# Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C2×C28

Direct product G=N×Q with N=C2×C4 and Q=C2×C28
dρLabelID
C22×C4×C28448C2^2xC4xC28448,1294

Semidirect products G=N:Q with N=C2×C4 and Q=C2×C28
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1(C2×C28) = C14×C23⋊C4φ: C2×C28/C14C4 ⊆ Aut C2×C4112(C2xC4):1(C2xC28)448,817
(C2×C4)⋊2(C2×C28) = C7×C23.8Q8φ: C2×C28/C14C22 ⊆ Aut C2×C4224(C2xC4):2(C2xC28)448,793
(C2×C4)⋊3(C2×C28) = C7×C23.23D4φ: C2×C28/C14C22 ⊆ Aut C2×C4224(C2xC4):3(C2xC28)448,794
(C2×C4)⋊4(C2×C28) = C7×C22.11C24φ: C2×C28/C14C22 ⊆ Aut C2×C4112(C2xC4):4(C2xC28)448,1301
(C2×C4)⋊5(C2×C28) = C7×C23.33C23φ: C2×C28/C14C22 ⊆ Aut C2×C4224(C2xC4):5(C2xC28)448,1303
(C2×C4)⋊6(C2×C28) = C22⋊C4×C28φ: C2×C28/C28C2 ⊆ Aut C2×C4224(C2xC4):6(C2xC28)448,785
(C2×C4)⋊7(C2×C28) = D4×C2×C28φ: C2×C28/C28C2 ⊆ Aut C2×C4224(C2xC4):7(C2xC28)448,1298
(C2×C4)⋊8(C2×C28) = C4○D4×C28φ: C2×C28/C28C2 ⊆ Aut C2×C4224(C2xC4):8(C2xC28)448,1300
(C2×C4)⋊9(C2×C28) = C14×C2.C42φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4448(C2xC4):9(C2xC28)448,783
(C2×C4)⋊10(C2×C28) = C4⋊C4×C2×C14φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4448(C2xC4):10(C2xC28)448,1296
(C2×C4)⋊11(C2×C28) = C14×C42⋊C2φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4224(C2xC4):11(C2xC28)448,1297

Non-split extensions G=N.Q with N=C2×C4 and Q=C2×C28
extensionφ:Q→Aut NdρLabelID
(C2×C4).1(C2×C28) = C7×C42⋊C4φ: C2×C28/C14C4 ⊆ Aut C2×C4564(C2xC4).1(C2xC28)448,157
(C2×C4).2(C2×C28) = C7×C423C4φ: C2×C28/C14C4 ⊆ Aut C2×C41124(C2xC4).2(C2xC28)448,158
(C2×C4).3(C2×C28) = C7×C42.C4φ: C2×C28/C14C4 ⊆ Aut C2×C41124(C2xC4).3(C2xC28)448,159
(C2×C4).4(C2×C28) = C7×C42.3C4φ: C2×C28/C14C4 ⊆ Aut C2×C41124(C2xC4).4(C2xC28)448,160
(C2×C4).5(C2×C28) = C14×C4.10D4φ: C2×C28/C14C4 ⊆ Aut C2×C4224(C2xC4).5(C2xC28)448,820
(C2×C4).6(C2×C28) = C7×M4(2).8C22φ: C2×C28/C14C4 ⊆ Aut C2×C41124(C2xC4).6(C2xC28)448,821
(C2×C4).7(C2×C28) = C7×C22.SD16φ: C2×C28/C14C22 ⊆ Aut C2×C4112(C2xC4).7(C2xC28)448,131
(C2×C4).8(C2×C28) = C7×C23.31D4φ: C2×C28/C14C22 ⊆ Aut C2×C4112(C2xC4).8(C2xC28)448,132
(C2×C4).9(C2×C28) = C7×C42.C22φ: C2×C28/C14C22 ⊆ Aut C2×C4224(C2xC4).9(C2xC28)448,133
(C2×C4).10(C2×C28) = C7×C42.2C22φ: C2×C28/C14C22 ⊆ Aut C2×C4448(C2xC4).10(C2xC28)448,134
(C2×C4).11(C2×C28) = C7×C4.D8φ: C2×C28/C14C22 ⊆ Aut C2×C4224(C2xC4).11(C2xC28)448,135
