Subgroups — #17950287

Order 4352.

486 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14544497	C₂	1	3	yes	maximal
2	#14543980	C₂	1	3	yes	maximal
3	C₈²×D₁₇	C₂	1	1	yes	maximal, characteristic
4	C₄×#63242	C₂²	1	3	yes	—
5	C₄²×#595	C₂²	1	1	yes	characteristic
6	#11763674	C₄	1	12	yes	—
7	#11763651	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	C₄×C₈×C₁₇	C₂×C₄	1	3	yes	—
17	C₈×Dic₁₇	C₂×C₄	1	6	yes	—
18	C₄×#3622	C₂×C₄	1	3	yes	—
19	C₂²×#595	C₄²	1	4	yes	—
20	C₂×C₄×D₁₇	C₂²×C₄	1	3	yes	—
21	C₂×#3624	C₄²	1	12	yes	—
22	C₄×#595	—	2	12	no	—
23	#63242	—	2	12	no	—
24	C₂×C₈×C₁₇	C₄²	1	6	yes	—
25	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
26	C₄×Dic₁₇	C₂²×C₄	1	3	yes	—
27	C₂×#3622	C₄²	1	6	yes	—
28	C₈×D₁₇	—	2	12	no	—
29	#7845	—	17	1	no	maximal, Sylow
30	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
31	C₂×#595	—	2	12	no	—
32	C₂×C₄×C₁₇	C₂×C₄²	1	3	yes	—
33	C₂×Dic₁₇	C₂×C₄²	1	3	yes	—
34	C₄×D₁₇	#131	1	12	yes	—
35	#3624	—	2	12	no	—
36	C₈×C₁₇	—	2	6	no	—
37	#3622	—	2	6	no	—
38	#1744	—	17	3	no	—
39	C₂×#322	—	17	3	no	—
40	C₂×C₈²	—	17	1	no	—
41	C₂²×C₁₇	C₄³	1	1	yes	characteristic
42	C₂×D₁₇	#405	1	6	yes	—
43	#595	—	4	4	no	—
44	C₄×C₁₇	#405	1	6	yes	—
45	Dic₁₇	#405	1	6	yes	—
46	C₂×C₄×C₈	—	17	3	no	—
47	C₂×C₄×C₈	—	17	3	no	—
48	C₄³	—	17	1	no	—
49	#336	—	17	12	no	—
50	#322	—	17	12	no	—
51	C₈²	—	17	3	no	—
52	C₈²	#595	1	1	yes	characteristic, complemented
53	C₂×C₁₇	#1726	1	3	yes	—
54	D₁₇	#1454	1	4	yes	—
55	C₂²×C₈	—	17	6	no	—
56	C₂²×C₈	—	17	6	no	—
57	C₂×C₄²	—	17	1	no	—
58	C₂×C₄²	—	17	6	no	—
59	C₄×C₈	—	17	12	no	—
60	C₄×C₈	—	17	6	no	—
61	C₄×C₈	—	17	3	no	—
62	C₄×C₈	C₂×#595	1	3	yes	—
63	C₁₇	#7845	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₄	—	17	3	no	—
65	C₂²×C₄	—	17	4	no	—
66	C₂×C₈	—	17	12	no	—
67	C₂×C₈	—	17	6	no	—
68	C₂×C₈	—	34	12	no	—
69	C₂×C₈	—	34	12	no	—
70	C₂×C₈	C₄×#595	1	6	yes	—
71	C₄²	—	17	3	no	—
72	C₄²	—	34	12	no	—
73	C₄²	C₂²×#595	1	1	yes	characteristic
74	C₂³	—	17	1	no	—
75	C₂×C₄	—	17	3	no	—
76	C₂×C₄	—	17	12	no	—
77	C₂×C₄	—	34	12	no	—
78	C₂×C₄	C₂×C₄×#595	1	3	yes	—
79	C₈	—	2	6	no	—
80	C₈	—	34	12	no	—
81	C₈	—	34	6	no	—
82	C₂²	—	17	6	no	—
83	C₂²	C₄²×#595	1	1	yes	characteristic
84	C₄	—	17	6	no	—
85	C₄	—	68	4	no	—
86	C₄	#11763772	1	6	yes	—
87	C₂	—	17	4	no	—
88	C₂	#14544440	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	#7845
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. #11763651	C₄	semidirect
9. C₈×#3622	C₄	semidirect
10. C₈²×C₁₇	C₄	semidirect
52. C₈²	#595	semidirect
63. C₁₇	#7845	semidirect

Maximal subgroups

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

subgroup	index
#14544497	2
#14543980	2
C₈²×D₁₇	2
#7845	17