Group #18081632 — subgroups

Subgroups — #18081632

Order 4864.

538 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 167 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	#14572033	C₂	1	1	yes	maximal, characteristic
2	#14563488	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926289	C₂	1	4	yes	maximal
4	C₁₉×#1831	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597315	—	2	1	no	—
6	C₂×#10597315	—	2	1	no	—
7	C₂×#10597315	C₂²	1	2	yes	—
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
9	C₂×#10597260	—	2	1	no	—
10	#11926414	—	2	2	no	—
11	#11926414	C₄	1	4	yes	—
12	#11926299	—	2	1	no	—
13	#11926289	—	2	8	no	—
14	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
15	C₄³×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#336	—	2	2	no	—
17	C₂²×Dic₃₈	—	2	2	no	—
18	C₂²×C₈×C₁₉	—	2	2	no	—
19	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	D₄	1	2	yes	—
22	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₉	—	2	4	no	—
25	C₂×C₄⋊Dic₁₉	—	2	4	no	—
26	C₂×C₄⋊Dic₁₉	—	2	2	no	—
27	C₂×C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
28	C₂²×C₁₉⋊C₈	—	2	2	no	—
29	#10597315	—	2	4	no	—
30	#10597315	—	2	4	no	—
31	#10597315	—	4	4	no	—
32	#10597315	—	4	2	no	—
33	#10597315	—	4	2	no	—
34	C₁₉×C₄⋊C₈	—	2	4	no	—
35	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
36	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
37	#10597260	—	4	2	no	—
38	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
39	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
40	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂²×Dic₁₉	—	2	4	no	—
44	C₂×Dic₃₈	—	4	4	no	—
45	C₂×Dic₃₈	—	4	2	no	—
46	C₂×Dic₃₈	—	4	2	no	—
47	C₂×Dic₃₈	—	4	4	no	—
48	C₂×C₈×C₁₉	—	4	2	no	—
49	C₂×C₈×C₁₉	—	4	4	no	—
50	C₄²×C₁₉	—	2	4	no	—
51	C₄²×C₁₉	—	2	2	no	—
52	C₄²×C₁₉	—	2	4	no	—
53	C₄²×C₁₉	D₈	1	2	yes	—
54	C₄²×C₁₉	SD₁₆	1	2	yes	—
55	C₄²×C₁₉	C₂×D₄	1	2	yes	—
56	C₄²×C₁₉	#41	1	2	yes	—
57	C₄⋊Dic₁₉	—	2	8	no	—
58	C₄⋊Dic₁₉	—	4	8	no	—
59	C₄⋊Dic₁₉	—	4	8	no	—
60	C₄⋊Dic₁₉	—	4	2	no	—
61	C₄⋊Dic₁₉	—	4	2	no	—
62	C₂×C₁₉⋊C₈	—	2	4	no	—
63	C₂×C₁₉⋊C₈	—	4	2	no	—
64	C₂×C₁₉⋊C₈	—	4	2	no	—
65	#9705	—	19	1	no	maximal, Sylow
66	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₉	—	2	2	no	—
68	C₂×C₄×C₁₉	—	2	2	no	—
69	C₂×C₄×C₁₉	—	2	2	no	—
70	C₂×C₄×C₁₉	—	2	2	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	#101	1	4	yes	—
73	C₂×C₄×C₁₉	#102	1	4	yes	—
74	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
75	C₂×C₄×C₁₉	#121	1	2	yes	—
76	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
77	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
78	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
79	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
80	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
81	C₂×C₄×C₁₉	#137	1	4	yes	—
82	C₂×Dic₁₉	—	4	4	no	—
83	C₂×Dic₁₉	—	4	4	no	—
84	C₂×Dic₁₉	—	4	4	no	—
85	Dic₃₈	—	8	4	no	—
86	Dic₃₈	—	8	4	no	—
87	C₈×C₁₉	—	8	2	no	—
88	C₁₉⋊C₈	—	4	4	no	—
89	#2868	—	19	1	no	—
90	#1831	D₁₉	1	1	yes	characteristic
91	#1767	—	19	1	no	—
92	C₂×#332	—	19	4	no	—
93	C₂²×C₁₉	#390	1	1	yes	characteristic
94	C₂²×C₁₉	C₂×#101	1	2	yes	—
95	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
96	C₂²×C₁₉	#418	1	1	yes	characteristic
97	C₂²×C₁₉	#419	1	2	yes	—
98	C₄×C₁₉	—	2	4	no	—
99	C₄×C₁₉	—	2	4	no	—
100	C₄×C₁₉	—	2	2	no	—