(C2×C4).12(C2×C28) = C7×C4.10D8φ: C2×C28/C14C22 ⊆ Aut C2×C4448(C2xC4).12(C2xC28)448,136
(C2×C4).13(C2×C28) = C7×C4.6Q16φ: C2×C28/C14C22 ⊆ Aut C2×C4448(C2xC4).13(C2xC28)448,137
(C2×C4).14(C2×C28) = C7×C22.C42φ: C2×C28/C14C22 ⊆ Aut C2×C4224(C2xC4).14(C2xC28)448,147
(C2×C4).15(C2×C28) = C7×M4(2)⋊4C4φ: C2×C28/C14C22 ⊆ Aut C2×C41124(C2xC4).15(C2xC28)448,148
(C2×C4).16(C2×C28) = C7×C23.65C23φ: C2×C28/C14C22 ⊆ Aut C2×C4448(C2xC4).16(C2xC28)448,797
(C2×C4).17(C2×C28) = C7×C23.67C23φ: C2×C28/C14C22 ⊆ Aut C2×C4448(C2xC4).17(C2xC28)448,799
(C2×C4).18(C2×C28) = C7×C23.C23φ: C2×C28/C14C22 ⊆ Aut C2×C41124(C2xC4).18(C2xC28)448,818
(C2×C4).19(C2×C28) = C14×C4.D4φ: C2×C28/C14C22 ⊆ Aut C2×C4112(C2xC4).19(C2xC28)448,819
(C2×C4).20(C2×C28) = C7×C23.36D4φ: C2×C28/C14C22 ⊆ Aut C2×C4224(C2xC4).20(C2xC28)448,825
(C2×C4).21(C2×C28) = C7×C23.37D4φ: C2×C28/C14C22 ⊆ Aut C2×C4112(C2xC4).21(C2xC28)448,826
(C2×C4).22(C2×C28) = C7×C23.38D4φ: C2×C28/C14C22 ⊆ Aut C2×C4224(C2xC4).22(C2xC28)448,827
(C2×C4).23(C2×C28) = C7×C42⋊C22φ: C2×C28/C14C22 ⊆ Aut C2×C41124(C2xC4).23(C2xC28)448,829
(C2×C4).24(C2×C28) = C7×C42.6C22φ: C2×C28/C14C22 ⊆ Aut C2×C4224(C2xC4).24(C2xC28)448,832
(C2×C4).25(C2×C28) = C7×M4(2)⋊C4φ: C2×C28/C14C22 ⊆ Aut C2×C4224(C2xC4).25(C2xC28)448,836
(C2×C4).26(C2×C28) = C7×M4(2).C4φ: C2×C28/C14C22 ⊆ Aut C2×C41124(C2xC4).26(C2xC28)448,838
(C2×C4).27(C2×C28) = C7×C42.7C22φ: C2×C28/C14C22 ⊆ Aut C2×C4224(C2xC4).27(C2xC28)448,841
(C2×C4).28(C2×C28) = C7×C89D4φ: C2×C28/C14C22 ⊆ Aut C2×C4224(C2xC4).28(C2xC28)448,843
(C2×C4).29(C2×C28) = C7×C86D4φ: C2×C28/C14C22 ⊆ Aut C2×C4224(C2xC4).29(C2xC28)448,844
(C2×C4).30(C2×C28) = C7×C84Q8φ: C2×C28/C14C22 ⊆ Aut C2×C4448(C2xC4).30(C2xC28)448,854
(C2×C4).31(C2×C28) = C7×C23.32C23φ: C2×C28/C14C22 ⊆ Aut C2×C4224(C2xC4).31(C2xC28)448,1302
(C2×C4).32(C2×C28) = C7×Q8○M4(2)φ: C2×C28/C14C22 ⊆ Aut C2×C41124(C2xC4).32(C2xC28)448,1351
(C2×C4).33(C2×C28) = C7×C23.63C23φ: C2×C28/C28C2 ⊆ Aut C2×C4448(C2xC4).33(C2xC28)448,795
(C2×C4).34(C2×C28) = C7×C24.C22φ: C2×C28/C28C2 ⊆ Aut C2×C4224(C2xC4).34(C2xC28)448,796
(C2×C4).35(C2×C28) = C7×C82M4(2)φ: C2×C28/C28C2 ⊆ Aut C2×C4224(C2xC4).35(C2xC28)448,813
(C2×C4).36(C2×C28) = D4×C56φ: C2×C28/C28C2 ⊆ Aut C2×C4224(C2xC4).36(C2xC28)448,842
(C2×C4).37(C2×C28) = Q8×C56φ: C2×C28/C28C2 ⊆ Aut C2×C4448(C2xC4).37(C2xC28)448,853
(C2×C4).38(C2×C28) = C7×D4⋊C8φ: C2×C28/C28C2 ⊆ Aut C2×C4224(C2xC4).38(C2xC28)448,129
