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Extensions 1→N→G→Q→1 with N=C8 and Q=C4⋊C4

Direct product G=N×Q with N=C8 and Q=C4⋊C4
dρLabelID
C8×C4⋊C4128C8xC4:C4128,501

Semidirect products G=N:Q with N=C8 and Q=C4⋊C4
extensionφ:Q→Aut NdρLabelID
C8⋊1(C4⋊C4) = C42.26Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C8128C8:1(C4:C4)128,579
C8⋊2(C4⋊C4) = C4.(C4×Q8)φ: C4⋊C4/C22 → C22 ⊆ Aut C8128C8:2(C4:C4)128,675
C8⋊3(C4⋊C4) = C8⋊(C4⋊C4)φ: C4⋊C4/C22 → C22 ⊆ Aut C8128C8:3(C4:C4)128,676
C8⋊4(C4⋊C4) = C42.59Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C8128C8:4(C4:C4)128,577
C8⋊5(C4⋊C4) = C8⋊5(C4⋊C4)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C8128C8:5(C4:C4)128,674
C8⋊6(C4⋊C4) = C42.58Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C8128C8:6(C4:C4)128,576
C8⋊7(C4⋊C4) = C8⋊7(C4⋊C4)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C8128C8:7(C4:C4)128,673
C8⋊8(C4⋊C4) = C4⋊C8⋊13C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C8128C8:8(C4:C4)128,502
C8⋊9(C4⋊C4) = C4⋊C8⋊14C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C8128C8:9(C4:C4)128,503

Non-split extensions G=N.Q with N=C8 and Q=C4⋊C4
extensionφ:Q→Aut NdρLabelID
C8.1(C4⋊C4) = C8.11C42φ: C4⋊C4/C22 → C22 ⊆ Aut C832C8.1(C4:C4)128,115
C8.2(C4⋊C4) = C23.9D8φ: C4⋊C4/C22 → C22 ⊆ Aut C8324C8.2(C4:C4)128,116
C8.3(C4⋊C4) = C8.13C42φ: C4⋊C4/C22 → C22 ⊆ Aut C8324C8.3(C4:C4)128,117
C8.4(C4⋊C4) = C8.(C4⋊C4)φ: C4⋊C4/C22 → C22 ⊆ Aut C8324C8.4(C4:C4)128,565
C8.5(C4⋊C4) = C42.106D4φ: C4⋊C4/C22 → C22 ⊆ Aut C864C8.5(C4:C4)128,581
C8.6(C4⋊C4) = C42.28Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C832C8.6(C4:C4)128,678
C8.7(C4⋊C4) = M4(2).5Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C864C8.7(C4:C4)128,683
C8.8(C4⋊C4) = M4(2).6Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C864C8.8(C4:C4)128,684
C8.9(C4⋊C4) = M4(2).27D4φ: C4⋊C4/C22 → C22 ⊆ Aut C8324C8.9(C4:C4)128,685
C8.10(C4⋊C4) = M5(2)⋊1C4φ: C4⋊C4/C22 → C22 ⊆ Aut C864C8.10(C4:C4)128,891
C8.11(C4⋊C4) = M5(2).1C4φ: C4⋊C4/C22 → C22 ⊆ Aut C8324C8.11(C4:C4)128,893
C8.12(C4⋊C4) = C8.7C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C8128C8.12(C4:C4)128,112
C8.13(C4⋊C4) = C8.2C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C864C8.13(C4:C4)128,119
C8.14(C4⋊C4) = M5(2).C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C8324C8.14(C4:C4)128,120
C8.15(C4⋊C4) = C32⋊3C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C8128C8.15(C4:C4)128,155
C8.16(C4⋊C4) = C32⋊4C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C8128C8.16(C4:C4)128,156
C8.17(C4⋊C4) = C32.C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C8642C8.17(C4:C4)128,157
C8.18(C4⋊C4) = C8.Q16φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C8324C8.18(C4:C4)128,158
C8.19(C4⋊C4) = C42.60Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C8128C8.19(C4:C4)128,578
C8.20(C4⋊C4) = C42.324D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C864C8.20(C4:C4)128,580
C8.21(C4⋊C4) = C42.62Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C832C8.21(C4:C4)128,677
C8.22(C4⋊C4) = M5(2)⋊3C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C8324C8.22(C4:C4)128,887
C8.23(C4⋊C4) = C2×C16⋊3C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C8128C8.23(C4:C4)128,888
C8.24(C4⋊C4) = C2×C16⋊4C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C8128C8.24(C4:C4)128,889
C8.25(C4⋊C4) = C2×C8.4Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C864C8.25(C4:C4)128,892
C8.26(C4⋊C4) = C8.8C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C864C8.26(C4:C4)128,113
C8.27(C4⋊C4) = C8.9C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C864C8.27(C4:C4)128,114
C8.28(C4⋊C4) = C8.C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C832C8.28(C4:C4)128,118
C8.29(C4⋊C4) = C8.4C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C8324C8.29(C4:C4)128,121
C8.30(C4⋊C4) = C2×C8.Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C832C8.30(C4:C4)128,886
C8.31(C4⋊C4) = C23.25D8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C864C8.31(C4:C4)128,890
C8.32(C4⋊C4) = C42.2C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C832C8.32(C4:C4)128,107
C8.33(C4⋊C4) = C42.7C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C832C8.33(C4:C4)128,108
C8.34(C4⋊C4) = M5(2)⋊C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C864C8.34(C4:C4)128,109
C8.35(C4⋊C4) = M4(2).C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C8324C8.35(C4:C4)128,110
C8.36(C4⋊C4) = C8.5C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C832C8.36(C4:C4)128,505
C8.37(C4⋊C4) = C4⋊M5(2)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C864C8.37(C4:C4)128,882
C8.38(C4⋊C4) = C4⋊C4.7C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C864C8.38(C4:C4)128,883
C8.39(C4⋊C4) = M4(2).1C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C8324C8.39(C4:C4)128,885
C8.40(C4⋊C4) = C22.7M5(2)central extension (φ=1)128C8.40(C4:C4)128,106
C8.41(C4⋊C4) = M5(2)⋊7C4central extension (φ=1)64C8.41(C4:C4)128,111
C8.42(C4⋊C4) = C4⋊C32central extension (φ=1)128C8.42(C4:C4)128,153
C8.43(C4⋊C4) = C8.C16central extension (φ=1)322C8.43(C4:C4)128,154
C8.44(C4⋊C4) = C8.14C42central extension (φ=1)32C8.44(C4:C4)128,504
C8.45(C4⋊C4) = C2×C4⋊C16central extension (φ=1)128C8.45(C4:C4)128,881
C8.46(C4⋊C4) = C2×C8.C8central extension (φ=1)32C8.46(C4:C4)128,884

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