Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
16T15 |
$C_2 \times (C_8:C_2)$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$, $C_8:C_2$ x 2 |
16T15, 32T1 |
16T16 |
$(C_8:C_2):C_2$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$ |
16T16 x 2, 32T2 |
16T17 |
$C_4^2:C_2$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$, $Q_8:C_2$ x 2 |
16T17, 32T3 |
16T18 |
$C_2 \times (C_4\times C_2):C_2$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2$ x 2 |
16T18 x 5, 32T4 |
16T19 |
$C_4 \times D_4$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ 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 |
$(C_2 \times Q_8):C_2$ |
$32$ |
$1$ |
✓ |
$2$ |
$17$ |
$C_2$ x 7, $C_2^2$ x 7, $C_2^3$ |
16T20 x 4, 32T6 |
16T21 |
$C_2 \times (C_2^2:C_4)$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ 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 |
$C_{16} : C_2$ |
$32$ |
$-1$ |
✓ |
$2$ |
$20$ |
$C_2$, $C_4$, $C_8$ |
32T8 |
16T23 |
$Q_8 : C_2^2$ |
$32$ |
$1$ |
✓ |
$2$ |
$17$ |
$C_2$ 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 |
$C_2^2 : C_8$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$, $C_4$, $D_{4}$ x 2, $C_8$, $C_8:C_2$, $C_2^2:C_4$ |
16T24, 32T10 |
16T25 |
$C_2^2 \times D_4$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ 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 |
$D_4:C_4$ |
$32$ |
$1$ |
✓ |
$3$ |
$14$ |
$C_2$, $C_4$, $D_{4}$ x 2, $D_{8}$, $QD_{16}$, $C_2^2:C_4$ |
16T26, 32T12 |
16T27 |
$C_4^2:C_2$ |
$32$ |
$1$ |
✓ |
$2$ |
$14$ |
$C_2$ x 3, $C_2^2$, $Q_8:C_2$ x 3 |
32T13 |
16T28 |
$C_4\wr C_2$ |
$32$ |
$1$ |
✓ |
$3$ |
$14$ |
$C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$ |
8T17 x 2, 16T42, 32T14 |
16T29 |
$C_2\times D_8$ |
$32$ |
$1$ |
✓ |
$3$ |
$14$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_{8}$ x 2, $D_4\times C_2$ |
16T29 x 3, 32T15 |
16T30 |
$C_4^2:C_2$ |
$32$ |
$1$ |
✓ |
$2$ |
$14$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$, $Q_8:C_2$ x 2 |
16T30, 32T16 |
16T31 |
$C_2^2:Q_8$ |
$32$ |
$1$ |
✓ |
$2$ |
$14$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $Q_8$, $D_4\times C_2$, $Q_8:C_2$ |
16T31, 32T17 |
16T32 |
$Q_{16}:C_2$ |
$32$ |
$1$ |
✓ |
$3$ |
$11$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$ |
16T50, 32T18 |
16T33 |
$C_2^3:C_4$ |
$32$ |
$1$ |
✓ |
$3$ |
$11$ |
$C_2$ 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 |
$C_4:D_4$ |
$32$ |
$1$ |
✓ |
$2$ |
$14$ |
$C_2$ 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 |
$D_8:C_2$ |
$32$ |
$1$ |
✓ |
$3$ |
$11$ |
$C_2$ 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 |
$\OD_{16}:C_2$ |
$32$ |
$1$ |
✓ |
$3$ |
$11$ |
$C_2$ 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 |
$C_2^2.D_4$ |
$32$ |
$1$ |
✓ |
$2$ |
$14$ |
$C_2$ 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 |
$D_8:C_2$ |
$32$ |
$1$ |
✓ |
$3$ |
$11$ |
$C_2$ 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 |
$C_2^2\wr C_2$ |
$32$ |
$1$ |
✓ |
$2$ |
$14$ |
$C_2$ 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 |
$C_4.D_4$ |
$32$ |
$1$ |
✓ |
$3$ |
$11$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$ |
32T25 |
16T41 |
$\OD_{16}:C_2$ |
$32$ |
$1$ |
✓ |
$3$ |
$11$ |
