Subgroups — #10587694

Order 544.

146 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	#63256	C₂	1	4	yes	maximal, complemented
3	Q₈×D₁₇	C₂	1	4	yes	maximal, complemented
4	#63252	C₂	1	6	yes	maximal, complemented
5	Q₈×C₁₇	C₂²	1	4	yes	—
6	C₂×C₄×C₁₇	C₂²	1	3	yes	—
7	C₂²⋊D₁₇	C₂²	1	4	yes	—
8	D₆₈	C₂²	1	6	yes	—
9	C₄×D₁₇	C₂²	1	12	yes	—
10	Dic₃₄	C₂²	1	6	yes	—
11	C₂²×C₁₇	C₂³	1	1	yes	characteristic
12	C₂×D₁₇	C₂³	1	4	yes	—
13	C₄×C₁₇	C₂³	1	6	yes	—
14	Dic₁₇	C₂³	1	4	yes	—
15	C₂×C₁₇	—	2	1	no	—
16	C₂×C₁₇	C₂⁴	1	1	yes	characteristic
17	D₁₇	—	2	4	no	—
18	2₋¹⁺⁴	—	17	1	no	maximal, Sylow
19	C₁₇	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
20	#41	—	17	4	no	—
21	#41	—	17	6	no	—
22	C₂×Q₈	—	17	4	no	—
23	C₂×Q₈	D₁₇	1	1	yes	characteristic, complemented
24	Q₈	—	17	6	no	—
25	Q₈	C₂×D₁₇	1	4	yes	—
26	D₄	—	17	4	no	—
27	D₄	—	17	6	no	—
28	C₂×C₄	—	17	12	no	—
29	C₂×C₄	C₂×D₁₇	1	3	yes	—
30	C₂²	—	17	4	no	—
31	C₂²	C₂²×D₁₇	1	1	yes	characteristic
32	C₄	—	17	4	no	—
33	C₄	C₂²×D₁₇	1	6	yes	—
34	C₂	—	2	1	no	—
35	C₂	—	34	4	no	—
36	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.