Finite Group Databasebeta

← C₄×C₁₇₄₁ #20294398

Subgroups — C₄×C₁₇₄₁ #20294398

Order 6964.

6 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇₄₁	C₂	1	1	yes	maximal, characteristic
2	C₁₇₄₁	C₄	1	1	yes	characteristic, direct product factor, Sylow
3	C₄	C₁₇₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂	C₂×C₁₇₄₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂	C₂×C₁₇₄₁
socle	C₂×C₁₇₄₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₇₄₁	C₄	direct (N × H)
3. C₄	C₁₇₄₁	direct (N × H)