Group #23764941 — subgroups

Subgroups — #23764941

Order 10112.

254 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14579093	C₂	1	1	yes	maximal, characteristic
2	C₂×#14579092	C₂	1	1	yes	maximal, characteristic
3	C₂×#14579085	C₂	1	1	yes	maximal, characteristic
4	#19098470	C₂	1	1	yes	maximal, characteristic
5	#19098432	C₂	1	1	yes	maximal, characteristic
6	#19098317	C₂	1	1	yes	maximal, characteristic
7	C₂×#103×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₇₉⋊C₄	—	2	2	no	—
12	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
13	#14579093	—	2	2	no	—
14	#14579092	—	2	2	no	—
15	#14579085	—	2	2	no	—
16	C₇₉⋊#95	—	2	2	no	—
17	C₂²×Q₈×C₇₉	C₂²	1	1	yes	characteristic
18	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
20	#103×C₇₉	—	2	2	no	—
21	C₂²×Dic₇₉	—	2	1	no	—
22	C₂²×Dic₇₉	—	2	1	no	—
23	C₂²×Dic₇₉	D₄	1	2	yes	—
24	C₂×C₇₉⋊C₈	—	2	1	no	—
25	C₂×C₇₉⋊C₈	—	2	1	no	—
26	C₂×C₇₉⋊C₈	D₄	1	2	yes	—
27	C₄⋊Dic₇₉	—	2	1	no	—
28	C₄⋊Dic₇₉	—	2	1	no	—
29	C₄⋊Dic₇₉	—	2	1	no	—
30	C₄⋊Dic₇₉	—	2	1	no	—
31	Dic₇₉⋊C₄	—	4	4	no	—
32	C₄×Dic₇₉	—	2	1	no	—
33	C₄×Dic₇₉	—	2	1	no	—
34	C₂×Q₈×C₇₉	—	2	1	no	—
35	C₂×Q₈×C₇₉	—	2	1	no	—
36	C₂×Q₈×C₇₉	—	2	1	no	—
37	C₂×Q₈×C₇₉	—	2	1	no	—
38	C₂×Q₈×C₇₉	—	2	1	no	—
39	C₂×Q₈×C₇₉	Q₈	1	2	yes	—
40	C₂²×C₄×C₇₉	—	2	1	no	—
41	C₂²×C₄×C₇₉	—	2	1	no	—
42	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
43	C₂×C₈×C₇₉	—	2	1	no	—
44	C₂×C₈×C₇₉	—	2	1	no	—
45	C₂×C₈×C₇₉	D₄	1	2	yes	—
46	C₄⋊C₄×C₇₉	—	2	1	no	—
47	C₄⋊C₄×C₇₉	—	2	1	no	—
48	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
49	Q₈×C₇₉	—	2	2	no	—
50	Q₈×C₇₉	—	2	2	no	—
51	Q₈×C₇₉	—	4	1	no	—
52	Q₈×C₇₉	—	4	1	no	—
53	C₂×C₄×C₇₉	—	2	2	no	—
54	C₂×C₄×C₇₉	—	4	1	no	—
55	C₂×C₄×C₇₉	—	4	1	no	—
56	C₂×C₄×C₇₉	—	4	1	no	—
57	C₂×C₄×C₇₉	—	4	2	no	—
58	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
59	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
60	C₂×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
61	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
62	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
63	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
64	C₂×Dic₇₉	—	2	2	no	—
65	C₂×Dic₇₉	—	2	2	no	—
66	C₂×Dic₇₉	—	4	1	no	—
67	C₂×Dic₇₉	—	4	1	no	—
68	C₂×Dic₇₉	—	4	2	no	—
69	C₂×Dic₇₉	—	4	2	no	—
70	C₂×Dic₇₉	SD₁₆	1	4	yes	—
71	C₈×C₇₉	—	2	2	no	—
72	C₇₉⋊C₈	—	2	2	no	—
73	C₂²×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
74	C₂²×C₇₉	#123	1	1	yes	characteristic
75	C₂²×C₇₉	#127	1	1	yes	characteristic
76	C₂²×C₇₉	C₂×SD₁₆	1	2	yes	—
77	C₂²×C₇₉	#137	1	2	yes	—
78	C₄×C₇₉	—	4	2	no	—
79	C₄×C₇₉	—	8	1	no	—
80	C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
81	C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
82	C₄×C₇₉	#123	1	1	yes	characteristic
83	C₄×C₇₉	#123	1	1	yes	characteristic
84	Dic₇₉	—	2	4	no	—
85	Dic₇₉	—	8	1	no	—
86	Dic₇₉	—	8	1	no	—
87	C₂×C₇₉	#399	1	1	yes	characteristic
