Group #11786188 — subgroups

Subgroups — #11786188

Order 1152.

384 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 158 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×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₉⋊C₈	C₂	1	4	yes	maximal
3	#10588612	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊(C₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
5	#70446	—	3	1	no	maximal
6	C₂²×C₈×C₉	C₂²	1	2	yes	—
7	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₉	C₂²	1	2	yes	—
9	C₂²×C₉⋊C₈	C₂²	1	2	yes	—
10	C₉×C₄⋊C₈	—	2	2	no	—
11	C₉⋊#95	C₄	1	2	yes	—
12	C₉⋊#95	C₄	1	2	yes	—
13	Dic₉⋊C₈	—	2	8	no	—
14	C₄⋊(C₉⋊C₈)	—	2	2	no	—
15	C₂×C₃×C₄⋊C₈	D₃	1	1	yes	characteristic
16	C₂×Dic₃⋊C₈	—	3	4	no	—
17	#4932	—	3	1	no	—
18	C₂×C₄⋊(C₃⋊C₈)	—	3	1	no	—
19	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
22	C₂²×Dic₉	C₂×C₄	1	4	yes	—
23	C₂×C₈×C₉	—	2	4	no	—
24	C₂×C₈×C₉	—	2	2	no	—
25	C₄²×C₉	D₄	1	2	yes	—
26	C₄²×C₉	Q₈	1	2	yes	—
27	C₄×Dic₉	D₄	1	4	yes	—
28	C₄×Dic₉	Q₈	1	4	yes	—
29	C₂×C₉⋊C₈	—	2	2	no	—
30	C₂×C₉⋊C₈	—	2	4	no	—
31	#1843	—	9	1	no	Sylow
32	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
33	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
34	C₂×C₄×Dic₃	—	3	2	no	—
35	C₂²×C₃⋊C₈	—	3	2	no	—
36	C₃×C₄⋊C₈	—	2	2	no	—
37	C₃⋊#95	—	3	2	no	—
38	C₃⋊#95	—	3	2	no	—
39	Dic₃⋊C₈	—	6	8	no	—
40	C₄⋊(C₃⋊C₈)	—	6	2	no	—
41	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₄×C₉	—	2	2	no	—
43	C₂×C₄×C₉	—	2	2	no	—
44	C₂×C₄×C₉	C₄⋊C₄	1	2	yes	—
45	C₂×C₄×C₉	C₄⋊C₄	1	2	yes	—
46	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₉	C₂×Q₈	1	1	yes	characteristic
49	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
50	C₂×Dic₉	—	2	4	no	—
51	C₂×Dic₉	—	2	4	no	—
52	C₂×Dic₉	C₄⋊C₄	1	8	yes	—
53	C₈×C₉	—	4	2	no	—
54	C₉⋊C₈	—	4	2	no	—
55	C₂×C₄⋊C₈	—	9	4	no	—
56	C₂×C₄⋊C₈	—	9	1	no	—
57	C₂×C₄⋊C₈	D₉	1	1	yes	characteristic
58	#376	—	9	1	no	—
59	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
60	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
61	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
62	C₂²×Dic₃	—	3	4	no	—
63	C₂×C₃×C₈	—	2	4	no	—
64	C₂×C₃×C₈	—	2	2	no	—
65	C₃×C₄²	Dic₆	1	2	yes	—
66	C₃×C₄²	#67	1	2	yes	—
67	C₄×Dic₃	—	3	4	no	—
68	C₄×Dic₃	—	3	4	no	—
69	C₂×C₃⋊C₈	—	6	4	no	—
70	C₂×C₃⋊C₈	—	6	2	no	—
71	C₂²×C₉	C₂×C₄⋊C₄	1	2	yes	—
72	C₂²×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₉	#131	1	2	yes	—
74	C₂²×C₉	#131	1	2	yes	—
75	C₄×C₉	—	2	2	no	—
76	C₄×C₉	—	2	2	no	—
77	C₄×C₉	#127	1	1	yes	characteristic
78	C₄×C₉	C₄⋊Q₈	1	2	yes	—
79	C₄×C₉	C₄⋊Q₈	1	1	yes	characteristic
80	Dic₉	—	2	8	no	—
81	C₂²×C₈	—	9	2	no	—
82	C₂²×C₈	C₂×D₉	1	2	yes	—
83	C₂×C₄²	—	9	2	no	—
