Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
32T1 |
$C_2\times \OD_{16}$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $C_8:C_2$ x 2, $C_4\times C_2^2$, $C_8: C_2$ x 2, $C_2 \times (C_8:C_2)$ x 2 |
16T15 x 2 |
32T2 |
$\OD_{16}:C_2$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $C_4\times C_2^2$, $(C_8:C_2):C_2$ x 3 |
16T16 x 3 |
32T3 |
$C_4^2:C_2$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $Q_8:C_2$ x 6, $C_4\times C_2^2$, $Q_8 : C_2$ x 2, $C_4^2:C_2$ x 2 |
16T17 x 2 |
32T4 |
$D_4:C_2^2$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ x 15, $C_2^2$ x 35, $C_2^3$ x 15, $Q_8:C_2$ x 6, $C_2^4$, $Q_8 : C_2$ x 2, $C_2 \times (C_4\times C_2):C_2$ x 6 |
16T18 x 6 |
32T5 |
$C_4\times D_4$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $D_{4}$ x 4, $C_4\times C_2$ x 6, $C_2^3$, $D_4$ x 2, $D_4\times C_2$ x 4, $Q_8:C_2$ x 3, $C_4\times C_2^2$, $D_4\times C_2$, $Q_8 : C_2$, $C_4 \times D_4$ x 4 |
16T19 x 4 |
32T6 |
$C_4.C_2^3$ |
$32$ |
$1$ |
✓ |
$2$ |
$17$ |
$C_2$ x 15, $C_2^2$ x 35, $C_2^3$ x 15, $C_2^4$, $(C_2 \times Q_8):C_2$ x 5 |
16T20 x 5 |
32T7 |
$C_2^3:C_4$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $D_{4}$ x 8, $C_4\times C_2$ x 6, $C_2^3$, $D_4$ x 4, $D_4\times C_2$ x 8, $C_2^2:C_4$ x 8, $C_4\times C_2^2$, $D_4\times C_2$ x 2, $C_2^2 : C_4$ x 4, $C_2 \times (C_2^2:C_4)$ x 4 |
16T21 x 4 |
32T8 |
$\OD_{32}$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_8$ x 2, $C_4\times C_2$, $C_8\times C_2$, $C_{16} : C_2$ |
16T22 |
32T9 |
$D_4:C_2^2$ |
$32$ |
$1$ |
✓ |
$2$ |
$17$ |
$C_2$ x 15, $C_2^2$ x 35, $C_2^3$ x 15, $Q_8:C_2^2$ x 6, $C_2^4$, $Q_8 : C_2^2$ x 9 |
8T22 x 6, 16T23 x 9 |
32T10 |
$C_2^2:C_8$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_8$ x 2, $C_4\times C_2$, $D_4$ x 2, $C_8:C_2$, $C_2^2:C_4$ x 2, $C_8\times C_2$, $C_8: C_2$, $C_2^2 : C_4$, $C_2^2 : C_8$ x 2 |
16T24 x 2 |
32T11 |
$C_2^2\times D_4$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ x 15, $C_2^2$ x 35, $D_{4}$ x 8, $C_2^3$ x 15, $D_4$ x 4, $D_4\times C_2$ x 24, $C_2^4$, $D_4\times C_2$ x 6, $C_2^2 \times D_4$ x 8 |
16T25 x 8 |
32T13 |
$C_4^2:C_2$ |
$32$ |
$1$ |
✓ |
$2$ |
$14$ |
$C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2$ x 9, $Q_8 : C_2$ x 3, $C_4^2:C_2$ |
16T27 |
32T16 |
$C_4^2:C_2$ |
$32$ |
$1$ |
✓ |
$2$ |
$14$ |
$C_2$ 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, $Q_8:C_2$ x 6, $D_4\times C_2$, $Q_8 : C_2$ x 2, $C_4^2:C_2$ x 2 |
16T30 x 2 |
32T17 |
$C_2^2:Q_8$ |
$32$ |
$1$ |
✓ |
$2$ |
$14$ |
$C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $Q_8$ x 2, $D_4\times C_2$ x 4, $Q_8:C_2$ x 3, $Q_8\times C_2$, $D_4\times C_2$, $Q_8 : C_2$, $C_2^2:Q_8$ x 2 |
