Subgroups — #14543933

Order 2176.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763740	C₂	1	1	yes	maximal, characteristic, complemented
2	#11763735	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic
4	D₈×D₁₇	—	2	1	no	—
5	#10587534	—	2	1	no	—
6	C₁₇×D₁₆	C₄	1	1	yes	characteristic, complemented
7	#10587497	—	2	1	no	—
8	D₂₇₂	C₄	1	1	yes	characteristic, complemented
9	C₁₆×D₁₇	C₂²	1	1	yes	characteristic
10	#10587467	—	2	1	no	—
11	D₄×D₁₇	—	4	1	no	—
12	C₄⋊#595	—	4	1	no	—
13	D₈×C₁₇	—	2	1	no	—
14	#63228	—	4	1	no	—
15	D₁₃₆	—	2	1	no	—
16	C₈×D₁₇	D₄	1	1	yes	characteristic
17	C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
18	#63214	D₄	1	1	yes	characteristic
19	C₂²×D₁₇	—	8	1	no	—
20	C₂×#595	—	8	1	no	—
21	D₄×C₁₇	—	4	1	no	—
22	C₂²⋊D₁₇	—	8	1	no	—
23	D₆₈	—	4	1	no	—
24	C₄×D₁₇	D₈	1	1	yes	characteristic
25	C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
26	#3622	SD₁₆	1	1	yes	characteristic
27	#1415	—	17	1	no	maximal, Sylow
28	C₂²×C₁₇	—	8	1	no	—
29	C₂×D₁₇	—	8	1	no	—
30	C₂×D₁₇	—	16	1	no	—
31	C₂×D₁₇	—	16	1	no	—
32	C₂×D₁₇	D₁₆	1	1	yes	characteristic
33	#595	—	16	1	no	—
34	C₄×C₁₇	#102	1	1	yes	characteristic
35	Dic₁₇	SD₃₂	1	1	yes	characteristic
36	C₂×D₁₆	—	17	1	no	—
37	C₂×C₃₂	—	17	1	no	—
38	#366	—	17	1	no	—
39	C₂×C₁₇	—	16	1	no	—
40	C₂×C₁₇	#357	1	1	yes	characteristic
41	D₁₇	—	16	1	no	—
42	D₁₇	D₃₂	1	1	yes	characteristic
43	D₁₇	SD₆₄	1	1	yes	characteristic
44	C₂×D₈	—	34	1	no	—
45	D₁₆	—	17	1	no	—
46	D₁₆	—	34	1	no	—
47	D₁₆	#595	1	1	yes	characteristic, complemented
48	C₂×C₁₆	—	17	1	no	—
49	#107	—	34	1	no	—
50	C₃₂	—	34	1	no	—
51	C₁₇	#1415	1	1	yes	characteristic, complemented, Sylow
52	C₂×D₄	—	68	1	no	—
53	D₈	—	2	1	no	—
54	D₈	—	34	1	no	—
55	D₈	—	68	1	no	—
56	C₂×C₈	—	17	1	no	—
57	C₄⋊C₄	—	68	1	no	—
58	C₁₆	—	17	1	no	—
59	C₁₆	C₂×#595	1	1	yes	characteristic
60	C₂³	—	136	1	no	—
61	D₄	—	4	1	no	—
62	D₄	—	68	1	no	—
63	D₄	—	136	1	no	—
64	C₂×C₄	—	17	1	no	—
65	C₂×C₄	—	136	1	no	—
66	C₈	—	17	1	no	—
67	C₈	C₂²⋊#595	1	1	yes	characteristic
68	C₂²	—	8	1	no	—
69	C₂²	—	272	1	no	—
70	C₂²	—	272	1	no	—
71	C₂²	—	17	1	no	—
72	C₂²	—	136	1	no	—
73	C₄	—	272	1	no	—
74	C₄	—	17	1	no	—
75	C₄	#10587547	1	1	yes	characteristic
76	C₂	—	16	1	no	—
77	C₂	—	272	1	no	—
78	C₂	—	17	1	no	—
79	C₂	—	17	1	no	—
80	C₂	#11763721	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11763721
commutator	C₁₆×C₁₇	C₂×C₄
Frattini	C₁₆	C₂×#595
Fitting	C₁₇×D₁₆	C₄
socle	C₂×C₁₇	#357
prime radical	D₁₆×D₁₇	C₂
cosocle	C₁₆×D₁₇	C₂²
hypercenter	D₁₆	#595
hypocenter	C₁₇	#1415
LCS	G ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. #11763740	C₂	semidirect
2. #11763735	C₂	semidirect
6. C₁₇×D₁₆	C₄	semidirect
8. D₂₇₂	C₄	semidirect
47. D₁₆	#595	semidirect
51. C₁₇	#1415	semidirect

Maximal subgroups

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

subgroup	index
#11763740	2
#11763735	2
D₁₆×D₁₇	2
#1415	17