Subgroups — C₇⋊C₉×D₁₅₇ #34089943

Order 19782.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊C₉×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₁₅₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇×C₁₅₇	C₂×C₃	1	1	yes	characteristic
4	C₉×D₁₅₇	—	7	1	no	maximal, Hall
5	C₇×D₁₅₇	C₉	1	1	yes	characteristic, complemented, Hall
6	C₉×C₁₅₇	—	7	1	no	Hall
7	C₇×C₁₅₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×D₁₅₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
9	C₃×C₁₅₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
10	D₁₅₇	C₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₁₅₇	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₇⋊C₉	—	157	1	no	maximal, Hall
13	C₇⋊C₉	D₁₅₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₇	—	157	1	no	—
15	C₃×C₇	C₃×D₁₅₇	1	1	yes	characteristic
16	C₂×C₉	—	1099	1	no	Hall
17	C₂×C₇	—	157	1	no	Hall
18	C₉	—	7	1	no	Sylow
19	C₇	C₉×D₁₅₇	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃	—	157	1	no	—
21	C₃	ΓL(1,𝔽₈)×D₁₅₇	1	1	yes	characteristic
22	C₂	—	157	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	ΓL(1,𝔽₈)×D₁₅₇
commutator, hypocenter	C₇×C₁₅₇	C₂×C₉
Fitting, socle, cosocle	C₃×C₇×C₁₅₇	C₂×C₃
prime radical	C₃×C₇×D₁₅₇	C₃
LCS	G ▷ C₇×C₁₅₇
UCS	C₁ ◁ C₃

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.