Subgroups — D₁₇×D₃₂ #14531080

Order 2176.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₆×D₁₇	C₂	1	2	yes	maximal, complemented
2	D₅₄₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#11762644	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×D₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	D₈×D₁₇	—	2	2	no	—
7	C₁₇×D₁₆	C₂²	1	2	yes	complemented
8	#10587497	—	2	2	no	—
9	D₂₇₂	C₂²	1	2	yes	complemented
10	C₁₆×D₁₇	C₂²	1	1	yes	characteristic
11	C₁₇×C₃₂	C₂²	1	1	yes	characteristic, complemented
12	#10587465	C₂²	1	1	yes	characteristic, complemented
13	D₄×D₁₇	—	4	2	no	—
14	D₈×C₁₇	—	2	2	no	—
15	#63228	—	4	2	no	—
16	D₁₃₆	—	2	2	no	—
17	C₈×D₁₇	D₄	1	1	yes	characteristic
18	C₁₆×C₁₇	C₂³	1	1	yes	characteristic
19	#63214	D₄	1	1	yes	characteristic
20	C₂²×D₁₇	—	8	2	no	—
21	D₄×C₁₇	—	4	2	no	—
22	C₂²⋊D₁₇	—	8	2	no	—
23	D₆₈	—	4	2	no	—
24	C₄×D₁₇	D₈	1	1	yes	characteristic
25	C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
26	#3622	D₈	1	1	yes	characteristic
27	C₂×D₃₂	—	17	1	no	maximal, Sylow
28	C₂²×C₁₇	—	8	2	no	—
29	C₂×D₁₇	—	8	2	no	—
30	C₂×D₁₇	—	16	4	no	—
31	C₂×D₁₇	D₁₆	1	1	yes	characteristic
32	C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
33	Dic₁₇	D₁₆	1	1	yes	characteristic
34	C₂×D₁₆	—	17	2	no	—
35	D₃₂	—	17	2	no	—
36	D₃₂	—	17	1	no	—
37	D₃₂	D₁₇	1	1	yes	characteristic, direct product factor
38	C₂×C₃₂	—	17	1	no	—
39	C₂×C₁₇	—	16	2	no	—
40	C₂×C₁₇	C₂×D₁₆	1	1	yes	characteristic
41	D₁₇	—	16	2	no	—
42	D₁₇	D₃₂	1	2	yes	direct product factor
43	C₂×D₈	—	34	2	no	—
44	D₁₆	—	17	2	no	—
45	D₁₆	—	34	2	no	—
46	D₁₆	C₂×D₁₇	1	2	yes	complemented
47	C₂×C₁₆	—	17	1	no	—
48	C₃₂	—	17	1	no	—
49	C₃₂	C₂×D₁₇	1	1	yes	characteristic, complemented
50	C₁₇	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
51	C₂×D₄	—	68	2	no	—
52	D₈	—	2	2	no	—
53	D₈	—	34	2	no	—
54	D₈	—	68	2	no	—
55	C₂×C₈	—	17	1	no	—
56	C₁₆	—	17	1	no	—
57	C₁₆	C₂²×D₁₇	1	1	yes	characteristic
58	C₂³	—	136	2	no	—
59	D₄	—	4	2	no	—
60	D₄	—	68	2	no	—
61	D₄	—	136	2	no	—
62	C₂×C₄	—	17	1	no	—
63	C₈	—	17	1	no	—
64	C₈	D₄×D₁₇	1	1	yes	characteristic
65	C₂²	—	8	2	no	—
66	C₂²	—	272	4	no	—
67	C₂²	—	17	1	no	—
68	C₂²	—	136	2	no	—
69	C₄	—	17	1	no	—
70	C₄	D₈×D₁₇	1	1	yes	characteristic
71	C₂	—	16	2	no	—
72	C₂	—	272	2	no	—
73	C₂	—	17	2	no	—
74	C₂	D₁₆×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₁₇
commutator, cosocle	C₁₆×C₁₇	C₂³
Frattini	C₁₆	C₂²×D₁₇
Fitting	C₁₇×D₃₂	C₂
socle	C₂×C₁₇	C₂×D₁₆
hypercenter	D₃₂	D₁₇
hypocenter	C₁₇	C₂×D₃₂
LCS	G ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₃₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. D₁₆×D₁₇	C₂	semidirect
2. D₅₄₄	C₂	semidirect
3. #11762644	C₂	semidirect
4. C₃₂×D₁₇	C₂	semidirect
5. C₁₇×D₃₂	C₂	semidirect
7. C₁₇×D₁₆	C₂²	semidirect
9. D₂₇₂	C₂²	semidirect
11. C₁₇×C₃₂	C₂²	semidirect
12. #10587465	C₂²	semidirect
37. D₃₂	D₁₇	direct (N × H)
42. D₁₇	D₃₂	direct (N × H)
46. D₁₆	C₂×D₁₇	semidirect
49. C₃₂	C₂×D₁₇	semidirect
50. C₁₇	C₂×D₃₂	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₁₆×D₁₇	2
D₅₄₄	2
#11762644	2
C₃₂×D₁₇	2
C₁₇×D₃₂	2
C₂×D₃₂	17

Subgroups — D17×D32 #14531080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₇×D₃₂ #14531080