| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 32T30 |
$\SD_{32}$ |
$32$ |
$1$ |
✓ |
$4$ |
$11$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $D_{8}$ x 2, $D_{8}$, $\SD_{32}$ |
16T55 |
| 32T31 |
$D_{16}$ |
$32$ |
$1$ |
✓ |
$4$ |
$11$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $D_{8}$ x 2, $D_{8}$, $D_{16}$ x 2 |
16T56 x 2 |
| 32T51 |
$Q_{32}$ |
$32$ |
$1$ |
✓ |
$4$ |
$11$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $D_{8}$ x 2, $D_{8}$ |
|
| 32T138 |
$C_2\wr C_4$ |
$64$ |
$1$ |
✓ |
$4$ |
$13$ |
$C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $C_2^3: C_4$, $((C_8 : C_2):C_2):C_2$ x 2, $(((C_4 \times C_2): C_2):C_2):C_2$, $C_2^3:C_4$, $C_2\wr C_4$, $C_2\wr C_4$, $C_2\wr C_4$, $C_2\wr C_4$ x 2 |
8T27 x 2, 8T28 x 2, 16T130, 16T157 x 2, 16T158 x 2, 16T159 x 2, 16T166, 16T170, 16T171, 16T172, 32T138, 32T139, 32T170, 32T176 |
| 32T139 |
$C_2\wr C_4$ |
$64$ |
$1$ |
✓ |
$4$ |
$13$ |
$C_2$ 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, $((C_8 : C_2):C_2):C_2$ x 2, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_2^2 : C_4$, $C_2\wr C_4$, $C_2\wr C_4$ x 2, $C_2\wr C_4$, $C_2\wr C_4$, $C_2\wr C_4$ |
8T27 x 2, 8T28 x 2, 16T130, 16T157 x 2, 16T158 x 2, 16T159 x 2, 16T166, 16T170, 16T171, 16T172, 32T138 x 2, 32T170, 32T176 |
| 32T140 |
$C_4^2.C_4$ |
$64$ |
$1$ |
✓ |
$4$ |
$13$ |
$C_2$ 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, $C_2^2 : C_4$, $C_4^2.C_4$, $C_4^2.C_4$ x 2 |
16T131, 16T151 x 2, 32T165 |
| 32T145 |
$D_{16}:C_2$ |
$64$ |
$1$ |
✓ |
$4$ |
$16$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $D_{8}$ x 2, $D_{8}$, $D_{16}:C_2$ x 2 |
16T134 x 2, 32T146 x 2, 32T298 |
| 32T146 |
$D_{16}:C_2$ |
$64$ |
$1$ |
✓ |
$4$ |
$16$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_{8}$ x 2, $D_4\times C_2$, $C_2\times D_8$, $D_{16}:C_2$ x 2 |
16T134 x 2, 32T145, 32T146, 32T298 |
| 32T149 |
$C_{16}:C_4$ |
$64$ |
$1$ |
✓ |
$4$ |
$16$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $QD_{16}$, $QD_{16}$, $C_{16}:C_4$ |
16T136 |
| 32T152 |
$C_4^2.C_4$ |
$64$ |
$1$ |
✓ |
$4$ |
$13$ |
$C_2$ 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 |
16T139 x 2 |
| 32T153 |
$C_2^3.D_4$ |
$64$ |
$1$ |
✓ |
$4$ |
$13$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$, $C_2^3: C_4$, $C_2^3: C_4$, $C_2^3:C_4$, $C_2^3.D_4$ |
16T140, 16T148, 16T153, 16T160, 32T154, 32T164 |
| 32T154 |
$C_2^3.D_4$ |
$64$ |
$1$ |
✓ |
$4$ |
$13$ |
