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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 187 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
648.723.1.a1.a1 $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ ✓ ✓ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $C_1$ $1$ ✓
648.723.2.a1.a1 $C_3\wr C_2^2$ $2^{2} \cdot 3^{4}$ ✓ ✓ ✓ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $C_2$ $2$ ✓
648.723.2.b1.a1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ ✓ ✓ ✓ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $C_2$ $2$ ✓
648.723.2.c1.a1 $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ ✓ ✓ ✓ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $C_2$ $2$ ✓
648.723.3.a1.a1 $S_3^2:S_3$ $2^{3} \cdot 3^{3}$ ✓ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $3$ $-$
648.723.3.b1.a1 $C_3^2:D_{12}$ $2^{3} \cdot 3^{3}$ ✓ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $3$ $-$
648.723.4.a1.a1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ ✓ ✓ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
648.723.4.b1.a1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2}$ $-$
648.723.4.c1.a1 $C_3^3:C_6$ $2 \cdot 3^{4}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2}$ $-$
648.723.6.a1.a1 $C_3:S_3^2$ $2^{2} \cdot 3^{3}$ ✓ ✓ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
648.723.6.b1.a1 $C_3^3:C_4$ $2^{2} \cdot 3^{3}$ ✓ ✓ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
648.723.6.c1.a1 $C_3\times S_3^2$ $2^{2} \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2 \cdot 3$ $-$
648.723.6.d1.a1 $C_3:S_3^2$ $2^{2} \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2 \cdot 3$ $-$
648.723.6.e1.a1 $C_3\times S_3^2$ $2^{2} \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2 \cdot 3$ $-$
648.723.6.f1.a1 $C_3:S_3^2$ $2^{2} \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2 \cdot 3$ $-$
648.723.6.g1.a1 $C_3:S_3^2$ $2^{2} \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2 \cdot 3$ $-$
648.723.6.h1.a1 $C_3:S_3^2$ $2^{2} \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2 \cdot 3$ $-$
648.723.6.i1.a1 $C_3^2:C_{12}$ $2^{2} \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2 \cdot 3$ $-$
648.723.8.a1.a1 $C_3^4$ $3^{4}$ $3$ ✓ ✓ ✓ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $D_4$ $2^{3}$
648.723.9.a1.a1 $C_3:D_{12}$ $2^{3} \cdot 3^{2}$ ✓ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $3^{2}$ $-$
648.723.9.b1.a1 $\SOPlus(4,2)$ $2^{3} \cdot 3^{2}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $3^{2}$ $-$
648.723.12.a1.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ ✓ ✓ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
648.723.12.b1.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ ✓ ✓ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
648.723.12.c1.a1 $S_3\times C_3^2$ $2 \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.723.12.d1.a1 $S_3\times C_3^2$ $2 \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.723.12.e1.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.723.12.f1.a1 $S_3\times C_3^2$ $2 \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.723.12.g1.a1 $S_3\times C_3^2$ $2 \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.723.12.h1.a1 $S_3\times C_3^2$ $2 \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.723.12.i1.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.723.12.j1.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.723.12.k1.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.723.12.l1.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.723.12.m1.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.723.12.n1.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.723.12.o1.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.723.12.p1.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.723.12.q1.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.723.12.q1.b1 $C_3^2:C_6$ $2 \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.723.12.r1.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.723.12.r1.a2 $C_3^2:C_6$ $2 \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.723.12.s1.a1 $C_3^2:S_3$ $2 \cdot 3^{3}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
648.723.18.a1.a1 $C_6\times S_3$ $2^{2} \cdot 3^{2}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.723.18.b1.a1 $C_6:S_3$ $2^{2} \cdot 3^{2}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.723.18.c1.a1 $C_3:C_{12}$ $2^{2} \cdot 3^{2}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.723.18.d1.a1 $C_6\times S_3$ $2^{2} \cdot 3^{2}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.723.18.e1.a1 $S_3^2$ $2^{2} \cdot 3^{2}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.723.18.f1.a1 $S_3^2$ $2^{2} \cdot 3^{2}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.723.18.g1.a1 $S_3^2$ $2^{2} \cdot 3^{2}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
648.723.18.h1.a1 $S_3^2$ $2^{2} \cdot 3^{2}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $2 \cdot 3^{2}$ $-$
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