Group #11766966 — subgroups

Subgroups — C₉×#2245 #11766966

Order 1152.

198 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 96 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	C₉×#499	C₂	1	1	yes	maximal, characteristic
2	C₉×#494	C₂	1	1	yes	maximal, characteristic
3	C₉×#358	C₂	1	4	yes	maximal
4	C₉×#346	C₂	1	1	yes	maximal, characteristic
5	C₃×#2245	C₃	1	1	yes	maximal, characteristic
6	C₂×C₉×Q₁₆	—	2	1	no	—
7	C₂×C₉×Q₁₆	C₂²	1	2	yes	—
8	C₉×C₄⋊Q₈	—	2	1	no	—
9	C₉×#125	—	2	1	no	—
10	C₂×C₉×C₁₆	C₂²	1	2	yes	—
11	C₉×#107	C₂²	1	2	yes	—
12	C₉×#106	—	2	1	no	—
13	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
14	C₃×#499	C₂×C₃	1	1	yes	characteristic
15	C₃×#494	C₂×C₃	1	1	yes	characteristic
16	C₃×#358	C₂×C₃	1	4	yes	—
17	C₃×#346	C₂×C₃	1	1	yes	characteristic
18	C₂×Q₈×C₉	—	2	2	no	—
19	C₉×Q₁₆	—	2	4	no	—
20	C₉×Q₁₆	—	4	2	no	—
21	C₂×C₈×C₉	D₄	1	1	yes	characteristic
22	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
23	C₉×C₄⋊C₄	—	2	2	no	—
24	C₉×C₄⋊C₄	—	4	2	no	—
25	C₉×C₄⋊C₄	—	4	2	no	—
26	C₄²×C₉	D₄	1	1	yes	characteristic
27	C₉×C₁₆	—	2	2	no	—
28	#2245	C₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₃×Q₁₆	—	2	1	no	—
30	C₂×C₃×Q₁₆	C₂²×C₃	1	2	yes	—
31	C₃×C₄⋊Q₈	—	2	1	no	—
32	C₃×#125	—	2	1	no	—
33	C₂×C₃×C₁₆	C₂²×C₃	1	2	yes	—
34	C₃×#107	C₂²×C₃	1	2	yes	—
35	C₃×#106	—	2	1	no	—
36	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
37	Q₈×C₉	—	4	2	no	—
38	Q₈×C₉	—	4	2	no	—
39	C₂×C₄×C₉	—	4	2	no	—
40	C₂×C₄×C₉	—	4	2	no	—
41	C₂×C₄×C₉	D₈	1	2	yes	—
42	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
43	C₈×C₉	SD₁₆	1	2	yes	—
44	C₈×C₉	#41	1	2	yes	—
45	#499	C₂×C₉	1	1	yes	characteristic
46	#494	C₂×C₉	1	1	yes	characteristic
47	#358	C₂×C₉	1	4	yes	—
48	#346	C₂×C₉	1	1	yes	characteristic
49	C₂×C₃×Q₈	—	2	2	no	—
50	C₃×Q₁₆	—	2	4	no	—
51	C₃×Q₁₆	—	4	2	no	—
52	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
53	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
54	C₃×C₄⋊C₄	—	2	2	no	—
