Extensions 1→N→G→Q→1 with N=C₂×C₄² and Q=C₄

Direct product G=N×Q with N=C₂×C₄² and Q=C₄

		d	ρ	Label	ID
C₂×C₄³		128		C2xC4^3	128,997

Semidirect products G=N:Q with N=C₂×C₄² and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₄²)⋊₁C₄ = C₂⁴.₄₆D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2):1C4	128,16
(C₂×C₄²)⋊₂C₄ = C₂⁴.₁₆₉C₂³	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2):2C4	128,552
(C₂×C₄²)⋊₃C₄ = C₂⁴.₆D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2):3C4	128,125
(C₂×C₄²)⋊₄C₄ = C₂×C₄.₉C₄²	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2):4C4	128,462
(C₂×C₄²)⋊₅C₄ = C₂⁴.₁₆₂C₂³	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2):5C4	128,472
(C₂×C₄²)⋊₆C₄ = C₄×C₂³⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2):6C4	128,486
(C₂×C₄²)⋊₇C₄ = C₂⁴.₁₆₇C₂³	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2):7C4	128,531
(C₂×C₄²)⋊₈C₄ = (C₂×C₄²)⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	16	4	(C2xC4^2):8C4	128,559
(C₂×C₄²)⋊₉C₄ = C₂×C₄²⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	16		(C2xC4^2):9C4	128,856
(C₂×C₄²)⋊₁₀C₄ = C₂×C₄²⋊₃C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2):10C4	128,857
(C₂×C₄²)⋊₁₁C₄ = C₄⋊Q₈⋊₂₉C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	16	4	(C2xC4^2):11C4	128,858
(C₂×C₄²)⋊₁₂C₄ = C₄×C₂.C₄²	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2):12C4	128,164
(C₂×C₄²)⋊₁₃C₄ = C₂⁴.₆₂₄C₂³	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2):13C4	128,166
(C₂×C₄²)⋊₁₄C₄ = C₂×C₄²⋊₄C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2):14C4	128,999
(C₂×C₄²)⋊₁₅C₄ = C₂×C₄²⋊₅C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2):15C4	128,1014
(C₂×C₄²)⋊₁₆C₄ = C₂⁴.₆₂₅C₂³	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2):16C4	128,167
(C₂×C₄²)⋊₁₇C₄ = C₂×C₄²⋊₆C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	32		(C2xC4^2):17C4	128,464
(C₂×C₄²)⋊₁₈C₄ = C₂×C₄×C₄⋊C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2):18C4	128,1001
(C₂×C₄²)⋊₁₉C₄ = C₄×C₄²⋊C₂	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	64		(C2xC4^2):19C4	128,1002
(C₂×C₄²)⋊₂₀C₄ = C₂×C₄²⋊₈C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2):20C4	128,1013
(C₂×C₄²)⋊₂₁C₄ = C₂³.₁₆₅C₂⁴	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	64		(C2xC4^2):21C4	128,1015
(C₂×C₄²)⋊₂₂C₄ = C₂×C₄²⋊₉C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2):22C4	128,1016
(C₂×C₄²)⋊₂₃C₄ = C₂³.₁₆₇C₂⁴	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	64		(C2xC4^2):23C4	128,1017

