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Label Name Order Parity Solvable Subfields Low Degree Siblings
32T12 $D_4:C_4$ $32$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_4\times C_2$, $D_4$ x 2, $D_{8}$ x 2, $QD_{16}$, $C_2^2:C_4$ x 2, $C_2^2 : C_4$, $QD_{16}$, $D_{8}$, $D_4:C_4$ x 2 16T26 x 2
32T14 $C_4\wr C_2$ $32$ $1$ $C_2$ 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, $C_4\wr C_2$ x 2, $C_2^2 : C_4$, $C_4\wr C_2$, $C_4\wr C_2$ 8T17 x 2, 16T28, 16T42
32T15 $C_2\times D_8$ $32$ $1$ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $D_{8}$ x 4, $D_4\times C_2$ x 4, $D_4\times C_2$, $D_{8}$ x 2, $C_2\times D_8$ x 4 16T29 x 4
32T18 $Q_{16}:C_2$ $32$ $1$ $C_2$ 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, $D_4\times C_2$, $Q_{16}:C_2$, $Q_{16}:C_2$ 16T32, 16T50
32T19 $C_2^3:C_4$ $32$ $1$ $C_2$ 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_2^3 : C_4 $ x 2, $C_2^3: C_4$, $C_2^3: C_4$, $C_2^2 : C_4$, $C_2^3:C_4$ x 2, $C_2^3:C_4$, $C_2^3:C_4$ 8T19 x 2, 8T20, 8T21, 16T33 x 2, 16T52, 16T53
32T21 $D_8:C_2$ $32$ $1$ $C_2$ 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, $Z_8 : Z_8^\times$ x 2, $D_4\times C_2$, $D_8:C_2$, $D_8:C_2$ x 2, $D_8:C_2$ 8T15 x 2, 16T35, 16T38 x 2, 16T45
32T22 $\OD_{16}:C_2$ $32$ $1$ $C_2$ 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, $(C_8:C_2):C_2$ x 2, $C_2^2 : C_4$, $\OD_{16}:C_2$, $\OD_{16}:C_2$ x 2 8T16 x 2, 16T36, 16T41 x 2
32T25 $C_4.D_4$ $32$ $1$ $C_2$ 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, $C_2^2 : C_4$, $C_4.D_4$ 16T40
32T26 $D_8:C_2$ $32$ $1$ $C_2$ 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, $D_4\times C_2$, $D_8:C_2$ x 2, $D_8:C_2$ 16T44 x 2, 16T47
32T27 $C_2\times \SD_{16}$ $32$ $1$ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $QD_{16}$ x 2, $D_4\times C_2$ x 4, $D_4\times C_2$, $QD_{16}$ x 2, $C_2\times \SD_{16}$ x 2 16T48 x 2
32T28 $C_8.C_4$ $32$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 2, $C_4\times C_2$, $D_4$, $Q_8$, $C_4:C_4$, $C_8.C_4$ 16T49
32T47 $C_8:C_4$ $32$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 2, $C_4\times C_2$, $D_4$, $Q_8$, $QD_{16}$ x 2, $C_4:C_4$, $QD_{16}$ x 2
32T48 $C_8:C_4$ $32$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 2, $C_4\times C_2$, $D_4$, $Q_8$, $D_{8}$ x 2, $C_4:C_4$, $D_{8}$, $Q_{16}$
32T49 $C_2\times Q_{16}$ $32$ $1$ $C_2$ 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, $D_4\times C_2$, $Q_{16}$ x 2
32T50 $Q_8:C_4$ $32$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_4\times C_2$, $D_4$ x 2, $QD_{16}$, $C_2^2:C_4$ x 2, $C_2^2 : C_4$, $QD_{16}$, $Q_{16}$