55	C₃×C₄⋊C₄	—	4	2	no	—
56	C₃×C₄⋊C₄	—	4	2	no	—
57	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
58	C₃×C₁₆	—	2	2	no	—
59	C₂²×C₉	C₂×D₈	1	1	yes	characteristic
60	C₄×C₉	—	2	2	no	—
61	C₄×C₉	—	8	2	no	—
62	C₄×C₉	—	8	2	no	—
63	C₄×C₉	#124	1	1	yes	characteristic
64	C₄×C₉	C₂×SD₁₆	1	1	yes	characteristic
65	C₂×Q₁₆	—	2	1	no	—
66	C₂×Q₁₆	C₂²×C₉	1	2	yes	—
67	C₄⋊Q₈	—	2	1	no	—
68	#125	—	2	1	no	—
69	C₂×C₁₆	C₂²×C₉	1	2	yes	—
70	#107	C₂²×C₉	1	2	yes	—
71	#106	—	2	1	no	—
72	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
73	C₃×Q₈	—	4	2	no	—
74	C₃×Q₈	—	4	2	no	—
75	C₂×C₃×C₄	—	4	2	no	—
76	C₂×C₃×C₄	—	4	2	no	—
77	C₂×C₃×C₄	C₃×D₈	1	2	yes	—
78	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
79	C₃×C₈	C₃×SD₁₆	1	2	yes	—
80	C₃×C₈	C₃×#41	1	2	yes	—
81	C₂×C₉	#486	1	1	yes	characteristic
82	C₂×C₉	#510	1	2	yes	—
83	C₂×Q₈	—	2	2	no	—
84	Q₁₆	—	2	4	no	—
85	Q₁₆	—	4	2	no	—
86	C₂×C₈	D₄×C₉	1	1	yes	characteristic
87	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
88	C₄⋊C₄	—	2	2	no	—
89	C₄⋊C₄	—	4	2	no	—
90	C₄⋊C₄	—	4	2	no	—
91	C₄²	D₄×C₉	1	1	yes	characteristic
92	C₁₆	—	2	2	no	—
93	C₂²×C₃	C₂×C₃×D₈	1	1	yes	characteristic
94	C₃×C₄	—	2	2	no	—
95	C₃×C₄	—	8	2	no	—
96	C₃×C₄	—	8	2	no	—
97	C₃×C₄	C₃×#124	1	1	yes	characteristic
98	C₃×C₄	C₂×C₃×SD₁₆	1	1	yes	characteristic
99	C₉	#2245	1	1	yes	characteristic, direct product factor, Sylow
100	Q₈	—	4	2	no	—
101	Q₈	—	4	2	no	—
102	C₂×C₄	—	4	2	no	—
103	C₂×C₄	—	4	2	no	—
104	C₂×C₄	C₉×D₈	1	2	yes	—
105	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
106	C₈	C₉×SD₁₆	1	2	yes	—
107	C₈	C₉×#41	1	2	yes	—
108	C₂×C₃	C₃×#486	1	1	yes	characteristic
109	C₂×C₃	C₃×#510	1	2	yes	—
110	C₂²	C₂×C₉×D₈	1	1	yes	characteristic
111	C₄	—	2	2	no	—
112	C₄	—	8	2	no	—
113	C₄	—	8	2	no	—
114	C₄	C₉×#124	1	1	yes	characteristic
115	C₄	C₂×C₉×SD₁₆	1	1	yes	characteristic
116	C₃	C₃×#2245	1	1	yes	characteristic
117	C₂	C₉×#486	1	1	yes	characteristic
118	C₂	C₉×#510	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#499

