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Note: Search results may be incomplete due to uncomputed quantities: Subgroup label (103813812 objects)

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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 55 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
432.58.2.b1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ ✓ $C_{12}.D_{18}$ $2^{4} \cdot 3^{3}$ $C_2$ $2$ ✓
432.59.2.b1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ ✓ $C_{12}.D_{18}$ $2^{4} \cdot 3^{3}$ $C_2$ $2$ ✓
432.60.2.b1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ ✓ $C_{12}.D_{18}$ $2^{4} \cdot 3^{3}$ $C_2$ $2$ ✓
432.61.2.b1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ ✓ $C_{12}.D_{18}$ $2^{4} \cdot 3^{3}$ $C_2$ $2$ ✓
432.62.2.c1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ ✓ $C_6.D_{36}$ $2^{4} \cdot 3^{3}$ $C_2$ $2$ ✓
432.63.2.c1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ ✓ $C_6.D_{36}$ $2^{4} \cdot 3^{3}$ $C_2$ $2$ ✓
432.64.2.c1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ ✓ $C_3:D_{72}$ $2^{4} \cdot 3^{3}$ $C_2$ $2$ ✓
432.65.2.c1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ ✓ $C_6.D_{36}$ $2^{4} \cdot 3^{3}$ $C_2$ $2$ ✓
432.109.2.c1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ ✓ $S_3\times C_{72}$ $2^{4} \cdot 3^{3}$ $C_2$ $2$ ✓
432.110.2.c1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ ✓ $C_{24}:C_{18}$ $2^{4} \cdot 3^{3}$ $C_2$ $2$ ✓
432.126.2.b1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_6:C_{72}$ $2^{4} \cdot 3^{3}$ $C_2$ $2$ ✓
432.126.2.b1.b1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_6:C_{72}$ $2^{4} \cdot 3^{3}$ $C_2$ $2$ ✓
432.127.2.b1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_{12}.C_{36}$ $2^{4} \cdot 3^{3}$ $C_2$ $2$ ✓
432.127.2.b1.b1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_{12}.C_{36}$ $2^{4} \cdot 3^{3}$ $C_2$ $2$ ✓
432.150.2.c1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ ✓ $D_{12}:C_{18}$ $2^{4} \cdot 3^{3}$ $C_2$ $2$ ✓
432.151.2.c1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ ✓ $C_{36}.D_6$ $2^{4} \cdot 3^{3}$ $C_2$ $2$ ✓
432.158.2.c1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ ✓ $C_{36}.D_6$ $2^{4} \cdot 3^{3}$ $C_2$ $2$ ✓
432.159.2.c1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ ✓ $C_{36}.D_6$ $2^{4} \cdot 3^{3}$ $C_2$ $2$ ✓
648.12.3.b1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $C_9:C_{72}$ $2^{3} \cdot 3^{4}$ $3$ $-$
648.13.3.b1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $C_3^2:C_{72}$ $2^{3} \cdot 3^{4}$ $3$ $-$
648.15.3.b1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $C_9:C_{72}$ $2^{3} \cdot 3^{4}$ $3$ $-$
648.17.3.a1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ ✓ $C_3:C_{216}$ $2^{3} \cdot 3^{4}$ $C_3$ $3$ ✓
648.21.3.b1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $\He_3.C_{24}$ $2^{3} \cdot 3^{4}$ $3$ $-$
648.23.3.b1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $\He_3.C_{24}$ $2^{3} \cdot 3^{4}$ $3$ $-$
648.233.3.b1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_3^2:C_{72}$ $2^{3} \cdot 3^{4}$ $C_3$ $3$ ✓
648.233.3.b1.b1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_3^2:C_{72}$ $2^{3} \cdot 3^{4}$ $C_3$ $3$ ✓
648.233.3.b1.c1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_3^2:C_{72}$ $2^{3} \cdot 3^{4}$ $C_3$ $3$ ✓
648.237.3.b1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_3^3.C_{24}$ $2^{3} \cdot 3^{4}$ $C_3$ $3$ ✓
648.237.3.b1.b1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_3^3.C_{24}$ $2^{3} \cdot 3^{4}$ $C_3$ $3$ ✓
648.237.3.b1.c1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_3^3.C_{24}$ $2^{3} \cdot 3^{4}$ $C_3$ $3$ ✓
648.239.3.b1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $C_3^2:C_{72}$ $2^{3} \cdot 3^{4}$ $3$ $-$
648.239.3.b1.b1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $C_3^2:C_{72}$ $2^{3} \cdot 3^{4}$ $3$ $-$
648.239.3.b1.c1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $C_3^2:C_{72}$ $2^{3} \cdot 3^{4}$ $3$ $-$
648.239.3.b1.d1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $C_3^2:C_{72}$ $2^{3} \cdot 3^{4}$ $3$ $-$
648.244.3.b1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $\He_3.C_{24}$ $2^{3} \cdot 3^{4}$ $3$ $-$
648.244.3.b1.b1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $\He_3.C_{24}$ $2^{3} \cdot 3^{4}$ $3$ $-$
648.244.3.b1.c1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $\He_3.C_{24}$ $2^{3} \cdot 3^{4}$ $3$ $-$
648.244.3.b1.d1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $\He_3.C_{24}$ $2^{3} \cdot 3^{4}$ $3$ $-$
864.681.4.b1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $A_4:C_{72}$ $2^{5} \cdot 3^{3}$ $2^{2}$ $-$
864.683.4.b1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $\SL(2,3):C_{36}$ $2^{5} \cdot 3^{3}$ $2^{2}$ $-$
864.729.4.b1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $C_6^2.C_{24}$ $2^{5} \cdot 3^{3}$ $2^{2}$ $-$
864.733.4.b1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $C_{12}.(S_3\times A_4)$ $2^{5} \cdot 3^{3}$ $2^{2}$ $-$
1080.37.5.a1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ ✓ $C_3:C_{360}$ $2^{3} \cdot 3^{3} \cdot 5$ $C_5$ $5$ ✓
1080.41.5.a1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $C_{15}:C_{72}$ $2^{3} \cdot 3^{3} \cdot 5$ $5$ $-$
1080.68.5.a1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $C_{15}:C_{72}$ $2^{3} \cdot 3^{3} \cdot 5$ $5$ $-$
1512.51.7.a1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $C_{21}:C_{72}$ $2^{3} \cdot 3^{3} \cdot 7$ $7$ $-$
1512.56.7.a1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $C_{21}:C_{72}$ $2^{3} \cdot 3^{3} \cdot 7$ $7$ $-$
1512.68.7.a1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ ✓ ✓ $C_3:C_{504}$ $2^{3} \cdot 3^{3} \cdot 7$ $C_7$ $7$ ✓
1512.72.7.a1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $C_{21}:C_{72}$ $2^{3} \cdot 3^{3} \cdot 7$ $7$ $-$
1944.2297.9.b1.a1 $C_3:C_{72}$ $2^{3} \cdot 3^{3}$ ✓ $\He_3:C_{72}$ $2^{3} \cdot 3^{5}$ $3^{2}$ $-$
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