Group #18085682 — subgroups

Subgroups — #18085682

Order 4864.

364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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	#14566940	C₂	1	1	yes	maximal, characteristic
2	#14562134	C₂	1	2	yes	maximal
3	#14561536	C₂	1	2	yes	maximal
4	#14561464	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1995	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	#11926486	—	2	2	no	—
8	#11926478	—	2	2	no	—
9	C₄×Dic₁₉⋊C₄	—	2	2	no	—
10	C₄×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	#11926281	—	2	2	no	—
12	#11926281	—	2	2	no	—
13	C₁₉×#533	C₂²	1	1	yes	characteristic
14	C₁₉×#423	C₂²	1	1	yes	characteristic
15	C₁₉×#376	C₂²	1	1	yes	characteristic
16	C₁₉×#339	—	2	2	no	—
17	C₂×M₁₆×C₁₉	—	2	1	no	—
18	C₁₉×C₄⋊Q₈	Q₈	1	2	yes	—
19	C₁₉×#125	—	2	1	no	—
20	C₁₉×C₂²⋊Q₈	—	2	2	no	—
21	C₄×Q₈×C₁₉	—	2	2	no	—
22	C₁₉×#117	—	2	1	no	—
23	C₂×C₄²×C₁₉	D₄	1	2	yes	—
24	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
25	C₂×C₄⋊Dic₁₉	—	2	2	no	—
26	C₂×Dic₁₉⋊C₄	—	2	2	no	—
27	C₂×Dic₁₉⋊C₄	—	2	2	no	—
28	C₂×C₄×Dic₁₉	—	2	2	no	—
29	C₁₉×C₄⋊C₈	—	2	2	no	—
30	C₁₉×#95	—	2	2	no	—
31	C₁₉⋊#95	—	2	2	no	—
32	C₁₉⋊#95	—	2	2	no	—
33	C₁₉⋊#95	D₄	1	2	yes	—
34	C₁₉⋊#95	D₄	1	2	yes	—
35	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
36	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
37	C₄×C₁₉⋊C₈	—	2	2	no	—
38	C₂×Q₈×C₁₉	—	2	2	no	—
39	C₂²×C₄×C₁₉	—	2	2	no	—
40	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
41	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×Dic₁₉	—	2	2	no	—
43	C₂²×Dic₁₉	—	2	2	no	—
44	M₁₆×C₁₉	—	4	2	no	—
45	C₂×C₈×C₁₉	—	4	1	no	—
46	C₄⋊C₄×C₁₉	—	2	2	no	—
47	C₄⋊C₄×C₁₉	—	2	2	no	—
48	C₄⋊C₄×C₁₉	—	4	2	no	—
49	C₂²⋊C₄×C₁₉	—	4	1	no	—
50	C₄²×C₁₉	—	2	2	no	—
51	C₄²×C₁₉	—	2	2	no	—
52	C₄²×C₁₉	—	4	1	no	—
53	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
54	C₄²×C₁₉	#41	1	1	yes	characteristic
55	C₄²×C₁₉	#41	1	2	yes	—
56	C₄⋊Dic₁₉	—	4	4	no	—
57	Dic₁₉⋊C₄	—	4	4	no	—
58	Dic₁₉⋊C₄	—	4	4	no	—
59	C₄×Dic₁₉	—	4	2	no	—
60	C₄×Dic₁₉	—	4	2	no	—
61	C₂×C₁₉⋊C₈	—	4	2	no	—
62	#10373	—	19	1	no	maximal, Sylow
63	C₂³×C₁₉	#120	1	1	yes	characteristic
64	Q₈×C₁₉	—	8	2	no	—
65	C₂×C₄×C₁₉	—	4	2	no	—
66	C₂×C₄×C₁₉	—	4	2	no	—
67	C₂×C₄×C₁₉	—	4	2	no	—
68	C₂×C₄×C₁₉	—	4	2	no	—
69	C₂×C₄×C₁₉	—	4	2	no	—
70	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
71	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
72	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
73	C₂×C₄×C₁₉	#124	1	2	yes	—
74	C₂×C₄×C₁₉	#135	1	2	yes	—
75	C₂×C₄×C₁₉	#137	1	2	yes	—
76	C₂×Dic₁₉	—	2	4	no	—
77	C₂×Dic₁₉	—	4	2	no	—
78	C₂×Dic₁₉	—	4	2	no	—
79	C₂×Dic₁₉	—	4	2	no	—
80	C₂×Dic₁₉	—	4	2	no	—
81	C₂×Dic₁₉	—	4	2	no	—
82	C₈×C₁₉	—	8	1	no	—
83	C₁₉⋊C₈	—	8	2	no	—
84	#2402	—	19	1	no	—
85	#1995	D₁₉	1	1	yes	characteristic
86	#1503	—	19	2	no	—
87	#1303	—	19	2	no	—
88	#1274	—	19	1	no	—
89	C₂²×C₁₉	—	2	2	no	—
90	C₂²×C₁₉	#393	1	1	yes	characteristic