84	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
85	C₄⋊C₈	—	2	2	no	—
86	C₄⋊C₈	—	18	8	no	—
87	C₄⋊C₈	—	18	2	no	—
88	#95	—	9	2	no	—
89	#95	—	9	2	no	—
90	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
91	C₂×C₃×C₄	—	2	2	no	—
92	C₂×C₃×C₄	—	2	2	no	—
93	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
94	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
95	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
96	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
97	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
98	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
99	C₂×Dic₃	—	3	8	no	—
100	C₂×Dic₃	—	6	4	no	—
101	C₂×Dic₃	—	6	4	no	—
102	C₃×C₈	—	4	2	no	—
103	C₃⋊C₈	—	12	2	no	—
104	C₂×C₉	#384	1	1	yes	characteristic
105	C₂×C₉	#424	1	4	yes	—
106	C₂×C₉	#424	1	1	yes	characteristic
107	C₂×C₉	#424	1	1	yes	characteristic
108	C₂²×C₄	—	9	4	no	—
109	C₂²×C₄	C₄×D₉	1	1	yes	characteristic
110	C₂²×C₄	C₄×D₉	1	1	yes	characteristic
111	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
112	C₂×C₈	—	2	4	no	—
113	C₂×C₈	—	2	2	no	—
114	C₂×C₈	—	18	4	no	—
115	C₂×C₈	—	18	2	no	—
116	C₄²	—	9	4	no	—
117	C₄²	—	9	4	no	—
118	C₄²	Dic₁₈	1	2	yes	—
119	C₄²	#611	1	2	yes	—
120	C₂²×C₃	D₃×C₄⋊C₄	1	2	yes	—
121	C₂²×C₃	#901	1	2	yes	—
122	C₂²×C₃	#907	1	2	yes	—
123	C₂²×C₃	C₂×Dic₃⋊C₄	1	1	yes	characteristic
124	C₃×C₄	—	2	2	no	—
125	C₃×C₄	—	2	2	no	—
126	C₃×C₄	#888	1	2	yes	—
127	C₃×C₄	#940	1	1	yes	characteristic
128	C₃×C₄	#944	1	1	yes	characteristic
129	Dic₃	—	6	8	no	—
130	C₉	#1843	1	1	yes	characteristic, complemented, Sylow
131	C₂³	C₂×C₄×D₉	1	1	yes	characteristic
132	C₂×C₄	—	2	2	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	9	8	no	—
135	C₂×C₄	—	18	4	no	—
136	C₂×C₄	—	18	4	no	—
137	C₂×C₄	Dic₉⋊C₄	1	2	yes	—
138	C₂×C₄	Dic₉⋊C₄	1	2	yes	—
139	C₂×C₄	C₂×Dic₁₈	1	1	yes	characteristic
140	C₂×C₄	D₄×D₉	1	2	yes	—
141	C₂×C₄	Q₈×D₉	1	2	yes	—
142	C₂×C₄	C₂×#611	1	1	yes	characteristic
143	C₈	—	4	2	no	—
144	C₈	—	36	2	no	—
145	C₂×C₃	#4839	1	4	yes	—
146	C₂×C₃	#4975	1	1	yes	characteristic
147	C₂×C₃	#5102	1	1	yes	characteristic
148	C₂×C₃	#5119	1	1	yes	characteristic
149	C₂²	C₄⋊C₄×D₉	1	2	yes	—
150	C₂²	#63464	1	2	yes	—
151	C₂²	#63469	1	2	yes	—
152	C₂²	C₂×Dic₉⋊C₄	1	1	yes	characteristic
153	C₄	—	2	2	no	—
154	C₄	—	2	2	no	—
155	C₄	—	18	8	no	—
156	C₄	#63450	1	2	yes	—
157	C₄	#63502	1	1	yes	characteristic
158	C₄	#63506	1	1	yes	characteristic
159	C₃	#70446	1	1	yes	characteristic
160	C₂	#10588523	1	4	yes	—
161	C₂	#10588655	1	1	yes	characteristic
162	C₂	#10588783	1	1	yes	characteristic
163	C₂	#10588803	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₉×C₄⋊C₈

