Subgroups — #11763162

Order 1088.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587622	C₂	1	1	yes	maximal, characteristic
2	#10587576	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#102	C₂	1	1	yes	maximal, characteristic
4	#10587503	C₂	1	1	yes	maximal, characteristic
5	#10587487	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×Dic₁₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#10587481	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₄×C₁₇	C₂²	1	1	yes	characteristic
9	C₂×Dic₃₄	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₁₇	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
12	C₂²⋊Dic₁₇	—	2	1	no	—
13	C₂²⋊Dic₁₇	—	2	1	no	—
14	C₄⋊Dic₁₇	—	2	1	no	—
15	C₄⋊Dic₁₇	C₂²	1	1	yes	characteristic
16	#63225	—	2	1	no	—
17	C₄×Dic₁₇	C₂²	1	1	yes	characteristic
18	C₂×#3622	C₂²	1	1	yes	characteristic
19	C₂³×C₁₇	—	2	1	no	—
20	D₄×C₁₇	—	2	1	no	—
21	D₄×C₁₇	—	2	1	no	—
22	C₂×C₄×C₁₇	—	2	1	no	—
23	C₂×C₄×C₁₇	C₂³	1	1	yes	characteristic
24	C₂×Dic₁₇	—	2	1	no	—
25	C₂×Dic₁₇	—	2	1	no	—
26	C₂×Dic₁₇	D₄	1	1	yes	characteristic
27	C₂×Dic₁₇	D₄	1	1	yes	characteristic
28	Dic₃₄	—	2	1	no	—
29	Dic₃₄	—	2	1	no	—
30	C₈×C₁₇	—	2	1	no	—
31	#3622	—	2	1	no	—
32	C₂²×C₁₇	—	4	1	no	—
33	C₂²×C₁₇	—	4	1	no	—
34	C₂²×C₁₇	—	4	1	no	—
35	C₂²×C₁₇	C₂×D₄	1	1	yes	characteristic
36	C₄×C₁₇	—	4	1	no	—
37	C₄×C₁₇	#41	1	1	yes	characteristic
38	C₄×C₁₇	#41	1	1	yes	characteristic
39	Dic₁₇	—	2	1	no	—
40	Dic₁₇	—	2	1	no	—
41	Dic₁₇	—	4	1	no	—
42	Dic₁₇	—	4	1	no	—
43	#488	—	17	1	no	maximal, Sylow
44	C₂×C₁₇	—	8	1	no	—
45	C₂×C₁₇	#124	1	1	yes	characteristic
46	C₂×C₁₇	#135	1	1	yes	characteristic
47	C₂×C₁₇	#135	1	1	yes	characteristic
48	#125	—	17	1	no	—
49	#124	—	17	1	no	—
50	#103	—	17	1	no	—
51	#103	—	17	1	no	—
52	#102	—	17	1	no	—
53	#102	D₁₇	1	1	yes	characteristic
54	C₄×C₈	—	17	1	no	—
55	C₁₇	#488	1	1	yes	characteristic, complemented, Sylow
56	C₂×Q₈	—	17	1	no	—
57	C₂×D₄	C₂×D₁₇	1	1	yes	characteristic
58	C₂×C₈	—	17	1	no	—
59	C₂×C₈	C₂×D₁₇	1	1	yes	characteristic
60	C₄⋊C₄	—	17	1	no	—
61	C₄⋊C₄	—	34	1	no	—
62	C₄⋊C₄	—	34	1	no	—
63	C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic
64	C₂²⋊C₄	—	34	1	no	—
65	C₂²⋊C₄	—	34	1	no	—
66	C₄²	—	17	1	no	—
67	C₂³	—	2	1	no	—
68	Q₈	—	34	1	no	—
69	Q₈	—	34	1	no	—
70	D₄	—	2	1	no	—
71	D₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	17	1	no	—
74	C₂×C₄	—	17	1	no	—
75	C₂×C₄	—	34	1	no	—
76	C₂×C₄	—	34	1	no	—
77	C₂×C₄	C₂²×D₁₇	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	34	1	no	—
80	C₂²	—	4	1	no	—
81	C₂²	—	4	1	no	—
82	C₂²	—	4	1	no	—
83	C₂²	D₄×D₁₇	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	34	1	no	—
86	C₄	—	34	1	no	—
87	C₄	—	68	1	no	—
88	C₄	—	68	1	no	—
89	C₄	#63252	1	1	yes	characteristic
90	C₄	#63254	1	1	yes	characteristic
91	C₂	—	8	1	no	—
92	C₂	#10587571	1	1	yes	characteristic
93	C₂	#10587598	1	1	yes	characteristic
94	C₂	#10587602	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₇
commutator, cosocle	C₂×C₄×C₁₇	C₂³
Frattini	C₂×C₄	C₂²×D₁₇
Fitting	C₁₇×#102	C₂
socle	C₂²×C₁₇	C₂×D₄
prime radical	C₂×D₄×C₁₇	C₂²
hypercenter	#102	D₁₇
hypocenter	C₁₇	#488
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

Complements

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

N	H ≅ G/N	type
2. #10587576	C₂	semidirect
5. #10587487	C₂	semidirect
6. C₈×Dic₁₇	C₂	semidirect
7. #10587481	C₂	semidirect
55. C₁₇	#488	semidirect

Maximal subgroups

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

subgroup	index
#10587622	2
#10587576	2
C₁₇×#102	2
#10587503	2
#10587487	2
C₈×Dic₁₇	2
#10587481	2
#488	17