Subgroups — #17981502

Order 4352.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763891	C₂	1	2	yes	maximal
2	#14543889	C₂	1	1	yes	maximal, characteristic
3	#11763891	—	2	2	no	—
4	C₂×#10587467	C₄	1	1	yes	characteristic
5	C₂×#10587467	C₂²	1	1	yes	characteristic
6	C₁₆×Dic₁₇	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₁₇	C₈	1	1	yes	characteristic
8	C₈×Dic₁₇	C₈	1	1	yes	characteristic
9	C₂×#63214	C₂×C₄	1	1	yes	characteristic
10	#10587467	—	2	1	no	—
11	#10587467	D₄	1	1	yes	characteristic
12	#10587467	Q₈	1	1	yes	characteristic
13	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
14	C₄×Dic₁₇	C₁₆	1	1	yes	characteristic
15	C₂×#3622	C₁₆	1	1	yes	characteristic
16	C₁₆×C₁₇	—	2	1	no	—
17	#63214	C₄⋊C₄	1	1	yes	characteristic
18	#63214	M₁₆	1	1	yes	characteristic
19	C₄⋊C₆₄	—	17	1	no	maximal, Sylow
20	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
21	C₂×Dic₁₇	C₃₂	1	1	yes	characteristic
22	C₂×Dic₁₇	C₃₂	1	1	yes	characteristic
23	C₈×C₁₇	C₄⋊C₈	1	1	yes	characteristic
24	C₈×C₁₇	M₃₂	1	1	yes	characteristic
25	#3622	—	2	1	no	—
26	C₂×C₆₄	—	17	2	no	—
27	C₄×C₃₂	—	17	1	no	—
28	C₂²×C₁₇	C₂×C₃₂	1	1	yes	characteristic
29	C₄×C₁₇	C₄⋊C₁₆	1	1	yes	characteristic
30	C₄×C₁₇	M₆₄	1	1	yes	characteristic
31	Dic₁₇	—	2	1	no	—
32	Dic₁₇	C₆₄	1	2	yes	complemented
33	C₂×C₃₂	—	17	1	no	—
34	C₂×C₃₂	—	17	1	no	—
35	C₄×C₁₆	—	17	1	no	—
36	C₆₄	—	34	2	no	—
37	C₂×C₁₇	C₄⋊C₃₂	1	1	yes	characteristic
38	C₂×C₁₇	C₂×C₆₄	1	1	yes	characteristic
39	C₂×C₁₇	M₁₂₈	1	1	yes	characteristic
40	C₂×C₁₆	—	17	1	no	—
41	C₂×C₁₆	#3633	1	1	yes	characteristic
42	C₄×C₈	—	17	1	no	—
43	C₃₂	—	17	1	no	—
44	C₃₂	—	17	1	no	—
45	C₃₂	—	34	1	no	—
46	C₁₇	C₄⋊C₆₄	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₈	—	17	1	no	—
48	C₂×C₈	C₂×#3633	1	1	yes	characteristic
49	C₄²	—	17	1	no	—
50	C₁₆	—	2	1	no	—
51	C₁₆	—	17	1	no	—
52	C₁₆	—	17	1	no	—
53	C₂×C₄	—	17	1	no	—
54	C₂×C₄	—	17	1	no	—
55	C₂×C₄	#10587665	1	1	yes	characteristic
56	C₈	—	34	1	no	—
57	C₈	C₄⋊#3633	1	1	yes	characteristic
58	C₈	#10587670	1	1	yes	characteristic
59	C₂²	#11763916	1	1	yes	characteristic
60	C₄	—	17	2	no	—
61	C₄	—	34	1	no	—
62	C₄	#11763912	1	1	yes	characteristic
63	C₄	#11763918	1	1	yes	characteristic
64	C₂	#14545883	1	1	yes	characteristic
65	C₂	#14545887	1	1	yes	characteristic
66	C₂	#14545889	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#3633
commutator	C₂×C₁₇	C₂×C₆₄
Fitting	C₂×C₁₆×C₁₇	C₈
socle, prime radical	C₂²×C₁₇	C₂×C₃₂
cosocle	C₂×#10587467	C₂²
hypercenter	C₂×C₁₆	#3633
hypocenter	C₁₇	C₄⋊C₆₄
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
32. Dic₁₇	C₆₄	semidirect
46. C₁₇	C₄⋊C₆₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11763891	2
#14543889	2
C₄⋊C₆₄	17