$C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(C_8:C_2):C_2$ |
8T16 x 2, 16T36, 16T41, 32T22 |
16T42 |
$C_4\wr C_2$ |
$32$ |
$1$ |
✓ |
$3$ |
$14$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $C_4\wr C_2$ x 2 |
8T17 x 2, 16T28, 32T14 |
16T43 |
$C_4:D_4$ |
$32$ |
$1$ |
✓ |
$2$ |
$14$ |
$C_2$ 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 |
$D_8:C_2$ |
$32$ |
$1$ |
✓ |
$3$ |
$14$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$ |
16T44, 16T47, 32T26 |
16T45 |
$D_8:C_2$ |
$32$ |
$1$ |
✓ |
$3$ |
$11$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$ |
8T15 x 2, 16T35, 16T38 x 2, 32T21 |
16T46 |
$C_2^2\wr C_2$ |
$32$ |
$1$ |
✓ |
$2$ |
$14$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 6, $D_4\times C_2$ x 3 |
8T18 x 8, 16T39 x 6, 32T24 |
16T47 |
$D_8:C_2$ |
$32$ |
$1$ |
✓ |
$3$ |
$14$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$ |
16T44 x 2, 32T26 |
16T48 |
$C_2\times \SD_{16}$ |
$32$ |
$1$ |
✓ |
$3$ |
$14$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $QD_{16}$ x 2, $D_4\times C_2$ |
16T48, 32T27 |
16T49 |
$C_8.C_4$ |
$32$ |
$1$ |
✓ |
$3$ |
$14$ |
$C_2$ x 3, $C_2^2$, $Q_8$ |
32T28 |
16T50 |
$Q_{16}:C_2$ |
$32$ |
$1$ |
✓ |
$3$ |
$11$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$ |
16T32, 32T18 |
16T51 |
$C_4^2:C_2$ |
$32$ |
$1$ |
✓ |
$2$ |
$14$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 6, $D_4\times C_2$ x 3 |
16T51 x 3, 32T29 |
16T52 |
$C_2^3:C_4$ |
$32$ |
$1$ |
✓ |
$3$ |
$11$ |
$C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $C_2^3: C_4$ |
8T19 x 2, 8T20, 8T21, 16T33 x 2, 16T53, 32T19 |
16T53 |
$C_2^3:C_4$ |
$32$ |
$1$ |
✓ |
$3$ |
$11$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$, $C_2^3: C_4$, $C_2^3: C_4$ |
8T19 x 2, 8T20, 8T21, 16T33 x 2, 16T52, 32T19 |
16T54 |
$C_2^2.D_4$ |
$32$ |
$1$ |
✓ |
$2$ |
$14$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $Q_8:C_2$ x 2 |
16T37, 16T54, 32T23 |
16T55 |
$\SD_{32}$ |
$32$ |
$-1$ |
✓ |
$4$ |
$11$ |
$C_2$, $D_{4}$, $D_{8}$ |
32T30 |
16T56 |
$D_{16}$ |
$32$ |
$-1$ |
✓ |
$4$ |
$11$ |
$C_2$, $D_{4}$, $D_{8}$ |
16T56, 32T31 |
16T57 |
$C_4\times A_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $C_4$, $A_4$, $A_4\times C_2$ |
12T29, 24T55, 24T56 |
16T58 |
$C_2^2\times A_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$ x 3, $C_2^2$, $A_4$, $A_4\times C_2$ x 3 |
12T25 x 3, 12T26 x 2, 24T49 x 3, 24T50 |
16T59 |
$C_2\times \SL(2,3)$ |
$48$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $A_4$, $\SL(2,3)$ x 2, $A_4\times C_2$ |
|
16T60 |
$\SL(2,3):C_2$ |
$48$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $A_4$, $A_4\times C_2$ |
24T21 |
16T61 |
$C_2\times S_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$10$ |
$C_2$ x 3, $C_2^2$, $S_4$, $S_4$, $S_4\times C_2$ x 2 |
6T11 x 2, 8T24 x 2, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 24T46, 24T47, 24T48 x 2 |
16T62 |
$A_4:C_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $C_4$, $S_4$, $S_4$ |
12T27, 12T30, 24T51, 24T57 |
16T63 |
$C_4^2:C_3$ |
$48$ |
$1$ |
✓ |
$-1$ |
$8$ |
$A_4$ |
12T31 x 2, 24T58 |
16T64 |
$C_2^2:A_4$ |
$48$ |
$1$ |
✓ |
$-1$ |
$8$ |
$A_4$ x 5 |
12T32 x 10, 24T59 x 5 |
Results are complete for degrees $\leq 23$.