Group #18076947 — subgroups

Subgroups — #18076947

Order 4864.

336 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 99 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	#14564617	C₂	1	1	yes	maximal, characteristic
2	#14562403	C₂	1	2	yes	maximal
3	#14562230	C₂	1	1	yes	maximal, characteristic
4	#14561527	C₂	1	2	yes	maximal
5	C₁₉×#2987	C₂	1	1	yes	maximal, characteristic
6	#11926568	C₂²	1	1	yes	characteristic
7	C₄×#64520	C₂²	1	2	yes	—
8	#11926390	C₂²	1	1	yes	characteristic
9	#11926303	—	2	2	no	—
10	#11926296	—	2	2	no	—
11	#11926294	—	2	2	no	—
12	#11926286	C₄	1	1	yes	characteristic, complemented
13	#11926286	C₄	1	2	yes	complemented
14	#11926286	C₄	1	1	yes	characteristic, complemented
15	C₁₉×#533	C₂²	1	1	yes	characteristic
16	C₁₉×#446	—	2	2	no	—
17	C₁₉×#446	—	2	2	no	—
18	C₁₉×#433	—	2	2	no	—
19	C₁₉×#432	C₂²	1	2	yes	—
20	C₁₉×C₄⋊Q₈	Q₈	1	2	yes	—
21	C₁₉×#125	C₂×C₄	1	1	yes	characteristic
22	C₁₉×#125	C₂×C₄	1	1	yes	characteristic
23	C₁₉×C₂²⋊Q₈	—	2	2	no	—
24	C₄×Q₈×C₁₉	—	2	2	no	—
25	C₁₉×#117	D₄	1	2	yes	—
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×C₄×Dic₁₉	—	2	1	no	—
28	C₂×#64520	—	2	2	no	—
29	C₂×#64520	—	2	1	no	—
30	C₁₉×C₄⋊C₈	—	2	2	no	—
31	C₁₉×C₄⋊C₈	—	2	2	no	—
32	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
33	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
34	C₁₉×C₂²⋊C₈	—	2	2	no	—
35	C₁₉×#97	—	2	2	no	—
36	C₁₉×#97	—	2	2	no	—
37	C₄×C₈×C₁₉	—	2	2	no	—
38	C₁₉⋊#95	—	2	2	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	#10597260	C₂×C₄	1	2	yes	—
41	#10597260	C₂×C₄	1	2	yes	—
42	C₄×C₁₉⋊C₈	—	2	2	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	C₂²×Dic₁₉	—	4	1	no	—
47	C₂×C₈×C₁₉	—	2	2	no	—
48	C₂×C₈×C₁₉	—	2	2	no	—
49	C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₄⋊C₄×C₁₉	—	2	2	no	—
52	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
53	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
54	C₂²⋊C₄×C₁₉	—	2	2	no	—
55	C₄²×C₁₉	—	2	2	no	—
56	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
57	C₄²×C₁₉	C₂×D₄	1	2	yes	—
58	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
59	C₄×Dic₁₉	—	2	2	no	—
60	C₄×Dic₁₉	—	4	1	no	—
61	#64520	—	4	4	no	—
62	#64520	—	4	2	no	—
63	C₂×C₁₉⋊C₈	—	2	2	no	—
64	C₂×C₁₉⋊C₈	—	2	2	no	—
65	C₂×C₁₉⋊C₈	—	4	1	no	—
66	#8919	—	19	1	no	maximal, Sylow
67	C₂³×C₁₉	#123	1	1	yes	characteristic
68	Q₈×C₁₉	—	8	2	no	—
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	—	4	2	no	—
74	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
76	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
77	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
78	C₂×Dic₁₉	—	4	2	no	—
79	C₂×Dic₁₉	—	8	2	no	—
80	C₈×C₁₉	—	4	2	no	—
81	C₈×C₁₉	—	4	2	no	—
82	C₁₉⋊C₈	—	2	4	no	—
83	C₁₉⋊C₈	—	4	2	no	—
84	C₁₉⋊C₈	—	8	1	no	—
85	#2987	D₁₉	1	1	yes	characteristic
86	#1995	—	19	1	no	—
87	#1569	—	19	2	no	—
88	#1526	—	19	1	no	—
89	#1300	—	19	2	no	—
90	C₂²×C₁₉	—	2	1	no	—
91	C₂²×C₁₉	—	2	2	no	—
92	C₂²×C₁₉	#385	1	1	yes	characteristic
