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The results below are complete, since the LMFDB contains all transitive groups of degree at most 47 (except 32)

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Parity Cyclic Solvable Primitive Equivalent siblings
Degree $T$-number Order Group Nilpotency class
$\#\Aut(F/K)$ Transitivity
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Results (11 matches)

  displayed columns for results
Label Name Order Parity Solvable $\#\Aut(F/K)$ Subfields Low Degree Siblings
8T6 $D_{8}$ $16$ $-1$ ✓ $2$ $C_2$, $D_{4}$ 8T6, 16T13
8T8 $QD_{16}$ $16$ $-1$ ✓ $2$ $C_2$, $D_{4}$ 16T12
8T15 $Z_8 : Z_8^\times$ $32$ $-1$ ✓ $2$ $C_2$, $D_{4}$ 8T15, 16T35, 16T38 x 2, 16T45, 32T21
8T16 $(C_8:C_2):C_2$ $32$ $-1$ ✓ $2$ $C_2$, $C_4$ 8T16, 16T36, 16T41 x 2, 32T22
8T17 $C_4\wr C_2$ $32$ $-1$ ✓ $4$ $C_2$, $D_{4}$ 8T17, 16T28, 16T42, 32T14
8T19 $C_2^3 : C_4 $ $32$ $1$ ✓ $2$ $C_2$, $D_{4}$ 8T19, 8T20, 8T21, 16T33 x 2, 16T52, 16T53, 32T19
8T20 $C_2^3: C_4$ $32$ $1$ ✓ $2$ $C_2$, $C_4$ 8T19 x 2, 8T21, 16T33 x 2, 16T52, 16T53, 32T19
8T21 $C_2^3: C_4$ $32$ $-1$ ✓ $2$ $C_2$ x 3, $C_2^2$ 8T19 x 2, 8T20, 16T33 x 2, 16T52, 16T53, 32T19
8T26 $(C_4^2 : C_2):C_2$ $64$ $-1$ ✓ $2$ $C_2$, $D_{4}$ 8T26 x 3, 16T135 x 2, 16T141 x 2, 16T142 x 2, 16T152 x 2, 32T147 x 2, 32T148 x 2, 32T155, 32T156
8T29 $(((C_4 \times C_2): C_2):C_2):C_2$ $64$ $1$ ✓ $2$ $C_2$, $D_{4}$ 8T29 x 5, 8T31 x 2, 16T127, 16T128 x 3, 16T129 x 3, 16T147, 16T149 x 6, 16T150 x 3, 32T136 x 3, 32T137 x 2, 32T163 x 3
8T31 $(((C_4 \times C_2): C_2):C_2):C_2$ $64$ $-1$ ✓ $2$ $C_2$ x 3, $C_2^2$ 8T29 x 6, 8T31, 16T127, 16T128 x 3, 16T129 x 3, 16T147, 16T149 x 6, 16T150 x 3, 32T136 x 3, 32T137 x 2, 32T163 x 3
  displayed columns for results