$C_2$ 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, $C_2^2 : C_4$, $C_2^3.D_4$, $C_2^3.D_4$, $C_2^3.D_4$ |
16T140, 16T148, 16T153, 16T160, 32T153, 32T164 |
| 32T157 |
$C_4^2:C_4$ |
$64$ |
$1$ |
✓ |
$4$ |
$13$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $C_2^3 : C_4 $, $C_2^3: C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_2^3:C_4$, $C_4^2:C_4$, $C_4^2:C_4$ |
8T30 x 4, 16T143 x 2, 16T167 x 2, 16T168 x 2, 16T169 x 2, 32T157, 32T177, 32T178 |
| 32T158 |
$\OD_{32}:C_2$ |
$64$ |
$1$ |
✓ |
$4$ |
$16$ |
$C_2$, $C_4$, $D_{4}$ x 2, $D_{8}$, $QD_{16}$, $C_2^2:C_4$, $D_4:C_4$, $\OD_{32}:C_2$ x 2 |
16T144 x 2, 32T158, 32T159 |
| 32T159 |
$\OD_{32}:C_2$ |
$64$ |
$1$ |
✓ |
$4$ |
$16$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $QD_{16}$, $QD_{16}$, $\OD_{32}:C_2$ x 2 |
16T144 x 2, 32T158 x 2 |
| 32T164 |
$C_2^3.D_4$ |
$64$ |
$1$ |
✓ |
$4$ |
$13$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $C_2^3 : C_4 $, $C_2^3: C_4$, $C_2^3:C_4$, $C_2^3.D_4$, $C_2^3.D_4$ |
16T140, 16T148, 16T153, 16T160, 32T153, 32T154 |
| 32T165 |
$C_4^2.C_4$ |
$64$ |
$1$ |
✓ |
$4$ |
$13$ |
$C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $C_2^3: C_4$, $C_2^3:C_4$, $C_4^2.C_4$ x 2 |
16T131, 16T151 x 2, 32T140 |
| 32T166 |
$C_4^2:C_4$ |
$64$ |
$1$ |
✓ |
$4$ |
$13$ |
$C_2$ 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, $C_2^2 : C_4$, $C_4^2:C_4$, $C_4^2:C_4$ x 2 |
16T154, 16T174 x 2, 16T176 x 2, 32T179 x 2 |
| 32T169 |
$D_8:C_4$ |
$64$ |
$1$ |
✓ |
$4$ |
$16$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $D_{8}$ x 2, $D_{8}$, $D_8:C_4$ |
16T156, 32T286 |
| 32T170 |
$C_2\wr C_4$ |
$64$ |
$1$ |
✓ |
$4$ |
$13$ |
$C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_4\times C_2$, $C_2^3: C_4$, $C_2^3: C_4$, $((C_8 : C_2):C_2):C_2$ x 2, $C_2^3:C_4$, $C_2\wr C_4$ x 2, $C_2\wr C_4$ x 2, $C_2\wr C_4$ |
8T27 x 2, 8T28 x 2, 16T130, 16T157 x 2, 16T158 x 2, 16T159 x 2, 16T166, 16T170, 16T171, 16T172, 32T138 x 2, 32T139, 32T176 |
| 32T176 |
$C_2\wr C_4$ |
$64$ |
$1$ |
✓ |
$4$ |
$13$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $C_2^3 : C_4 $, $C_2^3: C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_2^3:C_4$, $C_2\wr C_4$, $C_2\wr C_4$ |
8T27 x 2, 8T28 x 2, 16T130, 16T157 x 2, 16T158 x 2, 16T159 x 2, 16T166, 16T170, 16T171, 16T172, 32T138 x 2, 32T139, 32T170 |
| 32T177 |
$C_4^2:C_4$ |
$64$ |
$1$ |
✓ |
$4$ |
$13$ |
