Subgroups — #11763663

Order 1088.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587632	C₂	1	1	yes	maximal, characteristic
2	(C₂×#595)⋊C₄	C₂	1	1	yes	maximal, characteristic
3	#10587543	C₂	1	1	yes	maximal, characteristic
4	C₂²×#595	—	2	1	no	—
5	C₂×Q₈×C₁₇	C₄	1	1	yes	characteristic, complemented
6	C₂×C₄×D₁₇	C₂²	1	1	yes	characteristic
7	C₂×#3624	—	2	1	no	—
8	#63227	—	2	1	no	—
9	C₄⋊Dic₁₇	C₄	1	1	yes	characteristic, complemented
10	#63225	—	2	1	no	—
11	C₂²×D₁₇	D₄	1	1	yes	characteristic
12	C₂×#595	—	2	2	no	—
13	C₂×#595	—	4	1	no	—
14	C₂×#595	—	4	1	no	—
15	Q₈×C₁₇	—	4	1	no	—
16	C₂×C₄×C₁₇	—	2	1	no	—
17	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₁₇	—	2	1	no	—
19	C₂×Dic₁₇	D₄	1	1	yes	characteristic
20	C₄×D₁₇	—	4	1	no	—
21	#3624	—	4	1	no	—
22	C₂²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×D₁₇	—	2	1	no	—
24	C₂×D₁₇	—	2	1	no	—
25	C₂×D₁₇	SD₁₆	1	1	yes	characteristic
26	C₂×D₁₇	Q₁₆	1	1	yes	characteristic
27	#595	—	4	2	no	—
28	C₄×C₁₇	—	2	1	no	—
29	C₄×C₁₇	—	4	1	no	—
30	Dic₁₇	—	2	1	no	—
31	Dic₁₇	—	4	1	no	—
32	#328	—	17	1	no	maximal, Sylow
33	C₂×C₁₇	#99	1	1	yes	characteristic
34	C₂×C₁₇	#103	1	1	yes	characteristic
35	C₂×C₁₇	#104	1	1	yes	characteristic
36	D₁₇	—	2	1	no	—
37	D₁₇	—	2	1	no	—
38	C₂²⋊Q₈	—	17	1	no	—
39	C₂²⋊C₈	—	17	1	no	—
40	#95	—	17	1	no	—
41	C₁₇	#328	1	1	yes	characteristic, complemented, Sylow
42	C₂×Q₈	#595	1	1	yes	characteristic, complemented
43	C₂²×C₄	—	17	1	no	—
44	C₂²×C₄	—	34	1	no	—
45	C₂×C₈	—	34	1	no	—
46	C₄⋊C₄	—	17	1	no	—
47	C₄⋊C₄	—	34	1	no	—
48	C₂²⋊C₄	—	34	1	no	—
49	C₂³	—	17	1	no	—
50	Q₈	—	4	1	no	—
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	17	1	no	—
53	C₂×C₄	—	34	2	no	—
54	C₂×C₄	—	34	1	no	—
55	C₂×C₄	—	68	1	no	—
56	C₂×C₄	—	68	1	no	—
57	C₂×C₄	—	68	1	no	—
58	C₂×C₄	C₂×#595	1	1	yes	characteristic
59	C₈	—	68	1	no	—
60	C₂²	—	17	1	no	—
61	C₂²	—	17	1	no	—
62	C₂²	—	34	1	no	—
63	C₂²	—	34	1	no	—
64	C₂²	C₂²⋊#595	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	—	4	1	no	—
67	C₄	—	34	1	no	—
68	C₄	—	68	2	no	—
69	C₄	—	68	1	no	—
70	C₂	—	34	1	no	—
71	C₂	—	34	1	no	—
72	C₂	#10587549	1	1	yes	characteristic
73	C₂	#10587550	1	1	yes	characteristic
74	C₂	#10587551	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#595
commutator	C₂×C₄×C₁₇	C₂×C₄
Frattini	C₂×C₄	C₂×#595
Fitting	C₂×Q₈×C₁₇	C₄
socle	C₂²×C₁₇	C₂²⋊C₄
prime radical	C₂²×D₁₇	D₄
cosocle	C₂×C₄×D₁₇	C₂²
hypercenter	C₂×Q₈	#595
hypocenter	C₁₇	#328
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
5. C₂×Q₈×C₁₇	C₄	semidirect
9. C₄⋊Dic₁₇	C₄	semidirect
41. C₁₇	#328	semidirect
42. C₂×Q₈	#595	semidirect

Maximal subgroups

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

subgroup	index
#10587632	2
(C₂×#595)⋊C₄	2
#10587543	2
#328	17