Group #18080069 — subgroups

Subgroups — #18080069

Order 4864.

436 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 95 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	#14574011	C₂	1	1	yes	maximal, characteristic
2	#14572741	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562348	C₂	1	2	yes	maximal
4	#14561508	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1537	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597320	C₂²	1	1	yes	characteristic
7	#11926910	—	2	2	no	—
8	#11926892	C₄	1	4	yes	—
9	#11926675	—	2	4	no	—
10	#11926605	—	2	2	no	—
11	#11926601	C₂²	1	2	yes	—
12	#11926548	—	2	2	no	—
13	C₄×#64520	C₂²	1	1	yes	characteristic
14	#11926287	—	2	4	no	—
15	C₁₉×#533	C₂²	1	1	yes	characteristic
16	C₁₉×#432	C₂²	1	2	yes	—
17	C₁₉×#330	—	2	2	no	—
18	C₂²×D₇₆	—	2	1	no	—
19	C₂²×D₇₆	—	2	2	no	—
20	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
21	C₁₉×#125	D₄	1	2	yes	—
22	C₁₉×C₂²⋊Q₈	—	2	2	no	—
23	C₄×Q₈×C₁₉	—	2	2	no	—
24	C₁₉×#117	D₄	1	2	yes	—
25	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	C₂×#64520	—	2	1	no	—
27	#10597320	—	2	2	no	—
28	#10597320	—	2	1	no	—
29	#10597320	C₂×C₄	1	2	yes	—
30	C₁₉×C₄⋊C₈	—	2	2	no	—
31	C₁₉×C₂²⋊C₈	—	2	2	no	—
32	C₁₉×#97	—	2	2	no	—
33	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
34	#10597266	—	2	8	no	—
35	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
36	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
37	#10597260	—	2	2	no	—
38	#10597260	—	2	2	no	—
39	#10597260	—	2	1	no	—
40	C₄×C₁₉⋊C₈	—	2	2	no	—
41	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
42	C₂³×D₁₉	—	4	1	no	—
43	C₂×Q₈×C₁₉	—	2	2	no	—
44	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	#41	1	2	yes	—
46	C₂×D₇₆	—	2	2	no	—
47	C₂×D₇₆	—	2	4	no	—
48	C₂×D₇₆	—	4	4	no	—
49	C₂×D₇₆	—	4	1	no	—
50	C₂×D₇₆	—	4	2	no	—
51	C₂×D₇₆	—	8	4	no	—
52	C₂×C₈×C₁₉	—	4	2	no	—
53	C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₄⋊C₄×C₁₉	—	2	4	no	—
55	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
56	C₂²⋊C₄×C₁₉	—	2	2	no	—
57	C₄²×C₁₉	—	2	2	no	—
58	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
59	C₄²×C₁₉	C₂×D₄	1	2	yes	—
60	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
61	#64520	—	4	2	no	—
62	C₂×C₁₉⋊C₈	—	2	2	no	—
63	C₂×C₁₉⋊C₈	—	2	4	no	—
64	#9424	—	19	1	no	maximal, Sylow
65	C₂³×C₁₉	#123	1	1	yes	characteristic
66	C₂²×D₁₉	—	4	2	no	—
67	C₂²×D₁₉	—	8	2	no	—
68	C₂²×D₁₉	—	8	4	no	—
69	Q₈×C₁₉	—	8	2	no	—
70	C₂×C₄×C₁₉	—	2	2	no	—
71	C₂×C₄×C₁₉	—	2	4	no	—
72	C₂×C₄×C₁₉	—	4	2	no	—
73	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
75	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
76	C₂×C₄×C₁₉	#121	1	2	yes	—
77	D₇₆	—	4	4	no	—
78	D₇₆	—	8	4	no	—
79	D₇₆	—	8	4	no	—
80	D₇₆	—	8	2	no	—
81	C₈×C₁₉	—	8	2	no	—
82	C₁₉⋊C₈	—	4	2	no	—
83	C₁₉⋊C₈	—	4	4	no	—
84	#3138	—	19	1	no	—
85	#2987	—	19	1	no	—
86	#1555	—	19	2	no	—
87	#1537	D₁₉	1	1	yes	characteristic, complemented
