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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 $C_2$, $C_3$, $S_3$, $C_4$, $C_6$, $S_3$, $S_3\times C_3$, $S_3\times C_3$, $C_{12}$, $C_3 : C_4$, $C_3\times (C_3 : C_4)$, $S_3 \times C_3$ 12T19
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 12T18, 18T6 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 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 18T13 x 2
36T11 $C_2^2:C_9$ $36$ $1$ yes $C_3$, $A_4$, $A_4$, $C_9$, $A_4$, $C_2^2 : C_9$ 18T7
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, $A_4 \times C_3$ 12T20 x 3, 18T8
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, 12T16, 18T9, 18T11 x 2
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, 12T17 x 2, 18T10
36T15 $C_9\times D_4$ $72$ $-1$ yes $C_2$, $C_3$, $D_{4}$, $C_6$, $C_9$, $D_4 \times C_3$, $C_{18}$ 36T15
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 18T26, 36T30
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, $C_6 \times C_3$ 36T17
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 18T25, 24T71 x 3, 36T31
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, $S_3 \times C_3$ 12T42 x 2, 24T77, 36T26
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 12T45, 18T30, 18T33, 24T80, 24T84, 36T52
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 12T43, 18T31, 18T32, 24T78, 24T83, 36T50, 36T51
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, $C_3^2 : C_2$ 36T42
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 12T44 x 3, 18T37, 18T40, 24T79 x 3, 36T56
36T24 $C_9:D_4$ $72$ $-1$ yes $C_2$, $S_3$, $D_{4}$, $S_3$, $D_{9}$, $(C_6\times C_2):C_2$, $D_9$ 36T46
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 18T38, 18T39, 36T57
36T26 $C_3\times C_3:D_4$ $72$ $-1$ yes $C_2$, $C_3$, $S_3$, $D_{4}$, $C_6$, $D_{6}$, $S_3\times C_3$, $(C_6\times C_2):C_2$, $D_4 \times C_3$, $S_3 \times C_6$ 12T42 x 2, 24T77, 36T19
36T27 $C_{12}\times S_3$ $72$ $-1$ yes $C_2$, $C_3$, $S_3$, $C_4$, $C_6$, $D_{6}$, $S_3\times C_3$, $C_{12}$, $S_3 \times C_4$, $S_3 \times C_6$ 24T65, 36T27
36T28 $C_3\times D_{12}$ $72$ $-1$ yes $C_2$, $C_3$, $S_3$, $D_{4}$, $C_6$, $D_{6}$, $S_3\times C_3$, $D_{12}$, $D_4 \times C_3$, $S_3 \times C_6$ 24T67, 36T28
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 24T68, 36T29 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 18T26, 36T16
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 18T25, 24T71 x 3, 36T18
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, $S_3^2$ 12T39 x 2, 24T75, 36T32
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, $S_3^2$ 12T38 x 2, 24T74, 36T38
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 12T37 x 2, 18T29 x 4, 24T73, 36T34, 36T40 x 4
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, $C_3^2 : C_4$ 12T40 x 2, 12T41 x 2, 18T27 x 2, 24T76 x 2, 36T36
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 12T40 x 2, 12T41 x 2, 18T27 x 2, 24T76 x 2, 36T35
36T37 $S_3\times C_3:C_4$ $72$ $-1$ yes $C_2$, $S_3$ x 2, $C_4$, $S_3$, $D_{6}$, $S_3^2$, $C_3 : C_4$, $S_3 \times C_4$, $S_3^2$ 24T60, 36T37
36T38 $C_3^2:D_4$ $72$ $-1$ yes $C_2$, $S_3$ x 2, $D_{4}$, $S_3$, $D_{6}$, $S_3^2$, $D_{12}$, $(C_6\times C_2):C_2$, $S_3^2$ 12T38 x 2, 24T74, 36T33
36T39 $D_6:S_3$ $72$ $-1$ yes $C_2$, $S_3$ x 2, $D_{4}$, $S_3$, $D_{6}$, $S_3^2$, $(C_6\times C_2):C_2$, $(C_6\times C_2):C_2$, $S_3^2$ 24T61, 36T39
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 12T37 x 2, 18T29 x 4, 24T73, 36T34 x 2, 36T40 x 3
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 36T41
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 36T22
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 36T43
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 36T44 x 3
36T45 $C_4\times D_9$ $72$ $-1$ yes $C_2$, $S_3$, $C_4$, $D_{6}$, $D_{9}$, $S_3 \times C_4$, $D_{18}$ 36T45
36T46 $C_9:D_4$ $72$ $-1$ yes $C_2$, $S_3$, $D_{4}$, $D_{6}$, $D_{9}$, $(C_6\times C_2):C_2$, $D_{18}$ 36T24
36T47 $D_{36}$ $72$ $-1$ yes $C_2$, $S_3$, $D_{4}$, $D_{6}$, $D_{9}$, $D_{12}$, $D_{18}$ 36T47
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 36T48 x 3
36T49 $F_9$ $72$ $-1$ yes $C_2$, $C_4$, $C_3^2:C_8$, 12T46, 18T28 9T15, 12T46, 18T28, 24T81
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 12T43, 18T31, 18T32, 24T78, 24T83, 36T21, 36T51
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Results are complete for degrees $\leq 23$.