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

Direct product G=N×Q with N=C₄×C₈ and Q=C₄

		d	ρ	Label	ID
C₄²×C₈		128		C4^2xC8	128,456

Semidirect products G=N:Q with N=C₄×C₈ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₄×C₈)⋊₁C₄ = C₄²⋊₁C₈	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₈	32		(C4xC8):1C4	128,6
(C₄×C₈)⋊₂C₄ = C₄².₅Q₈	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₈	32		(C4xC8):2C4	128,18
(C₄×C₈)⋊₃C₄ = (C₄×C₈)⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₈	32	4	(C4xC8):3C4	128,146
(C₄×C₈)⋊₄C₄ = C₄⋊₁D₄⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₈	16	4+	(C4xC8):4C4	128,140
(C₄×C₈)⋊₅C₄ = C₈.(C₄⋊C₄)	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₈	32	4	(C4xC8):5C4	128,565
(C₄×C₈)⋊₆C₄ = (C₄×C₈)⋊₆C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₈	16	4	(C4xC8):6C4	128,141
(C₄×C₈)⋊₇C₄ = C₄².₆Q₈	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₈	32		(C4xC8):7C4	128,20
(C₄×C₈)⋊₈C₄ = C₈.₁₆C₄²	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₈	32	4	(C4xC8):8C4	128,479
(C₄×C₈)⋊₉C₄ = C₈⋊C₄⋊₁₇C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₈	16	4	(C4xC8):9C4	128,573
(C₄×C₈)⋊₁₀C₄ = C₄².₄₆Q₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8):10C4	128,11
(C₄×C₈)⋊₁₁C₄ = C₄²⋊₄C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8):11C4	128,476
(C₄×C₈)⋊₁₂C₄ = (C₄×C₈)⋊₁₂C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8):12C4	128,478
(C₄×C₈)⋊₁₃C₄ = C₈×C₄⋊C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8):13C4	128,501
(C₄×C₈)⋊₁₄C₄ = C₄².₅₅Q₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8):14C4	128,566
(C₄×C₈)⋊₁₅C₄ = C₄².₅₆Q₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8):15C4	128,567
(C₄×C₈)⋊₁₆C₄ = C₄×C₂.D₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8):16C4	128,507
(C₄×C₈)⋊₁₇C₄ = C₄².₅₉Q₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8):17C4	128,577
(C₄×C₈)⋊₁₈C₄ = C₄².₆₀Q₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8):18C4	128,578
(C₄×C₈)⋊₁₉C₄ = C₈.₁₄C₄²	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	32		(C4xC8):19C4	128,504
(C₄×C₈)⋊₂₀C₄ = C₄×C₄.Q₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8):20C4	128,506
(C₄×C₈)⋊₂₁C₄ = C₄².₅₈Q₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8):21C4	128,576
(C₄×C₈)⋊₂₂C₄ = C₄×C₈⋊C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8):22C4	128,457
(C₄×C₈)⋊₂₃C₄ = C₂.C₄³	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8):23C4	128,458
(C₄×C₈)⋊₂₄C₄ = C₄⋊C₈⋊₁₃C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8):24C4	128,502

Non-split extensions G=N.Q with N=C₄×C₈ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₄×C₈).₁C₄ = C₄².₂₀D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₈	64		(C4xC8).1C4	128,7
(C₄×C₈).₂C₄ = C₄².₂₃D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₈	64		(C4xC8).2C4	128,19
(C₄×C₈).₃C₄ = C₁₆⋊C₈	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₈	128		(C4xC8).3C4	128,45
(C₄×C₈).₄C₄ = (C₂×Q₈).D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₈	32	4-	(C4xC8).4C4	128,143
(C₄×C₈).₅C₄ = C₈.₁₉M₄(2)	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₈	32	4	(C4xC8).5C4	128,898
(C₄×C₈).₆C₄ = (C₄×C₈).C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₈	16	4	(C4xC8).6C4	128,142
(C₄×C₈).₇C₄ = C₄².₂₆D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₈	64		(C4xC8).7C4	128,23
(C₄×C₈).₈C₄ = C₃₂⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₈	32	4	(C4xC8).8C4	128,130
(C₄×C₈).₉C₄ = C₈.₂₃C₄²	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₈	32	4	(C4xC8).9C4	128,842
(C₄×C₈).₁₀C₄ = C₈.₅M₄(2)	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₈	16	4	(C4xC8).10C4	128,897
(C₄×C₈).₁₁C₄ = M₄(2)⋊C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	64		(C4xC8).11C4	128,10
(C₄×C₈).₁₂C₄ = C₁₆⋊₅C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8).12C4	128,43
(C₄×C₈).₁₃C₄ = C₈⋊C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8).13C4	128,44
(C₄×C₈).₁₄C₄ = C₄⋊C₃₂	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8).14C4	128,153
(C₄×C₈).₁₅C₄ = C₂×C₈⋊C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8).15C4	128,180
(C₄×C₈).₁₆C₄ = C₈×M₄(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	64		(C4xC8).16C4	128,181
(C₄×C₈).₁₇C₄ = C₂³.₂₇C₄²	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	64		(C4xC8).17C4	128,184
(C₄×C₈).₁₈C₄ = C₈⋊₈M₄(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	64		(C4xC8).18C4	128,298
(C₄×C₈).₁₉C₄ = C₈⋊₇M₄(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	64		(C4xC8).19C4	128,299
(C₄×C₈).₂₀C₄ = C₄².₄₃Q₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	64		(C4xC8).20C4	128,300
(C₄×C₈).₂₁C₄ = C₄².₃₂₂D₄	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	64		(C4xC8).21C4	128,569
(C₄×C₈).₂₂C₄ = C₂×C₄⋊C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8).22C4	128,881
(C₄×C₈).₂₃C₄ = C₄².₁₃C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	64		(C4xC8).23C4	128,894
(C₄×C₈).₂₄C₄ = C₈.₃₆D₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8).24C4	128,102
(C₄×C₈).₂₅C₄ = C₂×C₈⋊₁C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8).25C4	128,295
(C₄×C₈).₂₆C₄ = C₄².₄₂Q₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	64		(C4xC8).26C4	128,296
(C₄×C₈).₂₇C₄ = C₄².₃₂₄D₄	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	64		(C4xC8).27C4	128,580
(C₄×C₈).₂₈C₄ = C₈.C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	32	2	(C4xC8).28C4	128,154
(C₄×C₈).₂₉C₄ = C₂×C₈.C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	32		(C4xC8).29C4	128,884
(C₄×C₈).₃₀C₄ = C₈⋊₂C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8).30C4	128,99
(C₄×C₈).₃₁C₄ = C₂×C₈⋊₂C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8).31C4	128,294
(C₄×C₈).₃₂C₄ = C₄×C₈.C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	64		(C4xC8).32C4	128,509
(C₄×C₈).₃₃C₄ = C₃₂⋊₅C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8).33C4	128,129
(C₄×C₈).₃₄C₄ = C₈²⋊C₂	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	64		(C4xC8).34C4	128,182
(C₄×C₈).₃₅C₄ = C₈⋊₉M₄(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	64		(C4xC8).35C4	128,183
(C₄×C₈).₃₆C₄ = C₂×C₁₆⋊₅C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	128		(C4xC8).36C4	128,838
(C₄×C₈).₃₇C₄ = C₄×M₅(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	64		(C4xC8).37C4	128,839
(C₄×C₈).₃₈C₄ = C₄⋊M₅(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	64		(C4xC8).38C4	128,882
(C₄×C₈).₃₉C₄ = C₄².₆C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₈	64		(C4xC8).39C4	128,895

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

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