Subgroups — #14526921

Order 2176.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#10587465	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×D₁₇	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
6	C₂×#63214	C₄	1	1	yes	characteristic
7	C₁₆×D₁₇	—	2	1	no	—
8	C₁₆×D₁₇	—	2	1	no	—
9	C₁₇×C₃₂	—	2	1	no	—
10	#10587465	—	2	1	no	—
11	C₂×C₄×D₁₇	C₈	1	1	yes	characteristic
12	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
13	C₂×#3622	C₈	1	1	yes	characteristic
14	C₈×D₁₇	—	2	1	no	—
15	C₈×D₁₇	—	2	1	no	—
16	C₁₆×C₁₇	D₄	1	1	yes	characteristic
17	C₁₆×C₁₇	D₄	1	1	yes	characteristic
18	#63214	—	2	1	no	—
19	C₂²×D₁₇	C₁₆	1	1	yes	characteristic
20	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
21	C₂×Dic₁₇	C₁₆	1	1	yes	characteristic
22	C₄×D₁₇	—	2	1	no	—
23	C₄×D₁₇	—	2	1	no	—
24	C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₁₇	M₁₆	1	1	yes	characteristic
26	#3622	—	2	1	no	—
27	C₂²⋊C₃₂	—	17	1	no	maximal, Sylow
28	C₂²×C₁₇	C₂×C₁₆	1	1	yes	characteristic
29	C₂×D₁₇	—	2	1	no	—
30	C₂×D₁₇	—	2	1	no	—
31	C₂×D₁₇	C₃₂	1	2	yes	complemented
32	C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
33	C₄×C₁₇	M₃₂	1	1	yes	characteristic
34	Dic₁₇	—	2	1	no	—
35	C₂²×C₁₆	—	17	1	no	—
36	C₂×C₃₂	—	17	1	no	—
37	C₂×C₃₂	D₁₇	1	1	yes	characteristic, complemented
38	C₂×C₁₇	C₂²⋊C₁₆	1	1	yes	characteristic
39	C₂×C₁₇	C₂×C₃₂	1	1	yes	characteristic
40	C₂×C₁₇	M₆₄	1	1	yes	characteristic
41	D₁₇	—	2	2	no	—
42	C₂²×C₈	—	17	1	no	—
43	C₂×C₁₆	—	17	1	no	—
44	C₂×C₁₆	—	34	1	no	—
45	C₂×C₁₆	—	34	1	no	—
46	C₂×C₁₆	C₂×D₁₇	1	1	yes	characteristic
47	C₃₂	—	2	1	no	—
48	C₃₂	—	34	1	no	—
49	C₁₇	C₂²⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₄	—	17	1	no	—
51	C₂×C₈	—	17	1	no	—
52	C₂×C₈	—	34	1	no	—
53	C₂×C₈	—	34	1	no	—
54	C₂×C₈	C₄×D₁₇	1	1	yes	characteristic
55	C₁₆	—	34	1	no	—
56	C₁₆	D₆₈	1	1	yes	characteristic
57	C₁₆	C₂²⋊D₁₇	1	1	yes	characteristic
58	C₂³	—	17	1	no	—
59	C₂×C₄	—	17	1	no	—
60	C₂×C₄	—	34	1	no	—
61	C₂×C₄	—	34	1	no	—
62	C₂×C₄	C₈×D₁₇	1	1	yes	characteristic
63	C₈	—	34	1	no	—
64	C₈	#63218	1	1	yes	characteristic
65	C₈	#63227	1	1	yes	characteristic
66	C₂²	—	17	2	no	—
67	C₂²	—	34	1	no	—
68	C₂²	—	34	1	no	—
69	C₂²	C₁₆×D₁₇	1	1	yes	characteristic
70	C₄	—	34	1	no	—
71	C₄	#10587469	1	1	yes	characteristic
72	C₄	#10587491	1	1	yes	characteristic
73	C₂	—	34	2	no	—
74	C₂	#11762588	1	1	yes	characteristic
75	C₂	C₃₂×D₁₇	1	1	yes	characteristic
76	C₂	#11762642	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×D₁₇
commutator	C₂×C₁₇	C₂×C₃₂
Fitting	C₂×C₁₇×C₃₂	C₂
socle	C₂²×C₁₇	C₂×C₁₆
prime radical	C₂²×D₁₇	C₁₆
cosocle	C₂×C₁₆×C₁₇	C₂²
hypercenter	C₂×C₃₂	D₁₇
hypocenter	C₁₇	C₂²⋊C₃₂
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×#10587465	C₂	semidirect
3. C₂×C₁₇×C₃₂	C₂	semidirect
31. C₂×D₁₇	C₃₂	semidirect
37. C₂×C₃₂	D₁₇	semidirect
49. C₁₇	C₂²⋊C₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₆×D₁₇	2
C₂×#10587465	2
C₂×C₁₇×C₃₂	2
C₂²⋊C₃₂	17