$C_2$ 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, $(((C_4 \times C_2): C_2):C_2):C_2$ x 4, $C_2^2 : C_4$, $C_4^2:C_4$ x 2, $C_4^2:C_4$ x 2, $C_4^2:C_4$ x 2 |
8T30 x 4, 16T143 x 2, 16T167 x 2, 16T168 x 2, 16T169 x 2, 32T157 x 2, 32T178 |
| 32T178 |
$C_4^2:C_4$ |
$64$ |
$1$ |
✓ |
$4$ |
$13$ |
$C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $C_2^3: C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 4, $C_2^3:C_4$, $C_4^2:C_4$ x 2 |
8T30 x 4, 16T143 x 2, 16T167 x 2, 16T168 x 2, 16T169 x 2, 32T157 x 2, 32T177 |
| 32T179 |
$C_4^2:C_4$ |
$64$ |
$1$ |
✓ |
$4$ |
$13$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $C_2^3 : C_4 $, $C_2^3: C_4$, $C_2^3:C_4$, $C_4^2:C_4$, $C_4^2:C_4$ |
16T154, 16T174 x 2, 16T176 x 2, 32T166, 32T179 |
| 32T284 |
$C_4.D_8$ |
$64$ |
$1$ |
✓ |
$4$ |
$22$ |
$C_2$, $C_4$, $D_{4}$ x 2, $D_{8}$, $QD_{16}$, $C_2^2:C_4$, $D_4:C_4$ |
32T379 |
| 32T286 |
$D_8:C_4$ |
$64$ |
$1$ |
✓ |
$4$ |
$16$ |
$C_2$, $C_4$, $D_{4}$ x 2, $D_{8}$, $QD_{16}$, $C_2^2:C_4$, $D_4:C_4$ |
16T156, 32T169 |
| 32T287 |
$D_8:C_4$ |
$64$ |
$1$ |
✓ |
$4$ |
$22$ |
$C_2$, $C_4$, $D_{4}$ x 2, $D_{8}$, $QD_{16}$, $C_2^2:C_4$, $D_4:C_4$, $\SD_{32}$, $D_{16}$ |
32T287 |
| 32T297 |
$C_2\times D_{16}$ |
$64$ |
$1$ |
✓ |
$4$ |
$22$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_{8}$ x 2, $D_4\times C_2$, $C_2\times D_8$, $D_{16}$ x 2 |
32T297 x 3 |
| 32T298 |
$D_{16}:C_2$ |
$64$ |
$1$ |
✓ |
$4$ |
$16$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_{8}$ x 2, $D_4\times C_2$, $C_2\times D_8$ |
16T134 x 2, 32T145, 32T146 x 2 |
| 32T299 |
$C_2\times \SD_{32}$ |
$64$ |
$1$ |
✓ |
$4$ |
$22$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_{8}$ x 2, $D_4\times C_2$, $C_2\times D_8$, $\SD_{32}$ x 2 |
32T299 |
| 32T300 |
$Q_{32}:C_2$ |
$64$ |
$1$ |
✓ |
$4$ |
$16$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_{8}$ x 2, $D_4\times C_2$, $C_2\times D_8$ |
32T381 |
| 32T303 |
$D_{16}:C_2$ |
$64$ |
$1$ |
✓ |
$4$ |
$22$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_{8}$ x 2, $D_4\times C_2$, $C_2\times D_8$ |
32T303, 32T375 |
| 32T375 |
$D_{16}:C_2$ |
$64$ |
$1$ |
✓ |
$4$ |
$22$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $D_{8}$ x 2, $D_{8}$ |
32T303 x 2 |
| 32T376 |
$C_{16}.C_4$ |
$64$ |
$1$ |
✓ |
$4$ |
$22$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $Q_{16}$ |
|
| 32T379 |
$C_4.D_8$ |
$64$ |
$1$ |
✓ |
$4$ |
$22$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $QD_{16}$, $QD_{16}$ |
