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Parity Cyclic Solvable Primitive Equivalent siblings
Degree $T$-number Order Group Nilpotency class
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Results (1-50 of 166 matches)

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Label Name Order Parity Solvable Subfields Low Degree Siblings
16T72 $\OD_{16}:C_2^2$ $64$ $1$ ✓ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(C_8:C_2):C_2$ x 2 16T72 x 3, 16T99 x 4, 32T60 x 4, 32T61, 32T100
16T73 $C_4^2:C_2^2$ $64$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$, $Q_8:C_2^2$ x 2 16T73 x 7, 32T62 x 4, 32T63 x 2, 32T269 x 2
16T75 $C_2^3.D_4$ $64$ $1$ ✓ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $Z_8 : Z_8^\times$ x 2 16T75 x 7, 32T65 x 2, 32T66 x 4
16T82 $C_4^2:C_2^2$ $64$ $1$ ✓ $C_2$ x 3, $C_2^2$, $Q_8:C_2$, $Q_8:C_2^2$ x 2 16T82 x 3, 32T77 x 2, 32T78 x 2, 32T234 x 2
16T84 $C_2^3:C_8$ $64$ $1$ ✓ $C_2$, $C_4$, $C_8:C_2$, $(C_8:C_2):C_2$, $C_2^3: C_4$ 16T84, 16T85 x 2, 32T81 x 2, 32T82, 32T83
16T87 $C_2^3:D_4$ $64$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$, $Q_8:C_2^2$ x 2 16T87 x 7, 16T119 x 4, 32T85 x 4, 32T86 x 4, 32T128 x 2
16T89 $C_8:C_2^3$ $64$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$, $Z_8 : Z_8^\times$ x 2 16T89 x 7, 32T89 x 4, 32T90 x 2, 32T279 x 2
16T93 $C_2^4:C_4$ $64$ $1$ ✓ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $C_2^3: C_4$ x 2 16T76 x 4, 16T78, 16T92, 16T93, 16T94 x 2, 16T102 x 2, 32T67 x 2, 32T70 x 2, 32T71, 32T94 x 2, 32T95
16T118 $D_8:C_2^2$ $64$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$ 16T100, 16T118 x 3, 32T101 x 2, 32T102, 32T127 x 4
16T122 $C_4^2:C_2^2$ $64$ $1$ ✓ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$ 16T106, 16T107 x 2, 16T122, 32T110, 32T111, 32T112, 32T130 x 2
16T134 $D_{16}:C_2$ $64$ $-1$ ✓ $C_2$, $D_{4}$, $D_{8}$ 16T134, 32T145, 32T146 x 2, 32T298
16T142 $D_4:D_4$ $64$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$, $(C_4^2 : C_2):C_2$ x 2 8T26 x 4, 16T135 x 2, 16T141 x 2, 16T142, 16T152 x 2, 32T147 x 2, 32T148 x 2, 32T155, 32T156
16T144 $\OD_{32}:C_2$ $64$ $-1$ ✓ $C_2$, $D_{4}$, $QD_{16}$ 16T144, 32T158 x 2, 32T159
16T151 $C_4^2.C_4$ $64$ $1$ ✓ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$ 16T131, 16T151, 32T140, 32T165
16T159 $C_2\wr C_4$ $64$ $1$ ✓ $C_2$, $C_4$, $C_2^3: C_4$, $((C_8 : C_2):C_2):C_2$ x 2 8T27 x 2, 8T28 x 2, 16T130, 16T157 x 2, 16T158 x 2, 16T159, 16T166, 16T170, 16T171, 16T172, 32T138 x 2, 32T139, 32T170, 32T176
16T162 $D_4.D_4$ $64$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$ 16T162, 16T164, 32T172, 32T173, 32T345 x 2
16T169 $C_4^2:C_4$ $64$ $1$ ✓ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2 8T30 x 4, 16T143 x 2, 16T167 x 2, 16T168 x 2, 16T169, 32T157 x 2, 32T177, 32T178
