Group #11766541 — subgroups

Subgroups — C₉×#1820 #11766541

Order 1152.

450 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 156 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×#117	C₂	1	1	yes	maximal, characteristic
2	C₉×#381	C₂	1	2	yes	maximal
3	C₉×#342	C₂	1	4	yes	maximal
4	C₃×#1820	C₃	1	1	yes	maximal, characteristic
5	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
6	C₉×#117	—	2	4	no	—
7	C₂×C₉×C₄⋊C₄	C₄	1	2	yes	complemented
8	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	—
9	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
10	C₂×C₄²×C₉	C₄	1	2	yes	complemented
11	C₉×#95	—	2	4	no	—
12	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic
13	C₃×#381	C₂×C₃	1	2	yes	—
14	C₃×#342	C₂×C₃	1	4	yes	—
15	C₂⁴×C₉	C₂³	1	1	yes	characteristic
16	C₂²×C₄×C₉	—	2	4	no	—
17	C₂²×C₄×C₉	—	2	4	no	—
18	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₉	C₂×C₄	1	4	yes	—
21	C₂²×C₄×C₉	D₄	1	4	yes	—
22	C₉×C₄⋊C₄	—	2	4	no	—
23	C₉×C₂²⋊C₄	—	2	4	no	—
24	C₉×C₂²⋊C₄	—	2	8	no	—
25	C₄²×C₉	—	2	4	no	—
26	#1820	C₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
28	C₃×#117	—	2	4	no	—
29	C₂×C₃×C₄⋊C₄	C₃×C₄	1	2	yes	—
30	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
31	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
32	C₂×C₃×C₄²	C₃×C₄	1	2	yes	—
33	C₃×#95	—	2	4	no	—
34	C₂³×C₉	—	4	2	no	—
35	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
36	C₂³×C₉	C₂×D₄	1	2	yes	—
37	C₂³×C₉	#41	1	4	yes	—
38	C₂×C₄×C₉	—	2	2	no	—
39	C₂×C₄×C₉	—	2	2	no	—
40	C₂×C₄×C₉	—	2	8	no	—
41	C₂×C₄×C₉	—	2	4	no	—
42	C₂×C₄×C₉	—	4	4	no	—
43	C₂×C₄×C₉	—	4	8	no	—
44	C₂×C₄×C₉	—	4	4	no	—
45	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
46	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
47	C₂×#117	C₂×C₉	1	1	yes	characteristic
48	#381	C₂×C₉	1	2	yes	—
49	#342	C₂×C₉	1	4	yes	—
50	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
51	C₂²×C₃×C₄	—	2	4	no	—
52	C₂²×C₃×C₄	—	2	4	no	—
53	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
54	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
55	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
56	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
57	C₃×C₄⋊C₄	—	2	4	no	—
58	C₃×C₂²⋊C₄	—	2	4	no	—
59	C₃×C₂²⋊C₄	—	2	8	no	—
60	C₃×C₄²	—	2	4	no	—
61	C₂²×C₉	—	2	2	no	—
62	C₂²×C₉	—	2	4	no	—
63	C₂²×C₉	—	4	4	no	—
64	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₉	#117	1	2	yes	—
66	C₂²×C₉	#123	1	4	yes	—
67	C₄×C₉	—	2	2	no	—
