| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 16T636 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$, $D_{4}$ x 3, $C_2^2 \wr C_2$ |
16T636 x 3, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 16T652 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$ |
16T636 x 4, 16T652 x 3, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 16T657 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$ |
16T636 x 4, 16T652 x 4, 16T657 x 3, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 32T3110 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ 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, $C_2^2\wr C_2$, $D_4^2:C_2^2$, $D_4^2:C_2^2$ |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 3, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 32T3111 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 6, $D_4\times C_2$ x 3, $C_2^2 \wr C_2$ x 4, $C_2^3:D_4$, $D_4^2:C_2^2$ x 2 |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 32T3112 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ 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, $C_2^2\wr C_2$, $D_4^2:C_2^2$ x 2 |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 32T3113 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 6, $D_4\times C_2$ x 3, $C_2^2 \wr C_2$ x 4, $C_2^3:D_4$, $D_4^2:C_2^2$, $D_4^2:C_2^2$ |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 3, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 32T3114 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ 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, $C_2^2\wr C_2$, $D_4^2:C_2^2$ x 2 |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 32T3115 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 6, $D_4\times C_2$ x 3, $C_2^2 \wr C_2$ x 4, $C_2^3:D_4$, $D_4^2:C_2^2$ x 2 |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 32T3116 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 6, $D_4\times C_2$ x 3, $C_2^2 \wr C_2$ x 4, $C_2^3:D_4$, $D_4^2:C_2^2$ x 2 |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 32T3185 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ 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, $C_2^2\wr C_2$, $D_4^2:C_2^2$ x 2 |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 32T3186 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ 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, $C_2^2\wr C_2$, $D_4^2:C_2^2$ x 2 |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 32T3187 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4\times C_2$ x 6, $C_2^2 \times D_4$, $D_4^2:C_2^2$, $D_4^2:C_2^2$ |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 3, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 32T3188 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4\times C_2$ x 6, $C_2^2 \times D_4$, $D_4^2:C_2^2$ x 2 |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 32T3189 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ 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, $D_4\times C_2$, $D_4^2:C_2^2$ x 2 |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 32T3190 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ 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, $C_2^2\wr C_2$, $D_4^2:C_2^2$ x 2 |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 32T3209 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ 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, $D_4\times C_2$, $D_4^2:C_2^2$ x 2 |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 32T3210 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 6, $D_4\times C_2$ x 3, $C_2^2 \wr C_2$ x 4, $C_2^3:D_4$, $D_4^2:C_2^2$ x 2 |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 32T3211 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 6, $D_4\times C_2$ x 3, $C_2^2 \wr C_2$ x 4, $C_2^3:D_4$, $D_4^2:C_2^2$ x 2 |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 32T3212 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 6, $D_4\times C_2$ x 3, $C_2^2 \wr C_2$ x 4, $C_2^3:D_4$, $D_4^2:C_2^2$ x 2 |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 32T3213 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ x 7, $C_2^2$ x 7, $D_{4}$ x 4, $C_2^3$, $D_4\times C_2$ x 6, $C_2^2 \times D_4$, $D_4^2:C_2^2$ x 2 |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213, 32T4769 x 4, 32T7442 x 2, 32T7470 x 2 |
| 32T4769 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_2^4:D_4$ |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 3, 32T7442 x 2, 32T7470 x 2 |
| 32T7442 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$, $(((C_4 \times C_2): C_2):C_2):C_2$, $(((C_4 \times C_2): C_2):C_2):C_2$, $C_2\wr C_2^2$ |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442, 32T7470 x 2 |
| 32T7470 |
$D_4^2:C_2^2$ |
$256$ |
$1$ |
✓ |
$4$ |
$34$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $C_2\wr C_2^2$ |
16T636 x 4, 16T652 x 4, 16T657 x 4, 32T3110 x 4, 32T3111 x 2, 32T3112 x 2, 32T3113 x 4, 32T3114 x 2, 32T3115 x 2, 32T3116 x 2, 32T3185 x 2, 32T3186 x 2, 32T3187 x 4, 32T3188 x 2, 32T3189 x 2, 32T3190 x 2, 32T3209 x 2, 32T3210 x 2, 32T3211 x 2, 32T3212 x 2, 32T3213 x 2, 32T4769 x 4, 32T7442 x 2, 32T7470 |
Results are complete for degrees $\leq 23$.
