Subgroups — Q₁₆×#595 #11763847

Order 1088.

110 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	#10587534	C₂	1	1	yes	maximal, characteristic
5	C₈×#595	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	1	yes	characteristic
18	C₂×#595	D₄	1	1	yes	characteristic
19	Q₈×C₁₇	C₂×C₄	1	2	yes	—
20	C₄×D₁₇	—	2	2	no	—
21	C₄×D₁₇	C₂³	1	1	yes	characteristic
22	Dic₃₄	—	2	2	no	—
23	Dic₃₄	C₂×C₄	1	2	yes	—
24	#3624	—	2	1	no	—
25	C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
26	#3622	C₂×C₄	1	1	yes	characteristic
27	C₂×D₁₇	C₂×D₄	1	1	yes	characteristic
28	#595	—	2	1	no	—
29	#595	—	4	2	no	—
30	#595	Q₁₆	1	2	yes	direct product factor
31	C₄×C₁₇	—	2	2	no	—
32	C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
33	Dic₁₇	—	2	2	no	—
34	Dic₁₇	#41	1	1	yes	characteristic
35	C₄×Q₁₆	—	17	1	no	maximal, Sylow
36	C₂×C₁₇	C₄×D₄	1	1	yes	characteristic
37	D₁₇	C₂×Q₁₆	1	1	yes	characteristic
38	D₁₇	#135	1	1	yes	characteristic
39	C₂×Q₁₆	—	17	1	no	—
40	C₄×Q₈	—	17	2	no	—
41	#107	—	17	1	no	—
42	#103	—	17	2	no	—
43	C₄×C₈	—	17	1	no	—
44	C₁₇	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₈	—	17	2	no	—
46	Q₁₆	—	17	2	no	—
47	Q₁₆	—	17	1	no	—
48	Q₁₆	#595	1	1	yes	characteristic, direct product factor
49	C₂×C₈	—	17	1	no	—
50	C₂×C₈	—	17	1	no	—
51	C₄⋊C₄	—	17	2	no	—
52	C₄⋊C₄	—	34	2	no	—
53	C₄²	—	17	1	no	—
54	C₄²	—	34	2	no	—
55	Q₈	—	17	2	no	—
56	Q₈	—	34	2	no	—
57	Q₈	C₂×#595	1	2	yes	—
58	C₂×C₄	—	17	1	no	—
59	C₂×C₄	—	17	1	no	—
60	C₂×C₄	—	17	1	no	—
61	C₂×C₄	—	34	2	no	—
62	C₂×C₄	—	34	2	no	—
63	C₈	—	17	1	no	—
64	C₈	—	34	1	no	—
65	C₈	C₂×#595	1	1	yes	characteristic
66	C₂²	—	17	1	no	—
67	C₄	—	2	2	no	—
68	C₄	—	17	2	no	—
69	C₄	—	17	1	no	—
70	C₄	—	34	1	no	—
71	C₄	—	34	2	no	—
72	C₄	—	68	2	no	—
73	C₄	C₂²×#595	1	1	yes	characteristic
74	C₂	—	17	1	no	—
75	C₂	—	17	1	no	—
76	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	C₄×Q₁₆
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
30. #595	Q₁₆	direct (N × H)
44. C₁₇	C₄×Q₁₆	semidirect
48. Q₁₆	#595	direct (N × H)

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
#10587534	2
C₈×#595	2
C₄×Q₁₆	17

Subgroups — Q16×#595 #11763847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₁₆×#595 #11763847