| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 41T3 |
$C_{41}:C_{4}$ |
$164$ |
$1$ |
✓ |
$-1$ |
$14$ |
|
|
| 41T4 |
$C_{41}:C_{5}$ |
$205$ |
$1$ |
✓ |
$-1$ |
$13$ |
|
|
| 42T24 |
$A_4\times C_{14}$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$56$ |
$C_3$, $A_4\times C_2$, $C_7$, $C_{21}$ |
|
| 42T25 |
$C_3\times F_8$ |
$168$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_3$, $C_7$, $F_8$, $C_{21}$ |
24T282 |
| 42T26 |
$F_8:C_3$ |
$168$ |
$1$ |
✓ |
$-1$ |
$8$ |
$C_3$, $C_7:C_3$, $F_8:C_3$, $C_7:C_3$ |
8T36, 14T11, 24T283, 28T27 |
| 42T27 |
$C_{14}:A_4$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_3$, $A_4\times C_2$, $C_7:C_3$, $C_7:C_3$ |
|
| 42T28 |
$A_4\times D_7$ |
$168$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_3$, $A_4$, $D_{7}$, $C_3\times D_7$ |
28T29, 42T29 |
| 42T29 |
$A_4\times D_7$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_3$, $A_4\times C_2$, $D_{7}$, $C_3\times D_7$ |
28T29, 42T28 |
| 42T30 |
$D_7:A_4$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_3$, $A_4\times C_2$, $F_7$, $F_7$ |
28T28, 42T31 |
| 42T31 |
$D_7:A_4$ |
$168$ |
$1$ |
✓ |
$-1$ |
$12$ |
$C_3$, $A_4$, $F_7$, $F_7$ |
28T28, 42T30 |
| 42T32 |
$C_7:S_4$ |
$168$ |
$1$ |
✓ |
$-1$ |
$17$ |
$S_3$, $S_4$, $D_{7}$, $D_{21}$ |
28T30, 42T33 |
| 42T33 |
$C_7:S_4$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$S_3$, $S_4$, $D_{7}$, $D_{21}$ |
28T30, 42T32 |
| 42T34 |
$C_7\times S_4$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$35$ |
$S_3$, $S_4$, $C_7$, $S_3\times C_7$ |
28T31, 42T35 |
| 42T35 |
$C_7\times S_4$ |
$168$ |
$1$ |
✓ |
$-1$ |
$35$ |
$S_3$, $S_4$, $C_7$, $S_3\times C_7$ |
28T31, 42T34 |
| 42T36 |
$S_3\times D_{14}$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3$, $D_{6}$, $D_{7}$, $D_{14}$, $S_3\times D_7$ |
42T36 x 3 |
| 42T37 |
$\PSL(2,7)$ |
$168$ |
$1$ |
|
$-1$ |
$6$ |
$\GL(3,2)$ x 2, $\PSL(2,7)$ |
7T5 x 2, 8T37, 14T10 x 2, 21T14, 24T284, 28T32, 42T38 x 2 |
| 42T38 |
$\PSL(2,7)$ |
$168$ |
$1$ |
|
$-1$ |
$6$ |
$\GL(3,2)$ x 2, $\PSL(2,7)$, $\PSL(2,7)$ |
7T5 x 2, 8T37, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38 |
| 42T39 |
$A_4\times C_7:C_3$ |
$252$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_3$, $A_4$, $C_7:C_3$, $C_{21}:C_3$ |
28T40 |
| 42T40 |
$C_6\times F_7$ |
$252$ |
$-1$ |
✓ |
$-1$ |
$42$ |
$C_2$, $C_3$, $C_6$, $F_7$, $F_7 \times C_2$, $C_3\times F_7$ |
42T40 x 5 |
| 42T41 |
$C_{42}:C_6$ |
$252$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $S_3$, $D_{6}$, $F_7$, $F_7 \times C_2$, $C_{21}:C_6$ |
42T41 |
| 42T42 |
$C_{42}:C_6$ |
$252$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3$, $D_{6}$, $C_7:C_3$, $(C_7:C_3) \times C_2$, $C_{21}:C_6$ |
42T42 |
| 42T43 |
$S_3\times F_7$ |
$252$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$C_2$, $S_3$, $D_{6}$, $F_7$, $F_7 \times C_2$, $S_3\times F_7$ |
21T15, 42T44, 42T45, 42T52 |
| 42T44 |
$S_3\times F_7$ |
$252$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$C_2$, $S_3$, $D_{6}$, $F_7$, $F_7$, $S_3\times F_7$ |
21T15, 42T43, 42T45, 42T52 |
| 42T45 |
$S_3\times F_7$ |
$252$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$C_2$, $S_3$, $S_3$, $F_7$, $F_7 \times C_2$, $S_3\times F_7$ |
