Galois group search results

Results (1-50 of 512264 matches)

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Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
4T1	$C_4$	$4$	$-1$	✓	$1$	$4$	$C_2$
4T2	$C_2^2$	$4$	$1$	✓	$1$	$4$	$C_2$ x 3
4T3	$D_{4}$	$8$	$-1$	✓	$2$	$5$	$C_2$	4T3, 8T4
6T1	$C_6$	$6$	$-1$	✓	$1$	$6$	$C_2$, $C_3$
6T2	$S_3$	$6$	$-1$	✓	$-1$	$3$	$C_2$, $S_3$	3T2
6T3	$D_{6}$	$12$	$-1$	✓	$-1$	$6$	$C_2$, $S_3$	6T3, 12T3
6T4	$A_4$	$12$	$1$	✓	$-1$	$4$	$C_3$	4T4, 12T4
6T5	$S_3\times C_3$	$18$	$-1$	✓	$-1$	$9$	$C_2$	9T4, 18T3
6T6	$A_4\times C_2$	$24$	$-1$	✓	$-1$	$8$	$C_3$	8T13, 12T6, 12T7, 24T9
6T7	$S_4$	$24$	$1$	✓	$-1$	$5$	$S_3$	4T5, 6T8, 8T14, 12T8, 12T9, 24T10
6T8	$S_4$	$24$	$-1$	✓	$-1$	$5$	$S_3$	4T5, 6T7, 8T14, 12T8, 12T9, 24T10
6T9	$S_3^2$	$36$	$-1$	✓	$-1$	$9$	$C_2$	9T8, 12T16, 18T9, 18T11 x 2, 36T13
6T10	$C_3^2:C_4$	$36$	$1$	✓	$-1$	$6$	$C_2$	6T10, 9T9, 12T17 x 2, 18T10, 36T14
6T11	$S_4\times C_2$	$48$	$-1$	✓	$-1$	$10$	$S_3$	6T11, 8T24 x 2, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 16T61, 24T46, 24T47, 24T48 x 2
6T13	$C_3^2:D_4$	$72$	$-1$	✓	$-1$	$9$	$C_2$	6T13, 9T16, 12T34 x 2, 12T35 x 2, 12T36 x 2, 18T34 x 2, 18T36, 24T72 x 2, 36T53, 36T54 x 2
8T1	$C_8$	$8$	$-1$	✓	$1$	$8$	$C_2$, $C_4$
8T2	$C_4\times C_2$	$8$	$1$	✓	$1$	$8$	$C_2$ x 3, $C_4$ x 2, $C_2^2$
8T3	$C_2^3$	$8$	$1$	✓	$1$	$8$	$C_2$ x 7, $C_2^2$ x 7
8T4	$D_4$	$8$	$1$	✓	$2$	$5$	$C_2$ x 3, $C_2^2$, $D_{4}$ x 2	4T3 x 2
8T5	$Q_8$	$8$	$1$	✓	$2$	$5$	$C_2$ x 3, $C_2^2$
8T6	$D_{8}$	$16$	$-1$	✓	$3$	$7$	$C_2$, $D_{4}$	8T6, 16T13
8T7	$C_8:C_2$	$16$	$-1$	✓	$2$	$10$	$C_2$, $C_4$	16T6
8T8	$QD_{16}$	$16$	$-1$	✓	$3$	$7$	$C_2$, $D_{4}$	16T12
8T9	$D_4\times C_2$	$16$	$1$	✓	$2$	$10$	$C_2$ x 3, $C_2^2$, $D_{4}$ x 2	8T9 x 3, 16T9
8T10	$C_2^2:C_4$	$16$	$1$	✓	$2$	$10$	$C_2$, $C_4$, $D_{4}$ x 2	8T10, 16T10
8T11	$Q_8:C_2$	$16$	$1$	✓	$2$	$10$	$C_2$ x 3, $C_2^2$	8T11 x 2, 16T11
8T12	$\SL(2,3)$	$24$	$1$	✓	$-1$	$7$	$A_4$	24T7
8T13	$A_4\times C_2$	$24$	$1$	✓	$-1$	$8$	$C_2$, $A_4$	6T6, 12T6, 12T7, 24T9
8T14	$S_4$	$24$	$1$	✓	$-1$	$5$	$C_2$, $S_4$	4T5, 6T7, 6T8, 12T8, 12T9, 24T10
8T15	$Z_8 : Z_8^\times$	$32$	$-1$	✓	$3$	$11$	$C_2$, $D_{4}$	8T15, 16T35, 16T38 x 2, 16T45, 32T21
8T16	$(C_8:C_2):C_2$	$32$	$-1$	✓	$3$	$11$	$C_2$, $C_4$	8T16, 16T36, 16T41 x 2, 32T22
