Subgroups — D₄×D₁₇ #63253

Order 272.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₇	C₂	1	2	yes	maximal, complemented
2	D₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊D₁₇	C₂	1	2	yes	maximal, complemented
4	D₆₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₁₇	C₂²	1	2	yes	complemented
7	C₂×D₁₇	—	2	4	no	—
8	C₂×D₁₇	C₂²	1	1	yes	characteristic
9	C₂×D₁₇	C₂²	1	2	yes	complemented
10	C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
11	Dic₁₇	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₁₇	—	2	2	no	—
13	C₂×C₁₇	C₂³	1	1	yes	characteristic
14	D₁₇	—	2	2	no	—
15	D₁₇	D₄	1	2	yes	direct product factor
16	C₁₇	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
17	C₂×D₄	—	17	1	no	maximal, Sylow
18	C₂³	—	17	2	no	—
19	D₄	—	17	2	no	—
20	D₄	—	17	1	no	—
21	D₄	D₁₇	1	1	yes	characteristic, direct product factor
22	C₂×C₄	—	17	1	no	—
23	C₂²	—	17	1	no	—
24	C₂²	—	17	2	no	—
25	C₂²	—	34	4	no	—
26	C₂²	C₂×D₁₇	1	2	yes	complemented
27	C₄	—	17	1	no	—
28	C₄	C₂×D₁₇	1	1	yes	characteristic, complemented
29	C₂	—	2	2	no	—
30	C₂	—	17	2	no	—
31	C₂	—	34	2	no	—
32	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.