91	C₂²×C₁₉	#452	1	2	yes	—
92	C₄×C₁₉	—	2	2	no	—
93	C₄×C₁₉	—	2	2	no	—
94	C₄×C₁₉	—	8	2	no	—
95	C₄×C₁₉	—	8	2	no	—
96	C₄×C₁₉	#479	1	2	yes	—
97	C₄×C₁₉	#488	1	1	yes	characteristic
98	C₄×C₁₉	#491	1	1	yes	characteristic
99	Dic₁₉	—	4	4	no	—
100	Dic₁₉	—	8	2	no	—
101	#533	C₂×D₁₉	1	1	yes	characteristic
102	#431	—	19	2	no	—
103	#423	C₂×D₁₉	1	1	yes	characteristic
104	#400	—	38	2	no	—
105	#398	—	38	2	no	—
106	C₄×C₄⋊C₄	—	19	2	no	—
107	C₄×C₄⋊C₄	—	38	2	no	—
108	#376	C₂×D₁₉	1	1	yes	characteristic
109	#339	—	2	2	no	—
110	#328	—	38	2	no	—
111	#328	—	38	2	no	—
112	C₂×C₁₉	—	2	2	no	—
113	C₂×C₁₉	#2026	1	1	yes	characteristic
114	C₂×C₁₉	#2031	1	2	yes	—
115	C₂×M₁₆	—	2	1	no	—
116	C₄⋊Q₈	Dic₃₈	1	2	yes	—
117	#125	—	2	1	no	—
118	C₂²⋊Q₈	—	2	2	no	—
119	C₄×Q₈	—	2	2	no	—
120	#117	—	2	1	no	—
121	C₂×C₄⋊C₄	—	38	2	no	—
122	C₂×C₄⋊C₄	—	38	2	no	—
123	C₂×C₄⋊C₄	—	38	2	no	—
124	C₂×C₄²	—	38	2	no	—
125	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
126	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
127	C₄⋊C₈	—	2	2	no	—
128	C₄⋊C₈	—	38	2	no	—
129	C₂²⋊C₈	—	38	2	no	—
130	C₄×C₈	—	38	2	no	—
131	#95	—	2	2	no	—
132	#95	—	19	2	no	—
133	#95	—	19	2	no	—
134	#95	—	38	2	no	—
135	#95	—	38	2	no	—
136	C₁₉	#10373	1	1	yes	characteristic, complemented, Sylow
137	C₂×Q₈	—	2	2	no	—
138	C₂²×C₄	—	2	2	no	—
139	C₂²×C₄	—	38	2	no	—
140	C₂²×C₄	—	38	2	no	—
141	C₂²×C₄	D₄×D₁₉	1	2	yes	—
142	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
143	M₁₆	—	4	2	no	—
144	C₂×C₈	—	4	1	no	—
145	C₂×C₈	—	76	2	no	—
146	C₄⋊C₄	—	2	2	no	—
147	C₄⋊C₄	—	2	2	no	—
148	C₄⋊C₄	—	4	2	no	—
149	C₄⋊C₄	—	76	4	no	—
150	C₄⋊C₄	—	76	4	no	—
151	C₄⋊C₄	—	76	4	no	—
152	C₂²⋊C₄	—	4	1	no	—
153	C₄²	—	2	2	no	—
154	C₄²	—	2	2	no	—
155	C₄²	—	4	1	no	—
156	C₄²	—	76	2	no	—
157	C₄²	—	76	2	no	—
158	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
159	C₄²	#64541	1	1	yes	characteristic
160	C₄²	#64543	1	2	yes	—
161	C₂³	#10597383	1	1	yes	characteristic
162	Q₈	—	8	2	no	—
163	C₂×C₄	—	4	2	no	—
164	C₂×C₄	—	4	2	no	—
165	C₂×C₄	—	4	2	no	—
166	C₂×C₄	—	4	2	no	—
167	C₂×C₄	—	4	2	no	—
168	C₂×C₄	—	38	4	no	—
169	C₂×C₄	—	76	2	no	—
170	C₂×C₄	—	76	2	no	—
171	C₂×C₄	—	76	2	no	—
172	C₂×C₄	—	76	2	no	—
173	C₂×C₄	—	76	2	no	—
174	C₂×C₄	#10597324	1	2	yes	—
175	C₂×C₄	#10597331	1	2	yes	—
176	C₂×C₄	#10597370	1	1	yes	characteristic
177	C₂×C₄	#10597382	1	1	yes	characteristic
178	C₂×C₄	#10597388	1	2	yes	—
179	C₂×C₄	#10597396	1	2	yes	—
180	C₈	—	8	1	no	—
181	C₈	—	152	2	no	—
182	C₂²	—	2	2	no	—
183	C₂²	#11926456	1	1	yes	characteristic
184	C₂²	#11926704	1	2	yes	—
185	C₄	—	2	2	no	—
186	C₄	—	2	2	no	—
187	C₄	—	8	2	no	—
188	C₄	—	8	2	no	—
189	C₄	—	76	4	no	—
190	C₄	—	152	2	no	—
191	C₄	#11926851	1	2	yes	—
192	C₄	#11926898	1	1	yes	characteristic
193	C₄	#11926912	1	1	yes	characteristic
194	C₂	—	2	2	no	—
195	C₂	#14564786	1	1	yes	characteristic
196	C₂	#14564805	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14566940

