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The results below are complete, since the LMFDB contains all transitive groups of degree at most 47 (except 32)

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

  displayed columns for results
Label Name Order Parity Solvable Subfields Low Degree Siblings
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
8T25 $C_2^3:C_7$ $56$ $1$ ✓ 14T6, 28T11
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
8T36 $C_2^3:(C_7: C_3)$ $168$ $1$ ✓ 14T11, 24T283, 28T27, 42T26
8T37 $\PSL(2,7)$ $168$ $1$ 7T5 x 2, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38 x 2
8T38 $C_2\wr A_4$ $192$ $-1$ ✓ $A_4$ 8T38, 16T425, 16T427, 24T288 x 2, 24T425 x 2, 32T2185 x 2
8T39 $C_2^3:S_4$ $192$ $1$ ✓ $S_4$ 8T39 x 5, 16T442 x 3, 24T333 x 6, 24T431 x 2, 32T2213 x 2
8T40 $Q_8:S_4$ $192$ $-1$ ✓ $S_4$ 8T40, 16T444, 16T445, 24T332 x 2, 24T430 x 2, 32T2215 x 2
8T41 $V_4^2:(S_3\times C_2)$ $192$ $1$ ✓ $C_2$ 8T41, 12T108 x 2, 12T109 x 2, 12T110 x 2, 12T111 x 2, 16T435 x 2, 16T436, 24T516 x 2, 24T517 x 2, 24T518 x 2, 24T519 x 2, 24T520 x 2, 24T521 x 2, 24T522 x 2, 24T523, 24T524 x 2, 24T525 x 2, 24T526 x 2, 24T527, 24T528, 24T529, 32T2148, 32T2149 x 2
8T42 $A_4\wr C_2$ $288$ $1$ ✓ $C_2$ 12T126, 12T128, 12T129, 16T708, 18T112, 18T113, 24T692, 24T694, 24T695, 24T702, 24T703, 24T704, 32T9306, 36T316, 36T318, 36T456, 36T457, 36T458, 36T459
8T43 $\PGL(2,7)$ $336$ $-1$ 14T16, 16T713, 21T20, 24T707, 28T42, 28T46, 42T81, 42T82, 42T83
8T44 $C_2 \wr S_4$ $384$ $-1$ ✓ $S_4$ 8T44 x 3, 16T736 x 2, 16T743 x 2, 16T748 x 2, 16T752 x 2, 24T708 x 4, 24T1151 x 4, 32T9340, 32T9355, 32T9459 x 4
8T45 $(A_4\wr C_2):C_2$ $576$ $1$ ✓ $C_2$ 12T161, 12T163, 12T165 x 2, 16T1032, 16T1034, 18T179, 18T180, 18T185 x 2, 24T1490, 24T1492, 24T1493 x 2, 24T1494 x 2, 24T1495 x 2, 24T1503, 24T1504 x 2, 32T34597 x 2, 32T34598, 36T759, 36T760, 36T762, 36T763, 36T774 x 2, 36T775 x 2, 36T960, 36T961, 36T962 x 2, 36T963 x 2
8T46 $A_4^2:C_4$ $576$ $-1$ ✓ $C_2$ 12T160, 12T162, 16T1030, 16T1031, 18T182, 18T184, 24T1489, 24T1491, 24T1505, 24T1506 x 2, 24T1508, 32T34594, 36T764, 36T765, 36T766, 36T767, 36T964, 36T965
8T47 $S_4\wr C_2$ $1152$ $-1$ ✓ $C_2$ 12T200, 12T201, 12T202, 12T203, 16T1292, 16T1294, 16T1295, 16T1296, 18T272, 18T273, 18T274, 18T275, 24T2803, 24T2804, 24T2805, 24T2806, 24T2807, 24T2808, 24T2809, 24T2810, 24T2821, 24T2826, 32T96692, 32T96694, 32T96695, 32T96696, 36T1758, 36T1759, 36T1760, 36T1761, 36T1762, 36T1763, 36T1764, 36T1765, 36T1766, 36T1767, 36T1768, 36T1769, 36T1943, 36T1944, 36T1945, 36T1946
8T48 $C_2^3:\GL(3,2)$ $1344$ $1$ 8T48, 14T34 x 2, 28T153, 28T159 x 2, 42T210 x 2, 42T211 x 2
8T49 $A_8$ $20160$ $1$ 15T72 x 2, 28T433, 35T36
8T50 $S_8$ $40320$ $-1$ 16T1838, 28T502, 30T1153, 35T44
  displayed columns for results

Results are complete for degrees $\leq 23$.