C₂

yes

maximal, characteristic

C₂×Dic₉⋊C₈

C₂

yes

maximal

#10588612

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₉⋊C₈)

C₂

yes

maximal, characteristic

#70446

—

maximal

C₂²×C₈×C₉

C₂²

yes

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₂×C₄×Dic₉

C₂²

yes

—

C₂²×C₉⋊C₈

C₂²

yes

—

C₉×C₄⋊C₈

—

C₉⋊#95

C₄

yes

—

C₉⋊#95

C₄

yes

—

Dic₉⋊C₈

—

C₄⋊(C₉⋊C₈)

—

C₂×C₃×C₄⋊C₈

D₃

yes

characteristic

C₂×Dic₃⋊C₈

—

#4932

—

C₂×C₄⋊(C₃⋊C₈)

—

C₂²×C₄×C₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂²×Dic₉

C₂×C₄

yes

—

C₂×C₈×C₉

—

C₂×C₈×C₉

—

C₄²×C₉

D₄

yes

—

C₄²×C₉

Q₈

yes

—

C₄×Dic₉

D₄

yes

—

C₄×Dic₉

Q₈

yes

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

—

#1843

—

Sylow

C₂²×C₃×C₈

C₂×D₃

yes

—

C₂×C₃×C₄²

C₂×D₃

yes

characteristic

C₂×C₄×Dic₃

—

C₂²×C₃⋊C₈

—

C₃×C₄⋊C₈

—

C₃⋊#95

—

C₃⋊#95

—

Dic₃⋊C₈

—

C₄⋊(C₃⋊C₈)

