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Results (displaying both matches)

Label Name Order Parity Solvable Subfields Low Degree Siblings
4T3 $D_{4}$ $8$ $-1$ yes $C_2$ 4T3, 8T4
8T4 $D_4$ $8$ $1$ yes $C_2$ x 3, $C_2^2$, $D_{4}$ x 2 4T3 x 2

Results are complete for degrees $\leq 23$.