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Label | Name | Order | Parity | Solvable | Subfields | Low Degree Siblings |
---|---|---|---|---|---|---|
4T1 | $C_4$ | $4$ | $-1$ | ✓ | $C_2$ | |
4T2 | $C_2^2$ | $4$ | $1$ | ✓ | $C_2$ x 3 | |
4T3 | $D_{4}$ | $8$ | $-1$ | ✓ | $C_2$ | 4T3, 8T4 |
6T1 | $C_6$ | $6$ | $-1$ | ✓ | $C_2$, $C_3$ | |
6T2 | $S_3$ | $6$ | $-1$ | ✓ | $C_2$, $S_3$ | 3T2 |
6T3 | $D_{6}$ | $12$ | $-1$ | ✓ | $C_2$, $S_3$ | 6T3, 12T3 |
6T4 | $A_4$ | $12$ | $1$ | ✓ | $C_3$ | 4T4, 12T4 |
6T5 | $S_3\times C_3$ | $18$ | $-1$ | ✓ | $C_2$ | 9T4, 18T3 |
6T6 | $A_4\times C_2$ | $24$ | $-1$ | ✓ | $C_3$ | 8T13, 12T6, 12T7, 24T9 |
6T7 | $S_4$ | $24$ | $1$ | ✓ | $S_3$ | 4T5, 6T8, 8T14, 12T8, 12T9, 24T10 |
6T8 | $S_4$ | $24$ | $-1$ | ✓ | $S_3$ | 4T5, 6T7, 8T14, 12T8, 12T9, 24T10 |
6T9 | $S_3^2$ | $36$ | $-1$ | ✓ | $C_2$ | 9T8, 12T16, 18T9, 18T11 x 2, 36T13 |
6T10 | $C_3^2:C_4$ | $36$ | $1$ | ✓ | $C_2$ | 6T10, 9T9, 12T17 x 2, 18T10, 36T14 |
6T11 | $S_4\times C_2$ | $48$ | $-1$ | ✓ | $S_3$ | 6T11, 8T24 x 2, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 16T61, 24T46, 24T47, 24T48 x 2 |
6T13 | $C_3^2:D_4$ | $72$ | $-1$ | ✓ | $C_2$ | 6T13, 9T16, 12T34 x 2, 12T35 x 2, 12T36 x 2, 18T34 x 2, 18T36, 24T72 x 2, 36T53, 36T54 x 2 |
8T1 | $C_8$ | $8$ | $-1$ | ✓ | $C_2$, $C_4$ | |
8T2 | $C_4\times C_2$ | $8$ | $1$ | ✓ | $C_2$ x 3, $C_4$ x 2, $C_2^2$ | |
8T3 | $C_2^3$ | $8$ | $1$ | ✓ | $C_2$ x 7, $C_2^2$ x 7 | |
8T4 | $D_4$ | $8$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$, $D_{4}$ x 2 | 4T3 x 2 |
8T5 | $Q_8$ | $8$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$ | |
8T6 | $D_{8}$ | $16$ | $-1$ | ✓ | $C_2$, $D_{4}$ | 8T6, 16T13 |
8T7 | $C_8:C_2$ | $16$ | $-1$ | ✓ | $C_2$, $C_4$ | 16T6 |
8T8 | $QD_{16}$ | $16$ | $-1$ | ✓ | $C_2$, $D_{4}$ | 16T12 |
8T9 | $D_4\times C_2$ | $16$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$, $D_{4}$ x 2 | 8T9 x 3, 16T9 |
8T10 | $C_2^2:C_4$ | $16$ | $1$ | ✓ | $C_2$, $C_4$, $D_{4}$ x 2 | 8T10, 16T10 |
8T11 | $Q_8:C_2$ | $16$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$ | 8T11 x 2, 16T11 |
8T12 | $\SL(2,3)$ | $24$ | $1$ | ✓ | $A_4$ | 24T7 |
8T13 | $A_4\times C_2$ | $24$ | $1$ | ✓ | $C_2$, $A_4$ | 6T6, 12T6, 12T7, 24T9 |
8T14 | $S_4$ | $24$ | $1$ | ✓ | $C_2$, $S_4$ | 4T5, 6T7, 6T8, 12T8, 12T9, 24T10 |
8T15 | $Z_8 : Z_8^\times$ | $32$ | $-1$ | ✓ | $C_2$, $D_{4}$ | 8T15, 16T35, 16T38 x 2, 16T45, 32T21 |
8T16 | $(C_8:C_2):C_2$ | $32$ | $-1$ | ✓ | $C_2$, $C_4$ | 8T16, 16T36, 16T41 x 2, 32T22 |
8T17 | $C_4\wr C_2$ | $32$ | $-1$ | ✓ | $C_2$, $D_{4}$ | 8T17, 16T28, 16T42, 32T14 |
8T18 | $C_2^2 \wr C_2$ | $32$ | $1$ | ✓ | $C_2$, $D_{4}$ x 3 | 8T18 x 7, 16T39 x 6, 16T46, 32T24 |
