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Label Name Order Parity Solvable Subfields Low Degree Siblings
32T1 $C_2\times \OD_{16}$ $32$ $1$ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $C_8:C_2$ x 2, $C_4\times C_2^2$, $C_8: C_2$ x 2, $C_2 \times (C_8:C_2)$ x 2 16T15 x 2
32T2 $\OD_{16}:C_2$ $32$ $1$ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $C_4\times C_2^2$, $(C_8:C_2):C_2$ x 3 16T16 x 3
32T3 $C_4^2:C_2$ $32$ $1$ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $Q_8:C_2$ x 6, $C_4\times C_2^2$, $Q_8 : C_2$ x 2, $C_4^2:C_2$ x 2 16T17 x 2
32T4 $D_4:C_2^2$ $32$ $1$ $C_2$ x 15, $C_2^2$ x 35, $C_2^3$ x 15, $Q_8:C_2$ x 6, $C_2^4$, $Q_8 : C_2$ x 2, $C_2 \times (C_4\times C_2):C_2$ x 6 16T18 x 6
32T5 $C_4\times D_4$ $32$ $1$ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $D_{4}$ x 4, $C_4\times C_2$ x 6, $C_2^3$, $D_4$ x 2, $D_4\times C_2$ x 4, $Q_8:C_2$ x 3, $C_4\times C_2^2$, $D_4\times C_2$, $Q_8 : C_2$, $C_4 \times D_4$ x 4 16T19 x 4
32T6 $C_4.C_2^3$ $32$ $1$ $C_2$ x 15, $C_2^2$ x 35, $C_2^3$ x 15, $C_2^4$, $(C_2 \times Q_8):C_2$ x 5 16T20 x 5
32T7 $C_2^3:C_4$ $32$ $1$ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $D_{4}$ x 8, $C_4\times C_2$ x 6, $C_2^3$, $D_4$ x 4, $D_4\times C_2$ x 8, $C_2^2:C_4$ x 8, $C_4\times C_2^2$, $D_4\times C_2$ x 2, $C_2^2 : C_4$ x 4, $C_2 \times (C_2^2:C_4)$ x 4 16T21 x 4
32T8 $\OD_{32}$ $32$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_8$ x 2, $C_4\times C_2$, $C_8\times C_2$, $C_{16} : C_2$ 16T22
32T9 $D_4:C_2^2$ $32$ $1$ $C_2$ x 15, $C_2^2$ x 35, $C_2^3$ x 15, $Q_8:C_2^2$ x 6, $C_2^4$, $Q_8 : C_2^2$ x 9 8T22 x 6, 16T23 x 9
32T10 $C_2^2:C_8$ $32$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_8$ x 2, $C_4\times C_2$, $D_4$ x 2, $C_8:C_2$, $C_2^2:C_4$ x 2, $C_8\times C_2$, $C_8: C_2$, $C_2^2 : C_4$, $C_2^2 : C_8$ x 2 16T24 x 2
32T11 $C_2^2\times D_4$ $32$ $1$ $C_2$ x 15, $C_2^2$ x 35, $D_{4}$ x 8, $C_2^3$ x 15, $D_4$ x 4, $D_4\times C_2$ x 24, $C_2^4$, $D_4\times C_2$ x 6, $C_2^2 \times D_4$ x 8 16T25 x 8
32T13 $C_4^2:C_2$ $32$ $1$ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2$ x 9, $Q_8 : C_2$ x 3, $C_4^2:C_2$ 16T27
32T16 $C_4^2:C_2$ $32$ $1$ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $D_4\times C_2$ x 4, $Q_8:C_2$ x 6, $D_4\times C_2$, $Q_8 : C_2$ x 2, $C_4^2:C_2$ x 2 16T30 x 2
32T17 $C_2^2:Q_8$ $32$ $1$ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $Q_8$ x 2, $D_4\times C_2$ x 4, $Q_8:C_2$ x 3, $Q_8\times C_2$, $D_4\times C_2$, $Q_8 : C_2$, $C_2^2:Q_8$ x 2 16T31 x 2
32T20 $C_4:D_4$ $32$ $1$ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 8, $C_2^3$, $D_4$ x 4, $D_4\times C_2$ x 8, $Q_8:C_2$ x 3, $D_4\times C_2$ x 2, $Q_8 : C_2$, $C_4:D_4$ x 2, $C_4:D_4$ x 2 16T34 x 2, 16T43 x 2
32T23 $C_2^2.D_4$ $32$ $1$ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $D_4\times C_2$ x 4, $Q_8:C_2$ x 6, $D_4\times C_2$, $Q_8 : C_2$ x 2, $C_2^2.D_4$, $C_2^2.D_4$ x 2 16T37, 16T54 x 2
32T24 $C_2^2\wr C_2$ $32$ $1$ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 12, $C_2^3$, $D_4$ x 6, $D_4\times C_2$ x 12, $C_2^2 \wr C_2$ x 8, $D_4\times C_2$ x 3, $C_2^2\wr C_2$ x 6, $C_2^2\wr C_2$ 8T18 x 8, 16T39 x 6, 16T46