93	C₄×C₁₉	—	2	1	no	—
94	C₄×C₁₉	—	2	2	no	—
95	C₄×C₁₉	—	2	2	no	—
96	C₄×C₁₉	—	4	2	no	—
97	C₄×C₁₉	—	4	2	no	—
98	C₄×C₁₉	#454	1	1	yes	characteristic
99	C₄×C₁₉	#456	1	1	yes	characteristic
100	Dic₁₉	—	8	2	no	—
101	#533	C₂×D₁₉	1	1	yes	characteristic
102	#446	—	2	2	no	—
103	#446	—	2	2	no	—
104	#433	—	2	2	no	—
105	#432	C₂×D₁₉	1	2	yes	—
106	#423	—	19	1	no	—
107	C₄×M₁₆	—	19	2	no	—
108	#376	—	19	1	no	—
109	#339	—	38	2	no	—
110	#335	—	38	2	no	—
111	#334	—	38	2	no	—
112	#330	—	19	1	no	—
113	#330	—	19	2	no	—
114	#330	—	19	1	no	—
115	C₂×C₁₉	—	4	1	no	—
116	C₂×C₁₉	#1857	1	1	yes	characteristic
117	C₂×C₁₉	#1861	1	2	yes	—
118	C₂×M₁₆	—	38	2	no	—
119	C₂×M₁₆	—	38	1	no	—
120	C₄⋊Q₈	Dic₃₈	1	2	yes	—
121	#125	C₄×D₁₉	1	1	yes	characteristic
122	#125	C₄×D₁₉	1	1	yes	characteristic
123	C₂²⋊Q₈	—	2	2	no	—
124	C₄×Q₈	—	2	2	no	—
125	#117	C₂²⋊D₁₉	1	2	yes	—
126	C₂×C₄²	—	38	1	no	—
127	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
128	C₄⋊C₈	—	2	2	no	—
129	C₄⋊C₈	—	2	2	no	—
130	C₄⋊C₈	—	38	2	no	—
131	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
132	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
133	C₂²⋊C₈	—	2	2	no	—
134	#97	—	2	2	no	—
135	#97	—	2	2	no	—
136	#97	—	19	2	no	—
137	#97	—	19	2	no	—
138	C₄×C₈	—	2	2	no	—
139	C₄×C₈	—	38	2	no	—
140	#95	—	38	2	no	—
141	C₁₉	#8919	1	1	yes	characteristic, complemented, Sylow
142	C₂×Q₈	—	2	2	no	—
143	C₂²×C₄	—	76	1	no	—
144	C₂²×C₄	#64541	1	2	yes	—
145	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
146	M₁₆	—	76	4	no	—
147	M₁₆	—	76	2	no	—
148	C₂×C₈	—	2	2	no	—
149	C₂×C₈	—	2	2	no	—
150	C₂×C₈	—	38	2	no	—
151	C₂×C₈	—	38	2	no	—
152	C₂×C₈	—	76	1	no	—
153	C₄⋊C₄	—	2	2	no	—
154	C₄⋊C₄	—	2	2	no	—
155	C₄⋊C₄	—	2	2	no	—
156	C₄⋊C₄	Dic₁₉⋊C₄	1	2	yes	—
157	C₄⋊C₄	Dic₁₉⋊C₄	1	2	yes	—
158	C₂²⋊C₄	—	2	2	no	—
159	C₄²	—	2	2	no	—
160	C₄²	—	38	2	no	—
161	C₄²	—	76	1	no	—
162	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
163	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
164	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
165	C₂³	#10597375	1	1	yes	characteristic
166	Q₈	—	8	2	no	—
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	2	1	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	4	2	no	—
172	C₂×C₄	—	76	2	no	—
173	C₂×C₄	—	152	2	no	—
174	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
175	C₂×C₄	#10597370	1	2	yes	—
176	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
177	C₂×C₄	#10597399	1	1	yes	characteristic
178	C₈	—	4	2	no	—
179	C₈	—	4	2	no	—
180	C₈	—	38	4	no	—
181	C₈	—	76	2	no	—
182	C₈	—	152	1	no	—
183	C₂²	—	2	1	no	—
184	C₂²	—	2	2	no	—
185	C₂²	#11926417	1	1	yes	characteristic
186	C₄	—	2	1	no	—
187	C₄	—	2	2	no	—
188	C₄	—	2	2	no	—
189	C₄	—	4	2	no	—
190	C₄	—	4	2	no	—
191	C₄	—	152	2	no	—
192	C₄	#11926717	1	1	yes	characteristic
193	C₄	#11926727	1	1	yes	characteristic
194	C₂	—	4	1	no	—
195	C₂	#14563850	1	1	yes	characteristic
196	C₂	#14563875	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564617

