Subgroups — #14545205

Order 2176.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763742	C₂	1	2	yes	maximal, complemented
2	#11763741	C₂	1	2	yes	maximal, complemented
3	#11763740	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₈×D₁₇	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₁₇	C₄	1	1	yes	characteristic
7	C₂×#63214	C₂²	1	1	yes	characteristic
8	C₁₆×D₁₇	C₄	1	1	yes	characteristic
9	C₁₆×D₁₇	C₄	1	1	yes	characteristic
10	C₁₆×D₁₇	C₂²	1	1	yes	characteristic
11	C₁₆×D₁₇	C₂²	1	1	yes	characteristic
12	#10587467	C₂²	1	4	yes	complemented
13	C₂×C₄×D₁₇	C₈	1	1	yes	characteristic
14	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂×#3622	C₈	1	1	yes	characteristic
16	C₈×D₁₇	C₈	1	1	yes	characteristic
17	C₈×D₁₇	C₈	1	1	yes	characteristic
18	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
19	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
21	C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
22	#63214	C₂×C₄	1	1	yes	characteristic
23	#63214	C₂³	1	1	yes	characteristic
24	C₂²×D₁₇	C₁₆	1	1	yes	characteristic
25	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
26	C₂×Dic₁₇	C₁₆	1	1	yes	characteristic
27	C₄×D₁₇	C₁₆	1	1	yes	characteristic
28	C₄×D₁₇	C₁₆	1	1	yes	characteristic
29	C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
30	C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
31	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
32	C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
33	#3622	C₂×C₈	1	1	yes	characteristic
34	#3622	C₂×C₈	1	1	yes	characteristic
35	C₂×M₆₄	—	17	1	no	maximal, Sylow
36	C₂²×C₁₇	C₂×C₁₆	1	1	yes	characteristic
37	C₂×D₁₇	—	2	2	no	—
38	C₂×D₁₇	C₂×C₁₆	1	1	yes	characteristic
39	C₂×D₁₇	C₂×C₁₆	1	1	yes	characteristic
40	C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
41	C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
42	Dic₁₇	C₂×C₁₆	1	1	yes	characteristic
43	Dic₁₇	C₂×C₁₆	1	1	yes	characteristic
44	C₂²×C₁₆	—	17	1	no	—
45	M₆₄	—	17	2	no	—
46	M₆₄	—	17	2	no	—
47	C₂×C₃₂	—	17	2	no	—
48	C₂×C₁₇	—	2	1	no	—
49	C₂×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
50	D₁₇	—	2	1	no	—
51	D₁₇	M₆₄	1	2	yes	complemented
52	C₂²×C₈	—	17	1	no	—
53	C₂×C₁₆	—	17	1	no	—
54	C₂×C₁₆	—	17	1	no	—
55	C₂×C₁₆	—	17	1	no	—
56	C₂×C₁₆	—	17	1	no	—
57	C₂×C₁₆	—	17	1	no	—
58	C₂×C₁₆	#595	1	1	yes	characteristic
59	C₃₂	—	17	4	no	—
60	C₁₇	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₄	—	17	1	no	—
62	C₂×C₈	—	17	1	no	—
63	C₂×C₈	—	17	1	no	—
64	C₂×C₈	—	17	1	no	—
65	C₂×C₈	—	17	1	no	—
66	C₂×C₈	—	17	1	no	—
67	C₂×C₈	C₂×#595	1	1	yes	characteristic
68	C₁₆	—	17	1	no	—
69	C₁₆	—	17	1	no	—
70	C₁₆	C₂×#595	1	1	yes	characteristic
71	C₁₆	C₂×#595	1	1	yes	characteristic
72	C₂³	—	17	1	no	—
73	C₂×C₄	—	17	1	no	—
74	C₂×C₄	—	17	1	no	—
75	C₂×C₄	—	17	1	no	—
76	C₂×C₄	—	17	1	no	—
77	C₂×C₄	—	17	1	no	—
78	C₂×C₄	#63242	1	1	yes	characteristic
79	C₈	—	17	1	no	—
80	C₈	—	17	1	no	—
81	C₈	#63242	1	1	yes	characteristic
82	C₈	C₂²×#595	1	1	yes	characteristic
83	C₂²	—	17	1	no	—
84	C₂²	—	17	1	no	—
85	C₂²	—	34	2	no	—
86	C₂²	#10587529	1	1	yes	characteristic
87	C₄	—	17	1	no	—
88	C₄	—	17	1	no	—
89	C₄	#10587529	1	1	yes	characteristic
90	C₄	C₂×#63242	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	17	2	no	—
93	C₂	—	34	1	no	—
94	C₂	C₂×#10587529	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂×#595
commutator, socle	C₂×C₁₇	C₂²×C₁₆
Frattini	C₈	C₂²×#595
Fitting	C₂×C₁₆×C₁₇	C₄
prime radical	C₂²×D₁₇	C₁₆
cosocle	#63214	C₂³
hypercenter	C₂×C₁₆	#595
hypocenter	C₁₇	C₂×M₆₄
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. #11763742	C₂	semidirect
2. #11763741	C₂	semidirect
3. #11763740	C₂	semidirect
12. #10587467	C₂²	semidirect
51. D₁₇	M₆₄	semidirect
60. C₁₇	C₂×M₆₄	semidirect

Maximal subgroups

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

subgroup	index
#11763742	2
#11763741	2
#11763740	2
C₂×C₁₆×D₁₇	2
C₂×M₆₄	17