Subgroups — #17949608

Order 4352.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543952	C₂	1	1	yes	maximal, characteristic, complemented
2	#14543945	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₇×D₃₂	C₂	1	1	yes	maximal, characteristic
4	#11763735	—	2	1	no	—
5	#11763648	—	2	1	no	—
6	D₁₆×D₁₇	—	2	1	no	—
7	D₅₄₄	C₄	1	1	yes	characteristic, complemented
8	#11762644	—	2	1	no	—
9	C₃₂×D₁₇	C₂²	1	1	yes	characteristic
10	C₁₇×D₃₂	C₄	1	1	yes	characteristic, complemented
11	D₈×D₁₇	—	4	1	no	—
12	#10587534	—	4	1	no	—
13	C₁₇×D₁₆	—	2	1	no	—
14	#10587497	—	4	1	no	—
15	D₂₇₂	—	2	1	no	—
16	C₁₆×D₁₇	D₄	1	1	yes	characteristic
17	C₁₇×C₃₂	C₂×C₄	1	1	yes	characteristic
18	#10587465	D₄	1	1	yes	characteristic
19	D₄×D₁₇	—	8	1	no	—
20	C₄⋊#595	—	8	1	no	—
21	D₈×C₁₇	—	4	1	no	—
22	#63228	—	8	1	no	—
23	D₁₃₆	—	4	1	no	—
24	C₈×D₁₇	D₈	1	1	yes	characteristic
25	C₁₆×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
26	#63214	SD₁₆	1	1	yes	characteristic
27	#7537	—	17	1	no	maximal, Sylow
28	C₂²×D₁₇	—	16	1	no	—
29	C₂×#595	—	16	1	no	—
30	D₄×C₁₇	—	8	1	no	—
31	C₂²⋊D₁₇	—	16	1	no	—
32	D₆₈	—	8	1	no	—
33	C₄×D₁₇	D₁₆	1	1	yes	characteristic
34	C₈×C₁₇	#102	1	1	yes	characteristic
35	#3622	SD₃₂	1	1	yes	characteristic
36	C₂×D₃₂	—	17	1	no	—
37	C₂×C₆₄	—	17	1	no	—
38	#1423	—	17	1	no	—
39	C₂²×C₁₇	—	16	1	no	—
40	C₂×D₁₇	—	16	1	no	—
41	C₂×D₁₇	—	32	1	no	—
42	C₂×D₁₇	—	32	1	no	—
43	C₂×D₁₇	D₃₂	1	1	yes	characteristic
44	#595	—	32	1	no	—
45	C₄×C₁₇	#357	1	1	yes	characteristic
46	Dic₁₇	SD₆₄	1	1	yes	characteristic
47	C₂×D₁₆	—	34	1	no	—
48	D₃₂	—	17	1	no	—
49	D₃₂	—	34	1	no	—
50	D₃₂	#595	1	1	yes	characteristic, complemented
51	C₂×C₃₂	—	17	1	no	—
52	#366	—	34	1	no	—
53	C₆₄	—	34	1	no	—
54	C₂×C₁₇	—	32	1	no	—
55	C₂×C₁₇	#1415	1	1	yes	characteristic
56	D₁₇	—	32	1	no	—
57	D₁₇	D₆₄	1	1	yes	characteristic
58	D₁₇	SD₁₂₈	1	1	yes	characteristic
59	C₂×D₈	—	68	1	no	—
60	D₁₆	—	2	1	no	—
61	D₁₆	—	34	1	no	—
62	D₁₆	—	68	1	no	—
63	C₂×C₁₆	—	17	1	no	—
64	#107	—	68	1	no	—
65	C₃₂	—	17	1	no	—
66	C₃₂	C₂×#595	1	1	yes	characteristic
67	C₁₇	#7537	1	1	yes	characteristic, complemented, Sylow
68	C₂×D₄	—	136	1	no	—
69	D₈	—	4	1	no	—
70	D₈	—	68	1	no	—
71	D₈	—	136	1	no	—
72	C₂×C₈	—	17	1	no	—
73	C₄⋊C₄	—	136	1	no	—
74	C₁₆	—	17	1	no	—
75	C₁₆	C₂²⋊#595	1	1	yes	characteristic
76	C₂³	—	272	1	no	—
77	D₄	—	8	1	no	—
78	D₄	—	272	1	no	—
79	D₄	—	136	1	no	—
80	C₂×C₄	—	272	1	no	—
81	C₂×C₄	—	17	1	no	—
82	C₈	—	17	1	no	—
83	C₈	#10587547	1	1	yes	characteristic
84	C₂²	—	16	1	no	—
85	C₂²	—	272	1	no	—
86	C₂²	—	17	1	no	—
87	C₂²	—	544	1	no	—
88	C₂²	—	544	1	no	—
89	C₄	—	17	1	no	—
90	C₄	—	544	1	no	—
91	C₄	#11763721	1	1	yes	characteristic
92	C₂	—	17	1	no	—
93	C₂	—	17	1	no	—
94	C₂	—	32	1	no	—
95	C₂	—	544	1	no	—
96	C₂	#14543933	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14543933
commutator	C₁₇×C₃₂	C₂×C₄
Frattini	C₃₂	C₂×#595
Fitting	C₁₇×D₃₂	C₄
socle	C₂×C₁₇	#1415
prime radical	D₁₇×D₃₂	C₂
cosocle	C₃₂×D₁₇	C₂²
hypercenter	D₃₂	#595
hypocenter	C₁₇	#7537
LCS	G ▷ C₁₇×C₃₂ ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ D₃₂

Complements

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

N	H ≅ G/N	type
1. #14543952	C₂	semidirect
2. #14543945	C₂	semidirect
7. D₅₄₄	C₄	semidirect
10. C₁₇×D₃₂	C₄	semidirect
50. D₃₂	#595	semidirect
67. C₁₇	#7537	semidirect

Maximal subgroups

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

subgroup	index
#14543952	2
#14543945	2
D₁₇×D₃₂	2
#7537	17