Group #11795297 — subgroups

Subgroups — #11795297

Order 1152.

264 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 100 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	#10588805	C₂	1	2	yes	maximal
2	C₂×#63378	C₂	1	1	yes	maximal, characteristic
3	#10588783	C₂	1	1	yes	maximal, characteristic
4	C₉×#341	C₂	1	1	yes	maximal, characteristic
5	#10588234	C₂	1	2	yes	maximal
6	#68923	—	3	1	no	maximal
7	C₂×C₉×M₁₆	C₂²	1	2	yes	—
8	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
9	#63488	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
11	C₂×#3667	C₂²	1	1	yes	characteristic
12	#63378	—	2	2	no	—
13	#63378	—	2	2	no	—
14	#63377	—	2	2	no	—
15	Dic₉⋊C₈	—	2	2	no	—
16	#5121	—	3	2	no	—
17	C₂×#818	—	3	1	no	—
18	#5102	—	3	1	no	—
19	C₃×#341	D₃	1	1	yes	characteristic
20	#4554	—	3	2	no	—
21	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
22	C₂²×Dic₉	—	2	2	no	—
23	C₉×M₁₆	—	2	2	no	—
24	C₉×M₁₆	Q₈	1	4	yes	—
25	C₂×C₈×C₉	—	2	2	no	—
26	C₂×C₈×C₉	—	2	2	no	—
27	C₂×C₈×C₉	D₄	1	2	yes	—
28	#3676	—	2	1	no	—
29	C₄⋊Dic₉	—	2	2	no	—
30	C₄⋊Dic₉	—	2	2	no	—
31	C₄⋊Dic₉	D₄	1	1	yes	characteristic
32	C₄⋊Dic₉	D₄	1	1	yes	characteristic
33	C₄×Dic₉	—	2	1	no	—
34	#3667	—	2	2	no	—
35	C₂×C₉⋊C₈	—	2	1	no	—
36	#2089	—	9	1	no	Sylow
37	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
38	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
39	#926	—	3	1	no	—
40	C₂×C₄⋊Dic₃	—	3	2	no	—
41	C₂×#208	—	3	1	no	—
42	#818	—	6	2	no	—
43	#818	—	6	2	no	—
44	#817	—	6	2	no	—
45	Dic₃⋊C₈	—	6	2	no	—
46	C₂³×C₉	#41	1	1	yes	characteristic
47	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
50	C₂×C₄×C₉	#41	1	2	yes	—
51	C₂×Dic₉	—	2	1	no	—
52	C₂×Dic₉	—	2	1	no	—
53	C₂×Dic₉	—	4	2	no	—
54	C₂×Dic₉	—	8	2	no	—
55	C₈×C₉	—	2	4	no	—
56	C₈×C₉	—	2	2	no	—
57	C₉⋊C₈	—	4	1	no	—
58	#428	—	9	2	no	—
59	C₂×#107	—	9	1	no	—
60	#424	—	9	1	no	—
61	#343	—	9	2	no	—
62	#341	D₉	1	1	yes	characteristic
63	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
64	C₂²×Dic₃	—	6	2	no	—
65	C₃×M₁₆	—	2	2	no	—
66	C₃×M₁₆	Dic₆	1	4	yes	—
67	C₂×C₃×C₈	—	2	2	no	—
68	C₂×C₃×C₈	—	2	2	no	—
69	C₂×C₃×C₈	D₁₂	1	2	yes	—
70	#217	—	6	1	no	—
71	C₄⋊Dic₃	—	3	1	no	—
72	C₄⋊Dic₃	—	3	1	no	—
73	C₄⋊Dic₃	—	6	2	no	—
74	C₄⋊Dic₃	—	6	2	no	—
75	C₄×Dic₃	—	6	1	no	—
76	#208	—	6	2	no	—
77	C₂×C₃⋊C₈	—	6	1	no	—
78	C₂²×C₉	—	2	1	no	—
79	C₂²×C₉	—	2	1	no	—
80	C₂²×C₉	#121	1	1	yes	characteristic
81	C₂²×C₉	#125	1	2	yes	—
82	C₄×C₉	C₂²⋊Q₈	1	2	yes	—
83	C₄×C₉	#123	1	1	yes	characteristic
84	C₄×C₉	C₄⋊Q₈	1	1	yes	characteristic
