# Extensions 1→N→G→Q→1 with N=C4 and Q=C2×D4

Direct product G=N×Q with N=C4 and Q=C2×D4
dρLabelID
C2×C4×D432C2xC4xD464,196

Semidirect products G=N:Q with N=C4 and Q=C2×D4
extensionφ:Q→Aut NdρLabelID
C41(C2×D4) = C2×C41D4φ: C2×D4/C2×C4C2 ⊆ Aut C432C4:1(C2xD4)64,211
C42(C2×D4) = D42φ: C2×D4/D4C2 ⊆ Aut C416C4:2(C2xD4)64,226
C43(C2×D4) = C2×C4⋊D4φ: C2×D4/C23C2 ⊆ Aut C432C4:3(C2xD4)64,203

Non-split extensions G=N.Q with N=C4 and Q=C2×D4
extensionφ:Q→Aut NdρLabelID
C4.1(C2×D4) = C85D4φ: C2×D4/C2×C4C2 ⊆ Aut C432C4.1(C2xD4)64,173
C4.2(C2×D4) = C84D4φ: C2×D4/C2×C4C2 ⊆ Aut C432C4.2(C2xD4)64,174
C4.3(C2×D4) = C4⋊Q16φ: C2×D4/C2×C4C2 ⊆ Aut C464C4.3(C2xD4)64,175
C4.4(C2×D4) = C8.12D4φ: C2×D4/C2×C4C2 ⊆ Aut C432C4.4(C2xD4)64,176
C4.5(C2×D4) = C83D4φ: C2×D4/C2×C4C2 ⊆ Aut C432C4.5(C2xD4)64,177
C4.6(C2×D4) = C8.2D4φ: C2×D4/C2×C4C2 ⊆ Aut C432C4.6(C2xD4)64,178
C4.7(C2×D4) = C2×D16φ: C2×D4/C2×C4C2 ⊆ Aut C432C4.7(C2xD4)64,186
C4.8(C2×D4) = C2×SD32φ: C2×D4/C2×C4C2 ⊆ Aut C432C4.8(C2xD4)64,187
C4.9(C2×D4) = C2×Q32φ: C2×D4/C2×C4C2 ⊆ Aut C464C4.9(C2xD4)64,188
C4.10(C2×D4) = C4○D16φ: C2×D4/C2×C4C2 ⊆ Aut C4322C4.10(C2xD4)64,189
C4.11(C2×D4) = C16⋊C22φ: C2×D4/C2×C4C2 ⊆ Aut C4164+C4.11(C2xD4)64,190
C4.12(C2×D4) = Q32⋊C2φ: C2×D4/C2×C4C2 ⊆ Aut C4324-C4.12(C2xD4)64,191
C4.13(C2×D4) = C2×C4.4D4φ: C2×D4/C2×C4C2 ⊆ Aut C432C4.13(C2xD4)64,207
C4.14(C2×D4) = C2×C4⋊Q8φ: C2×D4/C2×C4C2 ⊆ Aut C464C4.14(C2xD4)64,212
C4.15(C2×D4) = C22.29C24φ: C2×D4/C2×C4C2 ⊆ Aut C416C4.15(C2xD4)64,216
C4.16(C2×D4) = C22×D8φ: C2×D4/C2×C4C2 ⊆ Aut C432C4.16(C2xD4)64,250
C4.17(C2×D4) = C22×SD16φ: C2×D4/C2×C4C2 ⊆ Aut C432C4.17(C2xD4)64,251
C4.18(C2×D4) = C22×Q16φ: C2×D4/C2×C4C2 ⊆ Aut C464C4.18(C2xD4)64,252
C4.19(C2×D4) = C22⋊D8φ: C2×D4/D4C2 ⊆ Aut C416C4.19(C2xD4)64,128
C4.20(C2×D4) = Q8⋊D4φ: C2×D4/D4C2 ⊆ Aut C432C4.20(C2xD4)64,129
C4.21(C2×D4) = D4⋊D4φ: C2×D4/D4C2 ⊆ Aut C432C4.21(C2xD4)64,130
C4.22(C2×D4) = C22⋊SD16φ: C2×D4/D4C2 ⊆ Aut C416C4.22(C2xD4)64,131
C4.23(C2×D4) = C22⋊Q16φ: C2×D4/D4C2 ⊆ Aut C432C4.23(C2xD4)64,132