101	C₄×C₁₉	#459	1	2	yes	—
102	C₄×C₁₉	#460	1	2	yes	—
103	C₄×C₁₉	#491	1	2	yes	—
104	C₄×C₁₉	#497	1	2	yes	—
105	Dic₁₉	—	8	4	no	—
106	C₂×C₄⋊Q₈	—	19	2	no	—
107	C₂×C₄⋊Q₈	—	38	1	no	—
108	C₂×C₄⋊Q₈	—	38	1	no	—
109	C₂×C₄⋊C₈	—	19	2	no	—
110	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
111	C₂×#97	—	38	1	no	—
112	#384	—	19	4	no	—
113	#384	—	38	2	no	—
114	C₄³	C₂×D₁₉	1	1	yes	characteristic
115	#336	—	2	2	no	—
116	#336	—	38	1	no	—
117	#332	—	38	8	no	—
118	C₂×C₁₉	#1546	1	2	yes	—
119	C₂×C₁₉	#1556	1	2	yes	—
120	C₂×C₁₉	#1960	1	1	yes	characteristic
121	C₂×C₁₉	#1966	1	1	yes	characteristic
122	C₂×C₁₉	#1982	1	1	yes	characteristic
123	C₂²×Q₈	—	38	2	no	—
124	C₂²×C₈	—	2	2	no	—
125	C₂²×C₈	—	38	2	no	—
126	C₄⋊Q₈	—	38	4	no	—
127	C₄⋊Q₈	—	38	4	no	—
128	C₄⋊Q₈	—	76	4	no	—
129	C₄⋊Q₈	—	76	2	no	—
130	C₄⋊Q₈	—	76	2	no	—
131	C₂×C₄⋊C₄	—	19	4	no	—
132	C₂×C₄⋊C₄	—	38	4	no	—
133	C₂×C₄⋊C₄	—	38	4	no	—
134	C₂×C₄⋊C₄	—	38	2	no	—
135	C₂×C₄²	C₄×D₁₉	1	2	yes	—
136	C₂×C₄²	D₇₆	1	1	yes	characteristic
137	C₂×C₄²	D₇₆	1	1	yes	characteristic
138	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
139	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
140	C₄⋊C₈	—	2	4	no	—
141	C₄⋊C₈	—	19	4	no	—
142	C₄⋊C₈	—	38	2	no	—
143	#97	—	76	2	no	—
144	C₁₉	#9705	1	1	yes	characteristic, complemented, Sylow
145	C₂×Q₈	—	76	4	no	—
146	C₂×Q₈	—	76	2	no	—
147	C₂×Q₈	—	76	2	no	—
148	C₂×Q₈	—	76	4	no	—
149	C₂²×C₄	—	38	4	no	—
150	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
151	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
152	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
153	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
154	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
155	C₂×C₈	—	4	2	no	—
156	C₂×C₈	—	4	4	no	—
157	C₂×C₈	—	38	4	no	—
158	C₂×C₈	—	76	2	no	—
159	C₂×C₈	—	76	2	no	—
160	C₄⋊C₄	—	38	8	no	—
161	C₄⋊C₄	—	76	8	no	—
162	C₄⋊C₄	—	76	2	no	—
163	C₄⋊C₄	—	76	2	no	—
164	C₄⋊C₄	—	76	8	no	—
165	C₄²	—	2	4	no	—
166	C₄²	—	2	4	no	—
167	C₄²	—	2	2	no	—
168	C₄²	#64516	1	2	yes	—
169	C₄²	D₁₅₂	1	2	yes	—
170	C₄²	D₄×D₁₉	1	2	yes	—
171	C₄²	#64545	1	2	yes	—
172	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
173	Q₈	—	152	4	no	—
174	Q₈	—	152	4	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	76	4	no	—
181	C₂×C₄	—	76	4	no	—
182	C₂×C₄	—	76	4	no	—
183	C₂×C₄	#10597278	1	4	yes	—
184	C₂×C₄	#10597281	1	4	yes	—
185	C₂×C₄	#10597339	1	2	yes	—
186	C₂×C₄	#10597341	1	2	yes	—
187	C₂×C₄	C₂×#64516	1	1	yes	characteristic
188	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
189	C₂×C₄	#10597354	1	2	yes	—
190	C₂×C₄	#10597386	1	1	yes	characteristic
191	C₂×C₄	#10597393	1	1	yes	characteristic
192	C₂×C₄	#10597397	1	4	yes	—
193	C₈	—	8	2	no	—
194	C₈	—	76	4	no	—
195	C₂²	#11926445	1	1	yes	characteristic
196	C₂²	C₂×#10597281	1	2	yes	—
197	C₂²	C₂×#10597278	1	1	yes	characteristic
198	C₂²	#11926550	1	1	yes	characteristic
199	C₂²	#11926552	1	2	yes	—
200	C₄	—	2	4	no	—
201	C₄	—	2	4	no	—
202	C₄	—	2	2	no	—
203	C₄	—	152	4	no	—
204	C₄	#11926740	1	2	yes	—
205	C₄	#11926745	1	2	yes	—
206	C₄	#11926914	1	2	yes	—
207	C₄	#11926939	1	2	yes	—
208	C₂	#14562306	1	2	yes	—
209	C₂	#14562351	1	2	yes	—
210	C₂	#14564454	1	1	yes	characteristic
211	C₂	#14564478	1	1	yes	characteristic
212	C₂	#14564561	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572033