8T19 | $C_2^3 : C_4 $ | $32$ | $1$ | ✓ | $C_2$, $D_{4}$ | 8T19, 8T20, 8T21, 16T33 x 2, 16T52, 16T53, 32T19 |
8T20 | $C_2^3: C_4$ | $32$ | $1$ | ✓ | $C_2$, $C_4$ | 8T19 x 2, 8T21, 16T33 x 2, 16T52, 16T53, 32T19 |
8T21 | $C_2^3: C_4$ | $32$ | $-1$ | ✓ | $C_2$ x 3, $C_2^2$ | 8T19 x 2, 8T20, 16T33 x 2, 16T52, 16T53, 32T19 |
8T22 | $Q_8:C_2^2$ | $32$ | $1$ | ✓ | $C_2$ x 3, $C_2^2$ | 8T22 x 5, 16T23 x 9, 32T9 |
8T23 | $\textrm{GL(2,3)}$ | $48$ | $-1$ | ✓ | $S_4$ | 8T23, 16T66, 24T22 |
8T24 | $S_4\times C_2$ | $48$ | $1$ | ✓ | $C_2$, $S_4$ | 6T11 x 2, 8T24, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 16T61, 24T46, 24T47, 24T48 x 2 |
8T26 | $(C_4^2 : C_2):C_2$ | $64$ | $-1$ | ✓ | $C_2$, $D_{4}$ | 8T26 x 3, 16T135 x 2, 16T141 x 2, 16T142 x 2, 16T152 x 2, 32T147 x 2, 32T148 x 2, 32T155, 32T156 |
8T27 | $((C_8 : C_2):C_2):C_2$ | $64$ | $-1$ | ✓ | $C_2$, $C_4$ | 8T27, 8T28 x 2, 16T130, 16T157 x 2, 16T158 x 2, 16T159 x 2, 16T166, 16T170, 16T171, 16T172, 32T138 x 2, 32T139, 32T170, 32T176 |
8T28 | $(((C_4 \times C_2): C_2):C_2):C_2$ | $64$ | $-1$ | ✓ | $C_2$, $D_{4}$ | 8T27 x 2, 8T28, 16T130, 16T157 x 2, 16T158 x 2, 16T159 x 2, 16T166, 16T170, 16T171, 16T172, 32T138 x 2, 32T139, 32T170, 32T176 |
8T29 | $(((C_4 \times C_2): C_2):C_2):C_2$ | $64$ | $1$ | ✓ | $C_2$, $D_{4}$ | 8T29 x 5, 8T31 x 2, 16T127, 16T128 x 3, 16T129 x 3, 16T147, 16T149 x 6, 16T150 x 3, 32T136 x 3, 32T137 x 2, 32T163 x 3 |
8T30 | $(((C_4 \times C_2): C_2):C_2):C_2$ | $64$ | $-1$ | ✓ | $C_2$, $D_{4}$ | 8T30 x 3, 16T143 x 2, 16T167 x 2, 16T168 x 2, 16T169 x 2, 32T157 x 2, 32T177, 32T178 |
8T31 | $(((C_4 \times C_2): C_2):C_2):C_2$ | $64$ | $-1$ | ✓ | $C_2$ x 3, $C_2^2$ | 8T29 x 6, 8T31, 16T127, 16T128 x 3, 16T129 x 3, 16T147, 16T149 x 6, 16T150 x 3, 32T136 x 3, 32T137 x 2, 32T163 x 3 |
8T32 | $((C_2 \times D_4): C_2):C_3$ | $96$ | $1$ | ✓ | $A_4$ | 8T32 x 2, 24T97 x 3, 24T149, 32T420 |
8T33 | $C_2^4:C_6$ | $96$ | $1$ | ✓ | $C_2$ | 8T33, 12T58 x 2, 12T59 x 2, 16T183, 24T181 x 2, 24T182 x 2, 24T183 x 2, 24T184 x 2, 24T185, 24T186, 32T389 |
8T34 | $V_4^2:S_3$ | $96$ | $1$ | ✓ | $C_2$ | 12T66 x 3, 12T67, 12T68 x 3, 12T69, 16T194, 24T195 x 3, 24T196 x 3, 24T197 x 3, 24T198, 24T199, 24T200 x 3, 32T398 |
8T35 | $C_2 \wr C_2\wr C_2$ | $128$ | $-1$ | ✓ | $C_2$, $D_{4}$ | 8T35 x 7, 16T376 x 4, 16T388 x 4, 16T390 x 4, 16T391 x 4, 16T393 x 4, 16T395 x 4, 16T396 x 4, 16T401 x 4, 32T852 x 4, 32T853 x 2, 32T854 x 2, 32T872 x 2, 32T876 x 4, 32T877 x 2, 32T880 x 2, 32T882 x 2, 32T883 x 4, 32T884 x 2, 32T885 x 2 |
8T38 | $C_2\wr A_4$ | $192$ | $-1$ | ✓ | $A_4$ | 8T38, 16T425, 16T427, 24T288 x 2, 24T425 x 2, 32T2185 x 2 |
Results are complete for degrees $\leq 23$.