C₂

yes

maximal, characteristic

#14562403

C₂

yes

maximal

#14562230

C₂

yes

maximal, characteristic

#14561527

C₂

yes

maximal

C₁₉×#2987

C₂

yes

maximal, characteristic

#11926568

C₂²

yes

characteristic

C₄×#64520

C₂²

yes

—

#11926390

C₂²

yes

—

—

—

C₄

yes

characteristic, complemented

#11926286

C₄

yes

complemented

#11926286

C₄

yes

characteristic, complemented

C₁₉×#533

C₂²

yes

characteristic

C₁₉×#446

—

C₁₉×#446

—

C₁₉×#433

—

C₁₉×#432

C₂²

yes

—

C₁₉×C₄⋊Q₈

Q₈

yes

—

C₁₉×#125

C₂×C₄

yes

characteristic

C₁₉×#125

C₂×C₄

yes

characteristic

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

—

C₂×#64520

—

C₂×#64520

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₁₉⋊#95

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

C₂×C₄

yes

—

#10597260

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₄⋊C₄

yes

—

C₄⋊C₄×C₁₉

C₄⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄×Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2987

D₁₉

yes

—

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#385

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

100

Dic₁₉

—

101

#533

C₂×D₁₉

yes

characteristic

102

#446

—

103

#446

—

104

#433

—

105

#432

C₂×D₁₉

yes

—

106

#423

—

107

C₄×M₁₆

—

108

#376

—

109

#339

—

110

#335

—

111

#334

—

112

#330

—

113

#330

—

114

#330

—

115

C₂×C₁₉

—

116

C₂×C₁₉

#1857

yes

characteristic

117

C₂×C₁₉

#1861

yes

—

118

C₂×M₁₆

—

119

C₂×M₁₆

—

120

C₄⋊Q₈

Dic₃₈

yes

—

121

#125

C₄×D₁₉

yes

characteristic

122

#125

C₄×D₁₉

yes

characteristic

123

C₂²⋊Q₈

—

124

C₄×Q₈

—

125

#117

C₂²⋊D₁₉

yes

—

126

C₂×C₄²

—

127

C₂×C₄²

C₂²×D₁₉

yes

characteristic

128

C₄⋊C₈

—

129

C₄⋊C₈

—

130

C₄⋊C₈

—

131

C₄⋊C₈

C₂²⋊D₁₉

yes

—

132

C₄⋊C₈

C₂²⋊D₁₉

yes

—

133

C₂²⋊C₈

—

134

#97

—

135

#97

—

136

#97

—

137

#97

—

138

C₄×C₈

—

139

C₄×C₈

—

140

#95

—

141

C₁₉

#8919

yes

characteristic, complemented, Sylow

142

C₂×Q₈

—

143

C₂²×C₄

—

144

C₂²×C₄

#64541

yes

—

145

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

146

M₁₆

—

147

M₁₆

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

Dic₁₉⋊C₄

yes

—

157

C₄⋊C₄

Dic₁₉⋊C₄

yes

—

158

C₂²⋊C₄

—

159

C₄²

—

160

C₄²

—

161

C₄²

—

162

C₄²

C₂×Dic₃₈

yes

characteristic

163

C₄²

C₂×C₄×D₁₉

yes

characteristic

164

C₄²

C₂×C₂²⋊D₁₉

yes

—

165

C₂³

#10597375

yes

characteristic

166

Q₈

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

152

—

174

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

175

C₂×C₄

#10597370

yes

—

176

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

177

C₂×C₄

#10597399

yes

characteristic

178

C₈

—

179

C₈

—

180

C₈

—

181

C₈

—

182

C₈

—

152

—

183

C₂²

—

184

C₂²

—

185

C₂²

#11926417

yes

characteristic

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

—

190

C₄

—

191

C₄

—

152

—

192

C₄

#11926717

yes

characteristic

193

C₄

#11926727

yes

characteristic

194

C₂

—

195

C₂

#14563850

yes

characteristic

196

C₂

#14563875

yes

—

	subgroup	G/H
center	C₂×C₄	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2987	C₂
socle	C₂²×C₁₉	#385
prime radical	C₂³×C₁₉	#123
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2987	D₁₉
hypocenter	C₁₉	#8919
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2987

subgroup

G/H

center

C₂×C₄

#10597399

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2987

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2987

N	H ≅ G/N	type
12. #11926286	C₄	semidirect
13. #11926286	C₄	semidirect
14. #11926286	C₄	semidirect
141. C₁₉	#8919	semidirect

H ≅ G/N

type

12. #11926286

C₄

semidirect

13. #11926286

C₄

semidirect

14. #11926286

C₄

semidirect

141. C₁₉

#8919

semidirect

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

subgroup	index
#14564617	2
#14562403	2
#14562230	2
#14561527	2
C₁₉×#2987	2
#8919	19

subgroup

index

C₁₉×#2987

Subgroups — #18076947

Conjugacy classes of subgroups

Complements

Maximal subgroups