88	#1291	—	19	2	no	—
89	C₂²×C₁₉	—	2	1	no	—
90	C₂²×C₁₉	—	2	2	no	—
91	C₂²×C₁₉	#386	1	1	yes	characteristic
92	C₂×D₁₉	—	8	2	no	—
93	C₂×D₁₉	—	8	4	no	—
94	C₂×D₁₉	—	16	4	no	—
95	C₄×C₁₉	—	2	1	no	—
96	C₄×C₁₉	—	2	2	no	—
97	C₄×C₁₉	—	2	2	no	—
98	C₄×C₁₉	—	4	4	no	—
99	C₄×C₁₉	#454	1	2	yes	—
100	#533	C₂×D₁₉	1	1	yes	characteristic
101	C₂×#127	—	19	1	no	—
102	#490	—	38	2	no	—
103	#486	—	19	4	no	—
104	#446	—	38	4	no	—
105	#433	—	38	2	no	—
106	#432	—	19	2	no	—
107	#432	C₂×D₁₉	1	2	yes	—
108	#418	—	38	2	no	—
109	C₄×M₁₆	—	19	1	no	—
110	#331	—	38	4	no	—
111	#330	—	2	2	no	—
112	C₂×C₁₉	—	4	1	no	—
113	C₂×C₁₉	#1888	1	1	yes	characteristic
114	C₂×C₁₉	#1903	1	2	yes	—
115	D₁₉	—	16	2	no	—
116	C₂²×D₄	—	38	1	no	—
117	C₂²×D₄	—	38	2	no	—
118	C₂×M₁₆	—	38	1	no	—
119	C₄⋊Q₈	C₄×D₁₉	1	2	yes	—
120	#127	—	19	2	no	—
121	#127	—	38	2	no	—
122	#127	—	38	1	no	—
123	#125	C₂²⋊D₁₉	1	2	yes	—
124	C₂²⋊Q₈	—	2	2	no	—
125	C₄×Q₈	—	2	2	no	—
126	#117	D₇₆	1	2	yes	—
127	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
128	C₄⋊C₈	—	2	2	no	—
129	C₄⋊C₈	—	19	4	no	—
130	C₄⋊C₈	—	38	4	no	—
131	#102	—	38	8	no	—
132	C₂²⋊C₈	—	2	2	no	—
133	C₂²⋊C₈	—	38	2	no	—
134	#97	—	2	2	no	—
135	#97	—	38	2	no	—
136	#97	—	38	2	no	—
137	#97	—	38	1	no	—
138	C₄×C₈	—	19	2	no	—
139	C₄×C₈	—	38	2	no	—
140	C₁₉	#9424	1	1	yes	characteristic, complemented, Sylow
141	C₂⁴	—	76	1	no	—
142	C₂×Q₈	—	2	2	no	—
143	C₂×D₄	—	38	4	no	—
144	C₂×D₄	—	38	2	no	—
145	C₂×D₄	—	76	4	no	—
146	C₂×D₄	—	76	2	no	—
147	C₂×D₄	—	76	1	no	—
148	C₂×D₄	—	152	4	no	—
149	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
150	C₂²×C₄	#64543	1	2	yes	—
151	M₁₆	—	76	2	no	—
152	C₂×C₈	—	4	2	no	—
153	C₂×C₈	—	38	4	no	—
154	C₂×C₈	—	38	2	no	—
155	C₄⋊C₄	—	2	4	no	—
156	C₄⋊C₄	—	2	2	no	—
157	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
158	C₂²⋊C₄	—	2	2	no	—
159	C₄²	—	2	2	no	—
160	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
161	C₄²	D₄×D₁₉	1	2	yes	—
162	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
163	C₂³	—	76	2	no	—
164	C₂³	—	152	2	no	—
165	C₂³	—	152	4	no	—
166	C₂³	#10597332	1	1	yes	characteristic
167	Q₈	—	8	2	no	—
168	D₄	—	76	4	no	—
169	D₄	—	152	4	no	—
170	D₄	—	152	4	no	—
171	D₄	—	152	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	4	no	—
174	C₂×C₄	—	4	2	no	—
175	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
176	C₂×C₄	#10597328	1	1	yes	characteristic
177	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
178	C₂×C₄	#10597385	1	2	yes	—
179	C₈	—	8	2	no	—
180	C₈	—	76	2	no	—
181	C₈	—	76	4	no	—
182	C₂²	—	2	2	no	—
183	C₂²	—	2	1	no	—
184	C₂²	—	304	4	no	—
185	C₂²	—	152	4	no	—
186	C₂²	—	152	2	no	—
187	C₂²	#11926421	1	1	yes	characteristic
188	C₄	—	2	2	no	—
189	C₄	—	2	2	no	—
190	C₄	—	2	1	no	—
191	C₄	—	4	4	no	—
192	C₄	#11926719	1	2	yes	—
193	C₂	—	4	1	no	—
194	C₂	—	304	2	no	—
195	C₂	#14564036	1	1	yes	characteristic
196	C₂	#14564113	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14574011

