Subgroups — #17953833

Order 4352.

486 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14544720	C₂	1	6	yes	maximal
2	C₈²×D₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#10587534	—	2	12	no	—
4	#11763755	C₂²	1	4	yes	—
5	C₄×C₈×D₁₇	C₂²	1	3	yes	—
6	C₈×#3622	C₄	1	3	yes	complemented
7	C₈²×C₁₇	C₄	1	1	yes	characteristic, complemented
8	C₂×C₄⋊#595	—	2	12	no	—
9	C₂×C₈×D₁₇	D₄	1	6	yes	—
10	C₄²×D₁₇	C₂³	1	1	yes	characteristic
11	#10587534	—	4	24	no	—
12	C₄×C₈×C₁₇	C₂×C₄	1	3	yes	—
13	C₈×Dic₁₇	Q₈	1	6	yes	—
14	C₄×#3622	C₂×C₄	1	3	yes	—
15	C₂²×#595	—	4	4	no	—
16	C₂×C₄×D₁₇	C₂×D₄	1	3	yes	—
17	C₄⋊#595	—	4	24	no	—
18	C₂×C₈×C₁₇	C₄⋊C₄	1	6	yes	—
19	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
20	C₄×Dic₁₇	C₂×Q₈	1	3	yes	—
21	C₂×#3622	C₄⋊C₄	1	6	yes	—
22	C₈×D₁₇	D₈	1	12	yes	—
23	C₈×D₁₇	Q₁₆	1	12	yes	—
24	#8818	—	17	1	no	maximal, Sylow
25	C₂²×D₁₇	#127	1	1	yes	characteristic
26	C₂×#595	—	8	12	no	—
27	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	3	yes	—
28	C₂×Dic₁₇	C₄⋊Q₈	1	3	yes	—
29	C₄×D₁₇	C₂×D₈	1	6	yes	—
30	C₄×D₁₇	C₂×Q₁₆	1	6	yes	—
31	C₈×C₁₇	#107	1	12	yes	complemented
32	#3622	#107	1	12	yes	complemented
33	#1845	—	17	6	no	—
34	C₂×C₈²	—	17	1	no	—
35	C₂²×C₁₇	#384	1	1	yes	characteristic
36	C₂×D₁₇	#493	1	3	yes	—
37	C₂×D₁₇	#494	1	3	yes	—
38	#595	—	16	4	no	—
39	C₄×C₁₇	C₂×#107	1	6	yes	—
40	Dic₁₇	#500	1	6	yes	—
41	C₂×#107	—	34	12	no	—
42	C₂×C₄×C₈	—	17	3	no	—
43	#384	—	17	4	no	—
44	C₈²	—	17	3	no	—
45	C₈²	#595	1	1	yes	characteristic, complemented
46	C₂×C₁₇	#1845	1	3	yes	—
47	D₁₇	#1712	1	1	yes	characteristic
48	D₁₇	#1713	1	3	yes	—
49	C₂²×C₈	—	17	6	no	—
50	C₂×C₄⋊C₄	—	34	12	no	—
51	C₂×C₄²	—	17	1	no	—
52	#107	—	68	24	no	—
53	C₄×C₈	—	17	6	no	—
54	C₄×C₈	—	17	3	no	—
55	C₄×C₈	C₂×#595	1	3	yes	—
56	C₁₇	#8818	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₄	—	17	3	no	—
58	C₂²×C₄	—	68	4	no	—
59	C₂×C₈	—	17	6	no	—
60	C₂×C₈	—	17	12	no	—
61	C₂×C₈	—	17	12	no	—
62	C₂×C₈	C₄⋊#595	1	6	yes	—
63	C₄⋊C₄	—	68	24	no	—
64	C₄²	—	17	3	no	—
65	C₄²	C₂²×#595	1	1	yes	characteristic
66	C₂³	—	17	1	no	—
67	C₂×C₄	—	17	3	no	—
68	C₂×C₄	—	17	6	no	—
69	C₂×C₄	—	17	6	no	—
70	C₂×C₄	—	136	12	no	—
71	C₂×C₄	C₂×C₄⋊#595	1	3	yes	—
72	C₈	—	17	12	no	—
73	C₈	#10587534	1	12	yes	complemented
74	C₂²	—	17	3	no	—
75	C₂²	—	17	3	no	—
76	C₂²	#11763755	1	1	yes	characteristic
77	C₄	—	272	4	no	—
78	C₄	—	17	6	no	—
79	C₄	C₂×#10587534	1	6	yes	—
80	C₂	—	17	1	no	—
81	C₂	—	17	3	no	—
82	C₂	#14544720	1	3	yes	—

	subgroup	G/H
center	C₂²	#11763755
commutator	C₄²×C₁₇	C₂²×C₄
Frattini	C₄²	C₂²×#595
Fitting	C₈²×C₁₇	C₄
socle	C₂²×C₁₇	#384
prime radical	C₂²×D₁₇	#127
cosocle	C₄²×D₁₇	C₂³
hypercenter	C₈²	#595
hypocenter	C₁₇	#8818
LCS	G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
6. C₈×#3622	C₄	semidirect
7. C₈²×C₁₇	C₄	semidirect
31. C₈×C₁₇	#107	semidirect
32. #3622	#107	semidirect
45. C₈²	#595	semidirect
56. C₁₇	#8818	semidirect
73. C₈	#10587534	semidirect

Maximal subgroups

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

subgroup	index
#14544720	2
C₈²×D₁₇	2
#8818	17