85	Dic₉	—	4	1	no	—
86	Dic₉	—	4	1	no	—
87	Dic₉	—	8	2	no	—
88	C₂×M₁₆	—	9	1	no	—
89	C₂×M₁₆	C₂×D₉	1	2	yes	—
90	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
91	#117	—	9	1	no	—
92	C₂×C₄⋊C₄	—	9	2	no	—
93	#107	—	18	2	no	—
94	#107	—	18	2	no	—
95	#106	—	18	2	no	—
96	C₄⋊C₈	—	18	2	no	—
97	C₂³×C₃	#239	1	1	yes	characteristic
98	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
99	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
100	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
101	C₂×C₃×C₄	#237	1	2	yes	—
102	C₂×Dic₃	—	6	1	no	—
103	C₂×Dic₃	—	6	1	no	—
104	C₂×Dic₃	—	12	2	no	—
105	C₂×Dic₃	—	24	2	no	—
106	C₃×C₈	—	2	4	no	—
107	C₃×C₈	—	2	2	no	—
108	C₃⋊C₈	—	12	1	no	—
109	C₂×C₉	—	2	2	no	—
110	C₂×C₉	#398	1	1	yes	characteristic
111	C₂×C₉	#472	1	1	yes	characteristic
112	C₂×C₉	#473	1	1	yes	characteristic
113	C₂²×C₄	—	18	2	no	—
114	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
115	M₁₆	—	2	2	no	—
116	M₁₆	—	18	2	no	—
117	M₁₆	Dic₁₈	1	4	yes	—
118	C₂×C₈	—	2	2	no	—
119	C₂×C₈	—	2	2	no	—
120	C₂×C₈	—	18	1	no	—
121	C₂×C₈	D₃₆	1	2	yes	—
122	C₄⋊C₄	—	9	1	no	—
123	C₄⋊C₄	—	9	1	no	—
124	C₄⋊C₄	—	18	2	no	—
125	C₄⋊C₄	—	18	2	no	—
126	C₂²⋊C₄	—	18	1	no	—
127	C₄²	—	18	1	no	—
128	C₂²×C₃	—	2	1	no	—
129	C₂²×C₃	—	2	1	no	—
130	C₂²×C₃	#890	1	2	yes	—
131	C₂²×C₃	#895	1	1	yes	characteristic
132	C₃×C₄	#869	1	1	yes	characteristic
133	C₃×C₄	#878	1	2	yes	—
134	C₃×C₄	#886	1	1	yes	characteristic
135	Dic₃	—	12	1	no	—
136	Dic₃	—	12	1	no	—
137	Dic₃	—	24	2	no	—
138	C₉	#2089	1	1	yes	characteristic, complemented, Sylow
139	C₂³	#3701	1	1	yes	characteristic
140	C₂×C₄	—	18	1	no	—
141	C₂×C₄	—	18	1	no	—
142	C₂×C₄	—	36	2	no	—
143	C₂×C₄	—	72	2	no	—
144	C₂×C₄	C₂×Dic₁₈	1	2	yes	—
145	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
146	C₂×C₄	D₄×D₉	1	1	yes	characteristic
147	C₂×C₄	#3699	1	2	yes	—
148	C₈	—	2	4	no	—
149	C₈	—	2	2	no	—
150	C₈	—	36	1	no	—
151	C₂×C₃	—	2	2	no	—
152	C₂×C₃	#4661	1	1	yes	characteristic
153	C₂×C₃	#4896	1	1	yes	characteristic
154	C₂×C₃	#4897	1	1	yes	characteristic
155	C₂²	—	2	1	no	—
156	C₂²	—	2	1	no	—
157	C₂²	#63452	1	2	yes	—
158	C₂²	#63457	1	1	yes	characteristic
159	C₄	—	36	1	no	—
160	C₄	—	36	1	no	—
161	C₄	—	72	2	no	—
162	C₄	#63431	1	1	yes	characteristic
163	C₄	#63440	1	2	yes	—
164	C₄	#63448	1	1	yes	characteristic
165	C₃	#68923	1	1	yes	characteristic
166	C₂	—	2	2	no	—
167	C₂	#10588341	1	1	yes	characteristic
168	C₂	#10588576	1	1	yes	characteristic
169	C₂	#10588577	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10588805

