↑

Learn more

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

Refine search

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

Results (1-50 of 55 matches)

Next   displayed columns for results
Label Name Order Parity Solvable $\#\Aut(F/K)$ Subfields Low Degree Siblings
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
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
16T27 $C_4^2:C_2$ $32$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $Q_8:C_2$ x 3 32T13
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
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
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
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
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
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
16T51 $C_4^2:C_2$ $32$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 6, $D_4\times C_2$ x 3 16T51 x 3, 32T29
16T54 $C_2^2.D_4$ $32$ $1$ ✓ $8$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $Q_8:C_2$ x 2 16T37, 16T54, 32T23
16T67 $C_4.C_2^4$ $64$ $1$ ✓ $4$ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$ 16T67 x 14, 32T52 x 15
16T68 $C_4^2:C_2^2$ $64$ $1$ ✓ $4$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$, $Q_8:C_2^2$ x 2 16T68 x 7, 32T53 x 8, 32T54 x 2
16T69 $D_4:C_2^3$ $64$ $1$ ✓ $4$ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2^2$ x 2 16T69 x 23, 32T55 x 18
16T70 $C_8.C_2^3$ $64$ $1$ ✓ $4$ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$ 16T70 x 2, 32T56 x 6, 32T57
16T73 $C_4^2:C_2^2$ $64$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$, $Q_8:C_2^2$ x 2 16T73 x 7, 32T62 x 4, 32T63 x 2, 32T269 x 2
16T74 $C_4^2:C_4$ $64$ $1$ ✓ $4$ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$ 16T74 x 3, 16T123, 32T64 x 2, 32T131
16T79 $C_2^4:C_4$ $64$ $1$ ✓ $8$ $C_2$, $C_4$, $D_{4}$ x 6, $C_2^2:C_4$ x 3, $C_2^2 \wr C_2$ x 4 16T79 x 31, 32T72 x 12
16T81 $C_4^2:C_2^2$ $64$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $Q_8:C_2$ x 2, $Q_8:C_2^2$ 16T81 x 3, 32T75 x 4, 32T76, 32T233
16T82 $C_4^2:C_2^2$ $64$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $Q_8:C_2$, $Q_8:C_2^2$ x 2 16T82 x 3, 32T77 x 2, 32T78 x 2, 32T234 x 2
16T83 $C_4^2:C_2^2$ $64$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $Q_8:C_2^2$ x 3 16T83 x 3, 32T79 x 2, 32T80, 32T270 x 3
16T87 $C_2^3:D_4$ $64$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$, $Q_8:C_2^2$ x 2 16T87 x 7, 16T119 x 4, 32T85 x 4, 32T86 x 4, 32T128 x 2
16T95 $C_2^2:\OD_{16}$ $64$ $1$ ✓ $8$ $C_2$, $C_4$, $D_{4}$ x 2, $C_8:C_2$ x 2, $C_2^2:C_4$ 16T95 x 7, 32T96 x 4, 32T97 x 2
16T97 $C_2^3:Q_8$ $64$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $Q_8$, $Q_8:C_2^2$ x 2 16T97 x 3, 32T98 x 6
16T98 $C_4^2:C_2^2$ $64$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $Q_8:C_2^2$ x 3 16T98 x 7, 32T99 x 6
16T105 $C_2^3:D_4$ $64$ $1$ ✓ $8$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 6, $D_4\times C_2$ x 3, $C_2^2 \wr C_2$ x 4 16T105 x 31, 32T109 x 12, 32T275 x 2
16T108 $C_4.C_4^2$ $64$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $Q_8$ 32T113 x 3
16T109 $D_4^2$ $64$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 4, $D_4\times C_2$ x 2, $Q_8:C_2^2$ 16T109 x 15, 32T114 x 8, 32T115 x 4
16T115 $D_4:D_4$ $64$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$, $Q_8:C_2$, $Q_8:C_2^2$ 16T115 x 7, 32T120 x 2, 32T121 x 4, 32T122 x 2, 32T225
16T117 $C_4^2:C_2^2$ $64$ $1$ ✓ $8$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$, $Q_8:C_2$ x 2 16T117 x 7, 32T125 x 4, 32T126 x 2, 32T236 x 2
16T119 $C_2^3:D_4$ $64$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $Q_8:C_2^2$ x 2 16T87 x 8, 16T119 x 3, 32T85 x 4, 32T86 x 4, 32T128 x 2
16T123 $C_4^2:C_4$ $64$ $1$ ✓ $4$ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$ 16T74 x 4, 32T64 x 2, 32T131
16T125 $C_{16}:C_4$ $64$ $-1$ ✓ $4$ $C_2$, $C_4$, $C_8:C_2$ 32T133
16T197 $C_2^4:C_2^3$ $128$ $1$ ✓ $2$ $C_2$ x 7, $C_2^2$ x 7, $C_2^3$ 16T197 x 29, 32T421 x 105
Next   displayed columns for results