—

C₂³×C₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₄⋊C₄

yes

—

C₂×C₄×C₉

C₄⋊C₄

yes

—

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₉

C₂×Q₈

yes

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

C₄⋊C₄

yes

—

C₈×C₉

—

C₉⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

D₉

yes

characteristic

#376

—

C₂²×C₃×C₄

C₄×D₃

yes

characteristic

C₂²×C₃×C₄

C₄×D₃

yes

characteristic

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂²×Dic₃

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₃×C₄²

Dic₆

yes

—

C₃×C₄²

#67

yes

—

C₄×Dic₃

—

C₄×Dic₃

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂²×C₉

C₂×C₄⋊C₄

yes

—

C₂²×C₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₉

#131

yes

—

C₂²×C₉

#131

yes

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

#127

yes

characteristic

C₄×C₉

C₄⋊Q₈

yes

—

C₄×C₉

C₄⋊Q₈

yes

characteristic

Dic₉

—

C₂²×C₈

—

C₂²×C₈

C₂×D₉

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

#95

—

#95

—

C₂³×C₃

C₂×C₄×D₃

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

Dic₃⋊C₄

yes

—

C₂×C₃×C₄

Dic₃⋊C₄

yes

—

C₂×C₃×C₄

C₂×Dic₆

yes

characteristic

C₂×C₃×C₄

D₃×D₄

yes

—

C₂×C₃×C₄

D₃×Q₈

yes

—

C₂×C₃×C₄

C₂×#67

yes

characteristic

C₂×Dic₃

—

100

C₂×Dic₃

—

101

C₂×Dic₃

—

102

C₃×C₈

—

103

C₃⋊C₈

—

104

C₂×C₉

#384

yes

characteristic

105

C₂×C₉

#424

yes

—

106

C₂×C₉

#424

yes

characteristic

107

C₂×C₉

#424

yes

characteristic

108

C₂²×C₄

—

109

C₂²×C₄

C₄×D₉

yes

characteristic

110

C₂²×C₄

C₄×D₉

yes

characteristic

111

C₂²×C₄

C₂²×D₉

yes

characteristic

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₄²

—

117

C₄²

—

118

C₄²

Dic₁₈

yes

—

119

C₄²

#611

yes

—

120

C₂²×C₃

D₃×C₄⋊C₄

yes

—

121

C₂²×C₃

#901

yes

—

122

C₂²×C₃

#907

yes

—

123

C₂²×C₃

C₂×Dic₃⋊C₄

yes

characteristic

124

C₃×C₄

—

125

C₃×C₄

—

126

C₃×C₄

#888

yes

—

127

C₃×C₄

#940

yes

characteristic

128

C₃×C₄

#944

yes

characteristic

129

Dic₃

—

130

C₉

#1843

yes

characteristic, complemented, Sylow

131

C₂³

C₂×C₄×D₉

yes

characteristic

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

Dic₉⋊C₄

yes

—

138

C₂×C₄

Dic₉⋊C₄

yes

—

139

C₂×C₄

C₂×Dic₁₈

yes

characteristic

140

C₂×C₄

D₄×D₉

yes

—

141

C₂×C₄

Q₈×D₉

yes

—

142

C₂×C₄

C₂×#611

yes

characteristic

143

C₈

—

144

C₈

—

145

C₂×C₃

#4839

yes

—

146

C₂×C₃

#4975

yes

characteristic

147

C₂×C₃

#5102

yes

characteristic

148

C₂×C₃

#5119

yes

characteristic

149

C₂²

C₄⋊C₄×D₉

yes

—

150

C₂²

#63464

yes

—

151

C₂²

#63469

yes

—

152

C₂²

C₂×Dic₉⋊C₄

yes

characteristic

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

#63450

yes

—

157

C₄

#63502

yes

characteristic

158

C₄

#63506

yes

characteristic

159

C₃

#70446

yes

characteristic

160

C₂

#10588523

yes

—

161

C₂

#10588655

yes

characteristic

162

C₂

#10588783

yes

characteristic

163

C₂

#10588803

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₉
commutator	C₂³×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₂×C₉×C₄⋊C₈	C₂
socle, prime radical	C₂³×C₃	C₂×C₄×D₃
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	C₂×C₄⋊C₈	D₉
hypocenter	C₉	#1843
LCS	G ▷ C₂³×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

subgroup

G/H

center

C₂²×C₄

C₂²×D₉

commutator

C₂³×C₉

C₂²×C₄

Frattini

C₂²×C₃×C₄

C₂²×D₃

Fitting

C₂×C₉×C₄⋊C₈

C₂

socle, prime radical

C₂³×C₃

C₂×C₄×D₃

cosocle

C₂²×C₄×C₉

C₂³

hypercenter

C₂×C₄⋊C₈

D₉

C₉

G ▷ C₂³×C₉ ▷ C₉

C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
130. C₉	#1843	semidirect

H ≅ G/N

type

130. C₉

#1843

semidirect

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

subgroup	index
C₂×C₉×C₄⋊C₈	2
C₂×Dic₉⋊C₈	2
#10588612	2
C₂×C₄⋊(C₉⋊C₈)	2
#70446	3

subgroup

index

C₂×C₉×C₄⋊C₈

C₂×Dic₉⋊C₈

#10588612

C₂×C₄⋊(C₉⋊C₈)

#70446

Subgroups — #11786188

Conjugacy classes of subgroups

Complements

Maximal subgroups