Subgroups — #11763865

Order 1088.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
2	#10587538	C₂	1	2	yes	maximal, complemented
3	#10587530	C₂	1	2	yes	maximal, complemented
4	#10587529	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×D₁₇	C₄	1	1	yes	characteristic
6	C₂×C₈×C₁₇	C₄	1	1	yes	characteristic
7	C₂×#3622	C₂²	1	1	yes	characteristic
8	C₈×D₁₇	C₄	1	1	yes	characteristic
9	C₈×D₁₇	C₄	1	1	yes	characteristic
10	C₈×D₁₇	C₂²	1	1	yes	characteristic
11	C₈×D₁₇	C₂²	1	1	yes	characteristic
12	#63216	C₂²	1	4	yes	complemented
13	C₂²×D₁₇	C₈	1	1	yes	characteristic
14	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂×Dic₁₇	C₈	1	1	yes	characteristic
16	C₄×D₁₇	C₈	1	1	yes	characteristic
17	C₄×D₁₇	C₈	1	1	yes	characteristic
18	C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
19	C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
20	C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
21	C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
22	#3622	C₂×C₄	1	1	yes	characteristic
23	#3622	C₂³	1	1	yes	characteristic
24	C₂²×C₁₇	C₂×C₈	1	1	yes	characteristic
25	C₂×D₁₇	—	2	2	no	—
26	C₂×D₁₇	C₂×C₈	1	1	yes	characteristic
27	C₂×D₁₇	C₂×C₈	1	1	yes	characteristic
28	C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
29	C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
30	Dic₁₇	C₂×C₈	1	1	yes	characteristic
31	Dic₁₇	C₂×C₈	1	1	yes	characteristic
32	C₂×M₃₂	—	17	1	no	maximal, Sylow
33	C₂×C₁₇	—	2	1	no	—
34	C₂×C₁₇	C₂²×C₈	1	1	yes	characteristic
35	D₁₇	—	2	1	no	—
36	D₁₇	M₃₂	1	2	yes	complemented
37	C₂²×C₈	—	17	1	no	—
38	M₃₂	—	17	2	no	—
39	M₃₂	—	17	2	no	—
40	C₂×C₁₆	—	17	2	no	—
41	C₁₇	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
42	C₂²×C₄	—	17	1	no	—
43	C₂×C₈	—	17	1	no	—
44	C₂×C₈	—	17	1	no	—
45	C₂×C₈	—	17	1	no	—
46	C₂×C₈	—	17	1	no	—
47	C₂×C₈	—	17	1	no	—
48	C₂×C₈	#595	1	1	yes	characteristic
49	C₁₆	—	17	4	no	—
50	C₂³	—	17	1	no	—
51	C₂×C₄	—	17	1	no	—
52	C₂×C₄	—	17	1	no	—
53	C₂×C₄	—	17	1	no	—
54	C₂×C₄	—	17	1	no	—
55	C₂×C₄	—	17	1	no	—
56	C₂×C₄	C₂×#595	1	1	yes	characteristic
57	C₈	—	17	1	no	—
58	C₈	—	17	1	no	—
59	C₈	C₂×#595	1	1	yes	characteristic
60	C₈	C₂×#595	1	1	yes	characteristic
61	C₂²	—	17	1	no	—
62	C₂²	—	17	1	no	—
63	C₂²	—	34	2	no	—
64	C₂²	#63242	1	1	yes	characteristic
65	C₄	—	17	1	no	—
66	C₄	—	17	1	no	—
67	C₄	#63242	1	1	yes	characteristic
68	C₄	C₂²×#595	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	—	17	2	no	—
71	C₂	—	34	1	no	—
72	C₂	C₂×#63242	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×#595
commutator, socle	C₂×C₁₇	C₂²×C₈
Frattini	C₄	C₂²×#595
Fitting	C₂×C₈×C₁₇	C₄
prime radical	C₂²×D₁₇	C₈
cosocle	#3622	C₂³
hypercenter	C₂×C₈	#595
hypocenter	C₁₇	C₂×M₃₂
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #10587538	C₂	semidirect
3. #10587530	C₂	semidirect
4. #10587529	C₂	semidirect
12. #63216	C₂²	semidirect
36. D₁₇	M₃₂	semidirect
41. C₁₇	C₂×M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₁₇	2
#10587538	2
#10587530	2
#10587529	2
C₂×M₃₂	17