Subgroups — #16922214

Order 4352.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14526995	C₂	1	1	yes	maximal, characteristic, complemented
2	#14526988	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×D₃₂	C₂	1	1	yes	maximal, characteristic
4	#11762639	—	2	1	no	—
5	#11762528	—	2	1	no	—
6	C₂×C₁₇×D₁₆	—	2	1	no	—
7	C₁₇×D₃₂	—	2	1	no	—
8	C₁₇×D₃₂	C₄	1	2	yes	—
9	C₂×C₁₇×C₃₂	C₂²	1	1	yes	characteristic
10	C₂×D₈×C₁₇	—	4	1	no	—
11	C₁₇×D₁₆	—	2	2	no	—
12	C₁₇×D₁₆	—	4	1	no	—
13	C₂×C₁₆×C₁₇	D₄	1	1	yes	characteristic
14	#10587490	—	4	1	no	—
15	C₁₇×C₃₂	C₂×C₄	1	1	yes	characteristic
16	C₁₇×C₃₂	D₄	1	1	yes	characteristic
17	C₂×D₄×C₁₇	—	8	1	no	—
18	D₈×C₁₇	—	4	2	no	—
19	D₈×C₁₇	—	8	1	no	—
20	C₂×C₈×C₁₇	D₈	1	1	yes	characteristic
21	#63223	—	8	1	no	—
22	C₁₆×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₆×C₁₇	SD₁₆	1	1	yes	characteristic
24	#7541	—	17	1	no	maximal, Sylow
25	C₂³×C₁₇	—	16	1	no	—
26	D₄×C₁₇	—	8	2	no	—
27	D₄×C₁₇	—	16	1	no	—
28	C₂×C₄×C₁₇	D₁₆	1	1	yes	characteristic
29	C₈×C₁₇	#102	1	1	yes	characteristic
30	C₈×C₁₇	SD₃₂	1	1	yes	characteristic
31	#3622	—	16	1	no	—
32	C₂×D₃₂	D₁₇	1	1	yes	characteristic
33	M₁₂₈	—	17	1	no	—
34	#1425	—	17	1	no	—
35	C₂²×C₁₇	—	16	2	no	—
36	C₂²×C₁₇	—	32	2	no	—
37	C₂²×C₁₇	SD₆₄	1	1	yes	characteristic
38	C₄×C₁₇	#357	1	1	yes	characteristic
39	C₄×C₁₇	D₃₂	1	1	yes	characteristic
40	C₂×D₁₆	—	2	1	no	—
41	D₃₂	—	2	1	no	—
42	D₃₂	Dic₁₇	1	2	yes	—
43	C₂×C₃₂	C₂×D₁₇	1	1	yes	characteristic
44	#368	—	34	1	no	—
45	C₆₄	—	34	1	no	—
46	C₂×C₁₇	—	2	1	no	—
47	C₂×C₁₇	—	32	2	no	—
48	C₂×C₁₇	#1415	1	1	yes	characteristic
49	C₂×D₈	—	4	1	no	—
50	D₁₆	—	2	2	no	—
51	D₁₆	—	4	1	no	—
52	C₂×C₁₆	C₂²⋊D₁₇	1	1	yes	characteristic
53	#108	—	68	1	no	—
54	C₃₂	C₂×Dic₁₇	1	1	yes	characteristic
55	C₃₂	C₂²⋊D₁₇	1	1	yes	characteristic
56	C₁₇	#7541	1	1	yes	characteristic, complemented, Sylow
57	C₂×D₄	—	8	1	no	—
58	D₈	—	4	2	no	—
59	D₈	—	8	1	no	—
60	M₁₆	—	136	1	no	—
61	C₂×C₈	#63228	1	1	yes	characteristic
62	C₁₆	#63229	1	1	yes	characteristic
63	C₁₆	C₂²⋊Dic₁₇	1	1	yes	characteristic
64	C₂³	—	16	1	no	—
65	D₄	—	8	2	no	—
66	D₄	—	16	1	no	—
67	C₂×C₄	#10587497	1	1	yes	characteristic
68	C₈	—	272	1	no	—
69	C₈	#10587498	1	1	yes	characteristic
70	C₈	#10587503	1	1	yes	characteristic
71	C₂²	—	16	2	no	—
72	C₂²	—	32	2	no	—
73	C₂²	#11762647	1	1	yes	characteristic
74	C₄	#11762610	1	1	yes	characteristic
75	C₄	#11762644	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	32	2	no	—
78	C₂	#14526962	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14526962
commutator	C₁₇×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₇
Fitting, prime radical	C₂×C₁₇×D₃₂	C₂
socle	C₂×C₁₇	#1415
cosocle	C₂×C₁₇×C₃₂	C₂²
hypercenter	C₂×D₃₂	D₁₇
hypocenter	C₁₇	#7541
LCS	G ▷ C₁₇×C₃₂ ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×D₃₂

Complements

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

N	H ≅ G/N	type
1. #14526995	C₂	semidirect
2. #14526988	C₂	semidirect
56. C₁₇	#7541	semidirect

Maximal subgroups

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

subgroup	index
#14526995	2
#14526988	2
C₂×C₁₇×D₃₂	2
#7541	17