Subgroups — #63227

Order 272.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Dic₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₇	C₂²	1	1	yes	characteristic
5	C₂×D₁₇	—	2	1	no	—
6	C₂×D₁₇	—	2	1	no	—
7	C₂×D₁₇	C₄	1	2	yes	complemented
8	C₄×C₁₇	—	2	1	no	—
9	Dic₁₇	—	2	1	no	—
10	C₂×C₁₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₁₇	D₄	1	1	yes	characteristic
12	C₂×C₁₇	D₄	1	1	yes	characteristic
13	D₁₇	—	2	2	no	—
14	C₁₇	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
15	C₂²⋊C₄	—	17	1	no	maximal, Sylow
16	C₂³	—	17	1	no	—
17	C₂×C₄	—	17	1	no	—
18	C₂×C₄	D₁₇	1	1	yes	characteristic, complemented
19	C₂²	—	17	2	no	—
20	C₂²	—	34	1	no	—
21	C₂²	—	34	1	no	—
22	C₂²	C₂×D₁₇	1	1	yes	characteristic
23	C₄	—	2	1	no	—
24	C₄	—	34	1	no	—
25	C₂	—	34	2	no	—
26	C₂	C₄×D₁₇	1	1	yes	characteristic
27	C₂	D₆₈	1	1	yes	characteristic
28	C₂	C₂²⋊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.