(C2×C4).39(C2×C28) = C7×Q8⋊C8φ: C2×C28/C28C2 ⊆ Aut C2×C4448(C2xC4).39(C2xC28)448,130
(C2×C4).40(C2×C28) = C7×C22.4Q16φ: C2×C28/C28C2 ⊆ Aut C2×C4448(C2xC4).40(C2xC28)448,144
(C2×C4).41(C2×C28) = C7×C4.C42φ: C2×C28/C28C2 ⊆ Aut C2×C4224(C2xC4).41(C2xC28)448,145
(C2×C4).42(C2×C28) = C7×D4.C8φ: C2×C28/C28C2 ⊆ Aut C2×C42242(C2xC4).42(C2xC28)448,154
(C2×C4).43(C2×C28) = C4⋊C4×C28φ: C2×C28/C28C2 ⊆ Aut C2×C4448(C2xC4).43(C2xC28)448,786
(C2×C4).44(C2×C28) = C7×C24.3C22φ: C2×C28/C28C2 ⊆ Aut C2×C4224(C2xC4).44(C2xC28)448,798
(C2×C4).45(C2×C28) = M4(2)×C28φ: C2×C28/C28C2 ⊆ Aut C2×C4224(C2xC4).45(C2xC28)448,812
(C2×C4).46(C2×C28) = C7×(C22×C8)⋊C2φ: C2×C28/C28C2 ⊆ Aut C2×C4224(C2xC4).46(C2xC28)448,816
(C2×C4).47(C2×C28) = C14×D4⋊C4φ: C2×C28/C28C2 ⊆ Aut C2×C4224(C2xC4).47(C2xC28)448,822
(C2×C4).48(C2×C28) = C14×Q8⋊C4φ: C2×C28/C28C2 ⊆ Aut C2×C4448(C2xC4).48(C2xC28)448,823
(C2×C4).49(C2×C28) = C7×C23.24D4φ: C2×C28/C28C2 ⊆ Aut C2×C4224(C2xC4).49(C2xC28)448,824
(C2×C4).50(C2×C28) = C14×C4≀C2φ: C2×C28/C28C2 ⊆ Aut C2×C4112(C2xC4).50(C2xC28)448,828
(C2×C4).51(C2×C28) = C7×D4○C16φ: C2×C28/C28C2 ⊆ Aut C2×C42242(C2xC4).51(C2xC28)448,912
(C2×C4).52(C2×C28) = Q8×C2×C28φ: C2×C28/C28C2 ⊆ Aut C2×C4448(C2xC4).52(C2xC28)448,1299
(C2×C4).53(C2×C28) = C14×C8○D4φ: C2×C28/C28C2 ⊆ Aut C2×C4224(C2xC4).53(C2xC28)448,1350
(C2×C4).54(C2×C28) = C7×C424C4φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4448(C2xC4).54(C2xC28)448,784
(C2×C4).55(C2×C28) = C7×C23.7Q8φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4224(C2xC4).55(C2xC28)448,788
(C2×C4).56(C2×C28) = C7×C23.34D4φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4224(C2xC4).56(C2xC28)448,789
(C2×C4).57(C2×C28) = C7×C425C4φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4448(C2xC4).57(C2xC28)448,791
(C2×C4).58(C2×C28) = C14×C8⋊C4φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4448(C2xC4).58(C2xC28)448,811
(C2×C4).59(C2×C28) = C14×C22⋊C8φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4224(C2xC4).59(C2xC28)448,814
(C2×C4).60(C2×C28) = C7×C42.6C4φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4224(C2xC4).60(C2xC28)448,840
(C2×C4).61(C2×C28) = C7×C82C8φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4448(C2xC4).61(C2xC28)448,138
(C2×C4).62(C2×C28) = C7×C81C8φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4448(C2xC4).62(C2xC28)448,139
