Subgroups — #17949096

Order 4352.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543889	C₂	1	1	yes	maximal, characteristic
2	C₁₆×#3624	C₂	1	1	yes	maximal, characteristic
3	C₃₂×Dic₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587467	C₄	1	2	yes	—
5	#11763695	C₄	1	1	yes	characteristic
6	C₈×#3624	C₄	1	1	yes	characteristic
7	C₂×#10587465	C₄	1	1	yes	characteristic
8	C₁₆×Dic₁₇	C₂²	1	1	yes	characteristic
9	C₂×C₁₇×C₃₂	C₄	1	1	yes	characteristic
10	C₄×#3624	C₈	1	1	yes	characteristic
11	C₄×#3624	C₈	1	1	yes	characteristic
12	C₂×#63216	C₈	1	2	yes	—
13	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
14	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂×#63214	C₂×C₄	1	1	yes	characteristic
16	#10587467	—	2	2	no	—
17	C₁₇×C₃₂	—	2	1	no	—
18	#10587465	—	2	1	no	—
19	C₂×#3624	C₁₆	1	2	yes	—
20	C₂×#3624	C₁₆	1	2	yes	—
21	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
22	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
23	C₂×#3622	C₂×C₈	1	1	yes	characteristic
24	#63216	—	2	2	no	—
25	C₁₆×C₁₇	M₁₆	1	1	yes	characteristic
26	C₁₆×C₁₇	M₁₆	1	1	yes	characteristic
27	#63214	M₁₆	1	2	yes	—
28	#7331	—	17	1	no	maximal, Sylow
29	C₂×C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
30	C₂×Dic₁₇	C₂×C₁₆	1	1	yes	characteristic
31	C₂×Dic₁₇	C₂×C₁₆	1	1	yes	characteristic
32	#3624	—	2	2	no	—
33	#3624	C₃₂	1	4	yes	complemented
34	C₈×C₁₇	#97	1	1	yes	characteristic
35	C₈×C₁₇	#97	1	1	yes	characteristic
36	#3622	M₃₂	1	2	yes	—
37	C₄×C₃₂	—	17	1	no	—
38	C₄×C₃₂	—	17	1	no	—
39	C₈×C₁₆	—	17	1	no	—
40	C₂²×C₁₇	C₄×C₁₆	1	1	yes	characteristic
41	C₄×C₁₇	#322	1	1	yes	characteristic
42	C₄×C₁₇	#346	1	1	yes	characteristic
43	Dic₁₇	C₂×C₃₂	1	2	yes	—
44	Dic₁₇	M₆₄	1	2	yes	—
45	C₂×C₃₂	—	17	2	no	—
46	C₂×C₃₂	—	17	1	no	—
47	C₂×C₃₂	#595	1	1	yes	characteristic
48	C₄×C₁₆	—	17	1	no	—
49	C₄×C₁₆	—	17	1	no	—
50	C₈²	—	17	1	no	—
51	C₂×C₁₇	#1312	1	1	yes	characteristic
52	C₂×C₁₇	C₄×C₃₂	1	1	yes	characteristic
53	C₂×C₁₇	#1397	1	1	yes	characteristic
54	C₂×C₁₆	—	17	1	no	—
55	C₂×C₁₆	—	17	2	no	—
56	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
57	C₄×C₈	—	17	1	no	—
58	C₄×C₈	—	17	1	no	—
59	C₄×C₈	—	17	1	no	—
60	C₃₂	—	2	1	no	—
61	C₃₂	—	34	2	no	—
62	C₃₂	—	34	1	no	—
63	C₁₇	#7331	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₈	—	17	2	no	—
65	C₂×C₈	—	17	1	no	—
66	C₂×C₈	—	17	2	no	—
67	C₂×C₈	C₄×#595	1	1	yes	characteristic
68	C₄²	—	17	1	no	—
69	C₁₆	—	17	2	no	—
70	C₁₆	—	34	2	no	—
71	C₁₆	#63243	1	1	yes	characteristic
72	C₁₆	#63247	1	1	yes	characteristic
73	C₂×C₄	—	17	1	no	—
74	C₂×C₄	—	17	1	no	—
75	C₂×C₄	C₈×#595	1	1	yes	characteristic
76	C₈	—	17	4	no	—
77	C₈	—	17	2	no	—
78	C₈	—	34	2	no	—
79	C₈	#10587532	1	1	yes	characteristic
80	C₈	#10587542	1	1	yes	characteristic
81	C₂²	C₁₆×#595	1	1	yes	characteristic
82	C₄	—	17	2	no	—
83	C₄	—	17	2	no	—
84	C₄	#11763651	1	1	yes	characteristic
85	C₄	#11763696	1	1	yes	characteristic
86	C₂	#14543698	1	1	yes	characteristic
87	C₂	C₃₂×#595	1	1	yes	characteristic
88	C₂	#14543890	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×#595
commutator	C₂×C₁₇	C₄×C₃₂
Fitting	C₂×C₁₇×C₃₂	C₄
socle, prime radical	C₂²×C₁₇	C₄×C₁₆
cosocle	C₁₆×Dic₁₇	C₂²
hypercenter	C₂×C₃₂	#595
hypocenter	C₁₇	#7331
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
33. #3624	C₃₂	semidirect
63. C₁₇	#7331	semidirect

Maximal subgroups

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

subgroup	index
#14543889	2
C₁₆×#3624	2
C₃₂×Dic₁₇	2
#7331	17