Subgroups — C₇⋊#19096904 #46828643

Order 34524.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊D₃×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇×C₁₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₇×C₁₃₇	—	6	2	no	—
4	#19096904	—	7	1	no	maximal, Hall
5	Dic₉₅₉	—	9	1	no	maximal, Hall
6	C₃×C₇×C₁₃₇	—	2	2	no	—
7	C₃⋊D₃×C₁₃₇	D₇	1	1	yes	characteristic
8	C₂×C₇×C₁₃₇	—	9	1	no	—
9	C₃²×C₁₃₇	Dic₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₁₃₇	#157	1	1	yes	characteristic, complemented, Hall
11	D₃×C₁₃₇	—	6	2	no	—
12	Dic₁₃₇	—	63	1	no	Hall
13	C₃×C₁₃₇	—	2	2	no	—
14	C₂×C₁₃₇	—	9	1	no	—
15	C₇⋊#157	—	137	1	no	maximal, Hall
16	C₁₃₇	C₇⋊#157	1	1	yes	characteristic, complemented, Sylow
17	C₇×C₃⋊D₃	D₁₃₇	1	1	yes	characteristic
18	C₃²×C₇	Dic₁₃₇	1	1	yes	characteristic, complemented, Hall
19	D₃×C₇	—	6	2	no	—
20	#157	—	959	1	no	Hall
21	Dic₇	—	1233	1	no	Hall
22	C₃×C₇	—	2	2	no	—
23	C₃⋊D₃	D₉₅₉	1	1	yes	characteristic
24	C₂×C₇	—	9	1	no	—
25	C₃²	Dic₉₅₉	1	1	yes	characteristic, complemented, Sylow
26	C₇	#19096904	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	6	2	no	—
28	C₄	—	8631	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₇×C₁₃₇	C₄
prime radical, cosocle	C₇×C₃⋊D₃×C₁₃₇	C₂
LCS	G ▷ C₃²×C₇×C₁₃₇
UCS	C₁

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.