Subgroups — #11763683

Order 1088.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#595	C₂	1	2	yes	maximal
2	C₂×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×#595	—	2	2	no	—
4	C₂×C₄×D₁₇	C₂²	1	1	yes	characteristic
5	C₄⋊#595	—	2	2	no	—
6	C₄⋊#595	C₄	1	4	yes	complemented
7	C₂×C₈×C₁₇	C₄	1	1	yes	characteristic, complemented
8	C₂×#3622	C₄	1	1	yes	characteristic, complemented
9	C₈×D₁₇	—	2	2	no	—
10	C₂²×D₁₇	D₄	1	1	yes	characteristic
11	C₂×#595	—	2	4	no	—
12	C₂×#595	—	4	2	no	—
13	C₂×#595	—	4	2	no	—
14	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂×Dic₁₇	Q₈	1	1	yes	characteristic
16	C₄×D₁₇	C₂×C₄	1	2	yes	—
17	C₄×D₁₇	D₄	1	2	yes	—
18	C₈×C₁₇	—	2	1	no	—
19	#3622	—	2	1	no	—
20	C₂²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
21	C₂×D₁₇	C₂²⋊C₄	1	2	yes	—
22	C₂×D₁₇	D₈	1	1	yes	characteristic
23	C₂×D₁₇	SD₁₆	1	2	yes	—
24	C₂×D₁₇	Q₁₆	1	1	yes	characteristic
25	#595	—	4	4	no	—
26	C₄×C₁₇	C₄²	1	1	yes	characteristic
27	C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
28	Dic₁₇	C₄⋊C₄	1	2	yes	—
29	#340	—	17	1	no	maximal, Sylow
30	C₂×C₁₇	#95	1	1	yes	characteristic
31	C₂×C₁₇	#106	1	1	yes	characteristic
32	C₂×C₁₇	#107	1	1	yes	characteristic
33	D₁₇	#102	1	2	yes	—
34	D₁₇	#103	1	2	yes	—
35	C₂²×C₈	—	17	1	no	—
36	C₂×C₄⋊C₄	—	17	2	no	—
37	C₁₇	#340	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₄	—	17	1	no	—
39	C₂²×C₄	—	34	2	no	—
40	C₂×C₈	—	17	1	no	—
41	C₂×C₈	—	34	2	no	—
42	C₂×C₈	#595	1	1	yes	characteristic, complemented
43	C₄⋊C₄	—	17	4	no	—
44	C₄⋊C₄	—	34	2	no	—
45	C₂³	—	17	1	no	—
46	C₂×C₄	—	17	1	no	—
47	C₂×C₄	—	17	2	no	—
48	C₂×C₄	—	17	2	no	—
49	C₂×C₄	—	34	4	no	—
50	C₂×C₄	—	68	2	no	—
51	C₂×C₄	—	68	2	no	—
52	C₂×C₄	C₂×#595	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	—	34	1	no	—
55	C₂²	—	17	2	no	—
56	C₂²	—	17	1	no	—
57	C₂²	—	17	1	no	—
58	C₂²	—	17	2	no	—
59	C₂²	C₄⋊#595	1	1	yes	characteristic
60	C₄	—	17	2	no	—
61	C₄	—	68	4	no	—
62	C₄	C₄×#595	1	1	yes	characteristic
63	C₄	C₂²⋊#595	1	1	yes	characteristic
64	C₂	—	17	2	no	—
65	C₂	—	17	2	no	—
66	C₂	#10587533	1	1	yes	characteristic
67	C₂	#10587534	1	1	yes	characteristic
68	C₂	(C₂×#595)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#595
commutator	C₄×C₁₇	C₄²
Frattini	C₂×C₄	C₂×#595
Fitting	C₂×C₈×C₁₇	C₄
socle	C₂²×C₁₇	C₄⋊C₄
prime radical	C₂²×D₁₇	D₄
cosocle	C₂×C₄×D₁₇	C₂²
hypercenter	C₂×C₈	#595
hypocenter	C₁₇	#340
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
6. C₄⋊#595	C₄	semidirect
7. C₂×C₈×C₁₇	C₄	semidirect
8. C₂×#3622	C₄	semidirect
37. C₁₇	#340	semidirect
42. C₂×C₈	#595	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊#595	2
C₂×C₈×D₁₇	2
#340	17