Subgroups — #11763849

Order 1088.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#595	C₂	1	2	yes	maximal
2	Q₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic
3	#10587549	C₂	1	2	yes	maximal
4	#10587533	C₂	1	1	yes	maximal, characteristic
5	#10587532	C₂	1	1	yes	maximal, characteristic
6	Q₈×D₁₇	C₂²	1	2	yes	—
7	C₄⋊#595	—	2	2	no	—
8	C₄⋊#595	C₂²	1	2	yes	—
9	C₄×#595	—	2	2	no	—
10	C₄×#595	C₂²	1	1	yes	characteristic
11	#63242	C₂²	1	1	yes	characteristic
12	Q₁₆×C₁₇	C₄	1	1	yes	characteristic, complemented
13	#63231	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	2	no	—
17	C₂×#595	D₄	1	2	yes	—
18	Q₈×C₁₇	C₂×C₄	1	2	yes	—
19	C₄×D₁₇	—	2	2	no	—
20	C₄×D₁₇	C₂³	1	1	yes	characteristic
21	Dic₃₄	—	2	2	no	—
22	Dic₃₄	C₂×C₄	1	2	yes	—
23	#3624	—	2	1	no	—
24	C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
25	#3622	C₂×C₄	1	1	yes	characteristic
26	C₂×D₁₇	C₂×D₄	1	1	yes	characteristic
27	#595	—	2	2	no	—
28	#595	—	4	2	no	—
29	C₄×C₁₇	—	2	2	no	—
30	C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
31	Dic₁₇	—	2	2	no	—
32	Dic₁₇	#41	1	1	yes	characteristic
33	#441	—	17	1	no	maximal, Sylow
34	C₂×C₁₇	C₄×D₄	1	1	yes	characteristic
35	D₁₇	#137	1	2	yes	—
36	C₂×Q₁₆	—	17	1	no	—
37	C₄×Q₈	—	17	2	no	—
38	#106	—	17	1	no	—
39	#103	—	17	2	no	—
40	#97	—	17	1	no	—
41	C₁₇	#441	1	1	yes	characteristic, complemented, Sylow
42	C₂×Q₈	—	17	2	no	—
43	Q₁₆	—	17	2	no	—
44	Q₁₆	—	17	1	no	—
45	Q₁₆	#595	1	1	yes	characteristic, complemented
46	C₂×C₈	—	17	1	no	—
47	C₂×C₈	—	17	1	no	—
48	C₄⋊C₄	—	17	2	no	—
49	C₄⋊C₄	—	34	2	no	—
50	C₄²	—	17	1	no	—
51	C₄²	—	34	2	no	—
52	Q₈	—	17	2	no	—
53	Q₈	—	34	2	no	—
54	Q₈	C₂×#595	1	2	yes	—
55	C₂×C₄	—	17	1	no	—
56	C₂×C₄	—	17	2	no	—
57	C₂×C₄	—	34	2	no	—
58	C₂×C₄	—	34	2	no	—
59	C₈	—	17	1	no	—
60	C₈	—	34	1	no	—
61	C₈	C₂×#595	1	1	yes	characteristic
62	C₂²	—	17	1	no	—
63	C₄	—	2	2	no	—
64	C₄	—	17	1	no	—
65	C₄	—	34	2	no	—
66	C₄	—	34	2	no	—
67	C₄	—	68	2	no	—
68	C₄	C₂²×#595	1	1	yes	characteristic
69	C₂	—	17	2	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	Q₁₆×C₁₇	C₄
socle	C₂×C₁₇	C₄×D₄
prime radical	C₂×D₁₇	C₂×D₄
cosocle	C₄×D₁₇	C₂³
hypercenter	Q₁₆	#595
hypocenter	C₁₇	#441
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
12. Q₁₆×C₁₇	C₄	semidirect
13. #63231	C₄	semidirect
14. Dic₆₈	C₄	semidirect
41. C₁₇	#441	semidirect
45. Q₁₆	#595	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#595	2
Q₁₆×D₁₇	2
#10587549	2
#10587533	2
#10587532	2
#441	17