21T15, 42T43, 42T44, 42T52 |
| 42T46 |
$C_7\times S_3^2$ |
$252$ |
$-1$ |
✓ |
$-1$ |
$63$ |
$C_2$, $S_3^2$, $C_7$, $C_{14}$ |
|
| 42T47 |
$C_3^2:C_{28}$ |
$252$ |
$1$ |
✓ |
$-1$ |
$42$ |
$C_2$, $C_3^2:C_4$, $C_7$, $C_{14}$ |
42T47 |
| 42T48 |
$(C_3\times C_{21}):C_4$ |
$252$ |
$1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $C_3^2:C_4$, $D_{7}$, $D_{7}$ |
42T48 |
| 42T49 |
$C_{21}:D_6$ |
$252$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $S_3^2$, $D_{7}$, $D_{7}$ |
|
| 42T50 |
$C_{21}:D_6$ |
$252$ |
$-1$ |
✓ |
$-1$ |
$45$ |
$C_2$, $S_3\times C_3$, $D_{7}$, $D_{14}$ |
|
| 42T51 |
$S_3\times D_{21}$ |
$252$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $S_3^2$, $D_{7}$, $D_{14}$ |
|
| 42T52 |
$S_3\times F_7$ |
$252$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$C_2$, $S_3\times C_3$, $F_7$, $F_7 \times C_2$ |
21T15, 42T43, 42T44, 42T45 |
| 43T3 |
$C_{43}:C_{3}$ |
$129$ |
$1$ |
✓ |
$-1$ |
$17$ |
|
|
| 44T11 |
$C_{11}\times A_4$ |
$132$ |
$1$ |
✓ |
$-1$ |
$44$ |
$A_4$, $C_{11}$ |
|
| 44T12 |
$D_4\times D_{11}$ |
$176$ |
$-1$ |
✓ |
$-1$ |
$35$ |
$C_2$, $D_{4}$, $D_{11}$, $D_{22}$ |
44T12 x 3 |
| 44T13 |
$C_{11}:C_{20}$ |
$220$ |
$-1$ |
✓ |
$-1$ |
$22$ |
$C_2$, $C_4$, $F_{11}$, $F_{11}$ |
|
| 44T14 |
$C_2\times F_{11}$ |
$220$ |
$1$ |
✓ |
$-1$ |
$22$ |
$C_2$ x 3, $C_2^2$, $F_{11}$, $F_{11}$, $C_2\times F_{11}$ x 2 |
22T6 x 2 |
| 44T15 |
$C_{11}:C_{20}$ |
$220$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$C_2$, $C_4$, $C_{11}:C_5$, $C_{11}:C_{10}$ |
|
| 44T16 |
$C_{22}:C_{10}$ |
$220$ |
$1$ |
✓ |
$-1$ |
$28$ |
$C_2$ x 3, $C_2^2$, $C_{11}:C_5$, $C_{11}:C_{10}$ x 3 |
|
| 45T11 |
$C_5\times \He_3$ |
$135$ |
$1$ |
✓ |
$2$ |
$55$ |
$C_3$, $C_5$, $C_3^2:C_3$, $C_{15}$ |
45T11 x 3 |
| 45T12 |
$C_9:C_{15}$ |
$135$ |
$1$ |
✓ |
$2$ |
$55$ |
$C_3$, $C_5$, $C_9:C_3$, $C_{15}$ |
|
| 45T13 |
$S_3\times D_{15}$ |
$180$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$S_3$ x 2, $D_{5}$, $S_3^2$, $D_{15}$, $D_5\times S_3$ |
30T42 |
| 45T14 |
$C_{15}:D_6$ |
$180$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_3$, $S_3$, $D_{5}$, $S_3\times C_3$, $D_5\times C_3$, $D_5\times S_3$ |
30T44 |
| 45T15 |
$C_5\times S_3^2$ |
$180$ |
$-1$ |
✓ |
$-1$ |
$45$ |
$S_3$ x 2, $C_5$, $S_3^2$, $S_3 \times C_5$ x 2 |
30T41 |
| 45T16 |
$\GL(2,4)$ |
$180$ |
$1$ |
|
$-1$ |
$15$ |
$C_3$, $A_5$, $A_5$, $\GL(2,4)$ x 2, $\GL(2,4)$ |
15T15 x 2, 15T16, 18T90, 30T45, 36T176 |
| 45T17 |
$C_{45}:C_4$ |
$180$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$S_3$, $F_5$, $D_{9}$, $C_{15} : C_4$ |
|
| 45T18 |
$C_{15}:C_{12}$ |
$180$ |
$1$ |
✓ |
$-1$ |
$27$ |
$C_3$, $S_3$, $F_5$, $S_3\times C_3$, $C_{15} : C_4$, $F_5\times C_3$ |
30T47 |
| 45T19 |
$C_3^2:F_5$ |
$180$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$S_3$ x 4, $F_5$, $C_3^2:C_2$, $C_{15} : C_4$ x 4 |
|
| 45T20 |
$D_5\times D_9$ |
$180$ |
$1$ |
✓ |
$-1$ |
$24$ |
$S_3$, $D_{5}$, $D_{9}$, $D_5\times S_3$ |
|
| 45T21 |
$C_{15}:D_6$ |
$180$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$S_3$ x 2, $D_{5}$, $S_3^2$, $D_5\times S_3$ x 2 |
30T43 |
| 45T22 |
$C_{15}:D_6$ |
$180$ |
$1$ |
✓ |
$-1$ |
$24$ |
$S_3$ x 4, $D_{5}$, $C_3^2:C_2$, $D_5\times S_3$ x 4 |
|
Results are complete for degrees $\leq 23$.