C₂

yes

maximal, characteristic

#14572741

C₂

yes

maximal, characteristic, complemented

#14562348

C₂

yes

maximal

#14561508

C₂

yes

maximal, complemented

C₁₉×#1537

C₂

yes

maximal, characteristic, complemented

C₂×#10597320

C₂²

yes

characteristic

#11926910

—

#11926892

C₄

yes

—

#11926675

—

#11926605

—

#11926601

C₂²

yes

—

#11926548

—

C₄×#64520

C₂²

yes

characteristic

#11926287

—

C₁₉×#533

C₂²

yes

characteristic

C₁₉×#432

C₂²

yes

—

C₁₉×#330

—

C₂²×D₇₆

—

C₂²×D₇₆

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×#125

D₄

yes

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₂²⋊(C₁₉⋊C₈)

—

#10597266

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₂³×D₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

—

—

D₁₉

yes

characteristic, complemented

#1291

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#386

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#454

yes

—

100

#533

C₂×D₁₉

yes

characteristic

101

C₂×#127

—

102

#490

—

103

#486

—

104

#446

—

105

#433

—

106

#432

—

107

#432

C₂×D₁₉

yes

—

108

#418

—

109

C₄×M₁₆

—

110

#331

—

111

#330

—

112

C₂×C₁₉

—

113

C₂×C₁₉

#1888

yes

characteristic

114

C₂×C₁₉

#1903

yes

—

115

D₁₉

—

116

C₂²×D₄

—

117

C₂²×D₄

—

118

C₂×M₁₆

—

119

C₄⋊Q₈

C₄×D₁₉

yes

—

120

#127

—

121

#127

—

122

#127

—

123

#125

C₂²⋊D₁₉

yes

—

124

C₂²⋊Q₈

—

125

C₄×Q₈

—

126

#117

D₇₆

yes

—

127

C₂×C₄²

C₂²×D₁₉

yes

characteristic

128

C₄⋊C₈

—

129

C₄⋊C₈

—

130

C₄⋊C₈

—

131

#102

—

132

C₂²⋊C₈

—

133

C₂²⋊C₈

—

134

#97

—

135

#97

—

136

#97

—

137

#97

—

138

C₄×C₈

—

139

C₄×C₈

—

140

C₁₉

#9424

yes

characteristic, complemented, Sylow

141

C₂⁴

—

142

C₂×Q₈

—

143

C₂×D₄

—

144

C₂×D₄

—

145

C₂×D₄

—

146

C₂×D₄

—

147

C₂×D₄

—

148

C₂×D₄

—

152

—

149

C₂²×C₄

C₂×D₇₆

yes

characteristic

150

C₂²×C₄

#64543

yes

—

151

M₁₆

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

(C₂×D₁₉)⋊C₄

yes

—

158

C₂²⋊C₄

—

159

C₄²

—

160

C₄²

C₂×C₄×D₁₉

yes

characteristic

161

C₄²

D₄×D₁₉

yes

—

162

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

163

C₂³

—

164

C₂³

—

152

—

165

C₂³

—

152

—

166

C₂³

#10597332

yes

characteristic

167

Q₈

—

168

D₄

—

169

D₄

—

152

—

170

D₄

—

152

—

171

D₄

—

152

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

—

176

C₂×C₄

#10597328

yes

characteristic

177

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

178

C₂×C₄

#10597385

yes

—

179

C₈

—

180

C₈

—

181

C₈

—

182

C₂²

—

183

C₂²

—

184

C₂²

—

304

—

185

C₂²

—

152

—

186

C₂²

—

152

—

187

C₂²

#11926421

yes

characteristic

188

C₄

—

189

C₄

—

190

C₄

—

191

C₄

—

192

C₄

#11926719

yes

—

193

C₂

—

194

C₂

—

304

—

195

C₂

#14564036

yes

characteristic

196

C₂

#14564113

yes

—

	subgroup	G/H
center	C₂²	#11926421
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1537	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂×#10597320	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1537	D₁₉
hypocenter	C₁₉	#9424
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1537

subgroup

G/H

center

C₂²

#11926421

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1537

C₂

C₂²×C₁₉

C₂²

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1537

N	H ≅ G/N	type
2. #14572741	C₂	semidirect
4. #14561508	C₂	semidirect
5. C₁₉×#1537	C₂	semidirect
87. #1537	D₁₉	semidirect
140. C₁₉	#9424	semidirect

H ≅ G/N

type

2. #14572741

C₂

semidirect

4. #14561508

C₂

semidirect

5. C₁₉×#1537

C₂

semidirect

87. #1537

D₁₉

semidirect

140. C₁₉

#9424

semidirect

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

subgroup	index
#14574011	2
#14572741	2
#14562348	2
#14561508	2
C₁₉×#1537	2
#9424	19

subgroup

index

C₁₉×#1537

Subgroups — #18080069

Conjugacy classes of subgroups

Complements

Maximal subgroups