16T31 x 2 |
32T20 |
$C_4:D_4$ |
$32$ |
$1$ |
✓ |
$2$ |
$14$ |
$C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 8, $C_2^3$, $D_4$ x 4, $D_4\times C_2$ x 8, $Q_8:C_2$ x 3, $D_4\times C_2$ x 2, $Q_8 : C_2$, $C_4:D_4$ x 2, $C_4:D_4$ x 2 |
16T34 x 2, 16T43 x 2 |
32T23 |
$C_2^2.D_4$ |
$32$ |
$1$ |
✓ |
$2$ |
$14$ |
$C_2$ 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, $Q_8:C_2$ x 6, $D_4\times C_2$, $Q_8 : C_2$ x 2, $C_2^2.D_4$, $C_2^2.D_4$ x 2 |
16T37, 16T54 x 2 |
32T24 |
$C_2^2\wr C_2$ |
$32$ |
$1$ |
✓ |
$2$ |
$14$ |
$C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 12, $C_2^3$, $D_4$ x 6, $D_4\times C_2$ x 12, $C_2^2 \wr C_2$ x 8, $D_4\times C_2$ x 3, $C_2^2\wr C_2$ x 6, $C_2^2\wr C_2$ |
8T18 x 8, 16T39 x 6, 16T46 |
32T29 |
$C_4:D_4$ |
$32$ |
$1$ |
✓ |
$2$ |
$14$ |
$C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 12, $C_2^3$, $D_4$ x 6, $D_4\times C_2$ x 12, $D_4\times C_2$ x 3, $C_4^2:C_2$ x 4 |
16T51 x 4 |
32T35 |
$C_2^2.D_4$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $D_{4}$ x 4, $C_4\times C_2$ x 6, $C_2^3$, $D_4$ x 2, $Q_8$ x 2, $D_4\times C_2$ x 4, $C_4\times C_2^2$, $Q_8\times C_2$, $C_4:C_4$ x 4, $D_4\times C_2$ |
|
32T38 |
$C_4\times Q_8$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $Q_8$ x 2, $Q_8:C_2$ x 3, $C_4\times C_2^2$, $Q_8\times C_2$, $Q_8 : C_2$ |
|
32T40 |
$C_2^2\times Q_8$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ x 15, $C_2^2$ x 35, $C_2^3$ x 15, $Q_8$ x 4, $C_2^4$, $Q_8\times C_2$ x 6 |
|
32T41 |
$C_2.C_4^2$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ x 3, $C_4$ x 6, $C_2^2$, $D_{4}$ x 6, $C_4\times C_2$ x 3, $D_4$ x 3, $Q_8$, $C_2^2:C_4$ x 6, $C_4^2$, $C_4:C_4$ x 3, $C_2^2 : C_4$ x 3 |
|
32T42 |
$C_8:C_4$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ x 3, $C_4$ x 6, $C_2^2$, $C_4\times C_2$ x 3, $C_8:C_2$ x 2, $C_4^2$, $C_8: C_2$ x 2 |
|
32T44 |
$C_4:C_8$ |
$32$ |
$1$ |
✓ |
$2$ |
$20$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 2, $C_8$ x 2, $C_4\times C_2$, $D_4$, $Q_8$, $C_8:C_2$, $C_8\times C_2$, $C_8: C_2$, $C_4:C_4$ |
|
32T45 |
$C_4:Q_8$ |
$32$ |
$1$ |
✓ |
$2$ |
$14$ |
$C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4$ x 2, $Q_8$ x 4, $D_4\times C_2$ x 4, $Q_8\times C_2$ x 2, $D_4\times C_2$ |
|
32T46 |
$C_4.Q_8$ |
$32$ |
$1$ |
✓ |
$2$ |
$14$ |
$C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8$ x 2, $Q_8:C_2$ x 6, $Q_8\times C_2$, $Q_8 : C_2$ x 2 |
|
32T52 |
$C_4.C_2^4$ |
$64$ |
$1$ |
✓ |
$2$ |
$34$ |
$C_2$ x 15, $C_2^2$ x 35, $C_2^3$ x 15, $C_2^4$, $C_4.C_2^4$ x 3 |
16T67 x 15, 32T52 x 14 |
32T53 |
$C_4^2:C_2^2$ |
$64$ |
