LMFDB - Subgroup search results

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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 278 matches)

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Label	Subgroup									Ambient			Quotient
Label	Name	Order	Sylow	norm	char	max	cent	cyc		ab	nilp		sup solv	solv	perf	simp	Agp	Zgp	metab	metacyc	Name	Order	Name	Size	max	cyc	ab	nilp	sup solv	solv	simp	Agp	metab
1944.2462.1.a1.a1	$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$		✓	✓							✓								$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$		$C_1$	$1$		✓	✓	✓	✓	✓		✓	✓
1944.2462.2.a1.a1	$C_6^2.C_3^3$	$2^{2} \cdot 3^{5}$		✓	✓	✓						✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$		$C_2$	$2$		✓	✓	✓	✓	✓	✓	✓	✓
1944.2462.3.a1.a1	$\He_3:S_4$	$2^{3} \cdot 3^{4}$		✓	✓	✓						✓								$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$		$C_3$	$3$		✓	✓	✓	✓	✓	✓	✓	✓
1944.2462.3.b1.a1	$C_3\times C_6^2:C_6$	$2^{3} \cdot 3^{4}$				✓					✓	✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.3.c1.a1	$C_3^3:S_4$	$2^{3} \cdot 3^{4}$				✓						✓								$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.3.d1.a1	$C_3^3.S_4$	$2^{3} \cdot 3^{4}$				✓						✓								$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.3.d1.b1	$C_3^3.S_4$	$2^{3} \cdot 3^{4}$				✓						✓								$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.4.a1.a1	$C_3\wr C_3:C_6$	$2 \cdot 3^{5}$				✓					✓	✓								$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$2^{2}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.6.a1.a1	$C_3^2:C_6^2$	$2^{2} \cdot 3^{4}$		✓	✓					✓	✓	✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$		$S_3$	$2 \cdot 3$					✓	✓		✓	✓
1944.2462.6.b1.a1	$C_3^3:A_4$	$2^{2} \cdot 3^{4}$		✓	✓							✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$		$S_3$	$2 \cdot 3$					✓	✓		✓	✓
1944.2462.6.c1.a1	$C_3^3.A_4$	$2^{2} \cdot 3^{4}$		✓								✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$		$S_3$	$2 \cdot 3$					✓	✓		✓	✓
1944.2462.6.c1.b1	$C_3^3.A_4$	$2^{2} \cdot 3^{4}$		✓								✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$		$S_3$	$2 \cdot 3$					✓	✓		✓	✓
1944.2462.6.d1.a1	$\He_3:A_4$	$2^{2} \cdot 3^{4}$		✓	✓							✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$		$C_6$	$2 \cdot 3$		✓	✓	✓	✓	✓		✓	✓
1944.2462.6.e1.a1	$C_3^2:C_6^2$	$2^{2} \cdot 3^{4}$									✓	✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$2 \cdot 3$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.6.f1.a1	$C_3^3:C_{12}$	$2^{2} \cdot 3^{4}$									✓	✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$2 \cdot 3$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.6.g1.a1	$\He_3:A_4$	$2^{2} \cdot 3^{4}$										✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$2 \cdot 3$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.6.h1.a1	$\He_3:A_4$	$2^{2} \cdot 3^{4}$										✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$2 \cdot 3$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.6.i1.a1	$\He_3:A_4$	$2^{2} \cdot 3^{4}$										✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$2 \cdot 3$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.6.i1.b1	$\He_3:A_4$	$2^{2} \cdot 3^{4}$										✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$2 \cdot 3$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.8.a1.a1	$C_3^3:C_3^2$	$3^{5}$	$3$							✓	✓	✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$2^{3}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.9.a1.a1	$C_6^2:C_6$	$2^{3} \cdot 3^{3}$									✓	✓					✓	?		$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3^{2}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.9.b1.a1	$C_6^2:C_6$	$2^{3} \cdot 3^{3}$									✓	✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3^{2}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.9.c1.a1	$C_3^2:S_4$	$2^{3} \cdot 3^{3}$										✓								$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3^{2}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.9.d1.a1	$C_3^2.S_4$	$2^{3} \cdot 3^{3}$										✓								$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3^{2}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.9.d1.b1	$C_3^2.S_4$	$2^{3} \cdot 3^{3}$										✓								$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3^{2}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.9.e1.a1	$C_6^2:C_6$	$2^{3} \cdot 3^{3}$									✓	✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3^{2}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.9.f1.a1	$C_3^2:S_4$	$2^{3} \cdot 3^{3}$										✓								$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3^{2}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.9.g1.a1	$C_3^2.S_4$	$2^{3} \cdot 3^{3}$										✓								$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3^{2}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.9.g1.b1	$C_3^2.S_4$	$2^{3} \cdot 3^{3}$										✓								$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3^{2}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.9.h1.a1	$C_6^2:C_6$	$2^{3} \cdot 3^{3}$									✓	✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3^{2}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.9.h1.b1	$C_6^2:C_6$	$2^{3} \cdot 3^{3}$									✓	✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3^{2}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.9.i1.a1	$C_3^2:S_4$	$2^{3} \cdot 3^{3}$										✓								$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3^{2}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.9.i1.b1	$C_3^2:S_4$	$2^{3} \cdot 3^{3}$										✓								$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3^{2}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.9.j1.a1	$C_3^2.S_4$	$2^{3} \cdot 3^{3}$										✓								$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3^{2}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.9.j1.b1	$C_3^2.S_4$	$2^{3} \cdot 3^{3}$										✓								$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3^{2}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.9.j2.a1	$C_3^2.S_4$	$2^{3} \cdot 3^{3}$										✓								$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3^{2}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.9.j2.b1	$C_3^2.S_4$	$2^{3} \cdot 3^{3}$										✓								$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$3^{2}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.12.a1.a1	$C_6\times \He_3$	$2 \cdot 3^{4}$								✓	✓	✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$2^{2} \cdot 3$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.12.b1.a1	$C_3^3:C_6$	$2 \cdot 3^{4}$									✓	✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$2^{2} \cdot 3$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.12.c1.a1	$C_3^3:C_6$	$2 \cdot 3^{4}$									✓	✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$2^{2} \cdot 3$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.12.d1.a1	$D_9:C_3^2$	$2 \cdot 3^{4}$									✓	✓					✓	?		$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$2^{2} \cdot 3$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.12.d1.b1	$D_9:C_3^2$	$2 \cdot 3^{4}$									✓	✓					✓	?		$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$2^{2} \cdot 3$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.12.e1.a1	$C_3^3:S_3$	$2 \cdot 3^{4}$									✓	✓								$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$2^{2} \cdot 3$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.18.a1.a1	$C_3\times C_6^2$	$2^{2} \cdot 3^{3}$		✓	✓				✓	✓	✓	✓			✓		✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$		$C_3:S_3$	$2 \cdot 3^{2}$					✓	✓		✓	✓
1944.2462.18.b1.a1	$C_2^2\times \He_3$	$2^{2} \cdot 3^{3}$		✓	✓					✓	✓	✓					✓	?		$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$		$C_3\times S_3$	$2 \cdot 3^{2}$					✓	✓		✓	✓
1944.2462.18.c1.a1	$C_3^2\times A_4$	$2^{2} \cdot 3^{3}$		✓	✓							✓			✓		✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$		$C_3\times S_3$	$2 \cdot 3^{2}$					✓	✓		✓	✓
1944.2462.18.d1.a1	$C_3^2.A_4$	$2^{2} \cdot 3^{3}$		✓								✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$		$C_3\times S_3$	$2 \cdot 3^{2}$					✓	✓		✓	✓
1944.2462.18.d1.b1	$C_3^2.A_4$	$2^{2} \cdot 3^{3}$		✓								✓					✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$		$C_3\times S_3$	$2 \cdot 3^{2}$					✓	✓		✓	✓
1944.2462.18.e1.a1	$C_3^2\times D_6$	$2^{2} \cdot 3^{3}$									✓	✓			✓		✓	?		$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$2 \cdot 3^{2}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$
1944.2462.18.f1.a1	$C_3^2:D_6$	$2^{2} \cdot 3^{3}$									✓	✓			✓		✓			$(C_3\times \He_3):S_4$	$2^{3} \cdot 3^{5}$			$2 \cdot 3^{2}$		$-$	$-$	$-$	$-$	$-$	$-$	$-$	$-$

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Elliptic curves over $\Q$
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