Group #11766970 — subgroups

Subgroups — C₉×#2249 #11766970

Order 1152.

276 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 108 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	C₂×C₉×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×SD₃₂	C₂	1	2	yes	maximal, complemented
3	C₂×C₉×D₁₆	C₂	1	1	yes	maximal, characteristic
4	C₉×#495	C₂	1	2	yes	maximal, complemented
5	C₄×C₉×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2249	C₃	1	1	yes	maximal, characteristic
7	C₂×C₉×Q₁₆	C₂²	1	2	yes	—
8	C₂×C₉×SD₁₆	—	2	2	no	—
9	C₂×C₉×D₈	C₂²	1	2	yes	—
10	C₉×#124	—	2	2	no	—
11	C₉×Q₃₂	—	2	2	no	—
12	C₉×SD₃₂	—	2	4	no	—
13	C₉×D₁₆	—	2	2	no	—
14	C₂×C₉×C₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₉×C₁₆	C₂²	1	1	yes	characteristic
16	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₃×Q₃₂	C₂×C₃	1	1	yes	characteristic
18	C₂×C₃×SD₃₂	C₂×C₃	1	2	yes	—
19	C₂×C₃×D₁₆	C₂×C₃	1	1	yes	characteristic
20	C₃×#495	C₂×C₃	1	2	yes	—
21	C₃×C₄×C₁₆	C₂×C₃	1	1	yes	characteristic
22	C₂×Q₈×C₉	—	2	2	no	—
23	C₂×D₄×C₉	—	2	2	no	—
24	C₉×Q₁₆	—	2	2	no	—
25	C₉×Q₁₆	—	2	2	no	—
26	C₉×SD₁₆	—	4	4	no	—
27	C₉×D₈	—	2	2	no	—
28	C₉×D₈	—	2	2	no	—
29	C₂×C₈×C₉	D₄	1	1	yes	characteristic
30	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
31	C₉×C₂²⋊C₄	—	4	4	no	—
32	C₄²×C₉	D₄	1	1	yes	characteristic
33	C₉×C₁₆	D₄	1	2	yes	—
34	C₉×C₁₆	D₄	1	2	yes	—
35	#2249	C₉	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₃×Q₁₆	C₂²×C₃	1	2	yes	—
37	C₂×C₃×SD₁₆	—	2	2	no	—
38	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
39	C₃×#124	—	2	2	no	—
40	C₃×Q₃₂	—	2	2	no	—
41	C₃×SD₃₂	—	2	4	no	—
42	C₃×D₁₆	—	2	2	no	—
43	C₂×C₃×C₁₆	C₂²×C₃	1	1	yes	characteristic
44	C₂×C₃×C₁₆	C₂²×C₃	1	1	yes	characteristic
45	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
46	C₂³×C₉	—	4	2	no	—
47	Q₈×C₉	—	4	2	no	—
48	Q₈×C₉	—	4	2	no	—
49	D₄×C₉	—	4	2	no	—
50	D₄×C₉	—	4	2	no	—
51	C₂×C₄×C₉	—	4	2	no	—
52	C₂×C₄×C₉	D₈	1	2	yes	—
53	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
54	C₈×C₉	D₈	1	2	yes	—
55	C₈×C₉	C₂×D₄	1	1	yes	characteristic
56	C₈×C₉	C₂×D₄	1	1	yes	characteristic
57	C₂×Q₃₂	C₂×C₉	1	1	yes	characteristic, complemented
58	C₂×SD₃₂	C₂×C₉	1	2	yes	complemented
59	C₂×D₁₆	C₂×C₉	1	1	yes	characteristic
60	#495	C₂×C₉	1	2	yes	complemented
61	C₄×C₁₆	C₂×C₉	1	1	yes	characteristic, complemented
62	C₂×C₃×Q₈	—	2	2	no	—
63	C₂×C₃×D₄	—	2	2	no	—
64	C₃×Q₁₆	—	2	2	no	—
65	C₃×Q₁₆	—	2	2	no	—
66	C₃×SD₁₆	—	4	4	no	—
67	C₃×D₈	—	2	2	no	—
68	C₃×D₈	—	2	2	no	—
69	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
