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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 (1-50 of 1954 matches)

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Label Name Order Parity Solvable $\#\Aut(F/K)$ Subfields Low Degree Siblings
16T1 $C_{16}$ $16$ $-1$ ✓ $16$ $C_2$, $C_4$, $C_8$
16T2 $C_4\times C_2^2$ $16$ $1$ ✓ $16$ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$
16T3 $C_2^4$ $16$ $1$ ✓ $16$ $C_2$ x 15, $C_2^2$ x 35, $C_2^3$ x 15
16T4 $C_4^2$ $16$ $1$ ✓ $16$ $C_2$ x 3, $C_4$ x 6, $C_2^2$, $C_4\times C_2$ x 3
16T5 $C_8\times C_2$ $16$ $1$ ✓ $16$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_8$ x 2, $C_4\times C_2$
16T6 $C_8: C_2$ $16$ $1$ ✓ $16$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$, $C_8:C_2$ 8T7
16T7 $Q_8\times C_2$ $16$ $1$ ✓ $16$ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8$ x 2
16T8 $C_4:C_4$ $16$ $1$ ✓ $16$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 2, $C_4\times C_2$, $D_4$, $Q_8$
16T9 $D_4\times C_2$ $16$ $1$ ✓ $16$ $C_2$ 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 8T9 x 4
16T10 $C_2^2 : C_4$ $16$ $1$ ✓ $16$ $C_2$ 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 8T10 x 2
16T11 $Q_8 : C_2$ $16$ $1$ ✓ $16$ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2$ x 3 8T11 x 3
16T12 $QD_{16}$ $16$ $1$ ✓ $16$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $QD_{16}$ 8T8
16T13 $D_{8}$ $16$ $1$ ✓ $16$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $D_{8}$ x 2 8T6 x 2
16T14 $Q_{16}$ $16$ $1$ ✓ $16$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$
16T15 $C_2 \times (C_8:C_2)$ $32$ $1$ ✓ $8$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$, $C_8:C_2$ x 2 16T15, 32T1
16T16 $(C_8:C_2):C_2$ $32$ $1$ ✓ $8$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$ 16T16 x 2, 32T2
16T17 $C_4^2:C_2$ $32$ $1$ ✓ $8$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$, $Q_8:C_2$ x 2 16T17, 32T3
16T18 $C_2 \times (C_4\times C_2):C_2$ $32$ $1$ ✓ $8$ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2$ x 2 16T18 x 5, 32T4
16T19 $C_4 \times D_4$ $32$ $1$ ✓ $8$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 2, $C_4\times C_2$, $D_4\times C_2$, $Q_8:C_2$ 16T19 x 3, 32T5
16T20 $(C_2 \times Q_8):C_2$ $32$ $1$ ✓ $8$ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$ 16T20 x 4, 32T6
16T21 $C_2 \times (C_2^2:C_4)$ $32$ $1$ ✓ $8$ $C_2$ 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 16T21 x 3, 32T7
16T22 $C_{16} : C_2$ $32$ $-1$ ✓ $8$ $C_2$, $C_4$, $C_8$ 32T8
16T23 $Q_8 : C_2^2$ $32$ $1$ ✓ $8$ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2^2$ x 2 8T22 x 6, 16T23 x 8, 32T9
16T24 $C_2^2 : C_8$ $32$ $1$ ✓ $8$ $C_2$, $C_4$, $D_{4}$ x 2, $C_8$, $C_8:C_2$, $C_2^2:C_4$ 16T24, 32T10
16T25 $C_2^2 \times D_4$ $32$ $1$ ✓ $8$ $C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4\times C_2$ x 6 16T25 x 7, 32T11
16T26 $D_4:C_4$ $32$ $1$ ✓ $4$ $C_2$, $C_4$, $D_{4}$ x 2, $D_{8}$, $QD_{16}$, $C_2^2:C_4$ 16T26, 32T12
16T27 $C_4^2:C_2$ $32$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $Q_8:C_2$ x 3 32T13
16T28 $C_4\wr C_2$ $32$ $1$ ✓ $4$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$ 8T17 x 2, 16T42, 32T14
16T29 $C_2\times D_8$ $32$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_{8}$ x 2, $D_4\times C_2$ 16T29 x 3, 32T15
16T30 $C_4^2:C_2$ $32$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$, $Q_8:C_2$ x 2 16T30, 32T16
16T31 $C_2^2:Q_8$ $32$ $1$ ✓ $8$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $Q_8$, $D_4\times C_2$, $Q_8:C_2$ 16T31, 32T17
16T32 $Q_{16}:C_2$ $32$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$ 16T50, 32T18
16T33 $C_2^3:C_4$ $32$ $1$ ✓ $8$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $C_2^3 : C_4 $, $C_2^3: C_4$ 8T19 x 2, 8T20, 8T21, 16T33, 16T52, 16T53, 32T19
16T34 $C_4:D_4$ $32$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 4, $D_4\times C_2$ x 2, $Q_8:C_2$ 16T34, 16T43 x 2, 32T20
16T35 $D_8:C_2$ $32$ $1$ ✓ $8$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $Z_8 : Z_8^\times$ x 2 8T15 x 2, 16T38 x 2, 16T45, 32T21
16T36 $\OD_{16}:C_2$ $32$ $1$ ✓ $8$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$, $(C_8:C_2):C_2$ x 2 8T16 x 2, 16T41 x 2, 32T22
16T37 $C_2^2.D_4$ $32$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$, $Q_8:C_2$ x 2 16T54 x 2, 32T23
16T38 $D_8:C_2$ $32$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$, $Z_8 : Z_8^\times$ x 2 8T15 x 2, 16T35, 16T38, 16T45, 32T21
16T39 $C_2^2\wr C_2$ $32$ $1$ ✓ $8$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 6, $D_4$, $D_4\times C_2$ x 2, $C_2^2 \wr C_2$ x 4 8T18 x 8, 16T39 x 5, 16T46, 32T24
16T40 $C_4.D_4$ $32$ $1$ ✓ $8$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$ 32T25
16T41 $\OD_{16}:C_2$ $32$ $1$ ✓ $4$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(C_8:C_2):C_2$ 8T16 x 2, 16T36, 16T41, 32T22
16T42 $C_4\wr C_2$ $32$ $1$ ✓ $8$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $C_4\wr C_2$ x 2 8T17 x 2, 16T28, 32T14
16T43 $C_4:D_4$ $32$ $1$ ✓ $8$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 4, $D_4$, $D_4\times C_2$, $Q_8:C_2$ 16T34 x 2, 16T43, 32T20
16T44 $D_8:C_2$ $32$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$ 16T44, 16T47, 32T26
16T45 $D_8:C_2$ $32$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$ 8T15 x 2, 16T35, 16T38 x 2, 32T21
16T46 $C_2^2\wr C_2$ $32$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 6, $D_4\times C_2$ x 3 8T18 x 8, 16T39 x 6, 32T24
16T47 $D_8:C_2$ $32$ $1$ ✓ $8$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$ 16T44 x 2, 32T26
16T48 $C_2\times \SD_{16}$ $32$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $QD_{16}$ x 2, $D_4\times C_2$ 16T48, 32T27
16T49 $C_8.C_4$ $32$ $1$ ✓ $8$ $C_2$ x 3, $C_2^2$, $Q_8$ 32T28
16T50 $Q_{16}:C_2$ $32$ $1$ ✓ $8$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$ 16T32, 32T18
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