Finite Group Databasebeta

← C₇⋊C₉×C₁₆₇ #24901949

Subgroups — C₇⋊C₉×C₁₆₇ #24901949

Order 10521.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₆₇	C₃	1	1	yes	maximal, characteristic
2	C₉×C₁₆₇	—	7	1	no	maximal, Hall
3	C₇×C₁₆₇	C₉	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₆₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
5	C₁₆₇	C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
6	C₇⋊C₉	C₁₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₇	C₃×C₁₆₇	1	1	yes	characteristic
8	C₉	—	7	1	no	Sylow
9	C₇	C₉×C₁₆₇	1	1	yes	characteristic, complemented, Sylow
10	C₃	ΓL(1,𝔽₈)×C₁₆₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₁₆₇	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₉×C₁₆₇
Frattini	C₃	ΓL(1,𝔽₈)×C₁₆₇
Fitting, socle, prime radical	C₃×C₇×C₁₆₇	C₃
cosocle	C₃×C₇	C₃×C₁₆₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₆₇

Complements

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

N	H ≅ G/N	type
3. C₇×C₁₆₇	C₉	semidirect
5. C₁₆₇	C₇⋊C₉	direct (N × H)
6. C₇⋊C₉	C₁₆₇	direct (N × H)
9. C₇	C₉×C₁₆₇	semidirect