C₂

yes

maximal, characteristic

#14563488

C₂

yes

maximal, characteristic

C₂×#11926289

C₂

yes

maximal

C₁₉×#1831

C₂

yes

maximal, characteristic

C₂×#10597315

—

C₂×#10597315

—

C₂×#10597315

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×#10597260

—

#11926414

—

#11926414

C₄

yes

—

#11926299

—

#11926289

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

—

—

—

—

—

—

C₁₉×C₄⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₈

yes

—

C₄²×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9705

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#101

yes

—

C₂×C₄×C₁₉

#102

yes

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2868

—

#1831

D₁₉

yes

characteristic

#1767

—

C₂×#332

—

C₂²×C₁₉

#390

yes

characteristic

C₂²×C₁₉

C₂×#101

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

100

C₄×C₁₉

—

101

C₄×C₁₉

#459

yes

—

102

C₄×C₁₉

#460

yes

—

103

C₄×C₁₉

#491

yes

—

104

C₄×C₁₉

#497

yes

—

105

Dic₁₉

—

106

C₂×C₄⋊Q₈

—

107

C₂×C₄⋊Q₈

—

108

C₂×C₄⋊Q₈

—

109

C₂×C₄⋊C₈

—

110

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

111

C₂×#97

—

112

#384

—

113

#384

—

114

C₄³

C₂×D₁₉

yes

characteristic

115

#336

—

116

#336

—

117

#332

—

118

C₂×C₁₉

#1546

yes

—

119

C₂×C₁₉

#1556

yes

—

120

C₂×C₁₉

#1960

yes

characteristic

121

C₂×C₁₉

#1966

yes

characteristic

122

C₂×C₁₉

#1982

yes

characteristic

123

C₂²×Q₈

—

124

C₂²×C₈

—

125

C₂²×C₈

—

126

C₄⋊Q₈

—

127

C₄⋊Q₈

—

128

C₄⋊Q₈

—

129

C₄⋊Q₈

—

130

C₄⋊Q₈

—

131

C₂×C₄⋊C₄

—

132

C₂×C₄⋊C₄

—

133

C₂×C₄⋊C₄

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄²

C₄×D₁₉

yes

—

136

C₂×C₄²

D₇₆

yes

characteristic

137

C₂×C₄²

D₇₆

yes

characteristic

138

C₂×C₄²

C₂²⋊D₁₉

yes

—

139

C₂×C₄²

C₂²×D₁₉

yes

characteristic

140

C₄⋊C₈

—

141

C₄⋊C₈

—

142

C₄⋊C₈

—

143

#97

—

144

C₁₉

#9705

yes

characteristic, complemented, Sylow

145

C₂×Q₈

—

146

C₂×Q₈

—

147

C₂×Q₈

—

148

C₂×Q₈

—

149

C₂²×C₄

—

150

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

151

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

152

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

153

C₂²×C₄

C₂×D₇₆

yes

characteristic

154

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₄⋊C₄

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄²

—

166

C₄²

—

167

C₄²

—

168

C₄²

#64516

yes

—

169

C₄²

D₁₅₂

yes

—

170

C₄²

D₄×D₁₉

yes

—

171

C₄²

#64545

yes

—

172

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

173

Q₈

—

152

—

174

Q₈

—

152

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

#10597278

yes

—

184

C₂×C₄

#10597281

yes

—

185

C₂×C₄

#10597339

yes

—

186

C₂×C₄

#10597341

yes

—

187

C₂×C₄

C₂×#64516

yes

characteristic

188

C₂×C₄

C₂×D₁₅₂

yes

characteristic

189

C₂×C₄

#10597354

yes

—

190

C₂×C₄

#10597386

yes

characteristic

191

C₂×C₄

#10597393

yes

characteristic

192

C₂×C₄

#10597397

yes

—

193

C₈

—

194

C₈

—

195

C₂²

#11926445

yes

characteristic

196

C₂²

C₂×#10597281

yes

—

197

C₂²

C₂×#10597278

yes

characteristic

198

C₂²

#11926550

yes

characteristic

199

C₂²

#11926552

yes

—

200

C₄

—

201

C₄

—

202

C₄

—

203

C₄

—

152

—

204

C₄

#11926740

yes

—

205

C₄

#11926745

yes

—

206

C₄

#11926914

yes

—

207

C₄

#11926939

yes

—

208

C₂

#14562306

yes

—

209

C₂

#14562351

yes

—

210

C₂

#14564454

yes

characteristic

211

C₂

#14564478

yes

characteristic

212

C₂

#14564561

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1831	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1831	D₁₉
hypocenter	C₁₉	#9705
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

subgroup

G/H

center

C₂³

C₂×(C₂×D₁₉)⋊C₄

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1831

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

N	H ≅ G/N	type
144. C₁₉	#9705	semidirect

H ≅ G/N

type

144. C₁₉

#9705

semidirect

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

subgroup	index
#14572033	2
#14563488	2
C₂×#11926289	2
C₁₉×#1831	2
#9705	19

subgroup

index

C₁₉×#1831

Subgroups — #18081632

Conjugacy classes of subgroups

Complements

Maximal subgroups