Subgroups — #11763850

Order 1088.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#595	C₂	1	2	yes	maximal, complemented
2	D₈×D₁₇	C₂	1	1	yes	maximal, characteristic
3	#10587547	C₂	1	2	yes	maximal, complemented
4	#10587533	C₂	1	1	yes	maximal, characteristic, complemented
5	#10587532	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#595	—	2	2	no	—
7	D₄×D₁₇	C₂²	1	2	yes	—
8	C₂²⋊#595	—	2	2	no	—
9	C₄⋊#595	C₂²	1	2	yes	—
10	C₄×#595	C₂²	1	1	yes	characteristic
11	#63242	C₂²	1	1	yes	characteristic
12	D₈×C₁₇	C₄	1	1	yes	characteristic, complemented
13	#63228	C₄	1	2	yes	complemented
14	D₁₃₆	C₄	1	1	yes	characteristic, complemented
15	C₈×D₁₇	C₂²	1	1	yes	characteristic
16	C₂²×D₁₇	—	2	2	no	—
17	C₂×#595	—	2	2	no	—
18	C₂×#595	—	4	4	no	—
19	C₂×#595	D₄	1	2	yes	—
20	D₄×C₁₇	C₂×C₄	1	2	yes	complemented
21	C₂²⋊D₁₇	—	2	2	no	—
22	D₆₈	C₂×C₄	1	2	yes	complemented
23	C₄×D₁₇	C₂³	1	1	yes	characteristic
24	#3624	—	2	1	no	—
25	C₈×C₁₇	C₂×C₄	1	1	yes	characteristic, complemented
26	#3622	C₂×C₄	1	1	yes	characteristic, complemented
27	C₂²×C₁₇	—	2	2	no	—
28	C₂×D₁₇	—	2	2	no	—
29	C₂×D₁₇	—	4	2	no	—
30	C₂×D₁₇	—	4	2	no	—
31	C₂×D₁₇	C₂×D₄	1	1	yes	characteristic
32	#595	—	2	2	no	—
33	#595	—	4	2	no	—
34	C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
35	Dic₁₇	#41	1	1	yes	characteristic
36	#442	—	17	1	no	maximal, Sylow
37	C₂×C₁₇	—	4	2	no	—
38	C₂×C₁₇	C₄×D₄	1	1	yes	characteristic
39	D₁₇	—	4	2	no	—
40	D₁₇	AGL(1,ℤ/8)	1	2	yes	—
41	C₂×D₈	—	17	1	no	—
42	C₄×D₄	—	17	2	no	—
43	#106	—	17	1	no	—
44	#102	—	17	2	no	—
45	#97	—	17	1	no	—
46	C₁₇	#442	1	1	yes	characteristic, complemented, Sylow
47	C₂×D₄	—	17	2	no	—
48	C₂²×C₄	—	34	2	no	—
49	D₈	—	17	2	no	—
50	D₈	—	17	1	no	—
51	D₈	#595	1	1	yes	characteristic, complemented
52	C₂×C₈	—	17	1	no	—
53	C₂×C₈	—	17	1	no	—
54	C₄⋊C₄	—	17	2	no	—
55	C₂²⋊C₄	—	34	2	no	—
56	C₄²	—	17	1	no	—
57	C₂³	—	34	2	no	—
58	D₄	—	17	2	no	—
59	D₄	—	34	2	no	—
60	D₄	C₂×#595	1	2	yes	complemented
61	C₂×C₄	—	17	1	no	—
62	C₂×C₄	—	17	2	no	—
63	C₂×C₄	—	34	2	no	—
64	C₂×C₄	—	68	4	no	—
65	C₈	—	17	1	no	—
66	C₈	—	34	1	no	—
67	C₈	C₂×#595	1	1	yes	characteristic, complemented
68	C₂²	—	2	2	no	—
69	C₂²	—	17	1	no	—
70	C₂²	—	34	2	no	—
71	C₂²	—	68	2	no	—
72	C₂²	—	68	2	no	—
73	C₄	—	17	1	no	—
74	C₄	—	34	2	no	—
75	C₄	—	68	2	no	—
76	C₄	C₂²×#595	1	1	yes	characteristic
77	C₂	—	4	2	no	—
78	C₂	—	17	2	no	—
79	C₂	—	68	2	no	—
80	C₂	D₄×#595	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#595
commutator	C₄×C₁₇	C₂²×C₄
Frattini	C₄	C₂²×#595
Fitting	D₈×C₁₇	C₄
socle	C₂×C₁₇	C₄×D₄
prime radical	D₈×D₁₇	C₂
cosocle	C₄×D₁₇	C₂³
hypercenter	D₈	#595
hypocenter	C₁₇	#442
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. D₄×#595	C₂	semidirect
3. #10587547	C₂	semidirect
4. #10587533	C₂	semidirect
5. #10587532	C₂	semidirect
12. D₈×C₁₇	C₄	semidirect
13. #63228	C₄	semidirect
14. D₁₃₆	C₄	semidirect
20. D₄×C₁₇	C₂×C₄	semidirect
22. D₆₈	C₂×C₄	semidirect
25. C₈×C₁₇	C₂×C₄	semidirect
26. #3622	C₂×C₄	semidirect
46. C₁₇	#442	semidirect
51. D₈	#595	semidirect
60. D₄	C₂×#595	semidirect
67. C₈	C₂×#595	semidirect

Maximal subgroups

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

subgroup	index
D₄×#595	2
D₈×D₁₇	2
#10587547	2
#10587533	2
#10587532	2
#442	17