Subgroups — D₁₇×C₆₄ #14526992

Order 2176.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₂×D₁₇	C₂	1	1	yes	maximal, characteristic
2	#11762528	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×D₁₇	C₄	1	1	yes	characteristic
5	C₁₇×C₃₂	C₂²	1	1	yes	characteristic
6	#10587465	C₄	1	1	yes	characteristic
7	C₈×D₁₇	C₈	1	1	yes	characteristic
8	C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
9	#63214	C₈	1	1	yes	characteristic
10	C₄×D₁₇	C₁₆	1	1	yes	characteristic
11	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
12	#3622	C₁₆	1	1	yes	characteristic
13	C₂×C₆₄	—	17	1	no	maximal, Sylow
14	C₂×D₁₇	C₃₂	1	1	yes	characteristic
15	C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
16	Dic₁₇	C₃₂	1	1	yes	characteristic
17	C₂×C₃₂	—	17	1	no	—
18	C₆₄	—	17	1	no	—
19	C₆₄	D₁₇	1	1	yes	characteristic, direct product factor
20	C₂×C₁₇	C₂×C₃₂	1	1	yes	characteristic
21	D₁₇	C₆₄	1	2	yes	direct product factor
22	C₂×C₁₆	—	17	1	no	—
23	C₃₂	—	17	1	no	—
24	C₃₂	C₂×D₁₇	1	1	yes	characteristic
25	C₁₇	C₂×C₆₄	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₈	—	17	1	no	—
27	C₁₆	—	17	1	no	—
28	C₁₆	C₄×D₁₇	1	1	yes	characteristic
29	C₂×C₄	—	17	1	no	—
30	C₈	—	17	1	no	—
31	C₈	C₈×D₁₇	1	1	yes	characteristic
32	C₂²	—	17	1	no	—
33	C₄	—	17	1	no	—
34	C₄	C₁₆×D₁₇	1	1	yes	characteristic
35	C₂	—	17	2	no	—
36	C₂	C₃₂×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.