Subgroups — #14545940

Order 2176.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587665	C₂	1	2	yes	maximal
2	#11763903	C₂	1	4	yes	maximal, complemented
3	C₄×#63242	C₂	1	1	yes	maximal, characteristic
4	C₂×#63242	C₄	1	1	yes	characteristic
5	C₂×#63242	C₂²	1	1	yes	characteristic
6	C₂×#63241	C₂²	1	4	yes	—
7	#10587665	C₄	1	8	yes	complemented
8	C₄²×D₁₇	C₄	1	1	yes	characteristic
9	C₄×#3624	C₄	1	2	yes	—
10	C₄×#3624	C₂²	1	2	yes	—
11	C₂×C₄×D₁₇	C₈	1	2	yes	—
12	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
13	C₂×#3624	C₂×C₄	1	1	yes	characteristic
14	C₂×#3624	C₂×C₄	1	2	yes	—
15	C₂×#3624	C₂³	1	1	yes	characteristic
16	#63242	C₈	1	4	yes	—
17	#63242	C₂×C₄	1	4	yes	—
18	#63241	C₂×C₄	1	8	yes	complemented
19	C₄²×C₁₇	C₈	1	1	yes	characteristic
20	C₄×Dic₁₇	C₈	1	1	yes	characteristic
21	C₄×Dic₁₇	C₂×C₄	1	2	yes	—
22	C₂²×D₁₇	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₁₇	C₂×C₈	1	2	yes	—
24	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
25	C₂×Dic₁₇	C₂×C₈	1	2	yes	—
26	C₂×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
27	C₄×D₁₇	—	2	4	no	—
28	C₄×D₁₇	C₄²	1	2	yes	—
29	C₄×D₁₇	C₂×C₈	1	2	yes	—
30	#3624	C₄²	1	2	yes	—
31	#3624	C₂×C₈	1	4	yes	—
32	#3624	C₂²×C₄	1	2	yes	—
33	C₂×#346	—	17	1	no	maximal, Sylow
34	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
35	C₂×D₁₇	C₄×C₈	1	2	yes	—
36	C₂×D₁₇	M₃₂	1	4	yes	—
37	C₄×C₁₇	—	2	2	no	—
38	C₄×C₁₇	C₄×C₈	1	2	yes	—
39	Dic₁₇	—	2	2	no	—
40	Dic₁₇	C₂×C₄²	1	1	yes	characteristic
41	Dic₁₇	C₂²×C₈	1	1	yes	characteristic
42	C₂²×C₁₆	—	17	2	no	—
43	C₂×C₄×C₈	—	17	1	no	—
44	#346	—	17	4	no	—
45	C₂×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
46	C₂×C₁₇	C₂×M₃₂	1	2	yes	—
47	D₁₇	#346	1	4	yes	complemented
48	C₂²×C₈	—	17	1	no	—
49	C₂²×C₈	—	17	1	no	—
50	C₂×C₄²	—	17	1	no	—
51	C₂×C₁₆	—	17	8	no	—
52	C₂×C₁₆	—	17	4	no	—
53	C₄×C₈	—	17	2	no	—
54	C₄×C₈	—	17	2	no	—
55	C₁₇	C₂×#346	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₄	—	17	1	no	—
57	C₂²×C₄	—	17	2	no	—
58	C₂×C₈	—	17	4	no	—
59	C₂×C₈	—	17	4	no	—
60	C₂×C₈	—	17	1	no	—
61	C₂×C₈	—	17	2	no	—
62	C₂×C₈	—	17	1	no	—
63	C₄²	—	17	2	no	—
64	C₄²	—	17	1	no	—
65	C₄²	#3633	1	1	yes	characteristic
66	C₁₆	—	17	8	no	—
67	C₂³	—	17	1	no	—
68	C₂×C₄	—	17	1	no	—
69	C₂×C₄	—	17	2	no	—
70	C₂×C₄	—	17	2	no	—
71	C₂×C₄	—	17	2	no	—
72	C₂×C₄	—	34	4	no	—
73	C₂×C₄	C₂×#3633	1	2	yes	—
74	C₂×C₄	C₂×#3633	1	1	yes	characteristic
75	C₈	—	17	2	no	—
76	C₈	—	17	2	no	—
77	C₈	—	17	4	no	—
78	C₂²	—	17	2	no	—
79	C₂²	—	17	4	no	—
80	C₂²	C₂²×#3633	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	17	1	no	—
83	C₄	—	17	1	no	—
84	C₄	—	34	2	no	—
85	C₄	C₄×#3633	1	2	yes	—
86	C₂	—	17	4	no	—
87	C₂	C₂×C₄×#3633	1	1	yes	characteristic
88	C₂	#11763928	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×#3633
commutator	C₂×C₁₇	C₂×C₄×C₈
Frattini	C₂²	C₂²×#3633
Fitting	C₄²×C₁₇	C₈
socle	C₂²×C₁₇	C₂²×C₈
prime radical	C₂²×D₁₇	C₂×C₈
cosocle	C₂×#3624	C₂³
hypercenter	C₄²	#3633
hypocenter	C₁₇	C₂×#346
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. #11763903	C₂	semidirect
7. #10587665	C₄	semidirect
18. #63241	C₂×C₄	semidirect
47. D₁₇	#346	semidirect
55. C₁₇	C₂×#346	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10587665	2
#11763903	2
C₄×#63242	2
C₂×#346	17