32T58 $\OD_{16}.C_2^2$ $64$ $1$ $C_2$ 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, $C_2^2 : C_4$, $\OD_{16}.C_2^2$ 16T71, 16T86 x 2, 32T58, 32T59, 32T84 x 2
32T59 $\OD_{16}.C_2^2$ $64$ $1$ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $C_4\times C_2^2$, $\OD_{16}.C_2^2$, $\OD_{16}.C_2^2$ x 2 16T71, 16T86 x 2, 32T58 x 2, 32T84 x 2
32T60 $\OD_{16}:C_2^2$ $64$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_4\times C_2$, $D_4\times C_2$ x 2, $C_2^2:C_4$ x 4, $(C_8:C_2):C_2$ x 2, $C_2 \times (C_2^2:C_4)$, $\OD_{16}:C_2$ x 2, $\OD_{16}:C_2^2$ x 2, $\OD_{16}:C_2^2$ 16T72 x 4, 16T99 x 4, 32T60 x 3, 32T61, 32T100
32T61 $\OD_{16}:C_2^2$ $64$ $1$ $C_2$ 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, $(C_8:C_2):C_2$ x 4, $C_2^2 : C_4$, $\OD_{16}:C_2$ x 2, $\OD_{16}:C_2^2$ x 4 16T72 x 4, 16T99 x 4, 32T60 x 4, 32T100
32T65 $C_2^3.D_4$ $64$ $1$ $C_2$ 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, $Z_8 : Z_8^\times$ x 4, $C_2^2 : C_4$, $D_8:C_2$ x 2, $C_2^3.D_4$ x 4 16T75 x 8, 32T65, 32T66 x 4
32T66 $C_2^3.D_4$ $64$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_4\times C_2$, $D_4\times C_2$ x 2, $C_2^2:C_4$ x 4, $Z_8 : Z_8^\times$ x 4, $C_2 \times (C_2^2:C_4)$, $D_8:C_2$ x 2, $C_2^3.D_4$ x 4 16T75 x 8, 32T65 x 2, 32T66 x 3
32T67 $C_2^4:C_4$ $64$ $1$ $C_2$ 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, $C_2^3 : C_4 $ x 2, $C_2^3: C_4$ x 2, $D_4\times C_2$, $C_2^3:C_4$ x 2, $C_2^4:C_4$ x 2, $C_2^4:C_4$, $C_2^4:C_4$ 16T76 x 4, 16T78, 16T92, 16T93 x 2, 16T94 x 2, 16T102 x 2, 32T67, 32T70 x 2, 32T71, 32T94 x 2, 32T95
32T68 $C_2^2.C_4^2$ $64$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 2, $C_4\times C_2$, $D_4$, $Q_8$, $C_2^3: C_4$ x 2, $C_2^3: C_4$ x 2, $C_4:C_4$, $C_2^3:C_4$ x 2, $C_2^2.C_4^2$, $C_2^2.C_4^2$ 16T77, 16T88 x 2, 16T91, 16T96 x 4, 32T69 x 2, 32T87, 32T88 x 2
32T69 $C_2^2.C_4^2$ $64$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 2, $C_4\times C_2$, $D_4$, $Q_8$, $C_2^3 : C_4 $ x 2, $C_2^3: C_4$ x 2, $C_4:C_4$, $C_2^3:C_4$ x 2, $C_2^2.C_4^2$, $C_2^2.C_4^2$ 16T77, 16T88 x 2, 16T91, 16T96 x 4, 32T68, 32T69, 32T87, 32T88 x 2
32T70 $C_2^4:C_4$ $64$ $1$ $C_2$ 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_2^3 : C_4 $ x 2, $C_2^3: C_4$ x 2, $C_2^2 : C_4$, $C_2^3:C_4$ x 2, $C_2^4:C_4$, $C_2^4:C_4$ 16T76 x 4, 16T78, 16T92, 16T93 x 2, 16T94 x 2, 16T102 x 2, 32T67 x 2, 32T70, 32T71, 32T94 x 2, 32T95
