Subgroups — C₂×#63223 #10587607

Order 544.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₁₇	C₂	1	1	yes	maximal, characteristic
2	#63223	C₂	1	4	yes	maximal, direct product factor
3	C₂×#3622	C₂	1	2	yes	maximal, complemented
4	C₂³×C₁₇	C₄	1	1	yes	characteristic
5	C₂×C₄×C₁₇	C₄	1	2	yes	—
6	C₂×C₄×C₁₇	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₇	C₂²	1	2	yes	—
8	C₂×C₄×C₁₇	C₂²	1	1	yes	characteristic
9	#3622	C₂²	1	4	yes	complemented
10	C₂²×C₁₇	—	2	2	no	—
11	C₂²×C₁₇	C₂×C₄	1	2	yes	—
12	C₂²×C₁₇	C₂×C₄	1	1	yes	characteristic
13	C₄×C₁₇	C₂×C₄	1	2	yes	—
14	C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₄×C₁₇	C₂³	1	1	yes	characteristic
16	C₂×C₁₇	—	2	2	no	—
17	C₂×C₁₇	M₁₆	1	2	yes	complemented
18	C₂×C₁₇	C₂²×C₄	1	1	yes	characteristic
19	C₂×M₁₆	—	17	1	no	maximal, Sylow
20	C₁₇	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₂²×C₄	D₁₇	1	1	yes	characteristic
22	M₁₆	—	17	4	no	—
23	C₂×C₈	—	17	2	no	—
24	C₂³	Dic₁₇	1	1	yes	characteristic
25	C₂×C₄	Dic₁₇	1	1	yes	characteristic
26	C₂×C₄	Dic₁₇	1	2	yes	—
27	C₂×C₄	C₂×D₁₇	1	2	yes	—
28	C₂×C₄	C₂×D₁₇	1	1	yes	characteristic
29	C₈	—	17	4	no	—
30	C₂²	—	2	2	no	—
31	C₂²	C₂×Dic₁₇	1	2	yes	—
32	C₂²	C₂×Dic₁₇	1	1	yes	characteristic
33	C₄	C₂×Dic₁₇	1	2	yes	—
34	C₄	C₂×Dic₁₇	1	1	yes	characteristic
35	C₄	C₂²×D₁₇	1	1	yes	characteristic
36	C₂	—	2	2	no	—
37	C₂	#63223	1	2	yes	direct product factor
38	C₂	C₂²×Dic₁₇	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.