| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 28T1 |
$C_{28}$ |
$28$ |
$-1$ |
✓ |
$1$ |
$28$ |
$C_2$, $C_4$, $C_7$, $C_{14}$ |
|
| 28T2 |
$C_2\times C_{14}$ |
$28$ |
$1$ |
✓ |
$1$ |
$28$ |
$C_2$ x 3, $C_2^2$, $C_7$, $C_{14}$ x 3 |
|
| 28T3 |
$C_7:C_4$ |
$28$ |
$-1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $C_4$, $D_{7}$, $D_{7}$ |
|
| 28T4 |
$D_{14}$ |
$28$ |
$1$ |
✓ |
$-1$ |
$10$ |
$C_2$ x 3, $C_2^2$, $D_{7}$, $D_{7}$, $D_{14}$ x 2 |
14T3 x 2 |
| 28T5 |
$C_7\times D_4$ |
$56$ |
$-1$ |
✓ |
$2$ |
$35$ |
$C_2$, $D_{4}$, $C_7$, $C_{14}$ |
28T5 |
| 28T6 |
$C_7:D_4$ |
$56$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$C_2$, $D_{4}$, $D_{7}$, $D_{7}$ |
28T7 |
| 28T7 |
$C_7:D_4$ |
$56$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$C_2$, $D_{4}$, $D_{7}$, $D_{14}$ |
28T6 |
| 28T8 |
$C_4\times D_7$ |
$56$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $C_4$, $D_{7}$, $D_{14}$ |
28T8 |
| 28T9 |
$C_2\times D_{14}$ |
$56$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$ x 3, $C_2^2$, $D_{7}$, $D_{14}$ x 3 |
28T9 x 3 |
| 28T10 |
$D_{28}$ |
$56$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$C_2$, $D_{4}$, $D_{7}$, $D_{14}$ |
28T10 |
| 28T11 |
$F_8$ |
$56$ |
$1$ |
✓ |
$-1$ |
$8$ |
$C_7$, $F_8$ |
8T25, 14T6 |
| 28T12 |
$C_7:C_{12}$ |
$84$ |
$-1$ |
✓ |
$-1$ |
$14$ |
$C_2$, $C_4$, $F_7$, $F_7$ |
|
| 28T13 |
$C_7:C_{12}$ |
$84$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $C_4$, $C_7:C_3$, $(C_7:C_3) \times C_2$ |
|
| 28T14 |
$C_{14}:C_6$ |
$84$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$ x 3, $C_2^2$, $C_7:C_3$, $(C_7:C_3) \times C_2$ x 3 |
|
| 28T15 |
$C_2\times F_7$ |
$84$ |
$1$ |
✓ |
$-1$ |
$14$ |
$C_2$ x 3, $C_2^2$, $F_7$, $F_7$, $F_7 \times C_2$ x 2 |
14T7 x 2, 42T10 x 2 |
| 28T16 |
$C_7:A_4$ |
$84$ |
$1$ |
✓ |
$-1$ |
$12$ |
$A_4$, $C_7:C_3$ |
42T8 |
| 28T17 |
$C_7\times A_4$ |
$84$ |
$1$ |
✓ |
$-1$ |
$28$ |
$A_4$, $C_7$ |
42T7 |
| 28T18 |
$D_4\times D_7$ |
$112$ |
$-1$ |
✓ |
$-1$ |
$25$ |
$C_2$, $D_{4}$, $D_{7}$, $D_{14}$ |
28T18 x 3 |
| 28T19 |
$C_2\times F_8$ |
$112$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_7$, $F_8$, $C_2\times F_8$ |
14T9, 16T196, 28T19 x 2, 28T20 |
| 28T20 |
$C_2\times F_8$ |
$112$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $C_7$, $C_{14}$, $F_8$, $C_2\times F_8$ |
14T9, 16T196, 28T19 x 3 |
| 28T21 |
$D_{14}:C_6$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$19$ |
$C_2$, $D_{4}$, $F_7$, $F_7$ |
28T25 |
| 28T22 |
$C_{28}:C_6$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$25$ |
$C_2$, $D_{4}$, $C_7:C_3$, $(C_7:C_3) \times C_2$ |
28T22 |
| 28T23 |
$C_{28}:C_6$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$19$ |
$C_2$, $D_{4}$, $F_7$, $F_7 \times C_2$ |
28T23 |
| 28T24 |
$C_2^2\times F_7$ |
$168$ |
$1$ |
✓ |
$-1$ |
$28$ |
$C_2$ x 3, $C_2^2$, $F_7$, $F_7 \times C_2$ x 3 |
28T24 x 3 |
| 28T25 |
$D_{14}:C_6$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$19$ |
$C_2$, $D_{4}$, $F_7$, $F_7 \times C_2$ |
