Subgroups — C₇⋊#10597479 #16862827

Order 4284.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊D₅₁	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×D₅₁	—	6	2	no	—
4	#10597479	—	7	1	no	maximal, Hall
5	C₇⋊#595	—	9	1	no	maximal, Hall
6	C₃×C₇×C₁₇	—	2	2	no	—
7	C₃⋊D₅₁	D₇	1	1	yes	characteristic
8	C₇⋊#157	—	17	1	no	maximal, Hall
9	C₇×D₁₇	—	9	1	no	—
10	C₃²×C₁₇	Dic₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₃⋊D₃	—	17	1	no	—
12	C₇×C₁₇	#157	1	1	yes	characteristic, complemented, Hall
13	D₅₁	—	6	2	no	—
14	#595	—	63	1	no	Hall
15	C₃²×C₇	#595	1	1	yes	characteristic, complemented, Hall
16	C₃×C₁₇	—	2	2	no	—
17	D₃×C₇	—	102	2	no	—
18	#157	—	119	1	no	Hall
19	D₁₇	—	9	1	no	—
20	Dic₇	—	153	1	no	Hall
21	C₃×C₇	—	2	2	no	—
22	C₃⋊D₃	—	17	1	no	—
23	C₁₇	C₇⋊#157	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₇	—	153	1	no	—
25	C₃²	C₇⋊#595	1	1	yes	characteristic, complemented, Sylow
26	C₇	#10597479	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	102	2	no	—
28	C₄	—	1071	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	153	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₇×C₁₇	C₄
prime radical, cosocle	C₇×C₃⋊D₅₁	C₂
LCS	G ▷ C₃²×C₇×C₁₇
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.