70	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
71	C₃×C₂²⋊C₄	—	4	4	no	—
72	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
73	C₃×C₁₆	C₃×D₄	1	2	yes	—
74	C₃×C₁₆	C₃×D₄	1	2	yes	—
75	C₂²×C₉	—	8	2	no	—
76	C₂²×C₉	—	8	4	no	—
77	C₂²×C₉	C₂×D₈	1	1	yes	characteristic
78	C₄×C₉	—	2	2	no	—
79	C₄×C₉	—	8	2	no	—
80	C₄×C₉	#127	1	1	yes	characteristic
81	C₄×C₉	C₂×D₈	1	1	yes	characteristic
82	C₂×Q₁₆	C₂²×C₉	1	2	yes	—
83	C₂×SD₁₆	—	2	2	no	—
84	C₂×D₈	C₂²×C₉	1	2	yes	—
85	#124	—	2	2	no	—
86	Q₃₂	—	2	2	no	—
87	SD₃₂	—	2	4	no	—
88	D₁₆	—	2	2	no	—
89	C₂×C₁₆	C₂²×C₉	1	1	yes	characteristic
90	C₂×C₁₆	C₂²×C₉	1	1	yes	characteristic
91	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
92	C₂³×C₃	—	4	2	no	—
93	C₃×Q₈	—	4	2	no	—
94	C₃×Q₈	—	4	2	no	—
95	C₃×D₄	—	4	2	no	—
96	C₃×D₄	—	4	2	no	—
97	C₂×C₃×C₄	—	4	2	no	—
98	C₂×C₃×C₄	C₃×D₈	1	2	yes	—
99	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
100	C₃×C₈	C₃×D₈	1	2	yes	—
101	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
102	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
103	C₂×C₉	—	16	2	no	—
104	C₂×C₉	#493	1	1	yes	characteristic
105	C₂×C₉	#508	1	2	yes	—
106	C₂×Q₈	—	2	2	no	—
107	C₂×D₄	—	2	2	no	—
108	Q₁₆	—	2	2	no	—
109	Q₁₆	—	2	2	no	—
110	SD₁₆	—	4	4	no	—
111	D₈	—	2	2	no	—
112	D₈	—	2	2	no	—
113	C₂×C₈	D₄×C₉	1	1	yes	characteristic
114	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
115	C₂²⋊C₄	—	4	4	no	—
116	C₄²	D₄×C₉	1	1	yes	characteristic
117	C₁₆	D₄×C₉	1	2	yes	—
118	C₁₆	D₄×C₉	1	2	yes	—
119	C₂²×C₃	—	8	4	no	—
120	C₂²×C₃	—	8	2	no	—
121	C₂²×C₃	C₂×C₃×D₈	1	1	yes	characteristic
122	C₃×C₄	—	2	2	no	—
123	C₃×C₄	—	8	2	no	—
124	C₃×C₄	C₃×#127	1	1	yes	characteristic
125	C₃×C₄	C₂×C₃×D₈	1	1	yes	characteristic
126	C₉	#2249	1	1	yes	characteristic, direct product factor, Sylow
127	C₂³	—	4	2	no	—
128	Q₈	—	4	2	no	—
129	Q₈	—	4	2	no	—
130	D₄	—	4	2	no	—
131	D₄	—	4	2	no	—
132	C₂×C₄	—	4	2	no	—
133	C₂×C₄	C₉×D₈	1	2	yes	—
134	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
135	C₈	C₉×D₈	1	2	yes	—
136	C₈	C₂×D₄×C₉	1	1	yes	characteristic
137	C₈	C₂×D₄×C₉	1	1	yes	characteristic
138	C₂×C₃	—	16	2	no	—
139	C₂×C₃	C₃×#493	1	1	yes	characteristic
140	C₂×C₃	C₃×#508	1	2	yes	—
141	C₂²	—	8	2	no	—
142	C₂²	—	8	4	no	—
143	C₂²	C₂×C₉×D₈	1	1	yes	characteristic
144	C₄	—	2	2	no	—
145	C₄	—	8	2	no	—
146	C₄	C₉×#127	1	1	yes	characteristic
147	C₄	C₂×C₉×D₈	1	1	yes	characteristic
148	C₃	C₃×#2249	1	1	yes	characteristic
149	C₂	—	16	2	no	—
150	C₂	C₉×#493	1	1	yes	characteristic
151	C₂	C₉×#508	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₉×Q₃₂