C4.24(C2×D4) = D4.7D4φ: C2×D4/D4C2 ⊆ Aut C432C4.24(C2xD4)64,133
C4.25(C2×D4) = D44D4φ: C2×D4/D4C2 ⊆ Aut C484+C4.25(C2xD4)64,134
C4.26(C2×D4) = D4.8D4φ: C2×D4/D4C2 ⊆ Aut C4164C4.26(C2xD4)64,135
C4.27(C2×D4) = D4.9D4φ: C2×D4/D4C2 ⊆ Aut C4164C4.27(C2xD4)64,136
C4.28(C2×D4) = D4.10D4φ: C2×D4/D4C2 ⊆ Aut C4164-C4.28(C2xD4)64,137
C4.29(C2×D4) = C4⋊D8φ: C2×D4/D4C2 ⊆ Aut C432C4.29(C2xD4)64,140
C4.30(C2×D4) = C4⋊SD16φ: C2×D4/D4C2 ⊆ Aut C432C4.30(C2xD4)64,141
C4.31(C2×D4) = D4.D4φ: C2×D4/D4C2 ⊆ Aut C432C4.31(C2xD4)64,142
C4.32(C2×D4) = C42Q16φ: C2×D4/D4C2 ⊆ Aut C464C4.32(C2xD4)64,143
C4.33(C2×D4) = D4.2D4φ: C2×D4/D4C2 ⊆ Aut C432C4.33(C2xD4)64,144
C4.34(C2×D4) = Q8.D4φ: C2×D4/D4C2 ⊆ Aut C432C4.34(C2xD4)64,145
C4.35(C2×D4) = D4.3D4φ: C2×D4/D4C2 ⊆ Aut C4164C4.35(C2xD4)64,152
C4.36(C2×D4) = D45D4φ: C2×D4/D4C2 ⊆ Aut C416C4.36(C2xD4)64,227
C4.37(C2×D4) = D46D4φ: C2×D4/D4C2 ⊆ Aut C432C4.37(C2xD4)64,228
C4.38(C2×D4) = Q85D4φ: C2×D4/D4C2 ⊆ Aut C432C4.38(C2xD4)64,229
C4.39(C2×D4) = D4×Q8φ: C2×D4/D4C2 ⊆ Aut C432C4.39(C2xD4)64,230
C4.40(C2×D4) = Q86D4φ: C2×D4/D4C2 ⊆ Aut C432C4.40(C2xD4)64,231
C4.41(C2×D4) = D4○D8φ: C2×D4/D4C2 ⊆ Aut C4164+C4.41(C2xD4)64,257
C4.42(C2×D4) = D4○SD16φ: C2×D4/D4C2 ⊆ Aut C4164C4.42(C2xD4)64,258
C4.43(C2×D4) = Q8○D8φ: C2×D4/D4C2 ⊆ Aut C4324-C4.43(C2xD4)64,259
C4.44(C2×D4) = C2×C4.D4φ: C2×D4/C23C2 ⊆ Aut C416C4.44(C2xD4)64,92
C4.45(C2×D4) = C2×C4.10D4φ: C2×D4/C23C2 ⊆ Aut C432C4.45(C2xD4)64,93
C4.46(C2×D4) = M4(2).8C22φ: C2×D4/C23C2 ⊆ Aut C4164C4.46(C2xD4)64,94
C4.47(C2×D4) = C2×D4⋊C4φ: C2×D4/C23C2 ⊆ Aut C432C4.47(C2xD4)64,95
C4.48(C2×D4) = C2×Q8⋊C4φ: C2×D4/C23C2 ⊆ Aut C464C4.48(C2xD4)64,96
C4.49(C2×D4) = C23.24D4φ: C2×D4/C23C2 ⊆ Aut C432C4.49(C2xD4)64,97
C4.50(C2×D4) = C23.36D4φ: C2×D4/C23C2 ⊆ Aut C432C4.50(C2xD4)64,98
C4.51(C2×D4) = C23.37D4φ: C2×D4/C23C2 ⊆ Aut C416C4.51(C2xD4)64,99
C4.52(C2×D4) = C23.38D4φ: C2×D4/C23C2 ⊆ Aut C432C4.52(C2xD4)64,100
C4.53(C2×D4) = C88D4φ: C2×D4/C23C2 ⊆ Aut C432C4.53(C2xD4)64,146
C4.54(C2×D4) = C87D4φ: C2×D4/C23C2 ⊆ Aut C432C4.54(C2xD4)64,147