32T29 $C_4:D_4$ $32$ $1$ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 12, $C_2^3$, $D_4$ x 6, $D_4\times C_2$ x 12, $D_4\times C_2$ x 3, $C_4^2:C_2$ x 4 16T51 x 4
32T35 $C_2^2.D_4$ $32$ $1$ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $D_{4}$ x 4, $C_4\times C_2$ x 6, $C_2^3$, $D_4$ x 2, $Q_8$ x 2, $D_4\times C_2$ x 4, $C_4\times C_2^2$, $Q_8\times C_2$, $C_4:C_4$ x 4, $D_4\times C_2$
32T38 $C_4\times Q_8$ $32$ $1$ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $Q_8$ x 2, $Q_8:C_2$ x 3, $C_4\times C_2^2$, $Q_8\times C_2$, $Q_8 : C_2$
32T40 $C_2^2\times Q_8$ $32$ $1$ $C_2$ x 15, $C_2^2$ x 35, $C_2^3$ x 15, $Q_8$ x 4, $C_2^4$, $Q_8\times C_2$ x 6
32T41 $C_2.C_4^2$ $32$ $1$ $C_2$ x 3, $C_4$ x 6, $C_2^2$, $D_{4}$ x 6, $C_4\times C_2$ x 3, $D_4$ x 3, $Q_8$, $C_2^2:C_4$ x 6, $C_4^2$, $C_4:C_4$ x 3, $C_2^2 : C_4$ x 3
32T42 $C_8:C_4$ $32$ $1$ $C_2$ x 3, $C_4$ x 6, $C_2^2$, $C_4\times C_2$ x 3, $C_8:C_2$ x 2, $C_4^2$, $C_8: C_2$ x 2
32T44 $C_4:C_8$ $32$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 2, $C_8$ x 2, $C_4\times C_2$, $D_4$, $Q_8$, $C_8:C_2$, $C_8\times C_2$, $C_8: C_2$, $C_4:C_4$
32T45 $C_4:Q_8$ $32$ $1$ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $Q_8$ x 4, $D_4\times C_2$ x 4, $Q_8\times C_2$ x 2, $D_4\times C_2$
32T46 $C_4.Q_8$ $32$ $1$ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8$ x 2, $Q_8:C_2$ x 6, $Q_8\times C_2$, $Q_8 : C_2$ x 2
32T52 $C_4.C_2^4$ $64$ $1$ $C_2$ x 15, $C_2^2$ x 35, $C_2^3$ x 15, $C_2^4$, $C_4.C_2^4$ x 3 16T67 x 15, 32T52 x 14
32T53 $C_4^2:C_2^2$ $64$ $1$ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $Q_8:C_2^2$ x 4, $C_4\times C_2^2$, $Q_8 : C_2^2$ x 2, $C_4^2:C_2^2$ x 2 16T68 x 8, 32T53 x 7, 32T54 x 2
32T54 $C_4^2:C_2^2$ $64$ $1$ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $Q_8:C_2^2$ x 4, $C_4\times C_2^2$, $Q_8 : C_2^2$ x 2, $C_4^2:C_2^2$ x 4 16T68 x 8, 32T53 x 8, 32T54
32T55 $D_4:C_2^3$ $64$ $1$ $C_2$ x 15, $C_2^2$ x 35, $C_2^3$ x 15, $Q_8:C_2^2$ x 4, $C_2^4$, $Q_8 : C_2^2$ x 2, $D_4:C_2^3$ x 4 16T69 x 24, 32T55 x 17
32T56 $C_8.C_2^3$ $64$ $1$ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $C_4\times C_2^2$, $C_8.C_2^3$ 16T70 x 3, 32T56 x 5, 32T57
32T57 $C_8.C_2^3$ $64$ $1$ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $C_4\times C_2^2$, $C_8.C_2^3$ x 3 16T70 x 3, 32T56 x 6
32T62 $C_4^2:C_2^2$ $64$ $1$ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4\times C_2$ x 6, $Q_8:C_2^2$ x 4, $Q_8 : C_2^2$ x 2, $C_2^2 \times D_4$, $C_4^2:C_2^2$ x 4 16T73 x 8, 32T62 x 3, 32T63 x 2, 32T269 x 2
32T63 $C_4^2:C_2^2$ $64$ $1$ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $D_4\times C_2$ x 4, $Q_8:C_2^2$ x 4, $D_4\times C_2$, $Q_8 : C_2^2$ x 2, $C_4^2:C_2^2$ x 4 16T73 x 8, 32T62 x 4, 32T63, 32T269 x 2
32T64 $C_4^2:C_4$ $64$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_4\times C_2$, $D_4$ x 2, $C_2^2:C_4$ x 2, $C_2^2 : C_4$, $C_4^2:C_4$ x 2, $C_4^2:C_4$ 16T74 x 4, 16T123, 32T64, 32T131
