Finite Group Databasebeta

← C₇⋊C₉×C₁₆₉ #24922380

Subgroups — C₇⋊C₉×C₁₆₉ #24922380

Order 10647.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₆₉	C₃	1	1	yes	maximal, characteristic
2	C₉×C₁₆₉	—	7	1	no	maximal, Hall
3	C₇×C₁₆₉	C₉	1	1	yes	characteristic, complemented, Hall
4	C₁₃×C₇⋊C₉	C₁₃	1	1	yes	maximal, characteristic
5	C₃×C₁₆₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
6	C₃×C₇×C₁₃	C₃×C₁₃	1	1	yes	characteristic
7	C₁₆₉	C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
8	C₉×C₁₃	—	7	1	no	—
9	C₇×C₁₃	C₉×C₁₃	1	1	yes	characteristic
10	C₇⋊C₉	C₁₆₉	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₁₃	C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
12	C₃×C₇	C₃×C₁₆₉	1	1	yes	characteristic
13	C₁₃	C₁₃×C₇⋊C₉	1	1	yes	characteristic
14	C₉	—	7	1	no	Sylow
15	C₇	C₉×C₁₆₉	1	1	yes	characteristic, complemented, Sylow
16	C₃	ΓL(1,𝔽₈)×C₁₆₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₁₆₉	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₉×C₁₆₉
Frattini	C₃×C₁₃	C₁₃×ΓL(1,𝔽₈)
Fitting	C₃×C₇×C₁₆₉	C₃
socle, prime radical, cosocle	C₃×C₇×C₁₃	C₃×C₁₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₆₉

Complements

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

N	H ≅ G/N	type
3. C₇×C₁₆₉	C₉	semidirect
7. C₁₆₉	C₇⋊C₉	direct (N × H)
10. C₇⋊C₉	C₁₆₉	direct (N × H)
15. C₇	C₉×C₁₆₉	semidirect