Finite Group Databasebeta

← C₄×C₆₇×C₁₂₁ #44569812

Subgroups — C₄×C₆₇×C₁₂₁ #44569812

Order 32428.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₇×C₁₂₁	C₂	1	1	yes	maximal, characteristic
2	C₆₇×C₁₂₁	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₁₁×C₆₇	C₁₁	1	1	yes	maximal, characteristic
4	C₂×C₁₁×C₆₇	C₂×C₁₁	1	1	yes	characteristic
5	C₁₁×C₆₇	C₄×C₁₁	1	1	yes	characteristic
6	C₄×C₁₂₁	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₄×C₆₇	C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₁₂₁	C₂×C₆₇	1	1	yes	characteristic
9	C₂×C₆₇	C₂×C₁₂₁	1	1	yes	characteristic
10	C₁₂₁	C₄×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
11	C₆₇	C₄×C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
12	C₄×C₁₁	C₁₁×C₆₇	1	1	yes	characteristic
13	C₂×C₁₁	C₂×C₁₁×C₆₇	1	1	yes	characteristic
14	C₁₁	C₄×C₁₁×C₆₇	1	1	yes	characteristic
15	C₄	C₆₇×C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
16	C₂	C₂×C₆₇×C₁₂₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₁₁	C₂×C₁₁×C₆₇
socle, prime radical	C₂×C₁₁×C₆₇	C₂×C₁₁
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×C₁₂₁	C₄	direct (N × H)
6. C₄×C₁₂₁	C₆₇	direct (N × H)
7. C₄×C₆₇	C₁₂₁	direct (N × H)
10. C₁₂₁	C₄×C₆₇	direct (N × H)
11. C₆₇	C₄×C₁₂₁	direct (N × H)
15. C₄	C₆₇×C₁₂₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₆₇×C₁₂₁	2
C₄×C₁₁×C₆₇	11
C₄×C₁₂₁	67