Group #22627059 — subgroups

Subgroups — Q₁₆×#10596842 #22627059

Order 9344.

164 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#10596842	C₂	1	2	yes	maximal
2	#17989677	C₂	1	1	yes	maximal, characteristic
3	Q₈⋊#10596842	C₂	1	2	yes	maximal
4	C₈×#10596842	C₂	1	1	yes	maximal, characteristic
5	Q₁₆×#64408	C₂	1	1	yes	maximal, characteristic
6	C₄⋊#10596842	—	2	2	no	—
7	C₄⋊#10596842	C₂²	1	2	yes	—
8	C₄×#10596842	—	2	2	no	—
9	C₄×#10596842	C₂²	1	1	yes	characteristic
10	C₄×#10596842	C₂²	1	1	yes	characteristic
11	Q₈×#64408	C₂²	1	2	yes	—
12	#14556660	C₄	1	1	yes	characteristic
13	#14556654	C₄	1	2	yes	—
14	C₈×#64408	C₂²	1	1	yes	characteristic
15	Q₁₆×D₇₃	C₄	1	1	yes	characteristic
16	C₂×#10596842	—	2	1	no	—
17	C₂×#10596842	—	2	2	no	—
18	C₂×#10596842	D₄	1	1	yes	characteristic
19	C₂×#10596842	D₄	1	1	yes	characteristic
20	#11924036	C₂×C₄	1	1	yes	characteristic
21	C₄⋊#64408	—	2	2	no	—
22	C₄⋊#64408	C₂×C₄	1	2	yes	—
23	C₄×#64408	—	2	2	no	—
24	C₄×#64408	C₂³	1	1	yes	characteristic
25	Q₈×D₇₃	C₂×C₄	1	2	yes	—
26	Dic₂₉₂	C₈	1	1	yes	characteristic, complemented
27	#11924018	C₈	1	2	yes	complemented
28	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
29	Q₁₆×C₇₃	C₈	1	1	yes	characteristic, complemented
30	C₂×#64408	—	2	2	no	—
31	C₂×#64408	C₂×D₄	1	1	yes	characteristic
32	C₂×#64408	#41	1	1	yes	characteristic
33	#10596842	—	2	2	no	—
34	#10596842	—	2	1	no	—
35	#10596842	—	4	2	no	—
36	#10596842	Q₁₆	1	2	yes	direct product factor
37	Q₈×C₇₃	C₂×C₈	1	2	yes	—
38	C₄×D₇₃	—	2	2	no	—
39	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
40	Dic₁₄₆	—	2	2	no	—
41	Dic₁₄₆	C₂×C₈	1	2	yes	—
42	#10596833	—	2	1	no	—
43	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
44	#10596831	C₂×C₈	1	1	yes	characteristic
45	C₂×D₇₃	C₄×D₄	1	1	yes	characteristic
46	#64408	—	2	1	no	—
47	#64408	—	4	2	no	—
48	#64408	C₂×Q₁₆	1	1	yes	characteristic
49	#64408	#135	1	1	yes	characteristic
50	C₄×C₇₃	—	2	2	no	—
51	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
52	Dic₇₃	—	2	2	no	—
53	Dic₇₃	#131	1	1	yes	characteristic
54	C₂×C₇₃	C₈×D₄	1	1	yes	characteristic
55	D₇₃	C₄×Q₁₆	1	1	yes	characteristic
56	D₇₃	#443	1	1	yes	characteristic
57	C₈×Q₁₆	—	73	1	no	maximal, Sylow
58	C₇₃	C₈×Q₁₆	1	1	yes	characteristic, complemented, Sylow
59	C₈×Q₈	—	73	2	no	—
60	C₄×Q₁₆	—	73	1	no	—
61	#335	—	73	1	no	—
62	Q₈⋊C₈	—	73	2	no	—
63	C₈²	—	73	1	no	—
64	C₂×Q₁₆	—	73	1	no	—
65	C₄×Q₈	—	73	2	no	—
66	#107	—	73	1	no	—
67	C₄⋊C₈	—	73	2	no	—
68	C₄⋊C₈	—	146	2	no	—
69	#103	—	73	2	no	—
70	C₄×C₈	—	73	1	no	—
71	C₄×C₈	—	73	1	no	—
72	C₄×C₈	—	73	1	no	—
73	C₄×C₈	—	146	2	no	—
74	C₂×Q₈	—	73	2	no	—
75	Q₁₆	—	73	2	no	—
76	Q₁₆	—	73	1	no	—
77	Q₁₆	#10596842	1	1	yes	characteristic, direct product factor
78	C₂×C₈	—	73	1	no	—
79	C₂×C₈	—	73	1	no	—
80	C₂×C₈	—	73	1	no	—
81	C₂×C₈	—	73	1	no	—
82	C₂×C₈	—	146	2	no	—
83	C₂×C₈	—	146	1	no	—
84	C₄⋊C₄	—	73	2	no	—
85	C₄⋊C₄	—	146	2	no	—
86	C₄²	—	73	1	no	—
87	C₄²	—	146	2	no	—
88	Q₈	—	73	2	no	—
89	Q₈	—	146	2	no	—
90	Q₈	C₂×#10596842	1	2	yes	—
91	C₂×C₄	—	73	1	no	—
92	C₂×C₄	—	73	1	no	—
93	C₂×C₄	—	73	1	no	—
94	C₂×C₄	—	146	2	no	—
95	C₂×C₄	—	146	2	no	—
96	C₈	—	292	2	no	—
97	C₈	—	73	2	no	—
98	C₈	—	73	1	no	—
99	C₈	—	146	1	no	—
100	C₈	—	146	1	no	—
101	C₈	—	146	2	no	—
102	C₈	C₂×#10596842	1	1	yes	characteristic
103	C₂²	—	73	1	no	—
104	C₄	—	2	2	no	—
105	C₄	—	292	2	no	—
106	C₄	—	73	1	no	—
107	C₄	—	73	1	no	—
108	C₄	—	73	1	no	—
109	C₄	—	146	1	no	—
110	C₄	—	146	2	no	—
111	C₄	C₂²×#10596842	1	1	yes	characteristic
112	C₂	—	73	1	no	—
113	C₂	—	73	1	no	—
114	C₂	D₄×#10596842	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₈×#10596842