68	C₄×C₉	—	2	2	no	—
69	C₄×C₉	—	4	4	no	—
70	C₄×C₉	—	8	4	no	—
71	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
72	#117	—	2	4	no	—
73	C₂×C₄⋊C₄	C₄×C₉	1	2	yes	complemented
74	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	—
75	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
76	C₂×C₄²	C₄×C₉	1	2	yes	complemented
77	#95	—	2	4	no	—
78	C₂³×C₃	—	4	2	no	—
79	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
80	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
81	C₂³×C₃	C₃×#41	1	4	yes	—
82	C₂×C₃×C₄	—	2	2	no	—
83	C₂×C₃×C₄	—	2	2	no	—
84	C₂×C₃×C₄	—	2	8	no	—
85	C₂×C₃×C₄	—	2	4	no	—
86	C₂×C₃×C₄	—	4	4	no	—
87	C₂×C₃×C₄	—	4	8	no	—
88	C₂×C₃×C₄	—	4	4	no	—
89	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
90	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
91	C₂×C₉	—	2	4	no	—
92	C₂×C₉	—	2	2	no	—
93	C₂×C₉	#381	1	1	yes	characteristic
94	C₂×C₉	#410	1	2	yes	—
95	C₂⁴	C₂³×C₉	1	1	yes	characteristic
96	C₂²×C₄	—	2	4	no	—
97	C₂²×C₄	—	2	4	no	—
98	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
99	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
100	C₂²×C₄	C₂×C₄×C₉	1	4	yes	—
101	C₂²×C₄	D₄×C₉	1	4	yes	—
102	C₄⋊C₄	—	2	4	no	—
103	C₂²⋊C₄	—	2	4	no	—
104	C₂²⋊C₄	—	2	8	no	—
105	C₄²	—	2	4	no	—
106	C₂²×C₃	—	2	2	no	—
107	C₂²×C₃	—	2	4	no	—
108	C₂²×C₃	—	4	4	no	—
109	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₃	C₃×#117	1	2	yes	—
111	C₂²×C₃	C₃×#123	1	4	yes	—
112	C₃×C₄	—	2	2	no	—
113	C₃×C₄	—	2	2	no	—
114	C₃×C₄	—	4	4	no	—
115	C₃×C₄	—	8	4	no	—
116	C₉	#1820	1	1	yes	characteristic, direct product factor, Sylow
117	C₂³	—	4	2	no	—
118	C₂³	C₂²×C₄×C₉	1	1	yes	characteristic
119	C₂³	C₂×D₄×C₉	1	2	yes	—
120	C₂³	C₉×#41	1	4	yes	—
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	—	2	8	no	—
124	C₂×C₄	—	2	4	no	—
125	C₂×C₄	—	4	4	no	—
126	C₂×C₄	—	4	8	no	—
127	C₂×C₄	—	4	4	no	—
128	C₂×C₄	C₉×C₂²⋊C₄	1	2	yes	—
129	C₂×C₄	C₉×C₂²⋊C₄	1	2	yes	—
130	C₂×C₃	—	2	4	no	—
131	C₂×C₃	—	2	2	no	—
132	C₂×C₃	C₃×#381	1	1	yes	characteristic
133	C₂×C₃	C₃×#410	1	2	yes	—
134	C₂²	—	2	2	no	—
135	C₂²	—	2	4	no	—
136	C₂²	—	4	4	no	—
137	C₂²	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
138	C₂²	C₉×#117	1	2	yes	—
139	C₂²	C₉×#123	1	4	yes	—
140	C₄	—	2	2	no	—
141	C₄	—	2	2	no	—
142	C₄	—	4	4	no	—
143	C₄	—	8	4	no	—
144	C₃	C₃×#1820	1	1	yes	characteristic
145	C₂	—	2	4	no	—
146	C₂	—	2	2	no	—
147	C₂	C₉×#381	1	1	yes	characteristic
148	C₂	C₉×#410	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₉×#117