C₂

yes

maximal, characteristic, complemented

C₂×C₉×SD₃₂

C₂

yes

maximal, complemented

C₂×C₉×D₁₆

C₂

yes

maximal, characteristic

C₉×#495

C₂

yes

maximal, complemented

C₄×C₉×C₁₆

C₂

yes

maximal, characteristic, complemented

C₃×#2249

C₃

yes

maximal, characteristic

C₂×C₉×Q₁₆

C₂²

yes

—

C₂×C₉×SD₁₆

—

C₂×C₉×D₈

C₂²

yes

—

C₉×#124

—

C₉×Q₃₂

—

C₉×SD₃₂

—

C₉×D₁₆

—

C₂×C₉×C₁₆

C₂²

yes

characteristic

C₂×C₉×C₁₆

C₂²

yes

characteristic

C₄×C₈×C₉

C₂²

yes

characteristic

C₂×C₃×Q₃₂

C₂×C₃

yes

characteristic

C₂×C₃×SD₃₂

C₂×C₃

yes

—

C₂×C₃×D₁₆

C₂×C₃

yes

characteristic

C₃×#495

C₂×C₃

yes

—

C₃×C₄×C₁₆

C₂×C₃

yes

characteristic

C₂×Q₈×C₉

—

C₂×D₄×C₉

—

C₉×Q₁₆

—

C₉×Q₁₆

—

C₉×SD₁₆

—

C₉×D₈

—

C₉×D₈

—

C₂×C₈×C₉

D₄

yes

characteristic

C₂×C₈×C₉

C₂³

yes

characteristic

C₉×C₂²⋊C₄

—

C₄²×C₉

D₄

yes

characteristic

C₉×C₁₆

D₄

yes

—

C₉×C₁₆

D₄

yes

—

#2249

C₉

yes

characteristic, direct product factor, Sylow

C₂×C₃×Q₁₆

C₂²×C₃

yes

—

C₂×C₃×SD₁₆

—

C₂×C₃×D₈

C₂²×C₃

yes

—

C₃×#124

—

C₃×Q₃₂

—

C₃×SD₃₂

—

C₃×D₁₆

—

C₂×C₃×C₁₆

C₂²×C₃

yes

characteristic

C₂×C₃×C₁₆

C₂²×C₃

yes

characteristic

C₃×C₄×C₈

C₂²×C₃

yes

characteristic

C₂³×C₉

—

Q₈×C₉

—

Q₈×C₉

—

D₄×C₉

—

D₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

D₈

yes

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₈×C₉

D₈

yes

—

C₈×C₉

C₂×D₄

yes

characteristic

C₈×C₉

C₂×D₄

yes

characteristic

C₂×Q₃₂

C₂×C₉

yes

characteristic, complemented

C₂×SD₃₂

C₂×C₉

yes

complemented

C₂×D₁₆

C₂×C₉

yes

characteristic

#495

C₂×C₉

yes

complemented

C₄×C₁₆

C₂×C₉

yes

characteristic, complemented

C₂×C₃×Q₈

—

C₂×C₃×D₄

—

C₃×Q₁₆

—

C₃×Q₁₆

—

C₃×SD₁₆

—

C₃×D₈

—

C₃×D₈

—

C₂×C₃×C₈

C₃×D₄

yes

characteristic

C₂×C₃×C₈

C₂³×C₃

yes

characteristic

C₃×C₂²⋊C₄

—

C₃×C₄²

C₃×D₄

yes

characteristic

C₃×C₁₆

C₃×D₄

yes

—

C₃×C₁₆

C₃×D₄

yes

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

C₂×D₈

yes

characteristic

C₄×C₉

—

C₄×C₉

—

C₄×C₉

#127

yes

characteristic

C₄×C₉

C₂×D₈

yes

characteristic

C₂×Q₁₆

C₂²×C₉

yes

—

C₂×SD₁₆

—

C₂×D₈

C₂²×C₉

yes

—

#124

—

Q₃₂

—

SD₃₂

—

D₁₆

—

C₂×C₁₆

C₂²×C₉

yes

characteristic

C₂×C₁₆

C₂²×C₉

yes

characteristic

C₄×C₈

C₂²×C₉

yes

characteristic

C₂³×C₃

—

C₃×Q₈

—

C₃×Q₈

—

C₃×D₄

—

C₃×D₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₃×D₈

yes

—

C₂×C₃×C₄

C₂×C₃×D₄

yes

characteristic

100

C₃×C₈

C₃×D₈

yes

—

101

C₃×C₈

C₂×C₃×D₄

yes

characteristic

102

C₃×C₈

C₂×C₃×D₄

yes

characteristic

103

C₂×C₉

