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Label | Name | Order | Parity | Solvable | Subfields | Low Degree Siblings |
---|---|---|---|---|---|---|
22T1 | $C_{22}$ | $22$ | $-1$ | ✓ | $C_2$, $C_{11}$ | |
22T2 | $D_{11}$ | $22$ | $-1$ | ✓ | $C_2$, $D_{11}$ | 11T2 |
22T3 | $D_{22}$ | $44$ | $-1$ | ✓ | $C_2$, $D_{11}$ | 22T3, 44T4 |
22T4 | $F_{11}$ | $110$ | $-1$ | ✓ | $C_2$, $F_{11}$ | 11T4 |
22T5 | $C_{11}:C_{10}$ | $110$ | $-1$ | ✓ | $C_2$, $C_{11}:C_5$ | |
22T6 | $C_2\times F_{11}$ | $220$ | $-1$ | ✓ | $C_2$, $F_{11}$ | 22T6, 44T14 |
22T7 | $C_{11}\times D_{11}$ | $242$ | $-1$ | ✓ | $C_2$ | 22T7 x 4 |
22T8 | $C_{11}^2:C_4$ | $484$ | $1$ | ✓ | $C_2$ | 22T8 x 5, 44T28 x 6 |
22T9 | $D_{11}^2$ | $484$ | $-1$ | ✓ | $C_2$ | 22T9 x 4, 44T29 x 5 |
22T10 | $D_{11}\wr C_2$ | $968$ | $-1$ | ✓ | $C_2$ | 22T10, 44T39 x 2, 44T40 x 2, 44T41 x 2, 44T44 x 2 |
22T11 | $C_{11}:F_{11}$ | $1210$ | $-1$ | ✓ | $C_2$ | 22T11 x 4 |
22T12 | $C_{11}^2:D_5$ | $1210$ | $-1$ | ✓ | $C_2$ | |
22T13 | $C_2\times \PSL(2,11)$ | $1320$ | $-1$ | $C_2$, $\PSL(2,11)$ | 22T13, 24T2948 | |
22T14 | $\PGL(2,11)$ | $1320$ | $-1$ | $C_2$ | 12T218, 24T2949 | |
22T15 | $D_{11}:F_{11}$ | $2420$ | $-1$ | ✓ | $C_2$ | 22T15 x 4, 44T59 x 5 |
22T16 | $C_{11}^2:C_5:C_4$ | $2420$ | $1$ | ✓ | $C_2$ | 44T60 |
22T17 | $C_{11}^2:D_{10}$ | $2420$ | $-1$ | ✓ | $C_2$ | 44T61 |
22T18 | $C_{11}^2:C_{20}$ | $2420$ | $1$ | ✓ | $C_2$ | 22T18 x 5, 44T62 x 6 |
22T19 | $D_{11}^2:D_5$ | $4840$ | $-1$ | ✓ | $C_2$ | 44T81, 44T82, 44T83 |
22T20 | $D_{11}^2:C_{10}$ | $4840$ | $-1$ | ✓ | $C_2$ | 22T20, 44T84 x 2, 44T85 x 2, 44T86 x 2, 44T89 x 2 |
22T21 | $C_{11}^2:(C_5\times D_5)$ | $6050$ | $-1$ | ✓ | $C_2$ | |
22T22 | $M_{11}$ | $7920$ | $1$ | $M_{11}$ | 11T6, 12T272 | |
22T23 | $C_2^{10}:C_{11}$ | $11264$ | $1$ | ✓ | $C_{11}$ | 22T23 x 92, 44T116 x 31, 44T117 x 465, 44T118 x 465, 44T119 x 465, 44T120 x 465, 44T121 x 930, 44T122 x 930, 44T123 x 930, 44T124 x 930, 44T125 x 930, 44T126 x 930, 44T127 x 930, 44T128 x 930, 44T129 x 930, 44T130 x 930, 44T131 x 930, 44T132 x 930, 44T133 x 930, 44T134 x 930, 44T135 x 930 |
22T24 | $C_{11}^2:C_5:C_{20}$ | $12100$ | $1$ | ✓ | $C_2$ | 44T138 |
22T25 | $C_{11}^2:(C_5\times D_{10})$ | $12100$ | $-1$ | ✓ | $C_2$ | 44T139 |
22T26 | $C_2\times M_{11}$ | $15840$ | $-1$ | $M_{11}$ | 22T27, 24T12204, 44T140 | |
22T27 | $C_2\times M_{11}$ | $15840$ | $-1$ | $C_2$, $M_{11}$ | 22T26, 24T12204, 44T140 | |
