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Label Name Order Parity Solvable Subfields Low Degree Siblings
32T3214 $(C_4\times C_8).D_4$ $256$ $1$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $(C_4\times C_8).D_4$ x 2 16T658 x 2, 32T3215, 32T3216, 32T7128, 32T7142, 32T7145, 32T7297
32T3215 $(C_4\times C_8).D_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $((C_8 : C_2):C_2):C_2$, $(((C_4 \times C_2): C_2):C_2):C_2$, $C_2\wr C_4$, $(C_4\times C_8).D_4$ x 2 16T658 x 2, 32T3214, 32T3216, 32T7128, 32T7142, 32T7145, 32T7297
32T3216 $(C_4\times C_8).D_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $(C_4\times C_8).D_4$ x 2 16T658 x 2, 32T3214, 32T3215, 32T7128, 32T7142, 32T7145, 32T7297
32T3233 $D_4^2:C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $((C_8 : C_2):C_2):C_2$, $(((C_4 \times C_2): C_2):C_2):C_2$, $C_2\wr C_4$, $D_4^2:C_4$, $D_4^2:C_4$ 16T663 x 2, 16T685 x 2, 16T688 x 2, 32T3233, 32T3234, 32T3235 x 4, 32T3236 x 4, 32T3237, 32T3314, 32T3315, 32T3316, 32T3322, 32T3323, 32T7298
32T3234 $D_4^2:C_4$ $256$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$, $((C_8 : C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $D_4^2:C_4$ x 2 16T663 x 2, 16T685 x 2, 16T688 x 2, 32T3233 x 2, 32T3235 x 4, 32T3236 x 4, 32T3237, 32T3314, 32T3315, 32T3316, 32T3322, 32T3323, 32T7298
32T3235 $D_4^2:C_4$ $256$ $1$ $C_2$, $C_4$, $C_2^3: C_4$, $((C_8 : C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $D_4^2:C_4$, $D_4^2:C_4$ 16T663 x 2, 16T685 x 2, 16T688 x 2, 32T3233 x 2, 32T3234, 32T3235 x 3, 32T3236 x 4, 32T3237, 32T3314, 32T3315, 32T3316, 32T3322, 32T3323, 32T7298
32T3236 $D_4^2:C_4$ $256$ $1$ $C_2$, $C_4$, $C_2^3: C_4$, $((C_8 : C_2):C_2):C_2$, $C_2\wr C_4$, $D_4^2:C_4$, $D_4^2:C_4$ 16T663 x 2, 16T685 x 2, 16T688 x 2, 32T3233 x 2, 32T3234, 32T3235 x 4, 32T3236 x 3, 32T3237, 32T3314, 32T3315, 32T3316, 32T3322, 32T3323, 32T7298
32T3237 $D_4^2:C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $((C_8 : C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $D_4^2:C_4$ x 2 16T663 x 2, 16T685 x 2, 16T688 x 2, 32T3233 x 2, 32T3234, 32T3235 x 4, 32T3236 x 4, 32T3314, 32T3315, 32T3316, 32T3322, 32T3323, 32T7298
32T3238 $C_8^2:C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_4^2:C_4$, $C_8^2:C_4$ x 2 16T664 x 8, 32T3238 x 3, 32T3239 x 4, 32T3240 x 4
32T3239 $C_8^2:C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_4^2:C_4$, $C_8^2:C_4$ x 2 16T664 x 8, 32T3238 x 4, 32T3239 x 3, 32T3240 x 4
32T3240 $C_8^2:C_4$ $256$ $1$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_4^2:C_4$, $C_8^2:C_4$ x 2 16T664 x 8, 32T3238 x 4, 32T3239 x 4, 32T3240 x 3
32T3254 $C_8:C_8:C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_4^2:C_4$, $C_8:C_8:C_4$ x 2 16T668 x 4, 32T3254, 32T3255 x 2, 32T3256 x 2, 32T7393 x 2
32T3255 $C_8:C_8:C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_4^2:C_4$, $C_8:C_8:C_4$ x 2 16T668 x 4, 32T3254 x 2, 32T3255, 32T3256 x 2, 32T7393 x 2
32T3256 $C_8:C_8:C_4$ $256$ $1$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_4^2:C_4$, $C_8:C_8:C_4$ x 2 16T668 x 4, 32T3254 x 2, 32T3255 x 2, 32T3256, 32T7393 x 2
32T3265 $D_4^2.C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $((C_8 : C_2):C_2):C_2$, $(((C_4 \times C_2): C_2):C_2):C_2$, $C_2\wr C_4$, $D_4^2.C_4$ 16T671 x 2, 16T692 x 2, 32T3265, 32T3266, 32T3267 x 4, 32T3268 x 4, 32T3269, 32T3333, 32T3334, 32T3335, 32T7344