C₂

yes

maximal, characteristic

C₉×#381

C₂

yes

maximal

C₉×#342

C₂

yes

maximal

C₃×#1820

C₃

yes

maximal, characteristic

C₂³×C₄×C₉

C₂²

yes

characteristic

C₉×#117

—

C₂×C₉×C₄⋊C₄

C₄

yes

complemented

C₂×C₉×C₂²⋊C₄

C₂²

yes

—

C₂×C₉×C₂²⋊C₄

C₂²

yes

—

C₂×C₄²×C₉

C₄

yes

complemented

C₉×#95

—

C₂×C₃×#117

C₂×C₃

yes

characteristic

C₃×#381

C₂×C₃

yes

—

C₃×#342

C₂×C₃

yes

—

C₂⁴×C₉

C₂³

yes

characteristic

C₂²×C₄×C₉

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₉

C₂×C₄

yes

—

C₂²×C₄×C₉

D₄

yes

—

C₉×C₄⋊C₄

—

C₉×C₂²⋊C₄

—

C₉×C₂²⋊C₄

—

C₄²×C₉

—

#1820

C₉

yes

characteristic, direct product factor, Sylow

C₂³×C₃×C₄

C₂²×C₃

yes

characteristic

C₃×#117

—

C₂×C₃×C₄⋊C₄

C₃×C₄

yes

—

C₂×C₃×C₂²⋊C₄

C₂²×C₃

yes

—

C₂×C₃×C₂²⋊C₄

C₂²×C₃

yes

—

C₂×C₃×C₄²

C₃×C₄

yes

—

C₃×#95

—

C₂³×C₉

—

C₂³×C₉

C₂²×C₄

yes

characteristic

C₂³×C₉

C₂×D₄

yes

—

C₂³×C₉

#41

yes

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂²⋊C₄

yes

—

C₂×C₄×C₉

C₂²⋊C₄

yes

—

C₂×#117

C₂×C₉

yes

characteristic

#381

C₂×C₉

yes

—

#342

C₂×C₉

yes

—

C₂⁴×C₃

C₂³×C₃

yes

characteristic

C₂²×C₃×C₄

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

C₂×C₃×C₄

yes

characteristic

C₂²×C₃×C₄

C₂×C₃×C₄

yes

characteristic

C₂²×C₃×C₄

C₂×C₃×C₄

yes

—

C₂²×C₃×C₄

C₃×D₄

yes

—

C₃×C₄⋊C₄

—

C₃×C₂²⋊C₄

—

C₃×C₂²⋊C₄

—

C₃×C₄²

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₉

#117

yes

—

C₂²×C₉

#123

yes

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

—

C₂³×C₄

C₂²×C₉

yes

characteristic

#117

—

C₂×C₄⋊C₄

C₄×C₉

yes

complemented

C₂×C₂²⋊C₄

C₂²×C₉

yes

—

C₂×C₂²⋊C₄

C₂²×C₉

yes

—

C₂×C₄²

C₄×C₉

yes

complemented

#95

—

C₂³×C₃

—

C₂³×C₃

C₂²×C₃×C₄

yes

characteristic

C₂³×C₃

C₂×C₃×D₄

yes

—

C₂³×C₃

C₃×#41

yes

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₃×C₂²⋊C₄

yes

—

C₂×C₃×C₄

C₃×C₂²⋊C₄

yes

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

#381

yes

characteristic

C₂×C₉

#410

yes

—

C₂⁴

C₂³×C₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₄×C₉

yes

characteristic

C₂²×C₄

C₂×C₄×C₉

yes

characteristic

100

C₂²×C₄

C₂×C₄×C₉

yes

—

101

C₂²×C₄

D₄×C₉

yes

—

102

C₄⋊C₄

—

103

C₂²⋊C₄

—

104

C₂²⋊C₄

—

105

C₄²

—

106

C₂²×C₃

—

107

C₂²×C₃

—

108

C₂²×C₃

—

109

C₂²×C₃

C₂×C₃×C₂²⋊C₄

yes

characteristic

110

C₂²×C₃

C₃×#117

yes

—

111

C₂²×C₃

C₃×#123

yes

—

112

C₃×C₄

—

113

C₃×C₄

—

114

C₃×C₄

—

115

C₃×C₄

—

116

C₉

#1820

yes

characteristic, direct product factor, Sylow

117

C₂³

—

118

C₂³

C₂²×C₄×C₉

yes

characteristic

119

C₂³

C₂×D₄×C₉

yes

—

120

C₂³

C₉×#41

yes

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

C₉×C₂²⋊C₄

yes

—

129

C₂×C₄

C₉×C₂²⋊C₄

yes

—

130

C₂×C₃

—

131

C₂×C₃

—

132

C₂×C₃

C₃×#381

yes

characteristic

133

C₂×C₃

C₃×#410

yes

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

C₂×C₉×C₂²⋊C₄

yes

characteristic

138

C₂²

C₉×#117

yes

—

139

C₂²

C₉×#123

yes

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₃

C₃×#1820

yes

characteristic

145

C₂

—

146

C₂

—

147

C₂

C₉×#381

yes

characteristic

148

C₂

C₉×#410

yes

—

	subgroup	G/H
center	C₂²×C₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₄×C₉
Frattini, prime radical, cosocle	C₂⁴×C₃	C₂³×C₃
socle	C₂²×C₃	C₂×C₃×C₂²⋊C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂³×C₄×C₉ ◁ G

subgroup

G/H

center

C₂²×C₉

C₂×C₂²⋊C₄

commutator

C₂³

C₂²×C₄×C₉

Frattini, prime radical, cosocle

C₂⁴×C₃

C₂³×C₃

socle

C₂²×C₃

C₂×C₃×C₂²⋊C₄

LCS

G ▷ C₂³ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₉ ◁ C₂³×C₄×C₉ ◁ G

N	H ≅ G/N	type
7. C₂×C₉×C₄⋊C₄	C₄	semidirect
10. C₂×C₄²×C₉	C₄	semidirect
26. #1820	C₉	direct (N × H)
73. C₂×C₄⋊C₄	C₄×C₉	semidirect
76. C₂×C₄²	C₄×C₉	semidirect
116. C₉	#1820	direct (N × H)

H ≅ G/N

type

7. C₂×C₉×C₄⋊C₄

C₄

semidirect

10. C₂×C₄²×C₉

C₄

semidirect

26. #1820

C₉

direct (N × H)

73. C₂×C₄⋊C₄

C₄×C₉

semidirect

76. C₂×C₄²

C₄×C₉

semidirect

116. C₉

#1820

direct (N × H)

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

subgroup	index
C₂×C₉×#117	2
C₉×#381	2
C₉×#342	2
C₃×#1820	3

subgroup

index

C₂×C₉×#117

C₉×#381

C₉×#342

C₃×#1820

Subgroups — C₉×#1820 #11766541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×#1820 #11766541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1820 #11766541