16T188 $C_2\times \GL(2,3)$ $96$ $1$ ✓ $C_2$, $S_4$, $\textrm{GL(2,3)}$ x 2, $S_4\times C_2$ 16T188 x 3, 32T394
16T189 $\GL(2,3):C_2$ $96$ $1$ ✓ $C_2$, $S_4$, $S_4\times C_2$ 16T189, 32T395
16T204 $D_8:C_2^3$ $128$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$ 16T204 x 5, 32T439 x 3, 32T440 x 12, 32T441 x 6, 32T1866 x 6
16T206 $D_4^2:C_2$ $128$ $1$ ✓ $C_2$ x 3, $C_2^2$, $Q_8:C_2^2$ x 3 16T206 x 15, 32T445 x 12, 32T446 x 4, 32T447 x 12, 32T1031 x 2, 32T1040 x 6
16T214 $C_4^2:C_2^3$ $128$ $1$ ✓ $C_2$, $D_{4}$ x 3, $C_2^2 \wr C_2$ 16T214 x 3, 16T262 x 4, 16T288 x 2, 32T469 x 4, 32T470 x 8, 32T471 x 4, 32T603 x 4, 32T604 x 2, 32T605 x 2, 32T665 x 2, 32T666
16T228 $C_2^4:C_8$ $128$ $1$ ✓ $C_2$, $C_4$, $(C_8:C_2):C_2$, $((C_8 : C_2):C_2):C_2$ x 2 16T228 x 7, 16T257 x 4, 16T258 x 4, 32T509 x 8, 32T510 x 4, 32T511 x 4, 32T512 x 2, 32T513 x 4, 32T591 x 2, 32T592 x 4, 32T593, 32T594, 32T1797
16T232 $(C_2^2\times D_4):C_4$ $128$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$ 16T232, 16T290 x 4, 32T519 x 4, 32T520 x 4, 32T521, 32T668 x 8, 32T669 x 2, 32T670 x 2, 32T1918 x 2
16T256 $D_{16}:C_4$ $128$ $-1$ ✓ $C_2$, $D_{4}$, $Z_8 : Z_8^\times$ 16T256, 32T588, 32T589, 32T590, 32T2022
16T259 $C_2^5:C_4$ $128$ $1$ ✓ $C_2$, $C_4$, $C_2^3: C_4$, $((C_8 : C_2):C_2):C_2$ x 2 16T227 x 4, 16T259 x 7, 16T261 x 4, 16T273 x 4, 16T283 x 4, 32T506, 32T507 x 2, 32T508 x 4, 32T595 x 4, 32T596 x 8, 32T597 x 2, 32T598 x 4, 32T599 x 4, 32T601, 32T602 x 2, 32T633, 32T657, 32T1130 x 2, 32T1796
16T263 $(C_2^2\times D_4):C_4$ $128$ $1$ ✓ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$ 16T244 x 4, 16T263, 32T556 x 2, 32T557 x 2, 32T558 x 4, 32T606, 32T607 x 4, 32T1136 x 4
16T267 $\OD_{16}.D_4$ $128$ $1$ ✓ $C_2$ x 3, $C_2^2$, $Q_8:C_2$ 16T267, 32T618 x 2, 32T619 x 2, 32T620 x 2, 32T621, 32T1973, 32T1984
16T277 $C_2^4:D_4$ $128$ $1$ ✓ $C_2$, $D_{4}$ x 3, $C_2^2 \wr C_2$ 16T241, 16T277, 16T301, 16T309 x 6, 16T320 x 3, 16T329 x 3, 32T547 x 3, 32T548 x 3, 32T549, 32T643 x 4, 32T644 x 6, 32T698 x 6, 32T716 x 6, 32T717 x 6, 32T749 x 3
16T282 $C_4^2.C_2^3$ $128$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$ 16T269 x 4, 16T282, 32T624 x 2, 32T625 x 4, 32T626 x 2, 32T655 x 4, 32T656, 32T1381 x 4, 32T1908 x 2
16T285 $C_4^2.(C_2\times C_4)$ $128$ $1$ ✓ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$ 16T226 x 4, 16T285, 32T503 x 2, 32T504 x 4, 32T505 x 2, 32T660 x 4, 32T661
16T290 $(C_2^2\times D_4):C_4$ $128$ $1$ ✓ $C_2$, $C_4$, $D_{4}$ x 2, $C_2^2:C_4$ 16T232 x 2, 16T290 x 3, 32T519 x 4, 32T520 x 4, 32T521, 32T668 x 8, 32T669 x 2, 32T670 x 2, 32T1918 x 2
16T297 $C_2^4.D_4$ $128$ $1$ ✓ $C_2$, $D_{4}$, $C_2^3 : C_4 $ 16T234 x 2, 16T250 x 2, 16T297 x 3, 16T310 x 2, 32T524 x 2, 32T525, 32T526 x 2, 32T569 x 2, 32T570, 32T689 x 4, 32T690 x 4, 32T718 x 2, 32T719
