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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 124 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
648.280.1.a1.a1 $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ ✓ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $C_1$ $1$ ✓
648.280.2.a1.a1 $C_6^2:C_9$ $2^{2} \cdot 3^{4}$ ✓ ✓ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $C_2$ $2$ ✓
648.280.3.a1.a1 $C_6^2:C_6$ $2^{3} \cdot 3^{3}$ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $3$ $-$
648.280.3.b1.a1 $C_3^2.S_4$ $2^{3} \cdot 3^{3}$ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $3$ $-$
648.280.3.b1.b1 $C_3^2.S_4$ $2^{3} \cdot 3^{3}$ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $3$ $-$
648.280.3.b1.c1 $C_3^2.S_4$ $2^{3} \cdot 3^{3}$ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $3$ $-$
648.280.4.a1.a1 $C_3^2:D_9$ $2 \cdot 3^{4}$ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2^{2}$ $-$
648.280.6.a1.a1 $C_3\times C_6^2$ $2^{2} \cdot 3^{3}$ ✓ ✓ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
648.280.6.b1.a1 $C_3^2.A_4$ $2^{2} \cdot 3^{3}$ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
648.280.6.b1.b1 $C_3^2.A_4$ $2^{2} \cdot 3^{3}$ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
648.280.6.b1.c1 $C_3^2.A_4$ $2^{2} \cdot 3^{3}$ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
648.280.6.c1.a1 $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2 \cdot 3$ $-$
648.280.6.d1.a1 $C_3^2:C_{12}$ $2^{2} \cdot 3^{3}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2 \cdot 3$ $-$
648.280.8.a1.a1 $C_3^2:C_9$ $3^{4}$ $3$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2^{3}$ $-$
648.280.9.a1.a1 $C_6\wr C_2$ $2^{3} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $3^{2}$ $-$
648.280.9.b1.a1 $C_6\wr C_2$ $2^{3} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $3^{2}$ $-$
648.280.9.b1.b1 $C_6\wr C_2$ $2^{3} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $3^{2}$ $-$
648.280.9.b1.c1 $C_6\wr C_2$ $2^{3} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $3^{2}$ $-$
648.280.9.c1.a1 $C_6^2:C_2$ $2^{3} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $3^{2}$ $-$
648.280.9.d1.a1 $C_2^2:D_9$ $2^{3} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $3^{2}$ $-$
648.280.9.d1.b1 $C_2^2:D_9$ $2^{3} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $3^{2}$ $-$
648.280.9.d1.c1 $C_2^2:D_9$ $2^{3} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $3^{2}$ $-$
648.280.12.a1.a1 $C_3^2\times C_6$ $2 \cdot 3^{3}$ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.280.12.b1.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.280.12.c1.a1 $C_3\times D_9$ $2 \cdot 3^{3}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.280.12.c1.b1 $C_3\times D_9$ $2 \cdot 3^{3}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.280.12.c1.c1 $C_3\times D_9$ $2 \cdot 3^{3}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.280.18.a1.a1 $C_6^2$ $2^{2} \cdot 3^{2}$ ✓ ✓ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $C_3:S_3$ $2 \cdot 3^{2}$
648.280.18.b1.a1 $C_6^2$ $2^{2} \cdot 3^{2}$ ✓ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $D_9$ $2 \cdot 3^{2}$
648.280.18.b1.b1 $C_6^2$ $2^{2} \cdot 3^{2}$ ✓ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $D_9$ $2 \cdot 3^{2}$
648.280.18.b1.c1 $C_6^2$ $2^{2} \cdot 3^{2}$ ✓ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $D_9$ $2 \cdot 3^{2}$
648.280.18.c1.a1 $C_6\times S_3$ $2^{2} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.280.18.d1.a1 $C_6\times S_3$ $2^{2} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.280.18.d1.b1 $C_6\times S_3$ $2^{2} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.280.18.d1.c1 $C_6\times S_3$ $2^{2} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.280.18.e1.a1 $C_6:S_3$ $2^{2} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.280.18.f1.a1 $C_3:C_{12}$ $2^{2} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.280.18.g1.a1 $C_3:C_{12}$ $2^{2} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.280.18.g1.b1 $C_3:C_{12}$ $2^{2} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.280.18.g1.c1 $C_3:C_{12}$ $2^{2} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.280.18.h1.a1 $C_3^2:C_4$ $2^{2} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.280.18.i1.a1 $C_6^2$ $2^{2} \cdot 3^{2}$ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.280.18.j1.a1 $C_2^2:C_9$ $2^{2} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.280.18.j1.b1 $C_2^2:C_9$ $2^{2} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.280.18.j1.c1 $C_2^2:C_9$ $2^{2} \cdot 3^{2}$ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.280.18.k1.a1 $C_6^2$ $2^{2} \cdot 3^{2}$ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.280.24.a1.a1 $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $S_4$ $2^{3} \cdot 3$
648.280.24.b1.a1 $C_3\times C_9$ $3^{3}$ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
648.280.24.b1.b1 $C_3\times C_9$ $3^{3}$ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
648.280.24.b1.c1 $C_3\times C_9$ $3^{3}$ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $2^{3} \cdot 3$ $-$
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