# Extensions 1→N→G→Q→1 with N=M4(2).8C22 and Q=C2

Direct product G=N×Q with N=M4(2).8C22 and Q=C2
dρLabelID
C2×M4(2).8C2232C2xM4(2).8C2^2128,1619

Semidirect products G=N:Q with N=M4(2).8C22 and Q=C2
extensionφ:Q→Out NdρLabelID
M4(2).8C221C2 = C42.313C23φ: C2/C1C2 ⊆ Out M4(2).8C22164M4(2).8C2^2:1C2128,1750
M4(2).8C222C2 = C42.12C23φ: C2/C1C2 ⊆ Out M4(2).8C22168+M4(2).8C2^2:2C2128,1753
M4(2).8C223C2 = C42.13C23φ: C2/C1C2 ⊆ Out M4(2).8C22328-M4(2).8C2^2:3C2128,1754
M4(2).8C224C2 = M4(2).10C23φ: C2/C1C2 ⊆ Out M4(2).8C22324M4(2).8C2^2:4C2128,1799
M4(2).8C225C2 = M4(2).37D4φ: C2/C1C2 ⊆ Out M4(2).8C22168+M4(2).8C2^2:5C2128,1800
M4(2).8C226C2 = M4(2).38D4φ: C2/C1C2 ⊆ Out M4(2).8C22328-M4(2).8C2^2:6C2128,1801
M4(2).8C227C2 = 2+ 1+4.2C4φ: C2/C1C2 ⊆ Out M4(2).8C22324M4(2).8C2^2:7C2128,523
M4(2).8C228C2 = C4○D4.D4φ: C2/C1C2 ⊆ Out M4(2).8C22168+M4(2).8C2^2:8C2128,527
M4(2).8C229C2 = (C22×Q8)⋊C4φ: C2/C1C2 ⊆ Out M4(2).8C22328-M4(2).8C2^2:9C2128,528
M4(2).8C2210C2 = (C2×C8)⋊D4φ: C2/C1C2 ⊆ Out M4(2).8C22164M4(2).8C2^2:10C2128,623
M4(2).8C2211C2 = M4(2)⋊21D4φ: C2/C1C2 ⊆ Out M4(2).8C22168+M4(2).8C2^2:11C2128,646
M4(2).8C2212C2 = M4(2).8D4φ: C2/C1C2 ⊆ Out M4(2).8C22168+M4(2).8C2^2:12C2128,780
M4(2).8C2213C2 = C42.131D4φ: C2/C1C2 ⊆ Out M4(2).8C22164M4(2).8C2^2:13C2128,782
M4(2).8C2214C2 = C4○C2≀C4φ: C2/C1C2 ⊆ Out M4(2).8C22164M4(2).8C2^2:14C2128,852
M4(2).8C2215C2 = C2≀C4⋊C2φ: C2/C1C2 ⊆ Out M4(2).8C22168+M4(2).8C2^2:15C2128,854
M4(2).8C2216C2 = (C2×D4).135D4φ: C2/C1C2 ⊆ Out M4(2).8C22164M4(2).8C2^2:16C2128,864
M4(2).8C2217C2 = C41D4.C4φ: C2/C1C2 ⊆ Out M4(2).8C22168+M4(2).8C2^2:17C2128,866
M4(2).8C2218C2 = M4(2).24C23φ: C2/C1C2 ⊆ Out M4(2).8C22168+M4(2).8C2^2:18C2128,1620
M4(2).8C2219C2 = M4(2).25C23φ: C2/C1C2 ⊆ Out M4(2).8C22328-M4(2).8C2^2:19C2128,1621

Non-split extensions G=N.Q with N=M4(2).8C22 and Q=C2
extensionφ:Q→Out NdρLabelID
M4(2).8C22.1C2 = M4(2).40D4φ: C2/C1C2 ⊆ Out M4(2).8C22324M4(2).8C2^2.1C2128,590
M4(2).8C22.2C2 = C42.427D4φ: C2/C1C2 ⊆ Out M4(2).8C22164M4(2).8C2^2.2C2128,664
M4(2).8C22.3C2 = C23.3C42φ: C2/C1C2 ⊆ Out M4(2).8C22324M4(2).8C2^2.3C2128,124
M4(2).8C22.4C2 = (C22×C8)⋊C4φ: C2/C1C2 ⊆ Out M4(2).8C22324M4(2).8C2^2.4C2128,127
M4(2).8C22.5C2 = (C2×C8).103D4φ: C2/C1C2 ⊆ Out M4(2).8C22324M4(2).8C2^2.5C2128,545
M4(2).8C22.6C2 = (C2×C42)⋊C4φ: C2/C1C2 ⊆ Out M4(2).8C22164M4(2).8C2^2.6C2128,559
M4(2).8C22.7C2 = M4(2).50D4φ: C2/C1C2 ⊆ Out M4(2).8C22328-M4(2).8C2^2.7C2128,647
M4(2).8C22.8C2 = M4(2).9D4φ: C2/C1C2 ⊆ Out M4(2).8C22328-M4(2).8C2^2.8C2128,781
M4(2).8C22.9C2 = C42.9D4φ: C2/C1C2 ⊆ Out M4(2).8C22324M4(2).8C2^2.9C2128,812
M4(2).8C22.10C2 = C23.(C2×D4)φ: C2/C1C2 ⊆ Out M4(2).8C22328-M4(2).8C2^2.10C2128,855
M4(2).8C22.11C2 = (C2×D4).137D4φ: C2/C1C2 ⊆ Out M4(2).8C22328-M4(2).8C2^2.11C2128,867
M4(2).8C22.12C2 = C23.5C42φ: trivial image324M4(2).8C2^2.12C2128,489

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