Finite Group Databasebeta

← C₇×C₁₅₁⋊C₉ #23748877

Subgroups — C₇×C₁₅₁⋊C₉ #23748877

Order 9513.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₅₁	C₃	1	1	yes	maximal, characteristic
2	C₁₅₁⋊C₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₅₁	C₉	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₅₁	C₃×C₇	1	1	yes	characteristic
5	C₁₅₁	C₇×C₉	1	1	yes	characteristic, complemented, Sylow
6	C₇×C₉	—	151	1	no	maximal, Hall
7	C₃×C₇	C₁₅₁⋊C₃	1	1	yes	characteristic
8	C₉	—	151	1	no	Sylow
9	C₇	C₁₅₁⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
10	C₃	C₇×C₁₅₁⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₇	C₁₅₁⋊C₃
commutator, hypocenter	C₁₅₁	C₇×C₉
Frattini	C₃	C₇×C₁₅₁⋊C₃
Fitting, socle, prime radical	C₃×C₇×C₁₅₁	C₃
cosocle	C₃×C₁₅₁	C₃×C₇
LCS	G ▷ C₁₅₁
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
2. C₁₅₁⋊C₉	C₇	direct (N × H)
3. C₇×C₁₅₁	C₉	semidirect
5. C₁₅₁	C₇×C₉	semidirect
9. C₇	C₁₅₁⋊C₉	direct (N × H)