32T3266 $D_4^2.C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $((C_8 : C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $D_4^2.C_4$ x 2 16T671 x 2, 16T692 x 2, 32T3265 x 2, 32T3267 x 4, 32T3268 x 4, 32T3269, 32T3333, 32T3334, 32T3335, 32T7344
32T3267 $D_4^2.C_4$ $256$ $1$ $C_2$, $C_4$, $C_2^3: C_4$, $((C_8 : C_2):C_2):C_2$, $C_2\wr C_4$, $D_4^2.C_4$, $D_4^2.C_4$ 16T671 x 2, 16T692 x 2, 32T3265 x 2, 32T3266, 32T3267 x 3, 32T3268 x 4, 32T3269, 32T3333, 32T3334, 32T3335, 32T7344
32T3268 $D_4^2.C_4$ $256$ $1$ $C_2$, $C_4$, $C_2^3: C_4$, $((C_8 : C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $D_4^2.C_4$, $D_4^2.C_4$ 16T671 x 2, 16T692 x 2, 32T3265 x 2, 32T3266, 32T3267 x 4, 32T3268 x 3, 32T3269, 32T3333, 32T3334, 32T3335, 32T7344
32T3269 $D_4^2.C_4$ $256$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$, $((C_8 : C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $D_4^2.C_4$ x 2 16T671 x 2, 16T692 x 2, 32T3265 x 2, 32T3266, 32T3267 x 4, 32T3268 x 4, 32T3333, 32T3334, 32T3335, 32T7344
32T3292 $C_2^2.C_2\wr C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $((C_8 : C_2):C_2):C_2$, $(((C_4 \times C_2): C_2):C_2):C_2$, $C_2\wr C_4$, $C_2^2.C_2\wr C_4$ x 2 16T680 x 2, 16T681 x 2, 32T3293 x 2, 32T3294, 32T3295, 32T3296, 32T7423, 32T7428
32T3293 $C_2^2.C_2\wr C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $C_2^2.C_2\wr C_4$, $C_2^2.C_2\wr C_4$ 16T680 x 2, 16T681 x 2, 32T3292, 32T3293, 32T3294, 32T3295, 32T3296, 32T7423, 32T7428
32T3294 $C_2^2.C_2\wr C_4$ $256$ $1$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $C_2^2.C_2\wr C_4$ x 2 16T680 x 2, 16T681 x 2, 32T3292, 32T3293 x 2, 32T3295, 32T3296, 32T7423, 32T7428
32T3295 $C_2^2.C_2\wr C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $((C_8 : C_2):C_2):C_2$, $(((C_4 \times C_2): C_2):C_2):C_2$, $C_2\wr C_4$, $C_2^2.C_2\wr C_4$ x 2 16T680 x 2, 16T681 x 2, 32T3292, 32T3293 x 2, 32T3294, 32T3296, 32T7423, 32T7428
32T3296 $C_2^2.C_2\wr C_4$ $256$ $1$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $C_2^2.C_2\wr C_4$ x 2 16T680 x 2, 16T681 x 2, 32T3292, 32T3293 x 2, 32T3294, 32T3295, 32T7423, 32T7428
32T3300 $(C_4\times C_8).D_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $(C_4\times C_8).D_4$ x 2 16T683 x 2, 32T3301, 32T3302, 32T7129, 32T7207, 32T7208, 32T7296
32T3301 $(C_4\times C_8).D_4$ $256$ $1$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $(C_4\times C_8).D_4$ x 2 16T683 x 2, 32T3300, 32T3302, 32T7129, 32T7207, 32T7208, 32T7296
32T3302 $(C_4\times C_8).D_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $((C_8 : C_2):C_2):C_2$, $(((C_4 \times C_2): C_2):C_2):C_2$, $C_2\wr C_4$, $(C_4\times C_8).D_4$ x 2 16T683 x 2, 32T3300, 32T3301, 32T7129, 32T7207, 32T7208, 32T7296
32T3314 $D_4^2:C_4$ $256$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$, $((C_8 : C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $D_4^2:C_4$ x 2 16T663 x 2, 16T685 x 2, 16T688 x 2, 32T3233 x 2, 32T3234, 32T3235 x 4, 32T3236 x 4, 32T3237, 32T3315, 32T3316, 32T3322, 32T3323, 32T7298
32T3315 $D_4^2:C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $((C_8 : C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $D_4^2:C_4$ x 2 16T663 x 2, 16T685 x 2, 16T688 x 2, 32T3233 x 2, 32T3234, 32T3235 x 4, 32T3236 x 4, 32T3237, 32T3314, 32T3316, 32T3322, 32T3323, 32T7298
32T3316 $D_4^2:C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $((C_8 : C_2):C_2):C_2$, $(((C_4 \times C_2): C_2):C_2):C_2$, $C_2\wr C_4$, $D_4^2:C_4$ x 2 16T663 x 2, 16T685 x 2, 16T688 x 2, 32T3233 x 2, 32T3234, 32T3235 x 4, 32T3236 x 4, 32T3237, 32T3314, 32T3315, 32T3322, 32T3323, 32T7298
