Subgroups — #11763170

Order 1088.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587633	C₂	1	1	yes	maximal, characteristic
2	#10587574	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#103	C₂	1	1	yes	maximal, characteristic, complemented
4	#10587506	C₂	1	1	yes	maximal, characteristic, complemented
5	#10587492	C₂	1	1	yes	maximal, characteristic
6	#10587486	C₂	1	1	yes	maximal, characteristic, complemented
7	#10587480	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₁₇	C₂²	1	1	yes	characteristic
9	C₂×D₆₈	C₂²	1	1	yes	characteristic
10	C₂×Dic₃₄	—	2	1	no	—
11	C₂×C₈×C₁₇	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
13	#63227	—	2	1	no	—
14	#63227	—	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	C₂²×D₁₇	—	2	1	no	—
20	Q₈×C₁₇	—	2	1	no	—
21	Q₈×C₁₇	—	2	1	no	—
22	C₂×C₄×C₁₇	—	2	1	no	—
23	C₂×C₄×C₁₇	—	2	1	no	—
24	C₂×C₄×C₁₇	C₂³	1	1	yes	characteristic
25	C₂×Dic₁₇	—	2	1	no	—
26	C₂×Dic₁₇	D₄	1	1	yes	characteristic
27	C₂×Dic₁₇	D₄	1	1	yes	characteristic
28	D₆₈	—	2	1	no	—
29	D₆₈	—	2	1	no	—
30	Dic₃₄	—	4	2	no	—
31	C₈×C₁₇	—	2	1	no	—
32	#3622	—	2	1	no	—
33	C₂²×C₁₇	C₂×D₄	1	1	yes	characteristic
34	C₂×D₁₇	—	4	1	no	—
35	C₂×D₁₇	—	4	1	no	—
36	C₂×D₁₇	—	4	1	no	—
37	C₄×C₁₇	—	4	1	no	—
38	C₄×C₁₇	—	4	1	no	—
39	C₄×C₁₇	#41	1	1	yes	characteristic
40	C₄×C₁₇	#41	1	1	yes	characteristic
41	Dic₁₇	—	2	1	no	—
42	Dic₁₇	—	2	1	no	—
43	Dic₁₇	—	4	1	no	—
44	#489	—	17	1	no	maximal, Sylow
45	C₂×C₁₇	#124	1	1	yes	characteristic
46	C₂×C₁₇	AGL(1,ℤ/8)	1	1	yes	characteristic
47	C₂×C₁₇	#137	1	1	yes	characteristic
48	D₁₇	—	8	1	no	—
49	C₄⋊Q₈	—	17	1	no	—
50	#124	—	17	1	no	—
51	#103	—	17	1	no	—
52	#103	D₁₇	1	1	yes	characteristic, complemented
53	#102	—	17	1	no	—
54	#102	—	17	1	no	—
55	#97	—	17	1	no	—
56	C₁₇	#489	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₈	—	34	1	no	—
58	C₂×Q₈	C₂×D₁₇	1	1	yes	characteristic
59	C₂×D₄	—	17	1	no	—
60	C₂×C₈	—	17	1	no	—
61	C₂×C₈	C₂×D₁₇	1	1	yes	characteristic
62	C₄⋊C₄	—	17	1	no	—
63	C₄⋊C₄	—	34	1	no	—
64	C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic
65	C₂²⋊C₄	—	34	1	no	—
66	C₂²⋊C₄	—	34	1	no	—
67	C₄²	—	17	1	no	—
68	C₂³	—	34	1	no	—
69	Q₈	—	2	1	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	68	2	no	—
72	D₄	—	34	1	no	—
73	D₄	—	34	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	17	1	no	—
77	C₂×C₄	—	17	1	no	—
78	C₂×C₄	—	34	1	no	—
79	C₂×C₄	C₂²×D₁₇	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	34	1	no	—
82	C₂²	—	68	1	no	—
83	C₂²	—	68	1	no	—
84	C₂²	—	68	1	no	—
85	C₂²	D₄×D₁₇	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	34	1	no	—
89	C₄	—	34	1	no	—
90	C₄	—	68	1	no	—
91	C₄	#63252	1	1	yes	characteristic
92	C₄	#63254	1	1	yes	characteristic
93	C₂	—	136	1	no	—
94	C₂	#10587571	1	1	yes	characteristic
95	C₂	#10587600	1	1	yes	characteristic
96	C₂	#10587604	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₇
commutator, cosocle	C₂×C₄×C₁₇	C₂³
Frattini	C₂×C₄	C₂²×D₁₇
Fitting	C₁₇×#103	C₂
socle	C₂²×C₁₇	C₂×D₄
prime radical	C₂×D₆₈	C₂²
hypercenter	#103	D₁₇
hypocenter	C₁₇	#489
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
2. #10587574	C₂	semidirect
3. C₁₇×#103	C₂	semidirect
4. #10587506	C₂	semidirect
6. #10587486	C₂	semidirect
52. #103	D₁₇	semidirect
56. C₁₇	#489	semidirect

Maximal subgroups

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

subgroup	index
#10587633	2
#10587574	2
C₁₇×#103	2
#10587506	2
#10587492	2
#10587486	2
#10587480	2
#489	17