ✓ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $C_3$ $3$ ✓
324.162.3.b1.a1 $C_3^2:C_{12}$ $2^{2} \cdot 3^{3}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $3$ $-$
324.162.4.a1.a1 $C_3^4$ $3^{4}$ $3$ ✓ ✓ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $C_4$ $2^{2}$ ✓
324.162.6.a1.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ ✓ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
324.162.6.b1.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ ✓ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $C_6$ $2 \cdot 3$ ✓
324.162.6.c1.a1 $S_3\times C_3^2$ $2 \cdot 3^{3}$ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2 \cdot 3$ $-$
324.162.6.c1.b1 $S_3\times C_3^2$ $2 \cdot 3^{3}$ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2 \cdot 3$ $-$
324.162.6.d1.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2 \cdot 3$ $-$
324.162.9.a1.a1 $C_3:C_{12}$ $2^{2} \cdot 3^{2}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $3^{2}$ $-$
324.162.9.b1.a1 $C_3^2:C_4$ $2^{2} \cdot 3^{2}$ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $3^{2}$ $-$
324.162.12.a1.a1 $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $C_3:C_4$ $2^{2} \cdot 3$
324.162.12.b1.a1 $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $C_{12}$ $2^{2} \cdot 3$ ✓
324.162.12.c1.a1 $C_3^3$ $3^{3}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
324.162.12.c1.b1 $C_3^3$ $3^{3}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
324.162.12.d1.a1 $C_3^3$ $3^{3}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
324.162.12.d1.b1 $C_3^3$ $3^{3}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
324.162.12.e1.a1 $C_3^3$ $3^{3}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
324.162.12.e1.b1 $C_3^3$ $3^{3}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
324.162.12.f1.a1 $C_3^3$ $3^{3}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
324.162.12.f1.b1 $C_3^3$ $3^{3}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
324.162.12.f1.c1 $C_3^3$ $3^{3}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
324.162.12.f1.d1 $C_3^3$ $3^{3}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
324.162.12.g1.a1 $C_3^3$ $3^{3}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
324.162.18.a1.a1 $C_3:S_3$ $2 \cdot 3^{2}$ ✓ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $C_3\times S_3$ $2 \cdot 3^{2}$
324.162.18.b1.a1 $C_3\times C_6$ $2 \cdot 3^{2}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
324.162.18.c1.a1 $C_3\times S_3$ $2 \cdot 3^{2}$ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
324.162.18.c1.b1 $C_3\times S_3$ $2 \cdot 3^{2}$ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
324.162.18.d1.a1 $C_3\times S_3$ $2 \cdot 3^{2}$ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
324.162.18.d1.b1 $C_3\times S_3$ $2 \cdot 3^{2}$ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
324.162.18.e1.a1 $C_3\times S_3$ $2 \cdot 3^{2}$ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
324.162.18.e1.b1 $C_3\times S_3$ $2 \cdot 3^{2}$ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
324.162.18.e1.c1 $C_3\times S_3$ $2 \cdot 3^{2}$ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
324.162.18.e1.d1 $C_3\times S_3$ $2 \cdot 3^{2}$ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
324.162.27.a1.a1 $C_{12}$ $2^{2} \cdot 3$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $3^{3}$ $-$
324.162.27.b1.a1 $C_3:C_4$ $2^{2} \cdot 3$ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $3^{3}$ $-$
324.162.36.a1.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $C_3^2:C_4$ $2^{2} \cdot 3^{2}$
324.162.36.b1.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $C_3:C_{12}$ $2^{2} \cdot 3^{2}$ ✓
324.162.36.c1.a1 $C_3^2$ $3^{2}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
324.162.36.c1.b1 $C_3^2$ $3^{2}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
324.162.36.d1.a1 $C_3^2$ $3^{2}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
324.162.36.d1.b1 $C_3^2$ $3^{2}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
324.162.36.e1.a1 $C_3^2$ $3^{2}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
324.162.36.e1.b1 $C_3^2$ $3^{2}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
324.162.36.f1.a1 $C_3^2$ $3^{2}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
324.162.36.f1.b1 $C_3^2$ $3^{2}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
324.162.36.g1.a1 $C_3^2$ $3^{2}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
324.162.36.g1.b1 $C_3^2$ $3^{2}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
324.162.36.g1.c1 $C_3^2$ $3^{2}$ ✓ $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $2^{2} \cdot 3^{2}$ $-$
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