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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 258 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
972.802.1.a1.a1 $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ ✓ ✓ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $C_1$ $1$ ✓
972.802.2.a1.a1 $C_3^3:(C_3\times S_3)$ $2 \cdot 3^{5}$ ✓ ✓ ✓ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $C_2$ $2$ ✓
972.802.2.b1.a1 $C_3^3:(C_3\times C_6)$ $2 \cdot 3^{5}$ ✓ ✓ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $C_2$ $2$ ✓
972.802.2.b1.b1 $C_3^3:(C_3\times C_6)$ $2 \cdot 3^{5}$ ✓ ✓ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $C_2$ $2$ ✓
972.802.3.a1.a1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ ✓ ✓ ✓ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $C_3$ $3$ ✓
972.802.3.b1.a1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ ✓ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $3$ $-$
972.802.3.b1.b1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ ✓ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $3$ $-$
972.802.3.c1.a1 $C_3^3:D_6$ $2^{2} \cdot 3^{4}$ ✓ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $3$ $-$
972.802.4.a1.a1 $C_3^3:C_3^2$ $3^{5}$ $3$ ✓ ✓ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $C_2^2$ $2^{2}$ ✓
972.802.6.a1.a1 $C_3^3:S_3$ $2 \cdot 3^{4}$ ✓ ✓ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $S_3$ $2 \cdot 3$
972.802.6.b1.a1 $C_3^3:S_3$ $2 \cdot 3^{4}$ ✓ ✓ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $C_6$ $2 \cdot 3$ ✓
972.802.6.c1.a1 $C_3^3:C_6$ $2 \cdot 3^{4}$ ✓ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $S_3$ $2 \cdot 3$
972.802.6.c1.b1 $C_3^3:C_6$ $2 \cdot 3^{4}$ ✓ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $S_3$ $2 \cdot 3$
972.802.6.d1.a1 $C_3^3:C_6$ $2 \cdot 3^{4}$ ✓ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $C_6$ $2 \cdot 3$ ✓
972.802.6.d1.b1 $C_3^3:C_6$ $2 \cdot 3^{4}$ ✓ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $C_6$ $2 \cdot 3$ ✓
972.802.6.e1.a1 $S_3\times \He_3$ $2 \cdot 3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2 \cdot 3$ $-$
972.802.6.e1.b1 $S_3\times \He_3$ $2 \cdot 3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2 \cdot 3$ $-$
972.802.6.f1.a1 $S_3\times \He_3$ $2 \cdot 3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2 \cdot 3$ $-$
972.802.6.g1.a1 $C_3^3:S_3$ $2 \cdot 3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2 \cdot 3$ $-$
972.802.6.h1.a1 $C_3^3:C_6$ $2 \cdot 3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2 \cdot 3$ $-$
972.802.6.h1.b1 $C_3^3:C_6$ $2 \cdot 3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2 \cdot 3$ $-$
972.802.6.i1.a1 $C_3^3:C_6$ $2 \cdot 3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2 \cdot 3$ $-$
972.802.6.i1.b1 $C_3^3:C_6$ $2 \cdot 3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2 \cdot 3$ $-$
972.802.6.j1.a1 $C_3^3:C_6$ $2 \cdot 3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2 \cdot 3$ $-$
972.802.6.j1.b1 $C_3^3:C_6$ $2 \cdot 3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2 \cdot 3$ $-$
972.802.6.k1.a1 $C_3^3:C_6$ $2 \cdot 3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2 \cdot 3$ $-$
972.802.6.k1.b1 $C_3^3:C_6$ $2 \cdot 3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2 \cdot 3$ $-$
972.802.9.a1.a1 $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $3^{2}$ $-$
972.802.9.b1.a1 $C_3\times S_3^2$ $2^{2} \cdot 3^{3}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $3^{2}$ $-$
972.802.9.b1.b1 $C_3\times S_3^2$ $2^{2} \cdot 3^{3}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $3^{2}$ $-$
972.802.9.c1.a1 $C_3:S_3^2$ $2^{2} \cdot 3^{3}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $3^{2}$ $-$
972.802.9.c1.b1 $C_3:S_3^2$ $2^{2} \cdot 3^{3}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $3^{2}$ $-$
972.802.9.d1.a1 $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $3^{2}$ $-$
972.802.12.a1.a1 $C_3\times \He_3$ $3^{4}$ ✓ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $D_6$ $2^{2} \cdot 3$
972.802.12.a1.b1 $C_3\times \He_3$ $3^{4}$ ✓ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $D_6$ $2^{2} \cdot 3$
972.802.12.b1.a1 $C_3\times \He_3$ $3^{4}$ ✓ ✓ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $D_6$ $2^{2} \cdot 3$
972.802.12.c1.a1 $C_3\times \He_3$ $3^{4}$ ✓ ✓ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
972.802.12.d1.a1 $C_3\times \He_3$ $3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
972.802.12.d1.b1 $C_3\times \He_3$ $3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
972.802.12.e1.a1 $C_3\times \He_3$ $3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
972.802.12.f1.a1 $C_3\times \He_3$ $3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
972.802.12.g1.a1 $C_3\times \He_3$ $3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
972.802.12.g1.b1 $C_3\times \He_3$ $3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
972.802.12.h1.a1 $C_3\times \He_3$ $3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
972.802.12.h1.b1 $C_3\times \He_3$ $3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
972.802.12.i1.a1 $C_3\times \He_3$ $3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
972.802.12.j1.a1 $C_3\times \He_3$ $3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
972.802.12.k1.a1 $C_3\times \He_3$ $3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
972.802.12.k1.b1 $C_3\times \He_3$ $3^{4}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $2^{2} \cdot 3$ $-$
972.802.18.a1.a1 $C_3^2:S_3$ $2 \cdot 3^{3}$ ✓ ✓ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$ $C_3\times S_3$ $2 \cdot 3^{2}$
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