C₂

yes

maximal, characteristic

#14562134

C₂

yes

maximal

#14561536

C₂

yes

maximal

#14561464

C₂

yes

maximal, characteristic

C₁₉×#1995

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

#11926486

—

#11926478

—

C₄×Dic₁₉⋊C₄

—

C₄×C₄⋊Dic₁₉

C₂²

yes

—

#11926281

—

#11926281

—

C₁₉×#533

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#376

C₂²

yes

characteristic

C₁₉×#339

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

Q₈

yes

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×Dic₁₉⋊C₄

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₁₉×C₄⋊C₈

—

C₁₉×#95

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

D₄

yes

—

C₁₉⋊#95

D₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×Q₈

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

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

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2402

—

#1995

D₁₉

yes

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

#393

yes

characteristic

C₂²×C₁₉

#452

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#479

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

100

Dic₁₉

—

101

#533

C₂×D₁₉

yes

characteristic

102

#431

—

103

#423

C₂×D₁₉

yes

characteristic

104

#400

—

105

#398

—

106

C₄×C₄⋊C₄

—

107

C₄×C₄⋊C₄

—

108

#376

C₂×D₁₉

yes

characteristic

109

#339

—

110

#328

—

111

#328

—

112

C₂×C₁₉

—

113

C₂×C₁₉

#2026

yes

characteristic

114

C₂×C₁₉

#2031

yes

—

115

C₂×M₁₆

—

116

C₄⋊Q₈

Dic₃₈

yes

—

117

#125

—

118

C₂²⋊Q₈

—

119

C₄×Q₈

—

120

#117

—

121

C₂×C₄⋊C₄

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

—

124

C₂×C₄²

—

125

C₂×C₄²

C₂²⋊D₁₉

yes

—

126

C₂×C₄²

C₂²×D₁₉

yes

characteristic

127

C₄⋊C₈

—

128

C₄⋊C₈

—

129

C₂²⋊C₈

—

130

C₄×C₈

—

131

#95

—

132

#95

—

133

#95

—

134

#95

—

135

#95

—

136

C₁₉

#10373

yes

characteristic, complemented, Sylow

137

C₂×Q₈

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

D₄×D₁₉

yes

—

142

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

143

M₁₆

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₄⋊C₄

—

147

C₄⋊C₄

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₂²⋊C₄

—

153

C₄²

—

154

C₄²

—

155

C₄²

—

156

C₄²

—

157

C₄²

—

158

C₄²

C₂×Dic₃₈

yes

characteristic

159

C₄²

#64541

yes

characteristic

160

C₄²

#64543

yes

—

161

C₂³

#10597383

yes

characteristic

162

Q₈

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

#10597324

yes

—

175

C₂×C₄

#10597331

yes

—

176

C₂×C₄

#10597370

yes

characteristic

177

C₂×C₄

#10597382

yes

characteristic

178

C₂×C₄

#10597388

yes

—

179

C₂×C₄

#10597396

yes

—

180

C₈

—

181

C₈

—

152

—

182

C₂²

—

183

C₂²

#11926456

yes

characteristic

184

C₂²

#11926704

yes

—

185

C₄

—

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

—

190

C₄

—

152

—

191

C₄

#11926851

yes

—

192

C₄

#11926898

yes

characteristic

193

C₄

#11926912

yes

characteristic

194

C₂

—

195

C₂

#14564786

yes

characteristic

196

C₂

#14564805

yes

—

	subgroup	G/H
center	C₂×C₄	#10597382
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1995	C₂
socle	C₂²×C₁₉	#393
prime radical	C₂³×C₁₉	#120
hypercenter	#1995	D₁₉
hypocenter	C₁₉	#10373
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1995

subgroup

G/H

center

C₂×C₄

#10597382

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1995

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1995

N	H ≅ G/N	type
136. C₁₉	#10373	semidirect

H ≅ G/N

type

136. C₁₉

#10373

semidirect

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

subgroup	index
#14566940	2
#14562134	2
#14561536	2
#14561464	2
C₁₉×#1995	2
#10373	19

subgroup

index

C₁₉×#1995

Subgroups — #18085682

Conjugacy classes of subgroups

Complements

Maximal subgroups