Subgroups — #14526751

Order 2176.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11762585	C₂	1	1	yes	maximal, characteristic, complemented
2	#11762560	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₈×C₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂×D₈×C₁₇	C₄	1	1	yes	characteristic
5	C₄×D₄×C₁₇	—	2	1	no	—
6	C₁₇×#107	C₄	1	1	yes	characteristic
7	C₁₇×#102	—	2	1	no	—
8	C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
9	C₂×#63214	—	2	1	no	—
10	C₄⋊#3622	—	2	1	no	—
11	C₂×D₄×C₁₇	—	2	1	no	—
12	C₂²×C₄×C₁₇	—	4	1	no	—
13	D₈×C₁₇	—	2	1	no	—
14	D₈×C₁₇	C₈	1	2	yes	complemented
15	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₇	D₄	1	1	yes	characteristic
17	C₄⋊C₄×C₁₇	—	2	1	no	—
18	C₂²⋊C₄×C₁₇	—	4	1	no	—
19	C₄²×C₁₇	D₄	1	1	yes	characteristic
20	C₂×#3622	—	4	1	no	—
21	#63214	—	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	—	4	1	no	—
26	C₂×C₄×C₁₇	—	8	2	no	—
27	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₇	D₈	1	1	yes	characteristic
29	C₂×C₄×C₁₇	SD₁₆	1	1	yes	characteristic
30	C₈×C₁₇	—	2	1	no	—
31	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
32	C₈×C₁₇	M₁₆	1	1	yes	characteristic
33	#3622	—	8	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	—	2	1	no	—
40	C₄×C₁₇	—	2	1	no	—
41	C₄×C₁₇	—	8	1	no	—
42	C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
43	C₄×C₁₇	#104	1	1	yes	characteristic
44	C₄×D₈	D₁₇	1	1	yes	characteristic
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	Dic₁₇	1	1	yes	characteristic
52	C₄×D₄	—	2	1	no	—
53	C₂×C₁₆	—	34	1	no	—
54	#107	Dic₁₇	1	1	yes	characteristic
55	C₄⋊C₈	—	34	1	no	—
56	#102	—	2	1	no	—
57	C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
58	C₁₇	#1333	1	1	yes	characteristic, complemented, Sylow
59	C₂×D₄	—	2	1	no	—
60	C₂²×C₄	—	4	1	no	—
61	D₈	—	2	1	no	—
62	D₈	#3622	1	2	yes	complemented
63	C₂×C₈	—	68	1	no	—
64	C₂×C₈	C₂×Dic₁₇	1	1	yes	characteristic
65	C₂×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
66	C₄⋊C₄	—	2	1	no	—
67	C₂²⋊C₄	—	4	1	no	—
68	C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
69	C₁₆	—	34	2	no	—
70	C₂³	—	4	1	no	—
71	D₄	—	2	2	no	—
72	D₄	—	4	1	no	—
73	C₂×C₄	—	4	1	no	—
74	C₂×C₄	—	8	2	no	—
75	C₂×C₄	#63228	1	1	yes	characteristic
76	C₂×C₄	#63229	1	1	yes	characteristic
77	C₂×C₄	C₂²⋊Dic₁₇	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	136	1	no	—
80	C₈	C₂×#3622	1	1	yes	characteristic
81	C₈	#63223	1	1	yes	characteristic
82	C₂²	—	4	2	no	—
83	C₂²	—	8	1	no	—
84	C₂²	—	8	1	no	—
85	C₂²	#10587503	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	2	1	no	—
88	C₄	—	8	1	no	—
89	C₄	C₂²⋊#3622	1	1	yes	characteristic
90	C₄	#10587508	1	1	yes	characteristic
91	C₂	—	8	2	no	—
92	C₂	D₄⋊#3622	1	1	yes	characteristic
93	C₂	#11762619	1	1	yes	characteristic
94	C₂	#11762622	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10587503
commutator	C₈×C₁₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₇
Fitting	C₄×D₈×C₁₇	C₂
socle	C₂²×C₁₇	#102
prime radical	C₂×D₈×C₁₇	C₄
cosocle	C₄×C₈×C₁₇	C₂²
hypercenter	C₄×D₈	D₁₇
hypocenter	C₁₇	#1333
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₈

Complements

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

N	H ≅ G/N	type
1. #11762585	C₂	semidirect
2. #11762560	C₂	semidirect
14. D₈×C₁₇	C₈	semidirect
58. C₁₇	#1333	semidirect
62. D₈	#3622	semidirect

Maximal subgroups

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

subgroup	index
#11762585	2
#11762560	2
C₄×D₈×C₁₇	2
#1333	17