C4.55(C2×D4) = C8.18D4φ: C2×D4/C23C2 ⊆ Aut C432C4.55(C2xD4)64,148
C4.56(C2×D4) = C8⋊D4φ: C2×D4/C23C2 ⊆ Aut C432C4.56(C2xD4)64,149
C4.57(C2×D4) = C82D4φ: C2×D4/C23C2 ⊆ Aut C432C4.57(C2xD4)64,150
C4.58(C2×D4) = C8.D4φ: C2×D4/C23C2 ⊆ Aut C432C4.58(C2xD4)64,151
C4.59(C2×D4) = D4.4D4φ: C2×D4/C23C2 ⊆ Aut C4164+C4.59(C2xD4)64,153
C4.60(C2×D4) = D4.5D4φ: C2×D4/C23C2 ⊆ Aut C4324-C4.60(C2xD4)64,154
C4.61(C2×D4) = C2×C22⋊Q8φ: C2×D4/C23C2 ⊆ Aut C432C4.61(C2xD4)64,204
C4.62(C2×D4) = C23.38C23φ: C2×D4/C23C2 ⊆ Aut C432C4.62(C2xD4)64,217
C4.63(C2×D4) = C22.31C24φ: C2×D4/C23C2 ⊆ Aut C432C4.63(C2xD4)64,218
C4.64(C2×D4) = C2×C8⋊C22φ: C2×D4/C23C2 ⊆ Aut C416C4.64(C2xD4)64,254
C4.65(C2×D4) = C2×C8.C22φ: C2×D4/C23C2 ⊆ Aut C432C4.65(C2xD4)64,255
C4.66(C2×D4) = C2×C22⋊C8central extension (φ=1)32C4.66(C2xD4)64,87
C4.67(C2×D4) = C24.4C4central extension (φ=1)16C4.67(C2xD4)64,88
C4.68(C2×D4) = (C22×C8)⋊C2central extension (φ=1)32C4.68(C2xD4)64,89
C4.69(C2×D4) = C2×C4≀C2central extension (φ=1)16C4.69(C2xD4)64,101
C4.70(C2×D4) = C42⋊C22central extension (φ=1)164C4.70(C2xD4)64,102
C4.71(C2×D4) = C2×C4⋊C8central extension (φ=1)64C4.71(C2xD4)64,103
C4.72(C2×D4) = C4⋊M4(2)central extension (φ=1)32C4.72(C2xD4)64,104
C4.73(C2×D4) = C42.6C22central extension (φ=1)32C4.73(C2xD4)64,105
C4.74(C2×D4) = C2×C8.C4central extension (φ=1)32C4.74(C2xD4)64,110
C4.75(C2×D4) = M4(2).C4central extension (φ=1)164C4.75(C2xD4)64,111
C4.76(C2×D4) = C8×D4central extension (φ=1)32C4.76(C2xD4)64,115
C4.77(C2×D4) = C89D4central extension (φ=1)32C4.77(C2xD4)64,116
C4.78(C2×D4) = C86D4central extension (φ=1)32C4.78(C2xD4)64,117
C4.79(C2×D4) = C8○D8central extension (φ=1)162C4.79(C2xD4)64,124
C4.80(C2×D4) = C8.26D4central extension (φ=1)164C4.80(C2xD4)64,125
C4.81(C2×D4) = C22.19C24central extension (φ=1)16C4.81(C2xD4)64,206
C4.82(C2×D4) = C22.26C24central extension (φ=1)32C4.82(C2xD4)64,213
C4.83(C2×D4) = C2×C4○D8central extension (φ=1)32C4.83(C2xD4)64,253
C4.84(C2×D4) = D8⋊C22central extension (φ=1)164C4.84(C2xD4)64,256

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