Refine search

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
Sort order Select

Results (1-50 of 253 matches)

Next   displayed columns for results
Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
243.61.243.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_3^3\times C_9$ $3^{5}$ $C_3^3\times C_9$ $3^{5}$ ✓
486.250.243.a1 $C_2$ $2$ $2$ ✓ ✓ ✓ ✓ $C_3^3\times C_{18}$ $2 \cdot 3^{5}$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
729.415.243.b1 $C_3$ $3$ ✓ ✓ ✓ $C_3^2\times C_9^2$ $3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
729.416.243.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3^4:C_9$ $3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
729.417.243.b1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3^2.C_3^4$ $3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
729.418.243.b1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_9^2:C_3^2$ $3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
729.419.243.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3^2.C_3^4$ $3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
729.420.243.c1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_9^2:C_3^2$ $3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
729.421.243.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_9^2.C_3^2$ $3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
729.422.243.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3^2.C_3^4$ $3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
729.423.243.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_9^2:C_3^2$ $3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
729.424.243.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_9^2.C_3^2$ $3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
729.475.243.b1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3^3\times C_{27}$ $3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
729.476.243.b1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_{27}:C_3^3$ $3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
729.477.243.b1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_{27}.C_3^3$ $3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
729.478.243.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_{27}.C_3^3$ $3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
729.497.243.a1 $C_3$ $3$ ✓ ✓ ✓ $C_3^4\times C_9$ $3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
972.751.243.a1 $C_4$ $2^{2}$ $2$ ✓ ✓ ✓ ✓ $C_3^3\times C_{36}$ $2^{2} \cdot 3^{5}$ $C_3^3\times C_9$ $3^{5}$ ✓
972.820.243.a1 $C_2^2$ $2^{2}$ $2$ ✓ ✓ ✓ $C_6^2.C_3^3$ $2^{2} \cdot 3^{5}$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
972.832.243.a1 $C_2^2$ $2^{2}$ $2$ ✓ ✓ ✓ $C_3^4.A_4$ $2^{2} \cdot 3^{5}$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
972.865.243.a1 $C_2^2$ $2^{2}$ $2$ ✓ ✓ ✓ ✓ $C_3^2\times C_6\times C_{18}$ $2^{2} \cdot 3^{5}$ $C_3^3\times C_9$ $3^{5}$ ✓
1215.61.243.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ ✓ $C_3^3\times C_{45}$ $3^{5} \cdot 5$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
1458.415.243.b1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_3^2\times C_9\times C_{18}$ $2 \cdot 3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓
1458.416.243.c1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_3^4:C_{18}$ $2 \cdot 3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓
1458.417.243.b1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_3^2\times C_9:C_{18}$ $2 \cdot 3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓
1458.418.243.b1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_3\times C_9^2:C_6$ $2 \cdot 3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓
1458.419.243.c1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_3\times C_{18}\times \He_3$ $2 \cdot 3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓
1458.420.243.c1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_9:C_3^2\times C_{18}$ $2 \cdot 3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓
1458.421.243.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_9.C_3^2\times C_{18}$ $2 \cdot 3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓
1458.422.243.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_3^3:(C_3\times C_{18})$ $2 \cdot 3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓
1458.423.243.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_2\times C_9^2:C_3^2$ $2 \cdot 3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓
1458.424.243.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_2\times C_9^2.C_3^2$ $2 \cdot 3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓
1458.475.243.b1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_3^3\times C_{54}$ $2 \cdot 3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓
1458.476.243.b1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_{54}:C_3^3$ $2 \cdot 3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓
1458.477.243.b1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_{18}.C_3^4$ $2 \cdot 3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓
1458.478.243.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_{18}.C_3^4$ $2 \cdot 3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓
1458.497.243.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_3^4\times C_{18}$ $2 \cdot 3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓
1458.1743.243.a1 $S_3$ $2 \cdot 3$ ✓ ✓ $C_3^4:C_{18}$ $2 \cdot 3^{6}$ $C_3^3\times C_9$ $3^{5}$ ✓
1701.61.243.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ ✓ $C_3^3\times C_{63}$ $3^{5} \cdot 7$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
1701.292.243.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{63}:C_3^3$ $3^{5} \cdot 7$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
1701.293.243.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{21}.C_3^4$ $3^{5} \cdot 7$ $C_3^3\times C_9$ $3^{5}$ ✓ ✓
1944.2283.243.a1 $C_8$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ $C_3^3\times C_{72}$ $2^{3} \cdot 3^{5}$ $C_3^3\times C_9$ $3^{5}$ ✓
1944.3251.243.a1 $Q_8$ $2^{3}$ $2$ ✓ ✓ $C_9\times C_3^2\times \SL(2,3)$ $2^{3} \cdot 3^{5}$ $C_3^3\times C_9$ $3^{5}$ ✓
1944.3263.243.a1 $Q_8$ $2^{3}$ $2$ ✓ ✓ $C_3^4.\SL(2,3)$ $2^{3} \cdot 3^{5}$ $C_3^3\times C_9$ $3^{5}$ ✓
1944.3416.243.a1 $C_2\times C_4$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ $C_3^2\times C_6\times C_{36}$ $2^{3} \cdot 3^{5}$ $C_3^3\times C_9$ $3^{5}$ ✓
1944.3422.243.a1 $D_4$ $2^{3}$ $2$ ✓ ✓ $D_4\times C_9\times C_3^3$ $2^{3} \cdot 3^{5}$ $C_3^3\times C_9$ $3^{5}$ ✓
1944.3428.243.a1 $Q_8$ $2^{3}$ $2$ ✓ ✓ $Q_8\times C_9\times C_3^3$ $2^{3} \cdot 3^{5}$ $C_3^3\times C_9$ $3^{5}$ ✓
1944.3731.243.a1 $C_2^3$ $2^{3}$ $2$ ✓ ✓ ✓ $C_6^3.C_3^2$ $2^{3} \cdot 3^{5}$ $C_3^3\times C_9$ $3^{5}$ ✓
1944.3743.243.a1 $C_2^3$ $2^{3}$ $2$ ✓ ✓ ✓ $C_6^3:C_9$ $2^{3} \cdot 3^{5}$ $C_3^3\times C_9$ $3^{5}$ ✓
1944.3776.243.a1 $C_2^3$ $2^{3}$ $2$ ✓ ✓ ✓ ✓ $C_3\times C_6^2\times C_{18}$ $2^{3} \cdot 3^{5}$ $C_3^3\times C_9$ $3^{5}$ ✓
Next   displayed columns for results