Subgroups — C₇×#10597480 #16862825

Order 4284.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₇×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₇×C₁₇	—	6	2	no	—
4	#10597480	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×Dic₁₇	—	9	1	no	maximal, Hall
6	C₃×C₇×C₁₇	—	2	2	no	—
7	C₁₇×C₃⋊D₃	C₂×C₇	1	1	yes	characteristic
8	C₇×#157	—	17	1	no	maximal, Hall
9	C₂×C₇×C₁₇	—	9	1	no	—
10	C₃²×C₁₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₃⋊D₃	D₁₇	1	1	yes	characteristic
12	C₇×C₁₇	#157	1	1	yes	characteristic, complemented, Hall
13	D₃×C₁₇	—	6	2	no	—
14	Dic₁₇	—	9	1	no	Hall
15	C₃²×C₇	Dic₁₇	1	1	yes	characteristic, complemented, Hall
16	C₃×C₁₇	—	2	2	no	—
17	D₃×C₇	—	6	2	no	—
18	#157	—	17	1	no	Hall
19	C₂×C₁₇	—	9	1	no	—
20	C₄×C₇	—	153	1	no	Hall
21	C₃×C₇	—	2	2	no	—
22	C₃⋊D₃	C₇×D₁₇	1	1	yes	characteristic
23	C₁₇	C₇×#157	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₇	—	9	1	no	—
25	C₃²	C₇×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
26	C₇	#10597480	1	1	yes	characteristic, direct product factor, Sylow
27	D₃	—	6	2	no	—
28	C₄	—	153	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	9	1	no	—

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.