C₂

yes

maximal

#17989677

C₂

yes

maximal, characteristic

Q₈⋊#10596842

C₂

yes

maximal

C₈×#10596842

C₂

yes

maximal, characteristic

Q₁₆×#64408

C₂

yes

maximal, characteristic

C₄⋊#10596842

—

C₄⋊#10596842

C₂²

yes

—

C₄×#10596842

—

C₄×#10596842

C₂²

yes

characteristic

C₄×#10596842

C₂²

yes

characteristic

Q₈×#64408

C₂²

yes

—

#14556660

C₄

yes

characteristic

#14556654

C₄

yes

—

C₈×#64408

C₂²

yes

characteristic

Q₁₆×D₇₃

C₄

yes

—

—

D₄

yes

characteristic

C₂×#10596842

D₄

yes

characteristic

#11924036

C₂×C₄

yes

characteristic

C₄⋊#64408

—

C₄⋊#64408

C₂×C₄

yes

—

C₄×#64408

—

C₄×#64408

C₂³

yes

characteristic

Q₈×D₇₃

C₂×C₄

yes

—

Dic₂₉₂

C₈

yes

characteristic, complemented

#11924018

C₈

yes

complemented

C₈×D₇₃

C₂×C₄

yes

characteristic

Q₁₆×C₇₃

C₈

yes

characteristic, complemented

C₂×#64408

—

C₂×#64408

C₂×D₄

yes

yes

—

—

—

Q₁₆

yes

direct product factor

Q₈×C₇₃

C₂×C₈

yes

—

C₄×D₇₃

—

C₄×D₇₃

C₂²×C₄

yes

characteristic

Dic₁₄₆

—

Dic₁₄₆

C₂×C₈

yes

—

#10596833

—

C₈×C₇₃

C₂×C₈

yes

characteristic

#10596831

C₂×C₈

yes

characteristic

C₂×D₇₃

C₄×D₄

yes

—

—

C₂×Q₁₆

yes

yes

C₄×C₇₃

—

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

—

Dic₇₃

#131

yes

characteristic

C₂×C₇₃

C₈×D₄

yes

characteristic

D₇₃

C₄×Q₁₆

yes

characteristic

D₇₃

#443

yes

characteristic

C₈×Q₁₆

—

maximal, Sylow

C₇₃

C₈×Q₁₆

yes

characteristic, complemented, Sylow

C₈×Q₈

—

C₄×Q₁₆

—

#335

—

Q₈⋊C₈

—

C₈²

—

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

#103

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

146

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

#10596842

yes

characteristic, direct product factor

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄²

—

C₄²

—

146

—

Q₈

—

Q₈

—

146

—

Q₈

C₂×#10596842

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₈

—

292

—

C₈

—

C₈

—

C₈

—

146

—

100

C₈

—

146

—

101

C₈

—

146

—

102

C₈

C₂×#10596842

yes

characteristic

103

C₂²

—

104

C₄

—

105

C₄

—

292

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

146

—

110

C₄

—

146

—

111

C₄

C₂²×#10596842

yes

characteristic

112

C₂

—

113

C₂

—

114

C₂

D₄×#10596842

yes

characteristic

	subgroup	G/H
center	C₂	D₄×#10596842
commutator	C₄×C₇₃	C₂²×C₈
Frattini	C₄	C₂²×#10596842
Fitting	Q₁₆×C₇₃	C₈
socle	C₂×C₇₃	C₈×D₄
hypercenter	Q₁₆	#10596842
hypocenter	C₇₃	C₈×Q₁₆
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

subgroup

G/H

center

C₂

D₄×#10596842

commutator

C₄×C₇₃

C₂²×C₈

Frattini

C₄

C₂²×#10596842

Fitting

Q₁₆×C₇₃

C₈

socle

C₂×C₇₃

C₈×D₄

hypercenter

Q₁₆

#10596842

hypocenter

C₇₃

C₈×Q₁₆

LCS

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

N	H ≅ G/N	type
26. Dic₂₉₂	C₈	semidirect
27. #11924018	C₈	semidirect
29. Q₁₆×C₇₃	C₈	semidirect
36. #10596842	Q₁₆	direct (N × H)
58. C₇₃	C₈×Q₁₆	semidirect
77. Q₁₆	#10596842	direct (N × H)

H ≅ G/N

type

26. Dic₂₉₂

C₈

semidirect

27. #11924018

C₈

semidirect

29. Q₁₆×C₇₃

C₈

semidirect

36. #10596842

Q₁₆

direct (N × H)

58. C₇₃

C₈×Q₁₆

semidirect

77. Q₁₆

#10596842

direct (N × H)

Subgroups — Q₁₆×#10596842 #22627059

Conjugacy classes of subgroups

Complements

Subgroups — Q16×#10596842 #22627059

Conjugacy classes of subgroups

Complements

Subgroups — Q₁₆×#10596842 #22627059