32T71 $C_2^4:C_4$ $64$ $1$ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $C_2^3: C_4$ x 2, $C_2^3: C_4$ x 2, $C_4\times C_2^2$, $C_2^3:C_4$ x 2, $C_2^4:C_4$, $C_2^4:C_4$, $C_2^4:C_4$ x 2 16T76 x 4, 16T78, 16T92, 16T93 x 2, 16T94 x 2, 16T102 x 2, 32T67 x 2, 32T70 x 2, 32T94 x 2, 32T95
32T73 $D_8:C_2^2$ $64$ $1$ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4\times C_2$ x 6, $C_2^2 \times D_4$, $D_8:C_2^2$ x 2 16T80 x 6, 32T73 x 5, 32T74 x 3
32T74 $D_8:C_2^2$ $64$ $1$ $C_2$ 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, $D_4\times C_2$, $D_8:C_2^2$ x 2 16T80 x 6, 32T73 x 6, 32T74 x 2
32T81 $C_2^3:C_8$ $64$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_8$, $C_8:C_2$, $C_2^2:C_4$, $(C_8:C_2):C_2$, $C_2^3: C_4$, $C_2^2 : C_8$, $\OD_{16}:C_2$, $C_2^3:C_4$, $C_2^3:C_8$ x 2, $C_2^3:C_8$ 16T84 x 2, 16T85 x 2, 32T81, 32T82, 32T83
32T82 $C_2^3:C_8$ $64$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$, $C_8:C_2$, $(C_8:C_2):C_2$ x 2, $C_2^3: C_4$, $C_2^3: C_4$, $C_8: C_2$, $\OD_{16}:C_2$, $C_2^3:C_4$, $C_2^3:C_8$ x 2 16T84 x 2, 16T85 x 2, 32T81 x 2, 32T83
32T83 $C_2^3:C_8$ $64$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_8$ x 2, $C_4\times C_2$, $(C_8:C_2):C_2$ x 2, $C_2^3: C_4$, $C_2^3: C_4$, $C_8\times C_2$, $\OD_{16}:C_2$, $C_2^3:C_4$, $C_2^3:C_8$ x 2 16T84 x 2, 16T85 x 2, 32T81 x 2, 32T82
32T84 $\OD_{16}.C_2^2$ $64$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_4\times C_2$, $D_4\times C_2$ x 2, $C_2^2:C_4$ x 4, $C_2 \times (C_2^2:C_4)$, $\OD_{16}.C_2^2$ 16T71, 16T86 x 2, 32T58 x 2, 32T59, 32T84
32T87 $C_2^2.C_4^2$ $64$ $1$ $C_2$ x 3, $C_4$ x 6, $C_2^2$, $C_4\times C_2$ x 3, $C_2^3: C_4$ x 2, $C_2^3: C_4$ x 2, $C_4^2$, $C_2^3:C_4$ x 2, $C_2^2.C_4^2$ x 2 16T77, 16T88 x 2, 16T91, 16T96 x 4, 32T68, 32T69 x 2, 32T88 x 2
32T88 $C_2^2.C_4^2$ $64$ $1$ $C_2$ 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_2^3 : C_4 $ x 2, $C_2^3: C_4$ x 2, $C_2^2 : C_4$, $C_2^3:C_4$ x 2, $C_2^2.C_4^2$, $C_2^2.C_4^2$, $C_2^2.C_4^2$ x 2 16T77, 16T88 x 2, 16T91, 16T96 x 4, 32T68, 32T69 x 2, 32T87, 32T88
32T89 $C_8:C_2^3$ $64$ $1$ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4\times C_2$ x 6, $Z_8 : Z_8^\times$ x 4, $C_2^2 \times D_4$, $D_8:C_2$ x 2, $C_8:C_2^3$ x 4 16T89 x 8, 32T89 x 3, 32T90 x 2, 32T279 x 2
32T90 $C_8:C_2^3$ $64$ $1$ $C_2$ 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, $Z_8 : Z_8^\times$ x 4, $D_4\times C_2$, $D_8:C_2$ x 2, $C_8:C_2^3$ x 4 16T89 x 8, 32T89 x 4, 32T90, 32T279 x 2
32T91 $\OD_{16}:C_4$ $64$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 2, $C_4\times C_2$, $D_4$, $Q_8$, $C_4:C_4$, $\OD_{16}:C_4$ 16T90, 16T110 x 2, 32T92, 32T93
