Subgroups — #17950290

Order 4352.

582 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10587532	C₂	1	3	yes	maximal
2	#14543978	C₂	1	3	yes	maximal
3	C₈²×D₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587532	C₄	1	12	yes	—
5	C₄×#63242	C₂²	1	3	yes	—
6	C₄²×#595	C₂²	1	1	yes	characteristic
7	#11763650	C₄	1	12	yes	complemented
8	C₄×C₈×D₁₇	C₂²	1	3	yes	—
9	C₈×#3622	C₄	1	3	yes	complemented
10	C₈²×C₁₇	C₄	1	1	yes	characteristic, complemented
11	C₂×C₄×#595	C₂×C₄	1	6	yes	—
12	C₂×#63242	C₂×C₄	1	6	yes	—
13	C₂×C₈×D₁₇	C₂×C₄	1	6	yes	—
14	C₄²×D₁₇	C₂³	1	1	yes	characteristic
15	C₄×#3624	C₂×C₄	1	12	yes	—
16	#10587532	—	2	24	no	—
17	C₄×C₈×C₁₇	C₂×C₄	1	3	yes	—
18	C₈×Dic₁₇	C₂×C₄	1	6	yes	—
19	C₄×#3622	C₂×C₄	1	3	yes	—
20	C₂²×#595	C₄²	1	4	yes	—
21	C₂×C₄×D₁₇	C₂²×C₄	1	3	yes	—
22	C₂×#3624	C₄²	1	12	yes	—
23	C₄×#595	—	2	12	no	—
24	#63242	—	2	12	no	—
25	C₂×C₈×C₁₇	C₄²	1	6	yes	—
26	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
27	C₄×Dic₁₇	C₂²×C₄	1	3	yes	—
28	C₂×#3622	C₄²	1	6	yes	—
29	C₈×D₁₇	M₁₆	1	24	yes	—
30	#7846	—	17	1	no	maximal, Sylow
31	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
32	C₂×#595	—	2	12	no	—
33	C₂×C₄×C₁₇	C₂×C₄²	1	3	yes	—
34	C₂×Dic₁₇	C₂×C₄²	1	3	yes	—
35	C₄×D₁₇	C₂×M₁₆	1	12	yes	—
36	#3624	—	2	12	no	—
37	C₈×C₁₇	#97	1	12	yes	complemented
38	#3622	#97	1	12	yes	complemented
39	C₄×#97	—	17	3	no	—
40	C₂×#322	—	17	3	no	—
41	C₂×C₈²	—	17	1	no	—
42	C₂²×C₁₇	C₄³	1	1	yes	characteristic
43	C₂×D₁₇	C₄×M₁₆	1	6	yes	—
44	#595	—	4	4	no	—
45	C₄×C₁₇	C₂×#97	1	6	yes	—
46	Dic₁₇	C₄×M₁₆	1	6	yes	—
47	C₂×#97	—	17	12	no	—
48	C₂×C₄×C₈	—	17	3	no	—
49	C₂×C₄×C₈	—	17	3	no	—
50	C₄³	—	17	1	no	—
51	#322	—	17	12	no	—
52	C₈²	—	17	3	no	—
53	C₈²	#595	1	1	yes	characteristic, complemented
54	C₂×C₁₇	C₄×#97	1	3	yes	—
55	D₁₇	#1455	1	4	yes	—
56	C₂²×C₈	—	17	6	no	—
57	C₂²×C₈	—	17	6	no	—
58	C₂×C₄²	—	17	1	no	—
59	C₂×C₄²	—	17	6	no	—
60	#97	—	34	24	no	—
61	C₄×C₈	—	17	12	no	—
62	C₄×C₈	—	17	6	no	—
63	C₄×C₈	—	17	3	no	—
64	C₄×C₈	C₂×#595	1	3	yes	—
65	C₁₇	#7846	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₄	—	17	3	no	—
67	C₂²×C₄	—	17	4	no	—
68	C₂×C₈	—	17	6	no	—
69	C₂×C₈	—	17	24	no	—
70	C₂×C₈	—	17	12	no	—
71	C₂×C₈	—	34	12	no	—
72	C₂×C₈	C₄×#595	1	6	yes	—
73	C₄²	—	17	3	no	—
74	C₄²	—	34	12	no	—
75	C₄²	C₂²×#595	1	1	yes	characteristic
76	C₂³	—	17	1	no	—
77	C₂×C₄	—	17	3	no	—
78	C₂×C₄	—	17	12	no	—
79	C₂×C₄	—	34	12	no	—
80	C₂×C₄	C₂×C₄×#595	1	3	yes	—
81	C₈	—	17	12	no	—
82	C₈	—	34	12	no	—
83	C₈	#10587532	1	12	yes	complemented
84	C₂²	—	17	6	no	—
85	C₂²	C₄²×#595	1	1	yes	characteristic
86	C₄	—	17	6	no	—
87	C₄	—	68	4	no	—
88	C₄	C₂×#10587532	1	6	yes	—
89	C₂	—	17	4	no	—
90	C₂	C₄×#10587532	1	3	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×#595
commutator, socle	C₂²×C₁₇	C₄³
Fitting	C₈²×C₁₇	C₄
prime radical	C₂²×D₁₇	C₂×C₄²
cosocle	C₄²×D₁₇	C₂³
hypercenter	C₈²	#595
hypocenter	C₁₇	#7846
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
7. #11763650	C₄	semidirect
9. C₈×#3622	C₄	semidirect
10. C₈²×C₁₇	C₄	semidirect
37. C₈×C₁₇	#97	semidirect
38. #3622	#97	semidirect
53. C₈²	#595	semidirect
65. C₁₇	#7846	semidirect
83. C₈	#10587532	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10587532	2
#14543978	2
C₈²×D₁₇	2
#7846	17