## Results (displaying matches 1-50 of at least 5000) Next

Label Name Order Parity Solvable Subfields Low Degree Siblings
36T1 $C_{36}$ 36 -1 Yes $C_2$, $C_3$, $C_4$, $C_6$, $C_9$, $C_{12}$, $C_{18}$
36T2 $C_2\times C_{18}$ 36 1 Yes $C_2$ x 3, $C_3$, $C_2^2$, $C_6$ x 3, $C_9$, $C_6\times C_2$, $C_{18}$ x 3
36T3 $C_3\times C_{12}$ 36 -1 Yes $C_2$, $C_3$ x 4, $C_4$, $C_6$ x 4, $C_3^2$, $C_{12}$ x 4, $C_6 \times C_3$
36T4 $C_6^2$ 36 1 Yes $C_2$ x 3, $C_3$ x 4, $C_2^2$, $C_6$ x 12, $C_3^2$, $C_6\times C_2$ x 4, $C_6 \times C_3$ x 3
36T5 $C_3\times C_3:C_4$ 36 -1 Yes $C_2$, $C_3$, $S_3$, $C_4$, $C_6$, $S_3$, $S_3\times C_3$, $S_3\times C_3$, $C_{12}$, $C_3 : C_4$, $C_3\times (C_3 : C_4)$, $S_3 \times C_3$
36T6 $C_6\times S_3$ 36 1 Yes $C_2$ x 3, $C_3$, $S_3$, $C_2^2$, $C_6$ x 3, $S_3$, $D_{6}$ x 2, $S_3\times C_3$, $S_3\times C_3$, $C_6\times C_2$, $D_6$, $C_6\times S_3$, $S_3 \times C_3$, $S_3 \times C_6$ x 2
36T7 $C_3^2:C_4$ 36 -1 Yes $C_2$, $S_3$ x 4, $C_4$, $S_3$ x 4, $C_3^2:C_2$, $C_3 : C_4$ x 4, $C_3^2 : C_2$
36T8 $C_2\times C_3:S_3$ 36 1 Yes $C_2$ x 3, $S_3$ x 4, $C_2^2$, $S_3$ x 4, $D_{6}$ x 8, $C_3^2:C_2$, $D_6$ x 4, $C_3^2 : C_2$, 18T12 x 2
36T9 $C_9:C_4$ 36 -1 Yes $C_2$, $S_3$, $C_4$, $S_3$, $D_{9}$, $C_3 : C_4$, $D_9$
36T10 $D_{18}$ 36 1 Yes $C_2$ x 3, $S_3$, $C_2^2$, $S_3$, $D_{6}$ x 2, $D_{9}$, $D_6$, $D_9$, $D_{18}$ x 2
36T11 $C_2^2:C_9$ 36 1 Yes $C_3$, $A_4$, $A_4$, $C_9$, $A_4$, $C_2^2 : C_9$
36T12 $C_3\times A_4$ 36 1 Yes $C_3$ x 4, $A_4$, $A_4$, $C_3^2$, $A_4$, $C_3\times A_4$ x 3, $A_4 \times C_3$
36T13 $S_3^2$ 36 1 Yes $C_2$ x 3, $S_3$ x 2, $C_2^2$, $S_3$ x 2, $D_{6}$ x 4, $S_3^2$, $S_3^2$, $D_6$ x 2, $S_3^2$, $S_3^2$, $S_3^2$ x 2 6T9, 9T8
36T14 $C_3:S_3.C_2$ 36 -1 Yes $C_2$, $C_4$, $C_3^2:C_4$ x 2, $C_3^2:C_4$, $(C_3\times C_3):C_4$ x 2, $C_3^2 : C_4$ 6T10 x 2, 9T9
36T15 $C_9\times D_4$ 72 -1 Yes $C_2$, $C_3$, $D_{4}$, $C_6$, $C_9$, $D_4 \times C_3$, $C_{18}$
36T16 $C_2\times C_2^2:C_9$ 72 1 Yes $C_2$, $C_3$, $C_6$, $A_4$, $A_4\times C_2$, $C_9$, $A_4 \times C_2$, $C_{18}$, $C_2^2 : C_9$, 18T26
36T17 $C_3^2\times D_4$ 72 -1 Yes $C_2$, $C_3$ x 4, $D_{4}$, $C_6$ x 4, $C_3^2$, $D_4 \times C_3$ x 4, $C_6 \times C_3$