(C2×C4).63(C2×C28) = C7×C4.9C42φ: C2×C28/C2×C14C2 ⊆ Aut C2×C41124(C2xC4).63(C2xC28)448,141
(C2×C4).64(C2×C28) = C7×C4.10C42φ: C2×C28/C2×C14C2 ⊆ Aut C2×C41124(C2xC4).64(C2xC28)448,142
(C2×C4).65(C2×C28) = C7×C426C4φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4112(C2xC4).65(C2xC28)448,143
(C2×C4).66(C2×C28) = C7×C16⋊C4φ: C2×C28/C2×C14C2 ⊆ Aut C2×C41124(C2xC4).66(C2xC28)448,151
(C2×C4).67(C2×C28) = C7×C23.C8φ: C2×C28/C2×C14C2 ⊆ Aut C2×C41124(C2xC4).67(C2xC28)448,153
(C2×C4).68(C2×C28) = C7×C8.C8φ: C2×C28/C2×C14C2 ⊆ Aut C2×C41122(C2xC4).68(C2xC28)448,168
(C2×C4).69(C2×C28) = C7×C428C4φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4448(C2xC4).69(C2xC28)448,790
(C2×C4).70(C2×C28) = C7×C429C4φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4448(C2xC4).70(C2xC28)448,792
(C2×C4).71(C2×C28) = C7×C24.4C4φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4112(C2xC4).71(C2xC28)448,815
(C2×C4).72(C2×C28) = C14×C4⋊C8φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4448(C2xC4).72(C2xC28)448,830
(C2×C4).73(C2×C28) = C7×C4⋊M4(2)φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4224(C2xC4).73(C2xC28)448,831
(C2×C4).74(C2×C28) = C14×C4.Q8φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4448(C2xC4).74(C2xC28)448,833
(C2×C4).75(C2×C28) = C14×C2.D8φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4448(C2xC4).75(C2xC28)448,834
(C2×C4).76(C2×C28) = C7×C23.25D4φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4224(C2xC4).76(C2xC28)448,835
(C2×C4).77(C2×C28) = C14×C8.C4φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4224(C2xC4).77(C2xC28)448,837
(C2×C4).78(C2×C28) = C7×C42.12C4φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4224(C2xC4).78(C2xC28)448,839
(C2×C4).79(C2×C28) = M4(2)×C2×C14φ: C2×C28/C2×C14C2 ⊆ Aut C2×C4224(C2xC4).79(C2xC28)448,1349
(C2×C4).80(C2×C28) = C7×C8⋊C8central extension (φ=1)448(C2xC4).80(C2xC28)448,126
(C2×C4).81(C2×C28) = C7×C22.7C42central extension (φ=1)448(C2xC4).81(C2xC28)448,140
(C2×C4).82(C2×C28) = C7×C165C4central extension (φ=1)448(C2xC4).82(C2xC28)448,150
(C2×C4).83(C2×C28) = C7×C22⋊C16central extension (φ=1)224(C2xC4).83(C2xC28)448,152
(C2×C4).84(C2×C28) = C7×C4⋊C16central extension (φ=1)448(C2xC4).84(C2xC28)448,167
(C2×C4).85(C2×C28) = C14×M5(2)central extension (φ=1)224(C2xC4).85(C2xC28)448,911

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