$1$ |
✓ |
$2$ |
$34$ |
$C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $Q_8:C_2^2$ x 4, $C_4\times C_2^2$, $Q_8 : C_2^2$ x 2, $C_4^2:C_2^2$ x 2 |
16T68 x 8, 32T53 x 7, 32T54 x 2 |
32T54 |
$C_4^2:C_2^2$ |
$64$ |
$1$ |
✓ |
$2$ |
$34$ |
$C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $Q_8:C_2^2$ x 4, $C_4\times C_2^2$, $Q_8 : C_2^2$ x 2, $C_4^2:C_2^2$ x 4 |
16T68 x 8, 32T53 x 8, 32T54 |
32T55 |
$D_4:C_2^3$ |
$64$ |
$1$ |
✓ |
$2$ |
$34$ |
$C_2$ x 15, $C_2^2$ x 35, $C_2^3$ x 15, $Q_8:C_2^2$ x 4, $C_2^4$, $Q_8 : C_2^2$ x 2, $D_4:C_2^3$ x 4 |
16T69 x 24, 32T55 x 17 |
32T56 |
$C_8.C_2^3$ |
$64$ |
$1$ |
✓ |
$2$ |
$34$ |
$C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $C_4\times C_2^2$, $C_8.C_2^3$ |
16T70 x 3, 32T56 x 5, 32T57 |
32T57 |
$C_8.C_2^3$ |
$64$ |
$1$ |
✓ |
$2$ |
$34$ |
$C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$, $C_4\times C_2^2$, $C_8.C_2^3$ x 3 |
16T70 x 3, 32T56 x 6 |
32T62 |
$C_4^2:C_2^2$ |
$64$ |
$1$ |
✓ |
$2$ |
$22$ |
$C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4\times C_2$ x 6, $Q_8:C_2^2$ x 4, $Q_8 : C_2^2$ x 2, $C_2^2 \times D_4$, $C_4^2:C_2^2$ x 4 |
16T73 x 8, 32T62 x 3, 32T63 x 2, 32T269 x 2 |
32T63 |
$C_4^2:C_2^2$ |
$64$ |
$1$ |
✓ |
$2$ |
$22$ |
$C_2$ 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, $Q_8:C_2^2$ x 4, $D_4\times C_2$, $Q_8 : C_2^2$ x 2, $C_4^2:C_2^2$ x 4 |
16T73 x 8, 32T62 x 4, 32T63, 32T269 x 2 |
32T64 |
$C_4^2:C_4$ |
$64$ |
$1$ |
✓ |
$2$ |
$22$ |
$C_2$ 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, $C_2^2 : C_4$, $C_4^2:C_4$ x 2, $C_4^2:C_4$ |
16T74 x 4, 16T123, 32T64, 32T131 |
32T72 |
$C_2^4:C_4$ |
$64$ |
$1$ |
✓ |
$2$ |
$28$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 12, $C_4\times C_2$, $D_4$ x 2, $D_4\times C_2$ x 4, $C_2^2:C_4$ x 10, $C_2^2 \wr C_2$ x 16, $C_2^2 : C_4$, $C_2 \times (C_2^2:C_4)$ x 2, $C_2^2\wr C_2$ x 4, $C_2^4:C_4$ x 8 |
16T79 x 32, 32T72 x 11 |
32T75 |
$C_4^2:C_2^2$ |
$64$ |
$1$ |
✓ |
$2$ |
$25$ |
$C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2$ x 5, $Q_8:C_2^2$ x 2, $Q_8 : C_2$, $C_2 \times (C_4\times C_2):C_2$, $Q_8 : C_2^2$, $C_4^2:C_2^2$ x 2 |
16T81 x 4, 32T75 x 3, 32T76, 32T233 |
32T76 |
$C_4^2:C_2^2$ |
$64$ |
$1$ |
✓ |
$2$ |
$25$ |
$C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2$ x 4, $Q_8:C_2^2$ x 2, $C_2 \times (C_4\times C_2):C_2$ x 2, $Q_8 : C_2^2$, $C_4^2:C_2^2$ x 4 |
16T81 x 4, 32T75 x 4, 32T233 |
32T77 |
$C_4^2:C_2^2$ |
$64$ |
$1$ |
✓ |
$2$ |
$22$ |
$C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2$ x 2, $Q_8:C_2^2$ x 4, $C_2 \times (C_4\times C_2):C_2$, $Q_8 : C_2^2$ x 2, $C_4^2:C_2^2$ x 4 |
16T82 x 4, 32T77, 32T78 x 2, 32T234 x 2 |