22T28 | $C_{15}\times C_{420}$ | $22528$ | $-1$ | ✓ | $C_{11}$ | 22T28 x 92, 44T146 x 93, 44T149 x 93, 44T150 x 465, 44T151 x 465, 44T152 x 465, 44T153 x 465, 44T154 x 465, 44T155 x 465, 44T156 x 930, 44T157 x 930, 44T158 x 930, 44T159 x 930, 44T160 x 930, 44T161 x 930, 44T162 x 930, 44T163 x 930, 44T164 x 930, 44T165 x 930, 44T166 x 930, 44T167 x 930, 44T168 x 930, 44T169 x 930, 44T170 x 930, 44T171 x 930, 44T172 x 930, 44T173 x 930, 44T174 x 930, 44T175 x 930, 44T176 x 930, 44T177 x 930, 44T178 x 930, 44T179 x 930, 44T180 x 930, 44T181 x 930, 44T182 x 930, 44T183 x 930, 44T184 x 930, 44T185 x 930, 44T186 x 930, 44T187 x 930, 44T188 x 930, 44T189 x 930, 44T190 x 930, 44T191 x 930, 44T192 x 930, 44T193 x 930, 44T194 x 930, 44T195 x 930, 44T196 x 930, 44T197 x 930, 44T198 x 930, 44T199 x 930, 44T200 x 930, 44T201 x 930, 44T202 x 930, 44T203 x 930 |
22T29 | $C_2^{10}.D_{11}$ | $22528$ | $-1$ | ✓ | $D_{11}$ | 22T29 x 30, 22T30 x 31, 44T147 x 31, 44T148 x 31, 44T204 x 155, 44T205 x 155, 44T206 x 155, 44T207 x 31, 44T208 x 155, 44T209 x 155, 44T210 x 155, 44T211 x 155 |
22T30 | $C_2^{10}.D_{11}$ | $22528$ | $1$ | ✓ | $D_{11}$ | 22T29 x 31, 22T30 x 30, 44T147 x 31, 44T148 x 31, 44T204 x 155, 44T205 x 155, 44T206 x 155, 44T207 x 31, 44T208 x 155, 44T209 x 155, 44T210 x 155, 44T211 x 155 |
22T31 | $F_{11}\wr C_2$ | $24200$ | $-1$ | ✓ | $C_2$ | 44T218, 44T219, 44T220 |
22T32 | $C_2^{10}.D_{22}$ | $45056$ | $-1$ | ✓ | $D_{11}$ | 22T32 x 61, 44T236 x 31, 44T239 x 31, 44T240 x 62, 44T241 x 62, 44T266 x 310, 44T267 x 310, 44T268 x 310, 44T269 x 31, 44T270 x 155, 44T271 x 155, 44T272 x 155, 44T273 x 310, 44T274 x 310, 44T275 x 310 |
22T33 | $C_2^{10}:C_{11}:C_5$ | $56320$ | $1$ | ✓ | $C_{11}:C_5$ | 22T33 x 2, 44T288 |
22T34 | $C_2^{10}.F_{11}$ | $112640$ | $1$ | ✓ | $F_{11}$ | 22T35, 44T312, 44T313, 44T316 |
22T35 | $C_2^{10}.F_{11}$ | $112640$ | $-1$ | ✓ | $F_{11}$ | 22T34, 44T312, 44T313, 44T316 |
22T36 | $C_2^{10}.C_{11}:C_{10}$ | $112640$ | $-1$ | ✓ | $C_{11}:C_5$ | 22T36 x 2, 44T314 x 3, 44T315 x 3 |
22T37 | $C_2\times C_2^{10}.F_{11}$ | $225280$ | $-1$ | ✓ | $F_{11}$ | 22T37, 44T333, 44T336, 44T339 x 2, 44T340 x 2, 44T341 |
22T38 | $M_{22}$ | $443520$ | $1$ | |||
22T39 | $C_2^{10}.\PSL(2,11)$ | $675840$ | $1$ | $\PSL(2,11)$ | 22T39 | |
22T40 | $\PSL(2,11)\wr C_2$ | $871200$ | $-1$ | $C_2$ | 22T40, 24T21362 | |
22T41 | $M_{22}:C_2$ | $887040$ | $-1$ | 44T405 | ||
22T42 | $C_2^{11}.\PSL(2,11)$ | $1351680$ | $-1$ | $\PSL(2,11)$ | 22T42, 44T433 x 2 | |
22T43 | $C_2^{10}.M_{11}$ | $8110080$ | $1$ | $M_{11}$ | 22T43, 44T554 | |
22T44 | $C_2^{11}.M_{11}$ | $16220160$ | $-1$ | $M_{11}$ | 22T44, 44T613, 44T615 x 2, 44T617 x 2 | |
22T45 | $S_{11}$ | $39916800$ | $-1$ | $C_2$, $S_{11}$ | 11T8 | |
22T46 | $C_2\times A_{11}$ | $39916800$ | $-1$ | $C_2$, $A_{11}$ | ||
22T47 | $C_2\times S_{11}$ | $79833600$ | $-1$ | $C_2$, $S_{11}$ | 22T47, 44T1258 | |
22T48 | $M_{11}\wr C_2$ | $125452800$ | $-1$ | $C_2$ | 24T24600, 44T1454 | |
22T49 | $C_2^{10}.A_{11}$ | $20437401600$ | $1$ | $A_{11}$ | ||
22T50 | $C_2^{10}.S_{11}$ | $40874803200$ | $-1$ | $S_{11}$ | 22T51, 44T1749 |
Results are complete for degrees $\leq 23$.