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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 438 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
2592.cm.1.a1 $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ ✓ ✓ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $C_1$ $1$ ✓
2592.cm.2.a1 $S_3^2:S_3^2$ $2^{4} \cdot 3^{4}$ ✓ ✓ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $C_2$ $2$ ✓
2592.cm.2.b1 $(C_3^2\times S_3^2):C_4$ $2^{4} \cdot 3^{4}$ ✓ ✓ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $C_2$ $2$ ✓
2592.cm.2.c1 $S_3^4$ $2^{4} \cdot 3^{4}$ ✓ ✓ ✓ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $C_2$ $2$ ✓
2592.cm.2.d1 $C_3^4:(C_2\times D_4)$ $2^{4} \cdot 3^{4}$ ✓ ✓ ✓ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $C_2$ $2$ ✓
2592.cm.2.e1 $C_3^2\wr C_2.D_4$ $2^{4} \cdot 3^{4}$ ✓ ✓ ✓ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $C_2$ $2$ ✓
2592.cm.4.a1 $C_3:S_3^3$ $2^{3} \cdot 3^{4}$ ✓ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
2592.cm.4.b1 $C_3:S_3^3$ $2^{3} \cdot 3^{4}$ ✓ ✓ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
2592.cm.4.c1 $C_3:S_3^3$ $2^{3} \cdot 3^{4}$ ✓ ✓ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
2592.cm.4.d1 $C_3^3:(C_4\times S_3)$ $2^{3} \cdot 3^{4}$ ✓ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
2592.cm.4.e1 $C_3^4:(C_2\times C_4)$ $2^{3} \cdot 3^{4}$ ✓ ✓ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
2592.cm.4.f1 $C_3:S_3^3$ $2^{3} \cdot 3^{4}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2}$ $-$
2592.cm.4.g1 $C_3\wr D_4$ $2^{3} \cdot 3^{4}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2}$ $-$
2592.cm.4.h1 $C_3:S_3^3$ $2^{3} \cdot 3^{4}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2}$ $-$
2592.cm.4.i1 $C_3\times S_3^3$ $2^{3} \cdot 3^{4}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2}$ $-$
2592.cm.4.j1 $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2}$ $-$
2592.cm.4.k1 $C_3^4:D_4$ $2^{3} \cdot 3^{4}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2}$ $-$
2592.cm.6.a1 $S_3^3:C_2$ $2^{4} \cdot 3^{3}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2 \cdot 3$ $-$
2592.cm.6.b1 $C_2\times S_3^3$ $2^{4} \cdot 3^{3}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2 \cdot 3$ $-$
2592.cm.8.a1 $C_3^2\times S_3^2$ $2^{2} \cdot 3^{4}$ ✓ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $D_4$ $2^{3}$
2592.cm.8.b1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ ✓ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $D_4$ $2^{3}$
2592.cm.8.c1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ ✓ ✓ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
2592.cm.8.d1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ ✓ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $D_4$ $2^{3}$
2592.cm.8.e1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{3}$ $-$
2592.cm.8.f1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{3}$ $-$
2592.cm.8.g1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{3}$ $-$
2592.cm.8.h1 $C_3^2\times S_3^2$ $2^{2} \cdot 3^{4}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{3}$ $-$
2592.cm.8.i1 $C_3\wr C_2^2$ $2^{2} \cdot 3^{4}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{3}$ $-$
2592.cm.8.j1 $C_3\wr C_2^2$ $2^{2} \cdot 3^{4}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{3}$ $-$
2592.cm.8.k1 $C_3\wr C_4$ $2^{2} \cdot 3^{4}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{3}$ $-$
2592.cm.8.l1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{3}$ $-$
2592.cm.8.m1 $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{3}$ $-$
2592.cm.8.n1 $C_3^4:C_4$ $2^{2} \cdot 3^{4}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{3}$ $-$
2592.cm.9.a1 $D_6\wr C_2$ $2^{5} \cdot 3^{2}$ ✓ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $3^{2}$ $-$
2592.cm.12.a1 $C_6:S_3^2$ $2^{3} \cdot 3^{3}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
2592.cm.12.b1 $S_3^3$ $2^{3} \cdot 3^{3}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
2592.cm.12.c1 $S_3^3$ $2^{3} \cdot 3^{3}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
2592.cm.12.d1 $C_6:S_3^2$ $2^{3} \cdot 3^{3}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
2592.cm.12.e1 $C_6:S_3^2$ $2^{3} \cdot 3^{3}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
2592.cm.12.f1 $S_3^2:C_6$ $2^{3} \cdot 3^{3}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
2592.cm.12.g1 $S_3^2:S_3$ $2^{3} \cdot 3^{3}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
2592.cm.12.h1 $S_3^3$ $2^{3} \cdot 3^{3}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
2592.cm.12.i1 $S_3^3$ $2^{3} \cdot 3^{3}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
2592.cm.12.j1 $S_3^3$ $2^{3} \cdot 3^{3}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
2592.cm.12.k1 $S_3^3$ $2^{3} \cdot 3^{3}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
2592.cm.12.l1 $C_6\times S_3^2$ $2^{3} \cdot 3^{3}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
2592.cm.12.m1 $C_6\times S_3^2$ $2^{3} \cdot 3^{3}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
2592.cm.12.n1 $S_3^3$ $2^{3} \cdot 3^{3}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
2592.cm.12.o1 $S_3^2:S_3$ $2^{3} \cdot 3^{3}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
2592.cm.12.p1 $C_3^2:D_{12}$ $2^{3} \cdot 3^{3}$ $S_3^2\wr C_2$ $2^{5} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
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