Subgroups — C₂×Q₈×D₁₇ #10587692

Order 544.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×D₁₇	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄×D₁₇	C₂	1	3	yes	maximal
4	C₂×Dic₃₄	C₂	1	3	yes	maximal, complemented
5	C₂²×D₁₇	C₂²	1	1	yes	characteristic
6	Q₈×C₁₇	C₂²	1	4	yes	complemented
7	C₂×C₄×C₁₇	C₂²	1	3	yes	—
8	C₂×Dic₁₇	C₂²	1	3	yes	—
9	C₄×D₁₇	C₂²	1	12	yes	—
10	Dic₃₄	C₂²	1	12	yes	complemented
11	C₂²×C₁₇	C₂³	1	1	yes	characteristic
12	C₂×D₁₇	Q₈	1	4	yes	direct product factor
13	C₂×D₁₇	C₂³	1	2	yes	—
14	C₄×C₁₇	C₂³	1	6	yes	—
15	Dic₁₇	C₂³	1	6	yes	—
16	C₂×C₁₇	C₂×Q₈	1	2	yes	complemented
17	C₂×C₁₇	C₂⁴	1	1	yes	characteristic
18	D₁₇	C₂×Q₈	1	4	yes	direct product factor
19	C₂²×Q₈	—	17	1	no	maximal, Sylow
20	C₁₇	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
21	C₂×Q₈	—	17	8	no	—
22	C₂×Q₈	—	17	3	no	—
23	C₂×Q₈	D₁₇	1	1	yes	characteristic, direct product factor
24	C₂²×C₄	—	17	3	no	—
25	C₂³	—	17	1	no	—
26	Q₈	—	17	12	no	—
27	Q₈	C₂×D₁₇	1	4	yes	direct product factor
28	C₂×C₄	—	17	3	no	—
29	C₂×C₄	—	17	12	no	—
30	C₂×C₄	C₂×D₁₇	1	3	yes	—
31	C₂²	—	17	4	no	—
32	C₂²	—	17	2	no	—
33	C₂²	C₂²×D₁₇	1	1	yes	characteristic
34	C₄	—	17	6	no	—
35	C₄	C₂²×D₁₇	1	6	yes	—
36	C₂	—	17	4	no	—
37	C₂	Q₈×D₁₇	1	2	yes	direct product factor
38	C₂	C₂³×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.