Non-split extensions G=N.Q with N=C₂×C₄² and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₄²).₁C₄ = C₄².₄Q₈	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2).1C4	128,17
(C₂×C₄²).₂C₄ = C₄².₄₂D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2).2C4	128,196
(C₂×C₄²).₃C₄ = (C₂²×C₄).₂₇₆D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2).3C4	128,554
(C₂×C₄²).₄C₄ = C₄²⋊₁C₈	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2).4C4	128,6
(C₂×C₄²).₅C₄ = (C₂×D₄)⋊C₈	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2).5C4	128,50
(C₂×C₄²).₆C₄ = (C₂×C₄²).C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2).6C4	128,51
(C₂×C₄²).₇C₄ = C₂².M₅(2)	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	64		(C2xC4^2).7C4	128,54
(C₂×C₄²).₈C₄ = C₄²⋊C₈	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2).8C4	128,56
(C₂×C₄²).₉C₄ = C₄²⋊₃C₈	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2).9C4	128,57
(C₂×C₄²).₁₀C₄ = C₄².C₈	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	16	4	(C2xC4^2).10C4	128,59
(C₂×C₄²).₁₁C₄ = C₄².₂C₈	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2).11C4	128,107
(C₂×C₄²).₁₂C₄ = M₅(2)⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	64		(C2xC4^2).12C4	128,109
(C₂×C₄²).₁₃C₄ = (C₂×Q₈).Q₈	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2).13C4	128,126
(C₂×C₄²).₁₄C₄ = C₄².₃₇₁D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2).14C4	128,190
(C₂×C₄²).₁₅C₄ = C₂³.₈M₄(2)	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2).15C4	128,191
(C₂×C₄²).₁₆C₄ = C₄².₃₉₄D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	64		(C2xC4^2).16C4	128,193
(C₂×C₄²).₁₇C₄ = C₂³⋊M₄(2)	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2).17C4	128,197
(C₂×C₄²).₁₈C₄ = C₄².₄₄D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	64		(C2xC4^2).18C4	128,199
(C₂×C₄²).₁₉C₄ = C₂³.₁₅C₄²	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2).19C4	128,474
(C₂×C₄²).₂₀C₄ = C₄×C₄.₁₀D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	64		(C2xC4^2).20C4	128,488
(C₂×C₄²).₂₁C₄ = C₄².₉₇D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	64		(C2xC4^2).21C4	128,533
(C₂×C₄²).₂₂C₄ = C₂×C₁₆⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2).22C4	128,841
(C₂×C₄²).₂₃C₄ = C₂×C₄².C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2).23C4	128,862
(C₂×C₄²).₂₄C₄ = C₂×C₄².₃C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	32		(C2xC4^2).24C4	128,863
(C₂×C₄²).₂₅C₄ = (C₂×D₄).₁₃₅D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	16	4	(C2xC4^2).25C4	128,864
(C₂×C₄²).₂₆C₄ = C₈.₅M₄(2)	φ: C₄/C₁ → C₄ ⊆ Aut C₂×C₄²	16	4	(C2xC4^2).26C4	128,897
(C₂×C₄²).₂₇C₄ = C₂².₇M₅(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2).27C4	128,106
(C₂×C₄²).₂₈C₄ = C₄×C₈⋊C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2).28C4	128,457
(C₂×C₄²).₂₉C₄ = C₂×C₂².₇C₄²	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2).29C4	128,459
(C₂×C₄²).₃₀C₄ = C₄²⋊₄C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2).30C4	128,476
(C₂×C₄²).₃₁C₄ = C₄³.C₂	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2).31C4	128,477
(C₂×C₄²).₃₂C₄ = C₄×C₂²⋊C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	64		(C2xC4^2).32C4	128,480
(C₂×C₄²).₃₃C₄ = C₄².₃₇₈D₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	64		(C2xC4^2).33C4	128,481
(C₂×C₄²).₃₄C₄ = C₄×C₄⋊C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2).34C4	128,498
(C₂×C₄²).₃₅C₄ = C₄³.₇C₂	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2).35C4	128,499
(C₂×C₄²).₃₆C₄ = C₄².₄₂₅D₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	64		(C2xC4^2).36C4	128,529
(C₂×C₄²).₃₇C₄ = C₂³.₃₂M₄(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	64		(C2xC4^2).37C4	128,549
(C₂×C₄²).₃₈C₄ = C₄²⋊₅C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2).38C4	128,571
(C₂×C₄²).₃₉C₄ = C₂×C₁₆⋊₅C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2).39C4	128,838
(C₂×C₄²).₄₀C₄ = C₂²×C₈⋊C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2).40C4	128,1602
(C₂×C₄²).₄₁C₄ = C₄²⋊₆C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	32		(C2xC4^2).41C4	128,8
(C₂×C₄²).₄₂C₄ = C₄².₇C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	32		(C2xC4^2).42C4	128,108
(C₂×C₄²).₄₃C₄ = C₂³.₂₈C₄²	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	64		(C2xC4^2).43C4	128,460
(C₂×C₄²).₄₄C₄ = C₄²⋊₈C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2).44C4	128,563
(C₂×C₄²).₄₅C₄ = C₄²⋊₉C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2).45C4	128,574
(C₂×C₄²).₄₆C₄ = C₄×M₅(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	64		(C2xC4^2).46C4	128,839
(C₂×C₄²).₄₇C₄ = C₂×C₄⋊C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2).47C4	128,881
(C₂×C₄²).₄₈C₄ = C₄⋊M₅(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	64		(C2xC4^2).48C4	128,882
(C₂×C₄²).₄₉C₄ = C₂×C₈.C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	32		(C2xC4^2).49C4	128,884
(C₂×C₄²).₅₀C₄ = C₄².₁₃C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	64		(C2xC4^2).50C4	128,894
(C₂×C₄²).₅₁C₄ = C₄².₆C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	64		(C2xC4^2).51C4	128,895
(C₂×C₄²).₅₂C₄ = C₂×C₄×M₄(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	64		(C2xC4^2).52C4	128,1603
(C₂×C₄²).₅₃C₄ = C₂²×C₄⋊C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	128		(C2xC4^2).53C4	128,1634
(C₂×C₄²).₅₄C₄ = C₂×C₄⋊M₄(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	64		(C2xC4^2).54C4	128,1635
(C₂×C₄²).₅₅C₄ = C₂×C₄².₁₂C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	64		(C2xC4^2).55C4	128,1649
(C₂×C₄²).₅₆C₄ = C₂×C₄².₆C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	64		(C2xC4^2).56C4	128,1650
(C₂×C₄²).₅₇C₄ = C₄².₆₇₇C₂³	φ: C₄/C₂ → C₂ ⊆ Aut C₂×C₄²	32		(C2xC4^2).57C4	128,1652

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Extensions 1→N→G→Q→1 with N=C2×C42 and Q=C4

Extensions 1→N→G→Q→1 with N=C₂×C₄² and Q=C₄