32T92 $\OD_{16}:C_4$ $64$ $1$ $C_2$ x 3, $C_4$ x 6, $C_2^2$, $C_4\times C_2$ x 3, $C_4^2$, $\OD_{16}:C_4$ 16T90, 16T110 x 2, 32T91, 32T93
32T93 $\OD_{16}:C_4$ $64$ $1$ $C_2$ 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, $C_2^2 : C_4$, $\OD_{16}:C_4$, $\OD_{16}:C_4$ x 2 16T90, 16T110 x 2, 32T91, 32T92
32T94 $C_2^4:C_4$ $64$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_4\times C_2$, $D_4\times C_2$ x 2, $C_2^2:C_4$ x 4, $C_2^3: C_4$ x 2, $C_2 \times (C_2^2:C_4)$, $C_2^3:C_4$ x 2, $C_2^4:C_4$ x 2, $C_2^4:C_4$ 16T76 x 4, 16T78, 16T92, 16T93 x 2, 16T94 x 2, 16T102 x 2, 32T67 x 2, 32T70 x 2, 32T71, 32T94, 32T95
32T95 $C_2^4:C_4$ $64$ $1$ $C_2$ 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, $C_2^3: C_4$ x 2, $C_2^3: C_4$ x 2, $C_2^2 : C_4$, $C_2^3:C_4$ x 2, $C_2^4:C_4$ x 2, $C_2^4:C_4$ x 2 16T76 x 4, 16T78, 16T92, 16T93 x 2, 16T94 x 2, 16T102 x 2, 32T67 x 2, 32T70 x 2, 32T71, 32T94 x 2
32T100 $\OD_{16}:C_2^2$ $64$ $1$ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $(C_8:C_2):C_2$ x 4, $C_4\times C_2^2$, $\OD_{16}:C_2$ x 2, $\OD_{16}:C_2^2$ x 4 16T72 x 4, 16T99 x 4, 32T60 x 4, 32T61
32T101 $D_8:C_2^2$ $64$ $1$ $C_2$ 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, $D_4\times C_2$, $D_8:C_2^2$, $D_8:C_2^2$ x 2 16T100, 16T118 x 4, 32T101, 32T102, 32T127 x 4
32T102 $D_8:C_2^2$ $64$ $1$ $C_2$ 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, $D_4\times C_2$, $D_8:C_2^2$ 16T100, 16T118 x 4, 32T101 x 2, 32T127 x 4
32T103 $C_2^3.C_2^3$ $64$ $1$ $C_2$ 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, $D_4\times C_2$, $C_2^3.C_2^3$, $C_2^3.C_2^3$ x 2 16T101, 16T112 x 2, 16T120 x 4, 32T103, 32T104, 32T117 x 2
32T104 $C_2^3.C_2^3$ $64$ $1$ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $C_4\times C_2^2$, $C_2^3.C_2^3$, $C_2^3.C_2^3$ x 2 16T101, 16T112 x 2, 16T120 x 4, 32T103 x 2, 32T117 x 2
32T105 $C_2^3.Q_8$ $64$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 2, $C_4\times C_2$, $D_4$, $Q_8$, $C_4:C_4$, $C_2^3.Q_8$ 16T103, 32T105, 32T106
32T106 $C_2^3.Q_8$ $64$ $1$ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8$ x 2, $Q_8\times C_2$, $C_2^3.Q_8$ 16T103, 32T105 x 2
32T107 $\OD_{32}:C_2$ $64$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_8$ x 2, $C_4\times C_2$, $C_8\times C_2$, $\OD_{32}:C_2$ 16T104, 32T108
32T108 $\OD_{32}:C_2$ $64$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_8$, $C_8:C_2$, $C_2^2:C_4$, $C_2^2 : C_8$, $\OD_{32}:C_2$ 16T104, 32T107
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Results are complete for degrees $\leq 23$.