32T3322 $D_4^2:C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $D_4^2:C_4$ x 2 16T663 x 2, 16T685 x 2, 16T688 x 2, 32T3233 x 2, 32T3234, 32T3235 x 4, 32T3236 x 4, 32T3237, 32T3314, 32T3315, 32T3316, 32T3323, 32T7298
32T3323 $D_4^2:C_4$ $256$ $1$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $D_4^2:C_4$ x 2 16T663 x 2, 16T685 x 2, 16T688 x 2, 32T3233 x 2, 32T3234, 32T3235 x 4, 32T3236 x 4, 32T3237, 32T3314, 32T3315, 32T3316, 32T3322, 32T7298
32T3329 $C_8:C_8:C_4$ $256$ $1$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_4^2:C_4$, $C_8:C_8:C_4$ x 2 16T690 x 4, 32T3329, 32T3330 x 2, 32T3331 x 2, 32T7243 x 2
32T3330 $C_8:C_8:C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_4^2:C_4$, $C_8:C_8:C_4$ x 2 16T690 x 4, 32T3329 x 2, 32T3330, 32T3331 x 2, 32T7243 x 2
32T3331 $C_8:C_8:C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_4^2:C_4$, $C_8:C_8:C_4$ x 2 16T690 x 4, 32T3329 x 2, 32T3330 x 2, 32T3331, 32T7243 x 2
32T3333 $D_4^2.C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $((C_8 : C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $D_4^2.C_4$ x 2 16T671 x 2, 16T692 x 2, 32T3265 x 2, 32T3266, 32T3267 x 4, 32T3268 x 4, 32T3269, 32T3334, 32T3335, 32T7344
32T3334 $D_4^2.C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $((C_8 : C_2):C_2):C_2$, $(((C_4 \times C_2): C_2):C_2):C_2$, $C_2\wr C_4$, $D_4^2.C_4$ x 2 16T671 x 2, 16T692 x 2, 32T3265 x 2, 32T3266, 32T3267 x 4, 32T3268 x 4, 32T3269, 32T3333, 32T3335, 32T7344
32T3335 $D_4^2.C_4$ $256$ $1$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$, $((C_8 : C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $D_4^2.C_4$ x 2 16T671 x 2, 16T692 x 2, 32T3265 x 2, 32T3266, 32T3267 x 4, 32T3268 x 4, 32T3269, 32T3333, 32T3334, 32T7344
32T3339 $C_8^2:C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_4^2:C_4$, $C_8^2:C_4$ 16T694 x 4, 32T3339 x 3, 32T3340 x 2, 32T3341 x 2
32T3340 $C_8^2:C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_4^2:C_4$, $C_8^2:C_4$ x 2 16T694 x 4, 32T3339 x 4, 32T3340, 32T3341 x 2
32T3341 $C_8^2:C_4$ $256$ $1$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_4^2:C_4$, $C_8^2:C_4$ x 2 16T694 x 4, 32T3339 x 4, 32T3340 x 2, 32T3341
32T3371 $Q_8^2:C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $((C_8 : C_2):C_2):C_2$, $(((C_4 \times C_2): C_2):C_2):C_2$, $C_2\wr C_4$, $Q_8^2:C_4$ 16T704 x 2, 32T3371, 32T3372, 32T3373, 32T7125, 32T7295
32T3372 $Q_8^2:C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $Q_8^2:C_4$ x 2 16T704 x 2, 32T3371 x 2, 32T3373, 32T7125, 32T7295
32T3373 $Q_8^2:C_4$ $256$ $1$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_2\wr C_4$, $Q_8^2:C_4$ x 2 16T704 x 2, 32T3371 x 2, 32T3372, 32T7125, 32T7295
32T6762 $C_8^2:C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_4^2:C_4$ 32T6762, 32T7392 x 4
32T6763 $C_8^2.C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_4^2:C_4$ 32T6763 x 3
32T6765 $C_8^2.C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_4^2:C_4$ 32T6765, 32T7240 x 4
32T6767 $C_8:C_8:C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_4^2:C_4$ 32T6767, 32T7394 x 2
32T6768 $C_8^2:C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_4^2:C_4$ 32T6768, 32T7241 x 2, 32T7395 x 2
32T6769 $C_8:C_8.C_4$ $256$ $1$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_4^2:C_4$ 32T6769, 32T7242 x 2
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Results are complete for degrees $\leq 23$.