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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 56 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
864.2220.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.(S_3\times S_4)$ $2^{5} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
864.2221.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.(S_3\times S_4)$ $2^{5} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
864.2222.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.(S_3\times S_4)$ $2^{5} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
864.2223.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.(S_3\times S_4)$ $2^{5} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
864.2224.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.(S_3\times S_4)$ $2^{5} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
864.2225.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_3\times \SL(2,3)):D_6$ $2^{5} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
864.2226.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.(S_3\times S_4)$ $2^{5} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
864.2227.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3^2:(C_2\times \GL(2,3))$ $2^{5} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
864.2235.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.(S_3\times S_4)$ $2^{5} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
864.2236.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3^2:(C_4\times S_4)$ $2^{5} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
864.2237.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3^2:(C_4\times S_4)$ $2^{5} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
864.2238.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3^2:\GL(2,\mathbb{Z}/4)$ $2^{5} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
864.2239.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3^2:\GL(2,\mathbb{Z}/4)$ $2^{5} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
864.2240.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6^2:D_{12}$ $2^{5} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
864.2241.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6.(S_3\times S_4)$ $2^{5} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
864.4000.432.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2\times C_6^2:D_6$ $2^{5} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
1296.1783.432.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
1296.1784.432.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
1296.1785.432.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
1296.1786.432.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
1296.1787.432.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
1296.1788.432.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
1296.1789.432.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_6^2:D_{18}$ $2^{4} \cdot 3^{4}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
1296.1790.432.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
1296.2923.432.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
1296.2928.432.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
1296.2933.432.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
1296.2940.432.b1.a1 $C_3$ $3$ ✓ ✓ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
1296.2940.432.b1.b1 $C_3$ $3$ ✓ ✓ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
1296.2940.432.b1.c1 $C_3$ $3$ ✓ ✓ $C_6^2:S_3^2$ $2^{4} \cdot 3^{4}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
1728.12316.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_{12}^2:D_6$ $2^{6} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
1728.12317.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_{12}^2:D_6$ $2^{6} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
1728.12469.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_2^2\times C_6^2):D_6$ $2^{6} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
1728.46099.432.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ $C_3.S_4^2$ $2^{6} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
1728.46099.432.a1.b1 $C_2^2$ $2^{2}$ ✓ ✓ $C_3.S_4^2$ $2^{6} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
1728.46119.432.a1 $C_2^2$ $2^{2}$ ✓ ✓ $C_6^2:(C_2\times S_4)$ $2^{6} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
6912.gf.432.a1 $C_2^4$ $2^{4}$ ✓ ✓ ✓ $(C_2^5\times C_6).S_3^2$ $2^{8} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
11664.bf.432.a1 $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^5:(C_2\times S_4)$ $2^{4} \cdot 3^{6}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
11664.bg.432.a1 $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^5:(C_2\times S_4)$ $2^{4} \cdot 3^{6}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
11664.bh.432.a1 $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^5:(C_2\times S_4)$ $2^{4} \cdot 3^{6}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
11664.bi.432.a1 $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^5:(C_2\times S_4)$ $2^{4} \cdot 3^{6}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
27648.m.432.A $C_2^6$ $2^{6}$ ✓ ✓ ✓ $C_2^4:A_4^2.D_6$ $2^{10} \cdot 3^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
54000.a.432.a1.a1 $C_5^3$ $5^{3}$ $5$ ✓ ✓ ✓ $C_{15}:D_5^2.S_3^2$ $2^{4} \cdot 3^{3} \cdot 5^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
54000.d.432.a1.a1 $C_5^3$ $5^{3}$ $5$ ✓ ✓ ✓ $C_{15}:D_5^2.S_3^2$ $2^{4} \cdot 3^{3} \cdot 5^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
54000.n.432.a1.a1 $C_5^3$ $5^{3}$ $5$ ✓ ✓ ✓ $C_{15}:D_5^2.S_3^2$ $2^{4} \cdot 3^{3} \cdot 5^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
54000.q.432.a1.a1 $C_5^3$ $5^{3}$ $5$ ✓ ✓ ✓ $C_3^2:D_5\wr S_3$ $2^{4} \cdot 3^{3} \cdot 5^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
6750000.m.432.a1 $C_5^6$ $5^{6}$ $5$ ✓ ✓ ✓ $C_5^6:(C_6^2:D_6)$ $2^{4} \cdot 3^{3} \cdot 5^{6}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
6750000.n.432.a1 $C_5^6$ $5^{6}$ $5$ ✓ ✓ ✓ $C_5^6:(C_6^2:D_6)$ $2^{4} \cdot 3^{3} \cdot 5^{6}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
93312000.a.432._.A $A_5^3$ $2^{6} \cdot 3^{3} \cdot 5^{3}$ ✓ ✓ $A_5^3.C_6^2:D_6$ $2^{10} \cdot 3^{6} \cdot 5^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
93312000.b.432._.A $A_5^3$ $2^{6} \cdot 3^{3} \cdot 5^{3}$ ✓ ✓ $A_5^3.C_6^2:D_6$ $2^{10} \cdot 3^{6} \cdot 5^{3}$ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓
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