# Extensions 1→N→G→Q→1 with N=M4(2) and Q=C23

Direct product G=N×Q with N=M4(2) and Q=C23
dρLabelID
C23×M4(2)64C2^3xM4(2)128,2302

Semidirect products G=N:Q with N=M4(2) and Q=C23
extensionφ:Q→Out NdρLabelID
M4(2)⋊1C23 = C2×D44D4φ: C23/C2C22 ⊆ Out M4(2)16M4(2):1C2^3128,1746
M4(2)⋊2C23 = C2×D4.9D4φ: C23/C2C22 ⊆ Out M4(2)32M4(2):2C2^3128,1747
M4(2)⋊3C23 = M4(2)⋊C23φ: C23/C2C22 ⊆ Out M4(2)168+M4(2):3C2^3128,1751
M4(2)⋊4C23 = C22×C8⋊C22φ: C23/C22C2 ⊆ Out M4(2)32M4(2):4C2^3128,2310
M4(2)⋊5C23 = C22×C8.C22φ: C23/C22C2 ⊆ Out M4(2)64M4(2):5C2^3128,2311
M4(2)⋊6C23 = C2×D8⋊C22φ: C23/C22C2 ⊆ Out M4(2)32M4(2):6C2^3128,2312
M4(2)⋊7C23 = C2×D4○D8φ: C23/C22C2 ⊆ Out M4(2)32M4(2):7C2^3128,2313
M4(2)⋊8C23 = C2×D4○SD16φ: C23/C22C2 ⊆ Out M4(2)32M4(2):8C2^3128,2314
M4(2)⋊9C23 = D8⋊C23φ: C23/C22C2 ⊆ Out M4(2)168+M4(2):9C2^3128,2317
M4(2)⋊10C23 = C22×C4.D4φ: C23/C22C2 ⊆ Out M4(2)32M4(2):10C2^3128,1617
M4(2)⋊11C23 = C22×C4≀C2φ: C23/C22C2 ⊆ Out M4(2)32M4(2):11C2^3128,1631
M4(2)⋊12C23 = C2×C42⋊C22φ: C23/C22C2 ⊆ Out M4(2)32M4(2):12C2^3128,1632
M4(2)⋊13C23 = C22×C8○D4φ: trivial image64M4(2):13C2^3128,2303
M4(2)⋊14C23 = C2×Q8○M4(2)φ: trivial image32M4(2):14C2^3128,2304

Non-split extensions G=N.Q with N=M4(2) and Q=C23
extensionφ:Q→Out NdρLabelID
M4(2).1C23 = C2×D4.8D4φ: C23/C2C22 ⊆ Out M4(2)32M4(2).1C2^3128,1748
M4(2).2C23 = C2×D4.10D4φ: C23/C2C22 ⊆ Out M4(2)32M4(2).2C2^3128,1749
M4(2).3C23 = C42.313C23φ: C23/C2C22 ⊆ Out M4(2)164M4(2).3C2^3128,1750
M4(2).4C23 = M4(2).C23φ: C23/C2C22 ⊆ Out M4(2)328-M4(2).4C2^3128,1752
M4(2).5C23 = C42.12C23φ: C23/C2C22 ⊆ Out M4(2)168+M4(2).5C2^3128,1753
M4(2).6C23 = C42.13C23φ: C23/C2C22 ⊆ Out M4(2)328-M4(2).6C2^3128,1754
M4(2).7C23 = C2×D4.3D4φ: C23/C2C22 ⊆ Out M4(2)32M4(2).7C2^3128,1796
M4(2).8C23 = C2×D4.4D4φ: C23/C2C22 ⊆ Out M4(2)32M4(2).8C2^3128,1797
M4(2).9C23 = C2×D4.5D4φ: C23/C2C22 ⊆ Out M4(2)64M4(2).9C2^3128,1798
M4(2).10C23 = M4(2).10C23φ: C23/C2C22 ⊆ Out M4(2)324M4(2).10C2^3128,1799
M4(2).11C23 = M4(2).37D4φ: C23/C2C22 ⊆ Out M4(2)168+M4(2).11C2^3128,1800
M4(2).12C23 = M4(2).38D4φ: C23/C2C22 ⊆ Out M4(2)328-M4(2).12C2^3128,1801
M4(2).13C23 = D811D4φ: C23/C2C22 ⊆ Out M4(2)168+M4(2).13C2^3128,2020
M4(2).14C23 = D8.13D4φ: C23/C2C22 ⊆ Out M4(2)328-M4(2).14C2^3128,2021
M4(2).15C23 = D8○SD16φ: C23/C2C22 ⊆ Out M4(2)324M4(2).15C2^3128,2022
M4(2).16C23 = D86D4φ: C23/C2C22 ⊆ Out M4(2)164M4(2).16C2^3128,2023
M4(2).17C23 = D8○D8φ: C23/C2C22 ⊆ Out M4(2)164+M4(2).17C2^3128,2024
M4(2).18C23 = D8○Q16φ: C23/C2C22 ⊆ Out M4(2)324-M4(2).18C2^3128,2025
M4(2).19C23 = C2×Q8○D8φ: C23/C22C2 ⊆ Out M4(2)64M4(2).19C2^3128,2315
M4(2).20C23 = C8.C24φ: C23/C22C2 ⊆ Out M4(2)324M4(2).20C2^3128,2316
M4(2).21C23 = C4.C25φ: C23/C22C2 ⊆ Out M4(2)328-M4(2).21C2^3128,2318
M4(2).22C23 = C22×C4.10D4φ: C23/C22C2 ⊆ Out M4(2)64M4(2).22C2^3128,1618
M4(2).23C23 = C2×M4(2).8C22φ: C23/C22C2 ⊆ Out M4(2)32M4(2).23C2^3128,1619
M4(2).24C23 = M4(2).24C23φ: C23/C22C2 ⊆ Out M4(2)168+M4(2).24C2^3128,1620
M4(2).25C23 = M4(2).25C23φ: C23/C22C2 ⊆ Out M4(2)328-M4(2).25C2^3128,1621
M4(2).26C23 = 2- 1+45C4φ: C23/C22C2 ⊆ Out M4(2)164M4(2).26C2^3128,1633
M4(2).27C23 = C22×C8.C4φ: C23/C22C2 ⊆ Out M4(2)64M4(2).27C2^3128,1646
M4(2).28C23 = C2×M4(2).C4φ: C23/C22C2 ⊆ Out M4(2)32M4(2).28C2^3128,1647
M4(2).29C23 = M4(2).29C23φ: C23/C22C2 ⊆ Out M4(2)324M4(2).29C2^3128,1648
M4(2).30C23 = C2×C8○D8φ: C23/C22C2 ⊆ Out M4(2)32M4(2).30C2^3128,1685
M4(2).31C23 = C2×C8.26D4φ: C23/C22C2 ⊆ Out M4(2)32M4(2).31C2^3128,1686
M4(2).32C23 = C42.283C23φ: C23/C22C2 ⊆ Out M4(2)324M4(2).32C2^3128,1687
M4(2).33C23 = M4(2).51D4φ: C23/C22C2 ⊆ Out M4(2)164M4(2).33C2^3128,1688
M4(2).34C23 = M4(2)○D8φ: C23/C22C2 ⊆ Out M4(2)324M4(2).34C2^3128,1689
M4(2).35C23 = C4.22C25φ: trivial image324M4(2).35C2^3128,2305

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