C₂

yes

maximal

C₂×#63378

C₂

yes

maximal, characteristic

#10588783

C₂

yes

maximal, characteristic

C₉×#341

C₂

yes

maximal, characteristic

#10588234

C₂

yes

maximal

#68923

—

maximal

C₂×C₉×M₁₆

C₂²

yes

—

C₂²×C₈×C₉

C₂²

yes

characteristic

#63488

C₂²

yes

characteristic

C₂×C₄⋊Dic₉

C₂²

yes

—

C₂×#3667

C₂²

yes

—

—

—

Dic₉⋊C₈

—

—

—

—

D₃

yes

characteristic

#4554

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂²×Dic₉

—

C₉×M₁₆

—

C₉×M₁₆

Q₈

yes

—

C₂×C₈×C₉

—

C₂×C₈×C₉

—

C₂×C₈×C₉

D₄

yes

—

#3676

—

C₄⋊Dic₉

—

C₄⋊Dic₉

—

C₄⋊Dic₉

D₄

yes

characteristic

C₄⋊Dic₉

D₄

yes

characteristic

C₄×Dic₉

—

#3667

—

C₂×C₉⋊C₈

—

#2089

—

Sylow

C₂×C₃×M₁₆

C₂×D₃

yes

—

C₂²×C₃×C₈

C₂×D₃

yes

characteristic

#926

—

C₂×C₄⋊Dic₃

—

—

—

—

—

Dic₃⋊C₈

—

C₂³×C₉

#41

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×Q₈

yes

—

C₂×C₄×C₉

#41

yes

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

C₈×C₉

—

C₈×C₉

—

C₉⋊C₈

—

—

—

—

—

D₉

yes

characteristic

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂²×Dic₃

—

C₃×M₁₆

—

C₃×M₁₆

Dic₆

yes

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

D₁₂

yes

—

#217

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₄×Dic₃

—

#208

—

C₂×C₃⋊C₈

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

#121

yes

characteristic

C₂²×C₉

#125

yes

—

C₄×C₉

C₂²⋊Q₈

yes

—

C₄×C₉

#123

yes

characteristic

C₄×C₉

C₄⋊Q₈

yes

characteristic

Dic₉

—

Dic₉

—

Dic₉

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₉

yes

—

C₂²×C₈

C₂×D₉

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

#107

—

#107

—

#106

—

C₄⋊C₈

—

C₂³×C₃

#239

yes

characteristic

C₂×C₃×C₄

C₂×Dic₆

yes

—

C₂×C₃×C₄

C₂×D₁₂

yes

characteristic

100

C₂×C₃×C₄

D₃×D₄

yes

characteristic

101

C₂×C₃×C₄

#237

yes

—

102

C₂×Dic₃

—

103

C₂×Dic₃

—

104

C₂×Dic₃

—

105

C₂×Dic₃

—

106

C₃×C₈

—

107

C₃×C₈

—

108

C₃⋊C₈

—

109

C₂×C₉

—

110

C₂×C₉

#398

yes

characteristic

111

C₂×C₉

#472

yes

characteristic

112

C₂×C₉

#473

yes

characteristic

113

C₂²×C₄

—

114

C₂²×C₄

C₂²×D₉

yes

characteristic

115

M₁₆

—

116

M₁₆

—

117

M₁₆

Dic₁₈

yes

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

D₃₆

yes

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₂²⋊C₄

—

127

C₄²

—

128

C₂²×C₃

—

129

C₂²×C₃

—

130

C₂²×C₃

#890

yes

—

131

C₂²×C₃

#895

yes

characteristic

132

C₃×C₄

#869

yes

characteristic

133

C₃×C₄

#878

yes

—

134

C₃×C₄

#886

yes

characteristic

135

Dic₃

—

136

Dic₃

—

137

Dic₃

—

138

C₉

#2089

yes

characteristic, complemented, Sylow

139

C₂³

#3701

yes

characteristic

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

C₂×Dic₁₈

yes

—

145

C₂×C₄

C₂×D₃₆

yes

characteristic

146

C₂×C₄

D₄×D₉

yes

characteristic

147

C₂×C₄

#3699

yes

—

148

C₈

—

149

C₈

—

150

C₈

—

151

C₂×C₃

—

152

C₂×C₃

#4661

yes

characteristic

153

C₂×C₃

#4896

yes

characteristic

154

C₂×C₃

#4897

yes

characteristic

155

C₂²

—

156

C₂²

—

157

C₂²

#63452

yes

—

158

C₂²

#63457

yes

characteristic

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

#63431

yes

characteristic

163

C₄

#63440

yes

—

164

C₄

#63448

yes

characteristic

165

C₃

#68923

yes

characteristic

166

C₂

—

167

C₂

#10588341

yes

characteristic

168

C₂

#10588576

yes

characteristic

169

C₂

#10588577

yes

characteristic

	subgroup	G/H
center	C₂²	#63457
commutator, cosocle	C₂²×C₄×C₉	C₂³
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#341	C₂
socle	C₂²×C₃	#895
prime radical	C₂³×C₃	#239
hypercenter	#341	D₉
hypocenter	C₉	#2089
LCS	G ▷ C₂²×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂²

#63457

commutator, cosocle

C₂²×C₄×C₉

C₂³

Frattini

C₂²×C₃×C₄

C₂²×D₃

C₂

C₂²×C₃

C₂³×C₃

D₉

C₉

G ▷ C₂²×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
138. C₉	#2089	semidirect

H ≅ G/N

type

138. C₉

#2089

semidirect

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

subgroup	index
#10588805	2
C₂×#63378	2
#10588783	2
C₉×#341	2
#10588234	2
#68923	3

subgroup

index

Subgroups — #11795297

Conjugacy classes of subgroups

Complements

Maximal subgroups