Subgroups — #11763856

Order 1088.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587678	C₂	1	2	yes	maximal, complemented
2	#10587598	C₂	1	1	yes	maximal, characteristic
3	#10587548	C₂	1	2	yes	maximal, complemented
4	#10587535	C₂	1	1	yes	maximal, characteristic, complemented
5	#10587532	C₂	1	1	yes	maximal, characteristic, complemented
6	#63254	C₂²	1	2	yes	—
7	#63247	—	2	2	no	—
8	C₂×#3624	—	2	2	no	—
9	C₄×#595	C₂²	1	1	yes	characteristic
10	#63243	C₂²	1	2	yes	—
11	#63242	C₂²	1	1	yes	characteristic
12	D₈×C₁₇	C₄	1	1	yes	characteristic, complemented
13	#63229	C₄	1	2	yes	complemented
14	Dic₆₈	C₄	1	1	yes	characteristic, complemented
15	C₈×D₁₇	C₂²	1	1	yes	characteristic
16	C₂×#595	—	2	1	no	—
17	D₄×C₁₇	C₂×C₄	1	2	yes	—
18	C₂²⋊D₁₇	—	2	2	no	—
19	C₂×Dic₁₇	—	2	2	no	—
20	C₄×D₁₇	C₂³	1	1	yes	characteristic
21	Dic₃₄	C₂×C₄	1	2	yes	—
22	#3624	—	2	2	no	—
23	#3624	D₄	1	2	yes	—
24	C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
25	#3622	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₁₇	—	2	2	no	—
27	C₂×D₁₇	#41	1	1	yes	characteristic
28	#595	—	4	1	no	—
29	C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
30	Dic₁₇	—	2	2	no	—
31	Dic₁₇	C₂×D₄	1	1	yes	characteristic
32	#444	—	17	1	no	maximal, Sylow
33	C₂×C₁₇	—	4	2	no	—
34	C₂×C₁₇	C₄×D₄	1	1	yes	characteristic
35	D₁₇	—	2	1	no	—
36	#135	—	17	1	no	—
37	#131	—	17	2	no	—
38	#108	—	17	1	no	—
39	#104	—	17	2	no	—
40	#97	—	17	1	no	—
41	C₁₇	#444	1	1	yes	characteristic, complemented, Sylow
42	#41	—	17	2	no	—
43	Q₁₆	—	17	1	no	—
44	SD₁₆	—	17	2	no	—
45	D₈	#595	1	1	yes	characteristic, complemented
46	M₁₆	—	17	2	no	—
47	M₁₆	—	34	2	no	—
48	C₂×C₈	—	17	1	no	—
49	C₂×C₈	—	17	1	no	—
50	C₂×C₈	—	34	2	no	—
51	C₄²	—	17	1	no	—
52	Q₈	—	17	2	no	—
53	D₄	—	34	2	no	—
54	D₄	C₂×#595	1	2	yes	—
55	C₂×C₄	—	17	1	no	—
56	C₂×C₄	—	34	2	no	—
57	C₂×C₄	—	34	1	no	—
58	C₈	—	17	2	no	—
59	C₈	—	17	1	no	—
60	C₈	—	34	2	no	—
61	C₈	C₂×#595	1	1	yes	characteristic
62	C₂²	—	2	2	no	—
63	C₂²	—	17	1	no	—
64	C₄	—	17	1	no	—
65	C₄	—	34	2	no	—
66	C₄	—	68	1	no	—
67	C₄	C₂²×#595	1	1	yes	characteristic
68	C₂	—	4	2	no	—
69	C₂	—	34	1	no	—
70	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	#10587598	C₂
cosocle	C₄×D₁₇	C₂³
hypercenter	D₈	#595
hypocenter	C₁₇	#444
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. #10587678	C₂	semidirect
3. #10587548	C₂	semidirect
4. #10587535	C₂	semidirect
5. #10587532	C₂	semidirect
12. D₈×C₁₇	C₄	semidirect
13. #63229	C₄	semidirect
14. Dic₆₈	C₄	semidirect
41. C₁₇	#444	semidirect
45. D₈	#595	semidirect

Maximal subgroups

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

subgroup	index
#10587678	2
#10587598	2
#10587548	2
#10587535	2
#10587532	2
#444	17