Finite Group Databasebeta

← C₂²×C₄₇×C₁₆₇ #44536039

Subgroups — C₂²×C₄₇×C₁₆₇ #44536039

Order 31396.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×C₁₆₇	C₂	1	3	yes	maximal, direct product factor
2	C₄₇×C₁₆₇	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₁₆₇	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₁₆₇	C₂×C₄₇	1	3	yes	direct product factor
5	C₂²×C₄₇	C₁₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₆₇	C₂²×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
7	C₂×C₄₇	C₂×C₁₆₇	1	3	yes	direct product factor
8	C₄₇	C₂²×C₁₆₇	1	1	yes	characteristic, direct product factor, Sylow
9	C₂²	C₄₇×C₁₆₇	1	1	yes	characteristic, direct product factor, Sylow
10	C₂	C₂×C₄₇×C₁₆₇	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇×C₁₆₇	C₂	direct (N × H)
2. C₄₇×C₁₆₇	C₂²	direct (N × H)
3. C₂²×C₁₆₇	C₄₇	direct (N × H)
4. C₂×C₁₆₇	C₂×C₄₇	direct (N × H)
5. C₂²×C₄₇	C₁₆₇	direct (N × H)
6. C₁₆₇	C₂²×C₄₇	direct (N × H)
7. C₂×C₄₇	C₂×C₁₆₇	direct (N × H)
8. C₄₇	C₂²×C₁₆₇	direct (N × H)
9. C₂²	C₄₇×C₁₆₇	direct (N × H)
10. C₂	C₂×C₄₇×C₁₆₇	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×C₄₇×C₁₆₇	2
C₂²×C₁₆₇	47
C₂²×C₄₇	167