Subgroups — C₄×C₁₂₁ #92144

Order 484.

9 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₂₁	C₂	1	1	yes	maximal, characteristic
2	C₁₂₁	C₄	1	1	yes	characteristic, direct product factor, Sylow
3	C₄×C₁₁	C₁₁	1	1	yes	maximal, characteristic
4	C₂×C₁₁	C₂×C₁₁	1	1	yes	characteristic
5	C₁₁	C₄×C₁₁	1	1	yes	characteristic
6	C₄	C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
7	C₂	C₂×C₁₂₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, socle, prime radical, cosocle	C₂×C₁₁	C₂×C₁₁
LCS	G ▷ C₁
UCS	C₁ ◁ G

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

N	H ≅ G/N	type
2. C₁₂₁	C₄	direct (N × H)
6. C₄	C₁₂₁	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₂₁	2
C₄×C₁₁	11