C₂

yes

maximal, characteristic

C₉×#494

C₂

yes

maximal, characteristic

C₉×#358

C₂

yes

maximal

C₉×#346

C₂

yes

maximal, characteristic

C₃×#2245

C₃

yes

maximal, characteristic

C₂×C₉×Q₁₆

—

C₂×C₉×Q₁₆

C₂²

yes

—

C₉×C₄⋊Q₈

—

C₉×#125

—

C₂×C₉×C₁₆

C₂²

yes

—

C₉×#107

C₂²

yes

—

C₉×#106

—

C₄×C₈×C₉

C₂²

yes

characteristic

C₃×#499

C₂×C₃

yes

characteristic

C₃×#494

C₂×C₃

yes

characteristic

C₃×#358

C₂×C₃

yes

—

C₃×#346

C₂×C₃

yes

characteristic

C₂×Q₈×C₉

—

C₉×Q₁₆

—

C₉×Q₁₆

—

C₂×C₈×C₉

D₄

yes

characteristic

C₂×C₈×C₉

C₂³

yes

characteristic

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

—

C₄²×C₉

D₄

yes

characteristic

C₉×C₁₆

—

#2245

C₉

yes

characteristic, direct product factor, Sylow

C₂×C₃×Q₁₆

—

C₂×C₃×Q₁₆

C₂²×C₃

yes

—

C₃×C₄⋊Q₈

—

C₃×#125

—

C₂×C₃×C₁₆

C₂²×C₃

yes

—

C₃×#107

C₂²×C₃

yes

—

C₃×#106

—

C₃×C₄×C₈

C₂²×C₃

yes

characteristic

Q₈×C₉

—

Q₈×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

D₈

yes

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₈×C₉

SD₁₆

yes

—

C₈×C₉

#41

yes

—

#499

C₂×C₉

yes

characteristic

#494

C₂×C₉

yes

characteristic

#358

C₂×C₉

yes

—

#346

C₂×C₉

yes

characteristic

C₂×C₃×Q₈

—

C₃×Q₁₆

—

C₃×Q₁₆

—

C₂×C₃×C₈

C₃×D₄

yes

characteristic

C₂×C₃×C₈

C₂³×C₃

yes

characteristic

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄²

C₃×D₄

yes

characteristic

C₃×C₁₆

—

C₂²×C₉

C₂×D₈

yes

characteristic

C₄×C₉

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

#124

yes

characteristic

C₄×C₉

C₂×SD₁₆

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

C₂²×C₉

yes

—

C₄⋊Q₈

—

#125

—

C₂×C₁₆

C₂²×C₉

yes

—

#107

C₂²×C₉

yes

—

#106

—

C₄×C₈

C₂²×C₉

yes

characteristic

C₃×Q₈

—

C₃×Q₈

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₃×D₈

yes

—

C₂×C₃×C₄

C₂×C₃×D₄

yes

characteristic

C₃×C₈

C₃×SD₁₆

yes

—

C₃×C₈

C₃×#41

yes

—

C₂×C₉

#486

yes

characteristic

C₂×C₉

#510

yes

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

C₂×C₈

D₄×C₉

yes

characteristic

C₂×C₈

C₂³×C₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₄×C₉

yes

characteristic

C₁₆

—

C₂²×C₃

C₂×C₃×D₈

yes

characteristic

C₃×C₄

—

C₃×C₄

—

C₃×C₄

—

C₃×C₄

C₃×#124

yes

characteristic

C₃×C₄

C₂×C₃×SD₁₆

yes

characteristic

C₉

#2245

yes

characteristic, direct product factor, Sylow

100

Q₈

—

101

Q₈

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₉×D₈

yes

—

105

C₂×C₄

C₂×D₄×C₉

yes

characteristic

106

C₈

C₉×SD₁₆

yes

—

107

C₈

C₉×#41

yes

—

108

C₂×C₃

C₃×#486

yes

characteristic

109

C₂×C₃

C₃×#510

yes

—

110

C₂²

C₂×C₉×D₈

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

C₉×#124

yes

characteristic

115

C₄

C₂×C₉×SD₁₆

yes

characteristic

116

C₃

C₃×#2245

yes

characteristic

117

C₂

C₉×#486

yes

characteristic

118

C₂

C₉×#510

yes

—

	subgroup	G/H
center	C₂²×C₉	C₂×D₈
commutator	C₂×C₈	C₂³×C₉
Frattini, cosocle	C₂×C₃×C₈	C₂³×C₃
socle, prime radical	C₂²×C₃	C₂×C₃×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₄²×C₉ ◁ C₄×C₈×C₉ ◁ G

subgroup

G/H

center

C₂²×C₉

C₂×D₈

commutator

C₂×C₈

C₂³×C₉

Frattini, cosocle

C₂×C₃×C₈

C₂³×C₃

socle, prime radical

C₂²×C₃

C₂×C₃×D₈

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₉ ◁ C₄²×C₉ ◁ C₄×C₈×C₉ ◁ G

N	H ≅ G/N	type
28. #2245	C₉	direct (N × H)
99. C₉	#2245	direct (N × H)

H ≅ G/N

type

28. #2245

C₉

direct (N × H)

99. C₉

#2245

direct (N × H)

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

subgroup	index
C₉×#499	2
C₉×#494	2
C₉×#358	2
C₉×#346	2
C₃×#2245	3

subgroup

index

Subgroups — C₉×#2245 #11766966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×#2245 #11766966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2245 #11766966