Subgroups — #11763712

Order 1088.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587572	C₂	1	1	yes	maximal, characteristic
2	#10587553	C₂	1	1	yes	maximal, characteristic
3	#10587551	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic
5	C₂²×Dic₁₇	C₄	1	1	yes	characteristic, complemented
6	C₂²⋊#595	—	2	1	no	—
7	#63247	—	2	1	no	—
8	C₂²⋊C₄×C₁₇	C₄	1	1	yes	characteristic, complemented
9	#63227	—	2	1	no	—
10	C₄⋊Dic₁₇	—	2	1	no	—
11	C₂³×C₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂²×D₁₇	D₄	1	1	yes	characteristic
13	C₂×#595	—	4	1	no	—
14	C₂×C₄×C₁₇	—	2	1	no	—
15	C₂²⋊D₁₇	—	4	1	no	—
16	C₂×Dic₁₇	—	2	1	no	—
17	C₂×Dic₁₇	—	4	1	no	—
18	C₂×Dic₁₇	D₄	1	1	yes	characteristic
19	#3624	—	4	1	no	—
20	C₂²×C₁₇	—	2	1	no	—
21	C₂²×C₁₇	—	4	1	no	—
22	C₂²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×D₁₇	—	2	1	no	—
24	C₂×D₁₇	—	4	1	no	—
25	#595	—	8	1	no	—
26	C₄×C₁₇	—	4	1	no	—
27	Dic₁₇	—	2	1	no	—
28	Dic₁₇	—	4	1	no	—
29	#352	—	17	1	no	maximal, Sylow
30	C₂×C₁₇	—	2	1	no	—
31	C₂×C₁₇	—	4	1	no	—
32	C₂×C₁₇	#99	1	1	yes	characteristic
33	D₁₇	—	4	1	no	—
34	#123	—	17	1	no	—
35	#100	—	17	1	no	—
36	#99	—	17	1	no	—
37	C₁₇	#352	1	1	yes	characteristic, complemented, Sylow
38	C₂×D₄	—	17	1	no	—
39	C₂²×C₄	—	17	1	no	—
40	M₁₆	—	34	1	no	—
41	C₄⋊C₄	—	34	1	no	—
42	C₂²⋊C₄	—	34	1	no	—
43	C₂²⋊C₄	—	34	1	no	—
44	C₂²⋊C₄	#595	1	1	yes	characteristic, complemented
45	C₂³	—	17	1	no	—
46	C₂³	C₂×#595	1	1	yes	characteristic
47	D₄	—	68	1	no	—
48	C₂×C₄	—	2	1	no	—
49	C₂×C₄	—	17	1	no	—
50	C₂×C₄	—	34	1	no	—
51	C₂×C₄	—	68	1	no	—
52	C₂×C₄	—	68	1	no	—
53	C₈	—	68	1	no	—
54	C₂²	—	2	1	no	—
55	C₂²	—	4	1	no	—
56	C₂²	—	34	1	no	—
57	C₂²	—	68	1	no	—
58	C₂²	C₂²⋊#595	1	1	yes	characteristic
59	C₄	—	4	1	no	—
60	C₄	—	34	1	no	—
61	C₄	—	68	1	no	—
62	C₄	—	136	1	no	—
63	C₂	—	2	1	no	—
64	C₂	—	4	1	no	—
65	C₂	—	68	1	no	—
66	C₂	#10587539	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10587539
commutator	C₂³×C₁₇	C₂×C₄
Frattini	C₂³	C₂×#595
Fitting	C₂²⋊C₄×C₁₇	C₄
socle	C₂×C₁₇	#99
prime radical, cosocle	C₂×C₂²⋊D₁₇	C₂²
hypercenter	C₂²⋊C₄	#595
hypocenter	C₁₇	#352
LCS	G ▷ C₂³×C₁₇ ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂³ ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
5. C₂²×Dic₁₇	C₄	semidirect
8. C₂²⋊C₄×C₁₇	C₄	semidirect
37. C₁₇	#352	semidirect
44. C₂²⋊C₄	#595	semidirect

Maximal subgroups

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

subgroup	index
#10587572	2
#10587553	2
#10587551	2
#352	17