Subgroups — C₇×#63256 #14274162

Order 1904.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×Q₈×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₆₈	C₂	1	3	yes	maximal, complemented
3	C₄×C₇×D₁₇	C₂	1	3	yes	maximal, complemented
4	C₂×C₇×D₁₇	C₂²	1	3	yes	—
5	C₄×C₇×C₁₇	C₂²	1	3	yes	—
6	C₇×Dic₁₇	C₂²	1	1	yes	characteristic
7	#63256	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇×C₁₇	C₂³	1	1	yes	characteristic
9	C₇×D₁₇	—	2	3	no	—
10	Q₈×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented
11	D₆₈	C₂×C₇	1	3	yes	complemented
12	C₄×D₁₇	C₂×C₇	1	3	yes	complemented
13	C₇×C₁₇	#41	1	1	yes	characteristic, complemented, Hall
14	C₇×#41	—	17	1	no	maximal, Hall
15	C₂×D₁₇	C₂²×C₇	1	3	yes	—
16	C₄×C₁₇	C₂²×C₇	1	3	yes	—
17	Dic₁₇	C₂²×C₇	1	1	yes	characteristic
18	C₇×Q₈	D₁₇	1	1	yes	characteristic, complemented
19	C₇×D₄	—	17	3	no	—
20	C₂×C₄×C₇	—	17	3	no	—
21	C₂×C₁₇	C₂³×C₇	1	1	yes	characteristic
22	D₁₇	—	2	3	no	—
23	C₂²×C₇	—	17	3	no	—
24	C₄×C₇	—	17	1	no	—
25	C₄×C₇	C₂×D₁₇	1	3	yes	—
26	C₁₇	C₇×#41	1	1	yes	characteristic, complemented, Sylow
27	#41	—	17	1	no	Sylow
28	C₂×C₇	—	34	3	no	—
29	C₂×C₇	C₂²×D₁₇	1	1	yes	characteristic
30	Q₈	C₇×D₁₇	1	1	yes	characteristic, complemented
31	D₄	—	17	3	no	—
32	C₂×C₄	—	17	3	no	—
33	C₇	#63256	1	1	yes	characteristic, direct product factor, Sylow
34	C₂²	—	17	3	no	—
35	C₄	—	17	1	no	—
36	C₄	C₂×C₇×D₁₇	1	3	yes	—
37	C₂	—	34	3	no	—
38	C₂	C₂²×C₇×D₁₇	1	1	yes	characteristic

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.