Subgroups — #11763819

Order 1088.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587677	C₂	1	2	yes	maximal
2	C₂×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
3	#10587534	C₂	1	2	yes	maximal, complemented
4	#10587533	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×D₁₇	C₂²	1	1	yes	characteristic
6	C₂²⋊#595	—	2	2	no	—
7	C₄⋊#595	C₂²	1	4	yes	—
8	C₄×#595	—	2	2	no	—
9	C₂×C₈×C₁₇	C₄	1	1	yes	characteristic, complemented
10	C₂×#3622	C₄	1	1	yes	characteristic, complemented
11	C₈×D₁₇	C₄	1	1	yes	characteristic, complemented
12	C₈×D₁₇	C₄	1	1	yes	characteristic, complemented
13	C₈×D₁₇	C₂²	1	1	yes	characteristic
14	C₈×D₁₇	C₂²	1	1	yes	characteristic
15	C₂²×D₁₇	D₄	1	1	yes	characteristic
16	C₂×#595	—	2	4	no	—
17	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₁₇	Q₈	1	1	yes	characteristic
19	C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
20	C₄×D₁₇	D₄	1	1	yes	characteristic
21	C₄×D₁₇	Q₈	1	1	yes	characteristic
22	C₄×D₁₇	C₂³	1	1	yes	characteristic
23	C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
24	C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
25	#3622	C₂×C₄	1	1	yes	characteristic
26	#3622	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
28	C₂×D₁₇	—	2	2	no	—
29	C₂×D₁₇	C₄⋊C₄	1	1	yes	characteristic
30	C₂×D₁₇	C₂×D₄	1	1	yes	characteristic
31	#595	—	4	4	no	—
32	C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
33	C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
34	Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
35	Dic₁₇	C₂×Q₈	1	1	yes	characteristic
36	#427	—	17	1	no	maximal, Sylow
37	C₂×C₁₇	—	2	1	no	—
38	C₂×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
39	D₁₇	—	2	1	no	—
40	D₁₇	#135	1	2	yes	—
41	C₂²×C₈	—	17	1	no	—
42	#117	—	17	2	no	—
43	#107	—	17	2	no	—
44	#106	—	17	2	no	—
45	C₁₇	#427	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₄	—	17	1	no	—
47	C₂×C₈	—	17	1	no	—
48	C₂×C₈	—	17	1	no	—
49	C₂×C₈	—	17	1	no	—
50	C₂×C₈	—	17	1	no	—
51	C₂×C₈	—	17	1	no	—
52	C₂×C₈	#595	1	1	yes	characteristic, complemented
53	C₄⋊C₄	—	17	4	no	—
54	C₂²⋊C₄	—	34	2	no	—
55	C₄²	—	34	2	no	—
56	C₂³	—	17	1	no	—
57	C₂×C₄	—	17	1	no	—
58	C₂×C₄	—	17	1	no	—
59	C₂×C₄	—	17	1	no	—
60	C₂×C₄	—	17	1	no	—
61	C₂×C₄	—	17	1	no	—
62	C₂×C₄	—	34	4	no	—
63	C₂×C₄	C₂×#595	1	1	yes	characteristic
64	C₈	—	17	1	no	—
65	C₈	—	17	1	no	—
66	C₈	C₂×#595	1	1	yes	characteristic
67	C₈	C₂×#595	1	1	yes	characteristic
68	C₂²	—	17	1	no	—
69	C₂²	—	17	1	no	—
70	C₂²	—	34	2	no	—
71	C₂²	C₄⋊#595	1	1	yes	characteristic
72	C₄	—	17	1	no	—
73	C₄	—	17	1	no	—
74	C₄	—	68	4	no	—
75	C₄	C₄⋊#595	1	1	yes	characteristic
76	C₄	C₂²×#595	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	—	17	2	no	—
79	C₂	—	34	1	no	—
80	C₂	C₂×C₄⋊#595	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄⋊#595
commutator	C₄×C₁₇	C₂²×C₄
Frattini	C₄	C₂²×#595
Fitting	C₂×C₈×C₁₇	C₄
socle	C₂×C₁₇	C₂×C₄⋊C₄
prime radical	C₂²×D₁₇	D₄
cosocle	C₄×D₁₇	C₂³
hypercenter	C₂×C₈	#595
hypocenter	C₁₇	#427
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
3. #10587534	C₂	semidirect
4. #10587533	C₂	semidirect
9. C₂×C₈×C₁₇	C₄	semidirect
10. C₂×#3622	C₄	semidirect
11. C₈×D₁₇	C₄	semidirect
12. C₈×D₁₇	C₄	semidirect
45. C₁₇	#427	semidirect
52. 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
#10587677	2
C₂×C₈×D₁₇	2
#10587534	2
#10587533	2
#427	17