Finite Group Databasebeta

← C₃×D₃₁×C₁₆₇ #44526939

Subgroups — C₃×D₃₁×C₁₆₇ #44526939

Order 31062.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₁×C₁₆₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₁×C₁₆₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₆₇	—	31	1	no	maximal, Hall
5	C₃×C₁₆₇	D₃₁	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₆₇	—	31	1	no	Hall
7	C₃×D₃₁	C₁₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₆₇	C₃×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
9	C₃×C₃₁	C₂×C₁₆₇	1	1	yes	characteristic, complemented, Hall
10	D₃₁	C₃×C₁₆₇	1	1	yes	characteristic, direct product factor, Hall
11	C₃₁	C₂×C₃×C₁₆₇	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	31	1	no	Hall
13	C₃	D₃₁×C₁₆₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₆₇	D₃₁
commutator, cosocle, hypocenter	C₃₁	C₂×C₃×C₁₆₇
Frattini	C₁	G
Fitting, socle	C₃×C₃₁×C₁₆₇	C₂
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₃×C₁₆₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₃₁×C₁₆₇	C₂	semidirect
2. D₃₁×C₁₆₇	C₃	direct (N × H)
3. C₃₁×C₁₆₇	C₂×C₃	semidirect
5. C₃×C₁₆₇	D₃₁	direct (N × H)
7. C₃×D₃₁	C₁₆₇	direct (N × H)
8. C₁₆₇	C₃×D₃₁	direct (N × H)
9. C₃×C₃₁	C₂×C₁₆₇	semidirect
10. D₃₁	C₃×C₁₆₇	direct (N × H)
11. C₃₁	C₂×C₃×C₁₆₇	semidirect
13. C₃	D₃₁×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
C₃×C₃₁×C₁₆₇	2
D₃₁×C₁₆₇	3
C₂×C₃×C₁₆₇	31
C₃×D₃₁	167