28T21 |
| 28T26 |
$C_4\times F_7$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$C_2$, $C_4$, $F_7$, $F_7 \times C_2$ |
28T26 |
| 28T27 |
$F_8:C_3$ |
$168$ |
$1$ |
✓ |
$-1$ |
$8$ |
$C_7:C_3$ |
8T36, 14T11, 24T283, 42T26 |
| 28T28 |
$D_7:A_4$ |
$168$ |
$1$ |
✓ |
$-1$ |
$12$ |
$A_4$, $F_7$ |
42T30, 42T31 |
| 28T29 |
$A_4\times D_7$ |
$168$ |
$1$ |
✓ |
$-1$ |
$20$ |
$A_4$, $D_{7}$ |
42T28, 42T29 |
| 28T30 |
$C_7:S_4$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$S_4$, $D_{7}$ |
42T32, 42T33 |
| 28T31 |
$C_7\times S_4$ |
$168$ |
$-1$ |
✓ |
$-1$ |
$35$ |
$S_4$, $C_7$ |
42T34, 42T35 |
| 28T32 |
$\PSL(2,7)$ |
$168$ |
$1$ |
|
$-1$ |
$6$ |
$\GL(3,2)$ x 2 |
7T5 x 2, 8T37, 14T10 x 2, 21T14, 24T284, 42T37, 42T38 x 2 |
| 28T33 |
$C_7:C_{28}$ |
$196$ |
$-1$ |
✓ |
$-1$ |
$70$ |
$C_2$, $C_4$, $C_7 \wr C_2$ |
28T33 x 2 |
| 28T34 |
$C_7\times D_{14}$ |
$196$ |
$1$ |
✓ |
$-1$ |
$70$ |
$C_2$ x 3, $C_2^2$, $C_7 \wr C_2$ |
28T34 x 2 |
| 28T35 |
$C_7^2:C_4$ |
$196$ |
$-1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $C_4$, $C_7^2:C_4$ |
14T12 x 4, 28T35 x 3 |
| 28T36 |
$D_7^2$ |
$196$ |
$1$ |
✓ |
$-1$ |
$25$ |
$C_2$ x 3, $C_2^2$, $D_7^2$ |
14T13 x 3, 28T36 x 2 |
| 28T37 |
$C_4\times F_8$ |
$224$ |
$-1$ |
✓ |
$-1$ |
$32$ |
$C_2$, $C_7$, $C_{14}$ |
32T2229 |
| 28T38 |
$C_2^2\times F_8$ |
$224$ |
$1$ |
✓ |
$-1$ |
$32$ |
$C_7$, $C_2\times F_8$ x 3 |
28T38 x 5, 28T39 x 3, 32T2228 |
| 28T39 |
$C_2^2\times F_8$ |
$224$ |
$1$ |
✓ |
$-1$ |
$32$ |
$C_2$, $C_7$, $C_{14}$, $C_2\times F_8$ x 2 |
28T38 x 6, 28T39 x 2, 32T2228 |
| 28T40 |
$A_4\times C_7:C_3$ |
$252$ |
$1$ |
✓ |
$-1$ |
$20$ |
$A_4$, $C_7:C_3$ |
42T39 |
| 28T41 |
$D_4\times F_7$ |
$336$ |
$-1$ |
✓ |
$-1$ |
$35$ |
$C_2$, $D_{4}$, $F_7$, $F_7 \times C_2$ |
28T41 x 3 |
| 28T42 |
$\PGL(2,7)$ |
$336$ |
$1$ |
|
$-1$ |
$9$ |
$C_2$, $\PGL(2,7)$ |
8T43, 14T16, 16T713, 21T20, 24T707, 28T46, 42T81, 42T82, 42T83 |
| 28T43 |
$C_2\times \GL(3,2)$ |
$336$ |
$1$ |
|
$-1$ |
$12$ |
$C_2$, $\GL(3,2)$, $\PSL(2,7)$, $C_2\times \GL(3,2)$, $\GL(3,2) \times C_2$ |
14T17 x 2, 14T19 x 2, 16T714, 28T43, 42T78, 42T79, 42T80 x 2 |
| 28T44 |
$F_8:C_6$ |
$336$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_2$, $C_7:C_3$, $(C_7:C_3) \times C_2$, $F_8:C_3$, $F_8:C_6$ |
14T18, 16T712, 42T67 |
| 28T45 |
$D_7\times S_4$ |
$336$ |
$-1$ |
✓ |
$-1$ |
$25$ |
$S_4$, $D_{7}$ |
42T74, 42T75, 42T76, 42T77 |
| 28T46 |
$\PGL(2,7)$ |
$336$ |
$1$ |
|
$-1$ |
$9$ |
|
8T43, 14T16, 16T713, 21T20, 24T707, 28T42, 42T81, 42T82, 42T83 |
| 28T47 |
$C_{14}\wr C_2$ |
$392$ |
$-1$ |
✓ |
$-1$ |
$119$ |
$C_2$, $D_{4}$, $C_7 \wr C_2$ |
28T47 x 5 |
| 28T48 |
$C_2\times C_7^2:C_4$ |
$392$ |
$1$ |
✓ |
$-1$ |
$32$ |
$C_2$ x 3, $C_2^2$, $C_7^2:C_4$ |
28T48 x 3, 28T49 x 4 |
| 28T49 |
$C_2\times C_7^2:C_4$ |
$392$ |
$-1$ |
✓ |
$-1$ |
$32$ |
$C_2$, $C_4$, $C_7^2:C_4$ |
28T48 x 4, 28T49 x 3 |
| 28T50 |
$C_7:D_{28}$ |
$392$ |
$-1$ |
✓ |
$-1$ |
$47$ |
$C_2$, $D_{4}$, $D_7^2$ |
28T50 x 5 |
Results are complete for degrees $\leq 23$.
