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 170 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
243.58.243.a1.a1	$C_1$	$1$		✓	✓		✓	✓	✓	✓	✓	✓	✓		✓	✓	✓	✓		$\He_3:C_3^2$	$3^{5}$		$\He_3:C_3^2$	$3^{5}$				✓	✓	✓			✓
486.217.243.a1	$C_2$	$2$	$2$	✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$(C_3\times C_{18}):C_3^2$	$2 \cdot 3^{5}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.149.243.b1	$C_3$	$3$		✓			✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.156.243.c1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.162.243.c1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.174.243.c1.a1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.177.243.b1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.180.243.b1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.182.243.a1.a1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.188.243.c1	$C_3$	$3$		✓			✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.192.243.c1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.196.243.b1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.200.243.c1.a1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.203.243.b1.a1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.208.243.c1.a1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.214.243.a1.a1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.216.243.b1	$C_3$	$3$		✓			✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.221.243.d1.a1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.225.243.b1	$C_3$	$3$		✓			✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.226.243.c1.a1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.227.243.b1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.228.243.b1.a1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.229.243.a1.a1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.251.243.c1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.258.243.d1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.282.243.a1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.297.243.a1	$C_3$	$3$		✓			✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.300.243.b1	$C_3$	$3$		✓			✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$\He_3:\He_3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.332.243.c1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.336.243.c1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.338.243.d1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.339.243.d1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.350.243.b1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.355.243.a1.a1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.367.243.d1.a1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.374.243.d1.a1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.379.243.d1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.380.243.c1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_3^3.C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.411.243.a1.a1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_9^2:C_3^2$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.412.243.a1.a1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_9^2.C_3^2$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.413.243.a1.a1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_9^2:C_3^2$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.414.243.a1.a1	$C_3$	$3$		✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$C_9^2.C_3^2$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
729.486.243.a1	$C_3$	$3$		✓			✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$\He_3:C_3^3$	$3^{6}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
972.401.243.a1	$C_4$	$2^{2}$	$2$	✓	✓		✓	✓	✓	✓	✓	✓			✓	✓	✓	✓		$(C_3\times C_{36}):C_3^2$	$2^{2} \cdot 3^{5}$		$\He_3:C_3^2$	$3^{5}$				✓	✓	✓			✓
972.534.243.a1	$C_2^2$	$2^{2}$	$2$	✓	✓				✓	✓	✓	✓			✓		✓	✓		$C_6^2.C_3^3$	$2^{2} \cdot 3^{5}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
972.562.243.a1	$C_2^2$	$2^{2}$	$2$	✓	✓				✓	✓	✓	✓			✓		✓	✓		$C_6^2.C_3^3$	$2^{2} \cdot 3^{5}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
972.577.243.a1	$C_2^2$	$2^{2}$	$2$	✓	✓				✓	✓	✓	✓			✓		✓	✓		$C_6^2.C_3^3$	$2^{2} \cdot 3^{5}$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
972.718.243.a1	$C_2^2$	$2^{2}$	$2$	✓	✓		✓		✓	✓	✓	✓			✓		✓	✓		$\He_3:C_6^2$	$2^{2} \cdot 3^{5}$		$\He_3:C_3^2$	$3^{5}$				✓	✓	✓			✓
1215.58.243.a1	$C_5$	$5$	$5$	✓	✓		✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓		$(C_3\times C_{45}):C_3^2$	$3^{5} \cdot 5$		$\He_3:C_3^2$	$3^{5}$	✓			✓	✓	✓			✓
1458.149.243.b1	$C_6$	$2 \cdot 3$		✓			✓	✓	✓	✓	✓	✓			✓	✓	✓	✓		$C_2\times C_3^3.C_3^3$	$2 \cdot 3^{6}$		$\He_3:C_3^2$	$3^{5}$				✓	✓	✓			✓

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