32T284 |
| 32T380 |
$C_4.D_8$ |
$64$ |
$1$ |
✓ |
$4$ |
$16$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $QD_{16}$, $QD_{16}$ |
|
| 32T381 |
$Q_{32}:C_2$ |
$64$ |
$1$ |
✓ |
$4$ |
$16$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $D_{8}$ x 2, $D_{8}$ |
32T300 |
| 32T466 |
$(C_2^2\times D_4):C_4$ |
$128$ |
$1$ |
✓ |
$4$ |
$23$ |
$C_2$ 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, $C_2^2 : C_4$, $(C_2^2\times D_4):C_4$ x 2 |
16T213 x 2, 16T281 x 2, 16T315 x 2, 32T467 x 2, 32T468 x 2, 32T653, 32T654 x 2, 32T729 x 4, 32T730, 32T1123 x 2 |
| 32T467 |
$(C_2^2\times D_4):C_4$ |
$128$ |
$1$ |
✓ |
$4$ |
$23$ |
$C_2$ 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, $C_2 \times (C_2^2:C_4)$, $(C_2^2\times D_4):C_4$, $(C_2^2\times D_4):C_4$ |
16T213 x 2, 16T281 x 2, 16T315 x 2, 32T466, 32T467, 32T468 x 2, 32T653, 32T654 x 2, 32T729 x 4, 32T730, 32T1123 x 2 |
| 32T468 |
$(C_2^2\times D_4):C_4$ |
$128$ |
$1$ |
✓ |
$4$ |
$23$ |
$C_2$ 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, $C_2 \times (C_2^2:C_4)$, $(C_2^2\times D_4):C_4$, $(C_2^2\times D_4):C_4$ |
16T213 x 2, 16T281 x 2, 16T315 x 2, 32T466, 32T467 x 2, 32T468, 32T653, 32T654 x 2, 32T729 x 4, 32T730, 32T1123 x 2 |
| 32T482 |
$C_2^4.D_4$ |
$128$ |
$1$ |
✓ |
$4$ |
$23$ |
$C_2$ 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, $C_2^2 : C_4$, $C_2^4.D_4$, $C_2^4.D_4$ |
16T219, 16T236, 16T266, 16T287, 16T317, 16T319 x 2, 16T324, 32T483, 32T484, 32T530, 32T531, 32T614, 32T615, 32T616, 32T617, 32T663, 32T664, 32T731 x 2, 32T733 x 2, 32T734 x 2, 32T743 |
| 32T483 |
$C_2^4.D_4$ |
$128$ |
$1$ |
✓ |
$4$ |
$23$ |
$C_2$ 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, $C_2 \times (C_2^2:C_4)$, $C_2^4.D_4$, $C_2^4.D_4$ |
16T219, 16T236, 16T266, 16T287, 16T317, 16T319 x 2, 16T324, 32T482, 32T484, 32T530, 32T531, 32T614, 32T615, 32T616, 32T617, 32T663, 32T664, 32T731 x 2, 32T733 x 2, 32T734 x 2, 32T743 |
| 32T484 |
$C_2^4.D_4$ |
$128$ |
$1$ |
✓ |
$4$ |
$23$ |
$C_2$ 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, $C_2 \times (C_2^2:C_4)$, $C_2^4.D_4$, $C_2^4.D_4$ |
16T219, 16T236, 16T266, 16T287, 16T317, 16T319 x 2, 16T324, 32T482, 32T483, 32T530, 32T531, 32T614, 32T615, 32T616, 32T617, 32T663, 32T664, 32T731 x 2, 32T733 x 2, 32T734 x 2, 32T743 |
| 32T503 |
$C_4^2.(C_2\times C_4)$ |
$128$ |
$1$ |
✓ |
$4$ |
$23$ |
$C_2$ 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, $C_2^2 : C_4$, $C_4^2.(C_2\times C_4)$ x 2 |
