Subgroups — #63252

Order 272.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊D₁₇	C₂	1	2	yes	maximal, complemented
3	D₆₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₁₇	C₂	1	2	yes	maximal, complemented
5	Dic₃₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₁₇	C₂²	1	1	yes	characteristic
7	C₂×D₁₇	C₂²	1	2	yes	—
8	C₄×C₁₇	C₂²	1	1	yes	characteristic
9	C₄×C₁₇	C₂²	1	1	yes	characteristic
10	Dic₁₇	C₂²	1	2	yes	—
11	C₂×C₁₇	—	2	1	no	—
12	C₂×C₁₇	C₂³	1	1	yes	characteristic
13	D₁₇	—	2	2	no	—
14	C₁₇	#41	1	1	yes	characteristic, complemented, Sylow
15	#41	—	17	1	no	maximal, Sylow
16	Q₈	—	17	1	no	—
17	D₄	—	17	2	no	—
18	D₄	—	17	1	no	—
19	C₂×C₄	—	17	2	no	—
20	C₂×C₄	D₁₇	1	1	yes	characteristic, complemented
21	C₂²	—	17	2	no	—
22	C₂²	C₂×D₁₇	1	1	yes	characteristic
23	C₄	—	17	2	no	—
24	C₄	C₂×D₁₇	1	1	yes	characteristic
25	C₄	C₂×D₁₇	1	1	yes	characteristic
26	C₂	—	2	1	no	—
27	C₂	—	34	2	no	—
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.