88	C₂×C₇₉	#475	1	2	yes	—
89	C₂×C₇₉	#483	1	2	yes	—
90	C₂×C₇₉	#492	1	1	yes	characteristic
91	C₂×C₇₉	#497	1	1	yes	characteristic
92	#2096	—	79	1	no	maximal, Sylow
93	C₇₉	#2096	1	1	yes	characteristic, complemented, Sylow
94	C₂×#106	—	79	1	no	—
95	C₂×#106	—	79	1	no	—
96	C₂×#103	—	79	1	no	—
97	C₂×#103	D₇₉	1	1	yes	characteristic
98	#391	—	79	1	no	—
99	#384	—	79	1	no	—
100	#336	—	79	1	no	—
101	C₂²×Q₈	C₂×D₇₉	1	1	yes	characteristic
102	C₂²×C₈	—	79	1	no	—
103	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
104	C₂×C₄⋊C₄	—	79	1	no	—
105	C₂×C₄⋊C₄	—	79	1	no	—
106	C₂×C₄⋊C₄	—	158	2	no	—
107	C₂×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
108	C₂×C₄²	—	79	1	no	—
109	#106	—	158	2	no	—
110	#106	—	158	2	no	—
111	#103	—	2	2	no	—
112	#103	—	158	2	no	—
113	#95	—	158	2	no	—
114	C₂×Q₈	—	2	1	no	—
115	C₂×Q₈	—	2	1	no	—
116	C₂×Q₈	—	2	1	no	—
117	C₂×Q₈	—	2	1	no	—
118	C₂×Q₈	—	2	1	no	—
119	C₂×Q₈	Dic₁₅₈	1	2	yes	—
120	C₂²×C₄	—	2	1	no	—
121	C₂²×C₄	—	2	1	no	—
122	C₂²×C₄	—	79	2	no	—
123	C₂²×C₄	—	158	1	no	—
124	C₂²×C₄	—	158	1	no	—
125	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
126	C₂×C₈	—	2	1	no	—
127	C₂×C₈	—	2	1	no	—
128	C₂×C₈	—	79	2	no	—
129	C₂×C₈	—	158	1	no	—
130	C₂×C₈	—	158	1	no	—
131	C₂×C₈	C₂²⋊D₇₉	1	2	yes	—
132	C₄⋊C₄	—	2	1	no	—
133	C₄⋊C₄	—	2	1	no	—
134	C₄⋊C₄	—	316	4	no	—
135	C₄⋊C₄	—	158	1	no	—
136	C₄⋊C₄	—	158	1	no	—
137	C₄⋊C₄	—	158	1	no	—
138	C₄⋊C₄	—	158	1	no	—
139	C₄²	—	158	1	no	—
140	C₄²	—	158	1	no	—
141	C₂³	D₄×D₇₉	1	1	yes	characteristic
142	Q₈	—	2	2	no	—
143	Q₈	—	2	2	no	—
144	Q₈	—	4	1	no	—
145	Q₈	—	4	1	no	—
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	4	1	no	—
148	C₂×C₄	—	4	1	no	—
149	C₂×C₄	—	4	1	no	—
150	C₂×C₄	—	4	2	no	—
151	C₂×C₄	—	316	1	no	—
152	C₂×C₄	—	316	1	no	—
153	C₂×C₄	—	316	2	no	—
154	C₂×C₄	—	316	2	no	—
155	C₂×C₄	—	79	4	no	—
156	C₂×C₄	—	158	2	no	—
157	C₂×C₄	—	158	2	no	—
158	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
159	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
160	C₂×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
161	C₂×C₄	#11929623	1	1	yes	characteristic
162	C₂×C₄	#11929623	1	1	yes	characteristic
163	C₂×C₄	#11929624	1	1	yes	characteristic
164	C₈	—	2	2	no	—
165	C₈	—	158	2	no	—
166	C₂²	#14579138	1	1	yes	characteristic
167	C₂²	#14579143	1	1	yes	characteristic
168	C₂²	#14579157	1	1	yes	characteristic
169	C₂²	SD₁₆×D₇₉	1	2	yes	—
170	C₂²	#14579193	1	2	yes	—
171	C₄	—	4	2	no	—
172	C₄	—	8	1	no	—
173	C₄	—	632	1	no	—
174	C₄	—	632	1	no	—
175	C₄	—	158	4	no	—
176	C₄	#14579138	1	1	yes	characteristic
177	C₄	#14579140	1	1	yes	characteristic
178	C₄	#14579142	1	1	yes	characteristic
179	C₄	#14579143	1	1	yes	characteristic
180	C₂	#19098499	1	1	yes	characteristic
181	C₂	#19098846	1	2	yes	—
182	C₂	#19098892	1	2	yes	—
183	C₂	#19098934	1	1	yes	characteristic
184	C₂	#19098956	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579093

