Subgroups — #14543742

Order 2176.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763698	C₂	1	1	yes	maximal, characteristic, complemented
2	#11763670	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×Dic₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂×D₈×C₁₇	C₄	1	1	yes	characteristic
5	D₄×Dic₁₇	—	2	1	no	—
6	C₄⋊#3624	—	2	1	no	—
7	C₂×#63216	—	2	1	no	—
8	#10587503	—	2	1	no	—
9	#10587489	C₄	1	1	yes	characteristic
10	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
11	C₂×D₄×C₁₇	—	2	1	no	—
12	C₂²×Dic₁₇	—	4	1	no	—
13	C₂×#3624	—	4	1	no	—
14	D₈×C₁₇	—	2	1	no	—
15	D₈×C₁₇	C₈	1	2	yes	complemented
16	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂²⋊Dic₁₇	—	4	1	no	—
18	C₄⋊Dic₁₇	—	2	1	no	—
19	C₄×Dic₁₇	D₄	1	1	yes	characteristic
20	C₂×#3622	D₄	1	1	yes	characteristic
21	#63216	—	2	2	no	—
22	C₂³×C₁₇	—	4	1	no	—
23	D₄×C₁₇	—	2	2	no	—
24	D₄×C₁₇	—	4	1	no	—
25	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×Dic₁₇	—	4	1	no	—
27	C₂×Dic₁₇	—	8	2	no	—
28	C₂×Dic₁₇	D₈	1	1	yes	characteristic
29	C₂×Dic₁₇	SD₁₆	1	1	yes	characteristic
30	#3624	—	8	1	no	—
31	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
32	C₈×C₁₇	M₁₆	1	1	yes	characteristic
33	#3622	—	2	1	no	—
34	#1333	—	17	1	no	maximal, Sylow
35	C₂²×C₁₇	—	4	2	no	—
36	C₂²×C₁₇	—	8	1	no	—
37	C₂²×C₁₇	—	8	1	no	—
38	C₂²×C₁₇	#102	1	1	yes	characteristic
39	C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
40	C₄×C₁₇	#104	1	1	yes	characteristic
41	Dic₁₇	—	2	1	no	—
42	Dic₁₇	—	2	1	no	—
43	Dic₁₇	—	8	1	no	—
44	C₄×D₈	—	17	1	no	—
45	#346	—	17	1	no	—
46	#334	—	17	1	no	—
47	C₂×C₁₇	—	8	2	no	—
48	C₂×C₁₇	D₄⋊C₈	1	1	yes	characteristic
49	C₂×C₁₇	#360	1	1	yes	characteristic
50	C₂×C₁₇	#361	1	1	yes	characteristic
51	C₂×D₈	#595	1	1	yes	characteristic
52	C₄×D₄	—	34	1	no	—
53	C₂×C₁₆	—	34	1	no	—
54	#107	—	17	1	no	—
55	C₄⋊C₈	—	34	1	no	—
56	#102	—	34	1	no	—
57	C₄×C₈	—	17	1	no	—
58	C₁₇	#1333	1	1	yes	characteristic, complemented, Sylow
59	C₂×D₄	—	2	1	no	—
60	C₂²×C₄	—	68	1	no	—
61	D₈	—	2	1	no	—
62	D₈	#3624	1	2	yes	complemented
63	C₂×C₈	—	17	1	no	—
64	C₂×C₈	—	68	1	no	—
65	C₂×C₈	C₂×#595	1	1	yes	characteristic
66	C₄⋊C₄	—	34	1	no	—
67	C₂²⋊C₄	—	68	1	no	—
68	C₄²	—	17	1	no	—
69	C₁₆	—	34	2	no	—
70	C₂³	—	4	1	no	—
71	D₄	—	2	2	no	—
72	D₄	—	4	1	no	—
73	C₂×C₄	—	17	1	no	—
74	C₂×C₄	—	17	1	no	—
75	C₂×C₄	—	68	1	no	—
76	C₂×C₄	—	136	2	no	—
77	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
78	C₈	—	34	1	no	—
79	C₈	—	136	1	no	—
80	C₈	C₂×#3624	1	1	yes	characteristic
81	C₈	#63247	1	1	yes	characteristic
82	C₂²	—	4	2	no	—
83	C₂²	—	8	1	no	—
84	C₂²	—	8	1	no	—
85	C₂²	#10587547	1	1	yes	characteristic
86	C₄	—	34	1	no	—
87	C₄	—	34	1	no	—
88	C₄	—	136	1	no	—
89	C₄	#10587548	1	1	yes	characteristic
90	C₄	C₂²⋊#3624	1	1	yes	characteristic
91	C₂	—	8	2	no	—
92	C₂	D₄⋊#3624	1	1	yes	characteristic
93	C₂	#11763725	1	1	yes	characteristic
94	C₂	#11763727	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10587547
commutator	C₈×C₁₇	C₂×C₈
Frattini	C₂×C₈	C₂×#595
Fitting, prime radical	C₂×D₈×C₁₇	C₄
socle	C₂²×C₁₇	#102
cosocle	C₈×Dic₁₇	C₂²
hypercenter	C₂×D₈	#595
hypocenter	C₁₇	#1333
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. #11763698	C₂	semidirect
2. #11763670	C₂	semidirect
15. D₈×C₁₇	C₈	semidirect
58. C₁₇	#1333	semidirect
62. D₈	#3624	semidirect

Maximal subgroups

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

subgroup	index
#11763698	2
#11763670	2
D₈×Dic₁₇	2
#1333	17