Subgroups — #14545160

Order 2176.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763732	C₂	1	2	yes	maximal, complemented
2	#11763706	C₂	1	2	yes	maximal
3	#11763702	C₂	1	2	yes	maximal, complemented
4	#11762766	C₂	1	1	yes	maximal, characteristic
5	C₂×#63218	C₂²	1	1	yes	characteristic
6	C₂×C₈×D₁₇	C₄	1	1	yes	characteristic
7	#10587558	C₄	1	1	yes	characteristic
8	#10587538	C₂²	1	4	yes	—
9	C₁₇×#97	C₄	1	1	yes	characteristic
10	#10587486	C₂²	1	1	yes	characteristic
11	C₈×Dic₁₇	C₄	1	1	yes	characteristic
12	C₄×#3622	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
16	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
17	#63227	—	2	1	no	—
18	#63225	—	2	1	no	—
19	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×#3622	C₂×C₄	1	1	yes	characteristic
21	C₂×#3622	C₂³	1	1	yes	characteristic
22	#63218	—	2	2	no	—
23	C₈×D₁₇	—	2	2	no	—
24	#63216	—	2	4	no	—
25	C₂²×D₁₇	M₁₆	1	1	yes	characteristic
26	C₂×C₄×C₁₇	—	2	1	no	—
27	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
28	C₂×Dic₁₇	—	2	1	no	—
29	C₂×Dic₁₇	M₁₆	1	1	yes	characteristic
30	C₄×D₁₇	—	2	1	no	—
31	C₄×D₁₇	—	2	1	no	—
32	C₈×C₁₇	—	2	1	no	—
33	C₈×C₁₇	—	2	1	no	—
34	#3622	M₁₆	1	2	yes	—
35	#3622	#41	1	2	yes	—
36	#2166	—	17	1	no	maximal, Sylow
37	C₂²×C₁₇	C₂×M₁₆	1	1	yes	characteristic
38	C₂×D₁₇	—	2	1	no	—
39	C₂×D₁₇	—	4	1	no	—
40	C₄×C₁₇	—	4	1	no	—
41	C₄×C₁₇	#117	1	1	yes	characteristic
42	C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
43	Dic₁₇	—	2	1	no	—
44	Dic₁₇	—	4	1	no	—
45	#405	—	17	1	no	—
46	#364	—	17	2	no	—
47	#349	—	17	2	no	—
48	#347	—	17	2	no	—
49	C₂×C₁₇	—	2	1	no	—
50	C₂×C₁₇	#432	1	1	yes	characteristic
51	D₁₇	—	4	1	no	—
52	C₂×M₁₆	—	17	1	no	—
53	C₂²×C₈	—	17	1	no	—
54	#117	—	17	1	no	—
55	M₃₂	—	17	4	no	—
56	#97	—	17	1	no	—
57	#97	#595	1	1	yes	characteristic
58	C₄×C₈	—	17	1	no	—
59	C₄×C₈	—	17	1	no	—
60	C₁₇	#2166	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₄	—	17	1	no	—
62	M₁₆	—	34	2	no	—
63	C₂×C₈	—	17	1	no	—
64	C₂×C₈	—	17	1	no	—
65	C₂×C₈	—	34	2	no	—
66	C₂×C₈	C₂×#595	1	1	yes	characteristic
67	C₂×C₈	C₂×#595	1	1	yes	characteristic
68	C₄⋊C₄	—	34	1	no	—
69	C₂²⋊C₄	—	34	1	no	—
70	C₄²	—	17	1	no	—
71	C₄²	C₂×#595	1	1	yes	characteristic
72	C₁₆	—	34	4	no	—
73	C₂³	—	17	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	17	1	no	—
76	C₂×C₄	—	34	1	no	—
77	C₂×C₄	—	34	1	no	—
78	C₂×C₄	—	34	1	no	—
79	C₂×C₄	C₂²×#595	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	2	1	no	—
82	C₈	—	17	2	no	—
83	C₈	—	17	2	no	—
84	C₂²	—	34	1	no	—
85	C₂²	—	68	1	no	—
86	C₂²	D₁₇⋊M₁₆	1	1	yes	characteristic
87	C₄	—	4	1	no	—
88	C₄	—	34	1	no	—
89	C₄	—	68	1	no	—
90	C₄	D₁₇⋊M₁₆	1	1	yes	characteristic
91	C₄	#10587677	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	68	1	no	—
94	C₂	#11763832	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10587677
commutator	C₂×C₄×C₁₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×#595
Fitting	C₁₇×#97	C₄
socle	C₂×C₁₇	#432
prime radical	C₂²×D₁₇	M₁₆
cosocle	C₂×#3622	C₂³
hypercenter	#97	#595
hypocenter	C₁₇	#2166
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #97

Complements

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

N	H ≅ G/N	type
1. #11763732	C₂	semidirect
3. #11763702	C₂	semidirect
60. C₁₇	#2166	semidirect

Maximal subgroups

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

subgroup	index
#11763732	2
#11763706	2
#11763702	2
#11762766	2
#2166	17