32T72 $C_2^4:C_4$ $64$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 12, $C_4\times C_2$, $D_4$ x 2, $D_4\times C_2$ x 4, $C_2^2:C_4$ x 10, $C_2^2 \wr C_2$ x 16, $C_2^2 : C_4$, $C_2 \times (C_2^2:C_4)$ x 2, $C_2^2\wr C_2$ x 4, $C_2^4:C_4$ x 8 16T79 x 32, 32T72 x 11
32T75 $C_4^2:C_2^2$ $64$ $1$ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2$ x 5, $Q_8:C_2^2$ x 2, $Q_8 : C_2$, $C_2 \times (C_4\times C_2):C_2$, $Q_8 : C_2^2$, $C_4^2:C_2^2$ x 2 16T81 x 4, 32T75 x 3, 32T76, 32T233
32T76 $C_4^2:C_2^2$ $64$ $1$ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2$ x 4, $Q_8:C_2^2$ x 2, $C_2 \times (C_4\times C_2):C_2$ x 2, $Q_8 : C_2^2$, $C_4^2:C_2^2$ x 4 16T81 x 4, 32T75 x 4, 32T233
32T77 $C_4^2:C_2^2$ $64$ $1$ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2$ x 2, $Q_8:C_2^2$ x 4, $C_2 \times (C_4\times C_2):C_2$, $Q_8 : C_2^2$ x 2, $C_4^2:C_2^2$ x 4 16T82 x 4, 32T77, 32T78 x 2, 32T234 x 2
32T78 $C_4^2:C_2^2$ $64$ $1$ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2$ x 3, $Q_8:C_2^2$ x 4, $Q_8 : C_2$, $Q_8 : C_2^2$ x 2, $C_4^2:C_2^2$ x 2 16T82 x 4, 32T77 x 2, 32T78, 32T234 x 2
32T79 $C_4^2:C_2^2$ $64$ $1$ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2^2$ x 6, $Q_8 : C_2^2$ x 3, $C_4^2:C_2^2$ x 4 16T83 x 4, 32T79, 32T80, 32T270 x 3
32T80 $C_4^2:C_2^2$ $64$ $1$ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2^2$ x 6, $Q_8 : C_2^2$ x 3, $C_4^2:C_2^2$ x 4 16T83 x 4, 32T79 x 2, 32T270 x 3
32T85 $C_2^3:D_4$ $64$ $1$ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4\times C_2$ x 6, $Q_8:C_2^2$ x 4, $Q_8 : C_2^2$ x 2, $C_2^2 \times D_4$, $C_2^3:D_4$ x 4 16T87 x 8, 16T119 x 4, 32T85 x 3, 32T86 x 4, 32T128 x 2
32T86 $C_2^3:D_4$ $64$ $1$ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $D_4\times C_2$ x 4, $Q_8:C_2^2$ x 4, $D_4\times C_2$, $Q_8 : C_2^2$ x 2, $C_2^3:D_4$ x 2, $C_2^3:D_4$ x 2 16T87 x 8, 16T119 x 4, 32T85 x 4, 32T86 x 3, 32T128 x 2
32T96 $C_2^2:\OD_{16}$ $64$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_4\times C_2$, $C_8:C_2$ x 3, $D_4\times C_2$ x 2, $C_2^2:C_4$ x 4, $C_8: C_2$, $C_2 \times (C_8:C_2)$, $C_2 \times (C_2^2:C_4)$, $C_2^2:\OD_{16}$ x 4 16T95 x 8, 32T96 x 3, 32T97 x 2
32T97 $C_2^2:\OD_{16}$ $64$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_4\times C_2$, $D_4$ x 2, $C_8:C_2$ x 4, $C_2^2:C_4$ x 2, $C_2^2 : C_4$, $C_2 \times (C_8:C_2)$ x 2, $C_2^2:\OD_{16}$ x 4 16T95 x 8, 32T96 x 4, 32T97
32T98 $C_2^3:Q_8$ $64$ $1$ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8$ x 2, $Q_8:C_2^2$ x 4, $Q_8\times C_2$, $Q_8 : C_2^2$ x 2, $C_2^3:Q_8$ x 2 16T97 x 4, 32T98 x 5
32T99 $C_4^2:C_2^2$ $64$ $1$ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2^2$ x 6, $Q_8 : C_2^2$ x 3, $C_4^2:C_2^2$ x 4 16T98 x 8, 32T99 x 5
32T109 $C_2^3:D_4$ $64$ $1$ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 12, $C_2^3$, $D_4$ x 2, $D_4\times C_2$ x 16, $C_2^2 \wr C_2$ x 16, $D_4\times C_2$, $C_2^2 \times D_4$ x 2, $C_2^2\wr C_2$ x 4, $C_2^3:D_4$ x 8 16T105 x 32, 32T109 x 11, 32T275 x 2
32T113 $C_4.C_4^2$ $64$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 2, $C_4\times C_2$, $D_4$, $Q_8$, $C_4:C_4$, $C_4.C_4^2$ 16T108, 32T113 x 2
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Results are complete for degrees $\leq 23$.