36T18 $C_6\times A_4$ 72 1 Yes $C_2$, $C_3$ x 4, $C_6$ x 4, $A_4$, $A_4\times C_2$, $C_3^2$, $A_4 \times C_2$, $C_6 \times C_3$, $A_4 \times C_3$, 18T25
36T19 $C_3\times C_3:D_4$ 72 -1 Yes $C_2$, $C_3$, $S_3$, $D_{4}$, $C_6$, $S_3$, $S_3\times C_3$, $S_3\times C_3$, $D_4 \times C_3$, $(C_6\times C_2):C_2$, 12T42 x 2, $S_3 \times C_3$
36T20 $C_3\times S_4$ 72 1 Yes $C_2$, $C_3$, $S_3$, $C_6$, $S_3$, $S_3\times C_3$, $S_4$, $S_4$, $S_3\times C_3$, $S_4$, $S_3 \times C_3$, 18T30, 18T33
36T21 $S_3\times A_4$ 72 1 Yes $C_2$, $C_3$, $S_3$, $C_6$, $S_3$, $A_4$, $S_3\times C_3$, $A_4\times C_2$, $S_3\times C_3$, $A_4 \times C_2$, $S_3 \times C_3$, 18T31, 18T32
36T22 $C_6^2:C_2$ 72 -1 Yes $C_2$, $S_3$ x 4, $D_{4}$, $S_3$ x 4, $C_3^2:C_2$, $(C_6\times C_2):C_2$ x 4, $C_3^2 : C_2$
36T23 $C_3:S_4$ 72 1 Yes $C_2$, $S_3$ x 4, $S_3$ x 4, $S_4$, $S_4$, $C_3^2:C_2$, $S_4$, $C_3^2 : C_2$, 18T37, 18T40
36T24 $C_9:D_4$ 72 -1 Yes $C_2$, $S_3$, $D_{4}$, $S_3$, $D_{9}$, $(C_6\times C_2):C_2$, $D_9$
36T25 $C_2^2:D_9$ 72 1 Yes $C_2$, $S_3$, $S_3$, $S_4$, $S_4$, $D_{9}$, $S_4$, $D_9$, 18T38, 18T39
36T26 $C_3\times C_3:D_4$ 72 -1 Yes $C_2$, $C_3$, $S_3$, $D_{4}$, $C_6$, $D_{6}$, $S_3\times C_3$, $(C_6\times C_2):C_2$, $D_4 \times C_3$, $S_3 \times C_6$
36T27 $C_{12}\times S_3$ 72 -1 Yes $C_2$, $C_3$, $S_3$, $C_4$, $C_6$, $D_{6}$, $S_3\times C_3$, $C_{12}$, $S_3 \times C_4$, $S_3 \times C_6$
36T28 $C_3\times D_{12}$ 72 -1 Yes $C_2$, $C_3$, $S_3$, $D_{4}$, $C_6$, $D_{6}$, $S_3\times C_3$, $D_{12}$, $D_4 \times C_3$, $S_3 \times C_6$
36T29 $C_2\times C_6\times S_3$ 72 1 Yes $C_2$ x 3, $C_3$, $S_3$, $C_2^2$, $C_6$ x 3, $D_{6}$ x 3, $S_3\times C_3$, $C_6\times C_2$, $S_3 \times C_2^2$, $S_3 \times C_6$ x 3
36T30 $C_2\times C_2^2:C_9$ 72 1 Yes $C_3$, $A_4$, $A_4\times C_2$, $C_9$, $A_4\times C_2$, $C_2^2 : C_9$, 18T26
36T31 $C_6\times A_4$ 72 1 Yes $C_3$ x 4, $A_4$, $A_4\times C_2$, $C_3^2$, $A_4\times C_2$, $A_4 \times C_3$, 18T25
36T32 $C_2.S_3^2$ 72 -1 Yes $C_2$, $S_3$ x 2, $C_4$, $D_{6}$ x 2, $S_3^2$, $S_3^2$, $S_3 \times C_4$ x 2, 12T39, $S_3^2$
