Subgroups — #11763721

Order 1088.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈×D₁₇	C₂	1	1	yes	maximal, characteristic
2	#10587534	C₂	1	1	yes	maximal, characteristic, complemented
3	#10587529	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×D₁₇	—	2	1	no	—
5	C₄⋊#595	—	2	1	no	—
6	D₈×C₁₇	C₄	1	1	yes	characteristic, complemented
7	#63228	—	2	1	no	—
8	D₁₃₆	C₄	1	1	yes	characteristic, complemented
9	C₈×D₁₇	C₂²	1	1	yes	characteristic
10	#63216	—	2	1	no	—
11	C₂²×D₁₇	—	4	1	no	—
12	C₂×#595	—	4	1	no	—
13	D₄×C₁₇	—	2	1	no	—
14	C₂²⋊D₁₇	—	4	1	no	—
15	D₆₈	—	2	1	no	—
16	C₄×D₁₇	D₄	1	1	yes	characteristic
17	C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
18	#3622	D₄	1	1	yes	characteristic
19	C₂²×C₁₇	—	4	1	no	—
20	C₂×D₁₇	—	4	1	no	—
21	C₂×D₁₇	—	8	1	no	—
22	C₂×D₁₇	—	8	1	no	—
23	C₂×D₁₇	D₈	1	1	yes	characteristic
24	#595	—	8	1	no	—
25	C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
26	Dic₁₇	SD₁₆	1	1	yes	characteristic
27	#357	—	17	1	no	maximal, Sylow
28	C₂×C₁₇	—	8	1	no	—
29	C₂×C₁₇	#102	1	1	yes	characteristic
30	D₁₇	—	8	1	no	—
31	D₁₇	D₁₆	1	1	yes	characteristic
32	D₁₇	SD₃₂	1	1	yes	characteristic
33	C₂×D₈	—	17	1	no	—
34	C₂×C₁₆	—	17	1	no	—
35	#107	—	17	1	no	—
36	C₁₇	#357	1	1	yes	characteristic, complemented, Sylow
37	C₂×D₄	—	34	1	no	—
38	D₈	—	17	1	no	—
39	D₈	—	34	1	no	—
40	D₈	#595	1	1	yes	characteristic, complemented
41	C₂×C₈	—	17	1	no	—
42	C₄⋊C₄	—	34	1	no	—
43	C₁₆	—	34	1	no	—
44	C₂³	—	68	1	no	—
45	D₄	—	2	1	no	—
46	D₄	—	34	1	no	—
47	D₄	—	68	1	no	—
48	C₂×C₄	—	17	1	no	—
49	C₂×C₄	—	68	1	no	—
50	C₈	—	17	1	no	—
51	C₈	C₂×#595	1	1	yes	characteristic
52	C₂²	—	4	1	no	—
53	C₂²	—	17	1	no	—
54	C₂²	—	68	1	no	—
55	C₂²	—	136	1	no	—
56	C₂²	—	136	1	no	—
57	C₄	—	17	1	no	—
58	C₄	—	136	1	no	—
59	C₄	C₂²⋊#595	1	1	yes	characteristic
60	C₂	—	8	1	no	—
61	C₂	—	17	1	no	—
62	C₂	—	17	1	no	—
63	C₂	—	136	1	no	—
64	C₂	#10587547	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10587547
commutator	C₈×C₁₇	C₂×C₄
Frattini	C₈	C₂×#595
Fitting	D₈×C₁₇	C₄
socle	C₂×C₁₇	#102
prime radical	D₈×D₁₇	C₂
cosocle	C₈×D₁₇	C₂²
hypercenter	D₈	#595
hypocenter	C₁₇	#357
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
2. #10587534	C₂	semidirect
3. #10587529	C₂	semidirect
6. D₈×C₁₇	C₄	semidirect
8. D₁₃₆	C₄	semidirect
36. C₁₇	#357	semidirect
40. D₈	#595	semidirect

Maximal subgroups

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

subgroup	index
D₈×D₁₇	2
#10587534	2
#10587529	2
#357	17