16T226 x 4, 16T285 x 2, 32T503, 32T504 x 4, 32T505 x 2, 32T660 x 4, 32T661 |
| 32T504 |
$C_4^2.(C_2\times C_4)$ |
$128$ |
$1$ |
✓ |
$4$ |
$23$ |
$C_2$ 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, $C_2 \times (C_2^2:C_4)$, $C_4^2.(C_2\times C_4)$, $C_4^2.(C_2\times C_4)$ |
16T226 x 4, 16T285 x 2, 32T503 x 2, 32T504 x 3, 32T505 x 2, 32T660 x 4, 32T661 |
| 32T505 |
$C_4^2.(C_2\times C_4)$ |
$128$ |
$1$ |
✓ |
$4$ |
$23$ |
$C_2$ 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, $C_2 \times (C_2^2:C_4)$, $C_4^2.(C_2\times C_4)$ x 2 |
16T226 x 4, 16T285 x 2, 32T503 x 2, 32T504 x 4, 32T505, 32T660 x 4, 32T661 |
| 32T506 |
$C_2^5:C_4$ |
$128$ |
$1$ |
✓ |
$4$ |
$26$ |
$C_2$ 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, $(((C_4 \times C_2): C_2):C_2):C_2$ x 4, $C_2^2 : C_4$, $C_2\wr C_4$ x 2, $C_2^5:C_4$ x 4 |
16T227 x 4, 16T259 x 8, 16T261 x 4, 16T273 x 4, 16T283 x 4, 32T507 x 2, 32T508 x 4, 32T595 x 4, 32T596 x 8, 32T597 x 2, 32T598 x 4, 32T599 x 4, 32T601, 32T602 x 2, 32T633, 32T657, 32T1130 x 2, 32T1796 |
| 32T507 |
$C_2^5:C_4$ |
$128$ |
$1$ |
✓ |
$4$ |
$26$ |
$C_2$ 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, $(((C_4 \times C_2): C_2):C_2):C_2$ x 4, $C_2 \times (C_2^2:C_4)$, $C_2\wr C_4$ x 2, $C_2^5:C_4$ x 2, $C_2^5:C_4$ x 2 |
16T227 x 4, 16T259 x 8, 16T261 x 4, 16T273 x 4, 16T283 x 4, 32T506, 32T507, 32T508 x 4, 32T595 x 4, 32T596 x 8, 32T597 x 2, 32T598 x 4, 32T599 x 4, 32T601, 32T602 x 2, 32T633, 32T657, 32T1130 x 2, 32T1796 |
| 32T508 |
$C_2^5:C_4$ |
$128$ |
$1$ |
✓ |
$4$ |
$26$ |
$C_2$ 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, $((C_8 : C_2):C_2):C_2$ x 2, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_2 \times (C_2^2:C_4)$, $C_2\wr C_4$ x 2, $C_2^5:C_4$, $C_2^5:C_4$, $C_2^5:C_4$, $C_2^5:C_4$ |
16T227 x 4, 16T259 x 8, 16T261 x 4, 16T273 x 4, 16T283 x 4, 32T506, 32T507 x 2, 32T508 x 3, 32T595 x 4, 32T596 x 8, 32T597 x 2, 32T598 x 4, 32T599 x 4, 32T601, 32T602 x 2, 32T633, 32T657, 32T1130 x 2, 32T1796 |
| 32T509 |
$C_2^4:C_8$ |
$128$ |
$1$ |
✓ |
$4$ |
$26$ |
$C_2$, $C_4$, $C_8:C_2$, $(C_8:C_2):C_2$, $C_2^3: C_4$, $((C_8 : C_2):C_2):C_2$ x 3, $C_2^3:C_8$, $C_2\wr C_4$, $C_2\wr C_4$, $C_2^4:C_8$ x 2, $C_2^4:C_8$ x 2 |
16T228 x 8, 16T257 x 4, 16T258 x 4, 32T509 x 7, 32T510 x 4, 32T511 x 4, 32T512 x 2, 32T513 x 4, 32T591 x 2, 32T592 x 4, 32T593, 32T594, 32T1797 |
Results are complete for degrees $\leq 23$.
