↑

Learn more

Refine search

Parity Cyclic Solvable Primitive Equivalent siblings
Degree $T$-number Order Group Nilpotency class
Sort order Select

Results (1-50 of 512264 matches)

Next   displayed columns for results
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
Next   displayed columns for results

Results are complete for degrees $\leq 23$.