36T33 $C_3^2:D_4$ 72 -1 Yes $C_2$, $S_3$ x 2, $D_{4}$, $D_{6}$ x 2, $S_3^2$, $S_3^2$, $D_{12}$, $(C_6\times C_2):C_2$, 12T38 x 2, $S_3^2$
36T34 $C_2\times S_3^2$ 72 1 Yes $C_2$ x 3, $S_3$ x 2, $C_2^2$, $D_{6}$ x 6, $S_3^2$, $S_3^2$, $S_3 \times C_2^2$ x 2, 12T37, $S_3^2$, 18T29 x 2
36T35 $C_2\times C_3:S_3.C_2$ 72 -1 Yes $C_2$, $C_4$, $C_3^2:C_4$ x 2, $C_3^2:C_4$, 12T41 x 2, $C_3^2 : C_4$
36T36 $C_2\times C_3:S_3.C_2$ 72 1 Yes $C_2$ x 3, $C_2^2$, $C_3^2:C_4$ x 2, $C_3^2:C_4$, 12T40 x 2, $C_3^2 : C_4$, 18T27 x 2
36T37 $S_3\times C_3:C_4$ 72 -1 Yes $C_2$, $S_3$ x 2, $C_4$, $S_3$, $D_{6}$, $S_3^2$, $C_3 : C_4$, $S_3 \times C_4$, $S_3^2$
36T38 $C_3^2:D_4$ 72 -1 Yes $C_2$, $S_3$ x 2, $D_{4}$, $S_3$, $D_{6}$, $S_3^2$, $D_{12}$, $(C_6\times C_2):C_2$, $S_3^2$
36T39 $D_6:S_3$ 72 -1 Yes $C_2$, $S_3$ x 2, $D_{4}$, $S_3$, $D_{6}$, $S_3^2$, $(C_6\times C_2):C_2$, $(C_6\times C_2):C_2$, $S_3^2$
36T40 $C_2\times S_3^2$ 72 1 Yes $C_2$ x 3, $S_3$ x 2, $C_2^2$, $S_3$, $D_{6}$ x 5, $S_3^2$, $D_6$, $S_3 \times C_2^2$, $S_3^2$, 18T29 x 2
36T41 $C_4\times C_3:S_3$ 72 -1 Yes $C_2$, $S_3$ x 4, $C_4$, $D_{6}$ x 4, $C_3^2:C_2$, $S_3 \times C_4$ x 4, 18T12
36T42 $C_6^2:C_2$ 72 -1 Yes $C_2$, $S_3$ x 4, $D_{4}$, $D_{6}$ x 4, $C_3^2:C_2$, $(C_6\times C_2):C_2$ x 4, 18T12
36T43 $C_3:D_{12}$ 72 -1 Yes $C_2$, $S_3$ x 4, $D_{4}$, $D_{6}$ x 4, $C_3^2:C_2$, $D_{12}$ x 4, 18T12
36T44 $C_2^2\times C_3:S_3$ 72 1 Yes $C_2$ x 3, $S_3$ x 4, $C_2^2$, $D_{6}$ x 12, $C_3^2:C_2$, $S_3 \times C_2^2$ x 4, 18T12 x 3
36T45 $C_4\times D_9$ 72 -1 Yes $C_2$, $S_3$, $C_4$, $D_{6}$, $D_{9}$, $S_3 \times C_4$, $D_{18}$
36T46 $C_9:D_4$ 72 -1 Yes $C_2$, $S_3$, $D_{4}$, $D_{6}$, $D_{9}$, $(C_6\times C_2):C_2$, $D_{18}$
36T47 $D_{36}$ 72 -1 Yes $C_2$, $S_3$, $D_{4}$, $D_{6}$, $D_{9}$, $D_{12}$, $D_{18}$
36T48 $C_2^2\times D_9$ 72 1 Yes $C_2$ x 3, $S_3$, $C_2^2$, $D_{6}$ x 3, $D_{9}$, $S_3 \times C_2^2$, $D_{18}$ x 3
36T49 $F_9$ 72 -1 Yes $C_2$, $C_4$, $C_3^2:C_8$, 12T46, 18T28 9T15
36T50 $S_3\times A_4$ 72 1 Yes $C_3$, $S_3$, $A_4$, $A_4\times C_2$, $S_3\times C_3$, $A_4\times C_2$, 18T31, 18T32

Next

Results are complete for degrees $\leq 23$.