8T17	$C_4\wr C_2$	$32$	$-1$	✓	$3$	$14$	$C_2$, $D_{4}$	8T17, 16T28, 16T42, 32T14
8T18	$C_2^2 \wr C_2$	$32$	$1$	✓	$2$	$14$	$C_2$, $D_{4}$ x 3	8T18 x 7, 16T39 x 6, 16T46, 32T24
8T19	$C_2^3 : C_4$	$32$	$1$	✓	$3$	$11$	$C_2$, $D_{4}$	8T19, 8T20, 8T21, 16T33 x 2, 16T52, 16T53, 32T19
8T20	$C_2^3: C_4$	$32$	$1$	✓	$3$	$11$	$C_2$, $C_4$	8T19 x 2, 8T21, 16T33 x 2, 16T52, 16T53, 32T19
8T21	$C_2^3: C_4$	$32$	$-1$	✓	$3$	$11$	$C_2$ x 3, $C_2^2$	8T19 x 2, 8T20, 16T33 x 2, 16T52, 16T53, 32T19
8T22	$Q_8:C_2^2$	$32$	$1$	✓	$2$	$17$	$C_2$ x 3, $C_2^2$	8T22 x 5, 16T23 x 9, 32T9
8T23	$\textrm{GL(2,3)}$	$48$	$-1$	✓	$-1$	$8$	$S_4$	8T23, 16T66, 24T22
8T24	$S_4\times C_2$	$48$	$1$	✓	$-1$	$10$	$C_2$, $S_4$	6T11 x 2, 8T24, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 16T61, 24T46, 24T47, 24T48 x 2
8T26	$(C_4^2 : C_2):C_2$	$64$	$-1$	✓	$3$	$16$	$C_2$, $D_{4}$	8T26 x 3, 16T135 x 2, 16T141 x 2, 16T142 x 2, 16T152 x 2, 32T147 x 2, 32T148 x 2, 32T155, 32T156
8T27	$((C_8 : C_2):C_2):C_2$	$64$	$-1$	✓	$4$	$13$	$C_2$, $C_4$	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	$(((C_4 \times C_2): C_2):C_2):C_2$	$64$	$-1$	✓	$4$	$13$	$C_2$, $D_{4}$	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	$(((C_4 \times C_2): C_2):C_2):C_2$	$64$	$1$	✓	$3$	$16$	$C_2$, $D_{4}$	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	$(((C_4 \times C_2): C_2):C_2):C_2$	$64$	$-1$	✓	$4$	$13$	$C_2$, $D_{4}$	8T30 x 3, 16T143 x 2, 16T167 x 2, 16T168 x 2, 16T169 x 2, 32T157 x 2, 32T177, 32T178
8T31	$(((C_4 \times C_2): C_2):C_2):C_2$	$64$	$-1$	✓	$3$	$16$	$C_2$ 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	$((C_2 \times D_4): C_2):C_3$	$96$	$1$	✓	$-1$	$11$	$A_4$	8T32 x 2, 24T97 x 3, 24T149, 32T420
8T33	$C_2^4:C_6$	$96$	$1$	✓	$-1$	$10$	$C_2$	8T33, 12T58 x 2, 12T59 x 2, 16T183, 24T181 x 2, 24T182 x 2, 24T183 x 2, 24T184 x 2, 24T185, 24T186, 32T389
8T34	$V_4^2:S_3$	$96$	$1$	✓	$-1$	$10$	$C_2$	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	$C_2 \wr C_2\wr C_2$	$128$	$-1$	✓	$4$	$20$	$C_2$, $D_{4}$	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	$C_2\wr A_4$	$192$	$-1$	✓	$-1$	$16$	$A_4$	8T38, 16T425, 16T427, 24T288 x 2, 24T425 x 2, 32T2185 x 2

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Results are complete for degrees $\leq 23$.