—

104

C₂×C₉

#493

yes

characteristic

105

C₂×C₉

#508

yes

—

106

C₂×Q₈

—

107

C₂×D₄

—

108

Q₁₆

—

109

Q₁₆

—

110

SD₁₆

—

111

D₈

—

112

D₈

—

113

C₂×C₈

D₄×C₉

yes

characteristic

114

C₂×C₈

C₂³×C₉

yes

characteristic

115

C₂²⋊C₄

—

116

C₄²

D₄×C₉

yes

characteristic

117

C₁₆

D₄×C₉

yes

—

118

C₁₆

D₄×C₉

yes

—

119

C₂²×C₃

—

120

C₂²×C₃

—

121

C₂²×C₃

C₂×C₃×D₈

yes

characteristic

122

C₃×C₄

—

123

C₃×C₄

—

124

C₃×C₄

C₃×#127

yes

characteristic

125

C₃×C₄

C₂×C₃×D₈

yes

characteristic

126

C₉

#2249

yes

characteristic, direct product factor, Sylow

127

C₂³

—

128

Q₈

—

129

Q₈

—

130

D₄

—

131

D₄

—

132

C₂×C₄

—

133

C₂×C₄

C₉×D₈

yes

—

134

C₂×C₄

C₂×D₄×C₉

yes

characteristic

135

C₈

C₉×D₈

yes

—

136

C₈

C₂×D₄×C₉

yes

characteristic

137

C₈

C₂×D₄×C₉

yes

characteristic

138

C₂×C₃

—

139

C₂×C₃

C₃×#493

yes

characteristic

140

C₂×C₃

C₃×#508

yes

—

141

C₂²

—

142

C₂²

—

143

C₂²

C₂×C₉×D₈

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

C₉×#127

yes

characteristic

147

C₄

C₂×C₉×D₈

yes

characteristic

148

C₃

C₃×#2249

yes

characteristic

149

C₂

—

150

C₂

C₉×#493

yes

characteristic

151

C₂

C₉×#508

yes

—

	subgroup	G/H
center	C₂²×C₉	C₂×D₈
commutator	C₂×C₈	C₂³×C₉
Frattini, cosocle	C₂×C₃×C₈	C₂³×C₃
socle	C₂²×C₃	C₂×C₃×D₈
prime radical	C₂×C₃×D₁₆	C₂×C₃
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

C₂²×C₃

C₂×C₃×D₈

prime radical

C₂×C₃×D₁₆

C₂×C₃

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₉ ◁ C₄²×C₉ ◁ C₄×C₈×C₉ ◁ G

N	H ≅ G/N	type
1. C₂×C₉×Q₃₂	C₂	semidirect
2. C₂×C₉×SD₃₂	C₂	semidirect
4. C₉×#495	C₂	semidirect
5. C₄×C₉×C₁₆	C₂	semidirect
35. #2249	C₉	direct (N × H)
57. C₂×Q₃₂	C₂×C₉	semidirect
58. C₂×SD₃₂	C₂×C₉	semidirect
60. #495	C₂×C₉	semidirect
61. C₄×C₁₆	C₂×C₉	semidirect
126. C₉	#2249	direct (N × H)

H ≅ G/N

type

1. C₂×C₉×Q₃₂

C₂

semidirect

2. C₂×C₉×SD₃₂

C₂

semidirect

4. C₉×#495

C₂

semidirect

5. C₄×C₉×C₁₆

C₂

semidirect

35. #2249

C₉

direct (N × H)

57. C₂×Q₃₂

C₂×C₉

semidirect

58. C₂×SD₃₂

C₂×C₉

semidirect

60. #495

C₂×C₉

semidirect

61. C₄×C₁₆

C₂×C₉

semidirect

126. C₉

#2249

direct (N × H)

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

subgroup	index
C₂×C₉×Q₃₂	2
C₂×C₉×SD₃₂	2
C₂×C₉×D₁₆	2
C₉×#495	2
C₄×C₉×C₁₆	2
C₃×#2249	3

subgroup

index

C₂×C₉×Q₃₂

C₂×C₉×SD₃₂

C₂×C₉×D₁₆

C₉×#495

C₄×C₉×C₁₆

C₃×#2249

Subgroups — C₉×#2249 #11766970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×#2249 #11766970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2249 #11766970