16T298 $(C_2\times C_8):D_4$ $128$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$ 16T238 x 4, 16T298, 32T537 x 2, 32T538 x 2, 32T539 x 4, 32T691 x 4, 32T692, 32T1983 x 2
16T307 $C_4^2.D_4$ $128$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$ 16T221 x 4, 16T307, 32T488 x 2, 32T489 x 4, 32T490 x 2, 32T711 x 2, 32T712, 32T713 x 2, 32T1971, 32T1992
16T308 $D_8:D_4$ $128$ $1$ ✓ $C_2$ x 3, $C_2^2$, $Q_8:C_2^2$ 16T308, 32T714, 32T715 x 2, 32T1424, 32T1431 x 2, 32T1967
16T312 $\OD_{16}.D_4$ $128$ $1$ ✓ $C_2$ x 3, $C_2^2$, $Q_8:C_2$ 16T312, 32T722 x 2, 32T723 x 2, 32T724, 32T725 x 2, 32T1870, 32T1961
16T319 $C_2^4.D_4$ $128$ $1$ ✓ $C_2$, $D_{4}$, $C_2^3 : C_4 $ 16T219, 16T236, 16T266, 16T287, 16T317, 16T319, 16T324, 32T482, 32T483, 32T484, 32T530, 32T531, 32T614, 32T615, 32T616, 32T617, 32T663, 32T664, 32T731 x 2, 32T733 x 2, 32T734 x 2, 32T743
16T323 $C_2^3.C_4^2$ $128$ $1$ ✓ $C_2$ x 3, $C_2^2$, $C_2^3: C_4$ x 3 16T323 x 15, 32T740 x 12, 32T741 x 12, 32T742 x 4, 32T1305 x 6
16T331 $\OD_{16}:D_4$ $128$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4\times C_2$ 16T331, 16T367 x 4, 32T753 x 4, 32T754 x 2, 32T755, 32T756 x 2, 32T836 x 2, 32T837 x 2, 32T1924, 32T1964
16T341 $C_4^2:D_4$ $128$ $1$ ✓ $C_2$, $D_{4}$, $(((C_4 \times C_2): C_2):C_2):C_2$ 16T336, 16T340, 16T341, 16T352, 16T359, 16T366, 16T402, 32T767, 32T768, 32T769, 32T777, 32T778, 32T779, 32T780 x 2, 32T781, 32T807, 32T808, 32T820, 32T821, 32T894, 32T1569, 32T1694
16T348 $C_2^3.\SD_{16}$ $128$ $-1$ ✓ $C_2$, $D_{4}$, $QD_{16}$ 16T348, 32T796, 32T797, 32T798, 32T2019
16T349 $C_4^2.D_4$ $128$ $1$ ✓ $C_2$, $D_{4}$ x 3, $C_2^2 \wr C_2$ 16T349, 16T357, 16T404 x 3, 32T799 x 4, 32T800 x 6, 32T817 x 3
16T355 $(C_2\times C_8).D_4$ $128$ $-1$ ✓ $C_2$, $C_4$, $(C_8:C_2):C_2$ 16T355, 32T813 x 2, 32T814, 32T2003
16T362 $C_4^2.(C_2\times C_4)$ $128$ $1$ ✓ $C_2$, $C_4$, $C_2^3: C_4$ 16T362, 32T826 x 2, 32T827, 32T1679, 32T1947
16T365 $C_4^2:D_4$ $128$ $1$ ✓ $C_2$, $D_{4}$, $(((C_4 \times C_2): C_2):C_2):C_2$ 16T342 x 2, 16T365 x 3, 16T381, 16T386, 16T394 x 2, 32T782 x 2, 32T783 x 2, 32T784 x 2, 32T833 x 2, 32T834 x 4, 32T835 x 2, 32T862, 32T871 x 2, 32T881 x 2
16T371 $C_2^3.D_8$ $128$ $-1$ ✓ $C_2$, $D_{4}$, $D_{8}$ 16T371, 32T841, 32T842, 32T843, 32T1772 x 2, 32T2013
16T374 $C_2^3.\SD_{16}$ $128$ $-1$ ✓ $C_2$, $D_{4}$, $QD_{16}$ 16T374, 32T847, 32T848, 32T849, 32T1954
16T375 $C_4^2.(C_2\times C_4)$ $128$ $-1$ ✓ $C_2$ x 3, $C_2^2$, $C_2^3: C_4$ 16T375, 32T850 x 2, 32T851, 32T1824 x 2, 32T2008
16T379 $D_8:D_4$ $128$ $-1$ ✓ $C_2$, $D_{4}$, $Z_8 : Z_8^\times$ 16T379 x 3, 32T859 x 2, 32T860 x 4
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Results are complete for degrees $\leq 23$.