32T78 |
$C_4^2:C_2^2$ |
$64$ |
$1$ |
✓ |
$2$ |
$22$ |
$C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2$ x 3, $Q_8:C_2^2$ x 4, $Q_8 : C_2$, $Q_8 : C_2^2$ x 2, $C_4^2:C_2^2$ x 2 |
16T82 x 4, 32T77 x 2, 32T78, 32T234 x 2 |
32T79 |
$C_4^2:C_2^2$ |
$64$ |
$1$ |
✓ |
$2$ |
$19$ |
$C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2^2$ x 6, $Q_8 : C_2^2$ x 3, $C_4^2:C_2^2$ x 4 |
16T83 x 4, 32T79, 32T80, 32T270 x 3 |
32T80 |
$C_4^2:C_2^2$ |
$64$ |
$1$ |
✓ |
$2$ |
$19$ |
$C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2^2$ x 6, $Q_8 : C_2^2$ x 3, $C_4^2:C_2^2$ x 4 |
16T83 x 4, 32T79 x 2, 32T270 x 3 |
32T85 |
$C_2^3:D_4$ |
$64$ |
$1$ |
✓ |
$2$ |
$22$ |
$C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4\times C_2$ x 6, $Q_8:C_2^2$ x 4, $Q_8 : C_2^2$ x 2, $C_2^2 \times D_4$, $C_2^3:D_4$ x 4 |
16T87 x 8, 16T119 x 4, 32T85 x 3, 32T86 x 4, 32T128 x 2 |
32T86 |
$C_2^3:D_4$ |
$64$ |
$1$ |
✓ |
$2$ |
$22$ |
$C_2$ 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, $Q_8:C_2^2$ x 4, $D_4\times C_2$, $Q_8 : C_2^2$ x 2, $C_2^3:D_4$ x 2, $C_2^3:D_4$ x 2 |
16T87 x 8, 16T119 x 4, 32T85 x 4, 32T86 x 3, 32T128 x 2 |
32T96 |
$C_2^2:\OD_{16}$ |
$64$ |
$1$ |
✓ |
$2$ |
$28$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_4\times C_2$, $C_8:C_2$ x 3, $D_4\times C_2$ x 2, $C_2^2:C_4$ x 4, $C_8: C_2$, $C_2 \times (C_8:C_2)$, $C_2 \times (C_2^2:C_4)$, $C_2^2:\OD_{16}$ x 4 |
16T95 x 8, 32T96 x 3, 32T97 x 2 |
32T97 |
$C_2^2:\OD_{16}$ |
$64$ |
$1$ |
✓ |
$2$ |
$28$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 4, $C_4\times C_2$, $D_4$ x 2, $C_8:C_2$ x 4, $C_2^2:C_4$ x 2, $C_2^2 : C_4$, $C_2 \times (C_8:C_2)$ x 2, $C_2^2:\OD_{16}$ x 4 |
16T95 x 8, 32T96 x 4, 32T97 |
32T98 |
$C_2^3:Q_8$ |
$64$ |
$1$ |
✓ |
$2$ |
$22$ |
$C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8$ x 2, $Q_8:C_2^2$ x 4, $Q_8\times C_2$, $Q_8 : C_2^2$ x 2, $C_2^3:Q_8$ x 2 |
16T97 x 4, 32T98 x 5 |
32T99 |
$C_4^2:C_2^2$ |
$64$ |
$1$ |
✓ |
$2$ |
$19$ |
$C_2$ x 7, $C_2^2$ x 7, $C_2^3$, $Q_8:C_2^2$ x 6, $Q_8 : C_2^2$ x 3, $C_4^2:C_2^2$ x 4 |
16T98 x 8, 32T99 x 5 |
32T109 |
$C_2^3:D_4$ |
$64$ |
$1$ |
✓ |
$2$ |
$28$ |
$C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 12, $C_2^3$, $D_4$ x 2, $D_4\times C_2$ x 16, $C_2^2 \wr C_2$ x 16, $D_4\times C_2$, $C_2^2 \times D_4$ x 2, $C_2^2\wr C_2$ x 4, $C_2^3:D_4$ x 8 |
16T105 x 32, 32T109 x 11, 32T275 x 2 |
32T113 |
$C_4.C_4^2$ |
$64$ |
$1$ |
✓ |
$2$ |
$22$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $D_{4}$ x 2, $C_4\times C_2$, $D_4$, $Q_8$, $C_4:C_4$, $C_4.C_4^2$ |
16T108, 32T113 x 2 |
Results are complete for degrees $\leq 23$.