C₂

yes

maximal, characteristic

C₂×#14579092

C₂

yes

maximal, characteristic

C₂×#14579085

C₂

yes

maximal, characteristic

#19098470

C₂

yes

maximal, characteristic

#19098432

C₂

yes

maximal, characteristic

#19098317

C₂

yes

maximal, characteristic

C₂×#103×C₇₉

C₂

yes

maximal, characteristic

C₂²×C₇₉⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

characteristic

C₂×Dic₇₉⋊C₄

—

C₂×C₄×Dic₇₉

C₂²

yes

—

—

—

C₇₉⋊#95

—

C₂²×Q₈×C₇₉

C₂²

yes

characteristic

C₂²×C₈×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₉

C₂²

yes

characteristic

#103×C₇₉

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

D₄

yes

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

D₄

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

Q₈

yes

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₈

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

SD₁₆

yes

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

C₂²⋊Q₈

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

C₂×SD₁₆

yes

—

C₂²×C₇₉

#137

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂²⋊Q₈

yes

characteristic

C₄×C₇₉

C₂²⋊Q₈

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

#399

yes

characteristic

C₂×C₇₉

#475

yes

—

C₂×C₇₉

#483

yes

—

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

—

—

—

D₇₉

yes

characteristic

#391

—

#384

—

100

#336

—

101

C₂²×Q₈

C₂×D₇₉

yes

characteristic

102

C₂²×C₈

—

103

C₂²×C₈

C₂×D₇₉

yes

characteristic

104

C₂×C₄⋊C₄

—

105

C₂×C₄⋊C₄

—

106

C₂×C₄⋊C₄

—

158

—

107

C₂×C₄⋊C₄

C₂×D₇₉

yes

characteristic

108

C₂×C₄²

—

109

#106

—

158

—

110

#106

—

158

—

111

#103

—

112

#103

—

158

—

113

#95

—

158

—

114

C₂×Q₈

—

115

C₂×Q₈

—

116

C₂×Q₈

—

117

C₂×Q₈

—

118

C₂×Q₈

—

119

C₂×Q₈

Dic₁₅₈

yes

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

—

158

—

124

C₂²×C₄

—

158

—

125

C₂²×C₄

C₂²×D₇₉

yes

characteristic

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

158

—

130

C₂×C₈

—

158

—

131

C₂×C₈

C₂²⋊D₇₉

yes

—

132

C₄⋊C₄

—

133

C₄⋊C₄

—

134

C₄⋊C₄

—

316

—

135

C₄⋊C₄

—

158

—

136

C₄⋊C₄

—

158

—

137

C₄⋊C₄

—

158

—

138

C₄⋊C₄

—

158

—

139

C₄²

—

158

—

140

C₄²

—

158

—

141

C₂³

D₄×D₇₉

yes

characteristic

142

Q₈

—

143

Q₈

—

144

Q₈

—

145

Q₈

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

316

—

152

C₂×C₄

—

316

—

153

C₂×C₄

—

316

—

154

C₂×C₄

—

316

—

155

C₂×C₄

—

156

C₂×C₄

—

158

—

157

C₂×C₄

—

158

—

158

C₂×C₄

D₄×D₇₉

yes

characteristic

159

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

160

C₂×C₄

C₂×Dic₁₅₈

yes

characteristic

161

C₂×C₄

#11929623

yes

characteristic

162

C₂×C₄

#11929623

yes

characteristic

163

C₂×C₄

#11929624

yes

characteristic

164

C₈

—

165

C₈

—

158

—

166

C₂²

#14579138

yes

characteristic

167

C₂²

#14579143

yes

characteristic

168

C₂²

#14579157

yes

characteristic

169

C₂²

SD₁₆×D₇₉

yes

—

170

C₂²

#14579193

yes

—

171

C₄

—

172

C₄

—

173

C₄

—

632

—

174

C₄

—

632

—

175

C₄

—

158

—

176

C₄

#14579138

yes

characteristic

177

C₄

#14579140

yes

characteristic

178

C₄

#14579142

yes

characteristic

179

C₄

#14579143

yes

characteristic

180

C₂

#19098499

yes

characteristic

181

C₂

#19098846

yes

—

182

C₂

#19098892

yes

—

183

C₂

#19098934

yes

characteristic

184

C₂

#19098956

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₇₉
commutator, cosocle	C₂²×C₄×C₇₉	C₂³
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	C₂×#103×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂×D₄
hypercenter	C₂×#103	D₇₉
hypocenter	C₇₉	#2096
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

subgroup

G/H

center

C₂³

D₄×D₇₉

commutator, cosocle

C₂²×C₄×C₇₉

C₂³

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

C₂×#103×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

C₂×D₄

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

N	H ≅ G/N	type
93. C₇₉	#2096	semidirect

H ≅ G/N

type

93. C₇₉

#2096

semidirect

Subgroups — #23764941

Conjugacy classes of subgroups

Complements