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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 427 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
216.165.216.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
432.619.216.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_3\times C_6).S_4$ $2^{4} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$ ✓
432.620.216.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3^2:\GL(2,3)$ $2^{4} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$ ✓
432.621.216.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_3^2\times A_4):C_4$ $2^{4} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$ ✓
432.762.216.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$ ✓
648.574.216.b1 $C_3$ $3$ ✓ ✓ ✓ $(C_3\times C_9):S_4$ $2^{3} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$ ✓
648.575.216.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $\He_3:S_4$ $2^{3} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$ ✓
648.576.216.b1 $C_3$ $3$ ✓ ✓ ✓ $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$ ✓
648.577.216.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3^3:S_4$ $2^{3} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$ ✓
648.737.216.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3^3:S_4$ $2^{3} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$ ✓
648.738.216.a1 $C_3$ $3$ ✓ ✓ $C_3^3:S_4$ $2^{3} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$ ✓
864.3013.216.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_{12}^2:S_3$ $2^{5} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$ ✓
864.3014.216.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $(C_3^2\times A_4):C_8$ $2^{5} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
864.3015.216.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_6^2.S_4$ $2^{5} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
864.3016.216.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_3^2:\Unitary(2,3)$ $2^{5} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
864.4430.216.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $(C_3\times C_{12}).S_4$ $2^{5} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
864.4431.216.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_4\times C_3^2:S_4$ $2^{5} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
864.4432.216.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_6^2:D_{12}$ $2^{5} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
864.4433.216.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_6^2.S_4$ $2^{5} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
864.4434.216.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_6^2.S_4$ $2^{5} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
864.4435.216.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_6^2.S_4$ $2^{5} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
864.4436.216.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $(C_3\times C_{12}).S_4$ $2^{5} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
864.4437.216.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $(C_3\times C_{12}).S_4$ $2^{5} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
864.4438.216.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $(C_3\times \SL(2,3)):D_6$ $2^{5} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
864.4439.216.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_6^2.S_4$ $2^{5} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
864.4440.216.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_6^2:S_4$ $2^{5} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
864.4679.216.a1 $C_2^2$ $2^{2}$ ✓ ✓ $A_4^2:S_3$ $2^{5} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$ ✓
864.4707.216.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_6^2:S_4$ $2^{5} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
864.4710.216.a1 $C_2^2$ $2^{2}$ ✓ ✓ $C_6^2:S_4$ $2^{5} \cdot 3^{3}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$ ✓
1080.546.216.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ ✓ $C_5\times C_3^2:S_4$ $2^{3} \cdot 3^{3} \cdot 5$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$ ✓
1080.547.216.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_6^2:D_{15}$ $2^{3} \cdot 3^{3} \cdot 5$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$ ✓
1296.2132.216.b1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_3\times C_{18}).S_4$ $2^{4} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
1296.2133.216.b1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_3\times C_9):\GL(2,3)$ $2^{4} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
1296.2134.216.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $(C_2\times \He_3).S_4$ $2^{4} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
1296.2135.216.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $\He_3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
1296.2136.216.b1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_3\times C_{18}).S_4$ $2^{4} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
1296.2137.216.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $(A_4\times \He_3):C_4$ $2^{4} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
1296.2138.216.b1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_3^2\times C_6).S_4$ $2^{4} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
1296.2139.216.b1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_3^3.\GL(2,3)$ $2^{4} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
1296.2140.216.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $(C_3^2\times C_6).S_4$ $2^{4} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
1296.2141.216.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_3^3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
1296.2142.216.b1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_6^3.S_3$ $2^{4} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
1296.2143.216.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_6^3.S_3$ $2^{4} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
1296.3004.216.b1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_3\times C_{18}):S_4$ $2^{4} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
1296.3005.216.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_2\times \He_3:S_4$ $2^{4} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
1296.3006.216.b1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_6^2:D_{18}$ $2^{4} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
1296.3007.216.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_6^3:S_3$ $2^{4} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
1296.3279.216.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $(C_3^2\times C_6).S_4$ $2^{4} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
1296.3280.216.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_3^3:\GL(2,3)$ $2^{4} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
1296.3281.216.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_6^3.S_3$ $2^{4} \cdot 3^{4}$ $C_3^2:S_4$ $2^{3} \cdot 3^{3}$
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