Group #18081355 — subgroups

Subgroups — #18081355

Order 4864.

558 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 159 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	C₄×#10597315	C₂	1	1	yes	maximal, characteristic
2	#14563752	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926276	C₂	1	4	yes	maximal
4	C₄×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597315	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₃₈	C₂²	1	2	yes	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	#11926450	C₄	1	2	yes	—
9	#11926442	—	2	2	no	—
10	#11926414	C₄	1	1	yes	characteristic
11	C₄×C₄⋊Dic₁₉	—	2	2	no	—
12	#11926299	—	2	2	no	—
13	#11926276	—	2	8	no	—
14	C₂×C₁₉×#97	—	2	2	no	—
15	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
16	C₄³×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
18	C₂²×C₈×C₁₉	—	2	2	no	—
19	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	D₄	1	2	yes	—
22	C₂×C₄²×C₁₉	D₄	1	2	yes	—
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₉	—	2	2	no	—
25	C₂×C₄⋊Dic₁₉	—	2	2	no	—
26	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
27	C₂×Dic₁₉⋊C₄	—	2	2	no	—
28	C₂×C₄×Dic₁₉	—	2	2	no	—
29	C₂²×C₁₉⋊C₈	—	2	2	no	—
30	#10597315	—	2	4	no	—
31	C₄×Dic₃₈	—	2	4	no	—
32	C₄×Dic₃₈	—	2	4	no	—
33	C₁₉×#97	—	2	8	no	—
34	C₄×C₈×C₁₉	—	2	2	no	—
35	C₄×C₈×C₁₉	D₄	1	4	yes	—
36	C₁₉⋊#95	—	2	4	no	—
37	C₄⋊(C₁₉⋊C₈)	—	2	4	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	2	no	—
44	C₂²×Dic₁₉	—	2	2	no	—
45	C₂×Dic₃₈	—	2	4	no	—
46	C₂×Dic₃₈	—	2	4	no	—
47	C₂×Dic₃₈	—	2	2	no	—
48	C₂×Dic₃₈	M₁₆	1	4	yes	—
49	C₂×C₈×C₁₉	—	2	8	no	—
50	C₂×C₈×C₁₉	—	2	4	no	—
51	C₄²×C₁₉	—	2	4	no	—
52	C₄²×C₁₉	—	2	2	no	—
53	C₄²×C₁₉	—	2	2	no	—
54	C₄²×C₁₉	—	2	4	no	—
55	C₄²×C₁₉	C₂×D₄	1	2	yes	—
56	C₄²×C₁₉	#41	1	2	yes	—
57	C₄⋊Dic₁₉	—	2	8	no	—
58	C₄⋊Dic₁₉	—	2	4	no	—
59	C₄⋊Dic₁₉	—	4	4	no	—
60	Dic₁₉⋊C₄	—	4	4	no	—
61	C₄×Dic₁₉	—	4	2	no	—
62	C₄×Dic₁₉	—	4	2	no	—
63	C₂×C₁₉⋊C₈	—	4	2	no	—
64	C₂×C₁₉⋊C₈	—	4	4	no	—
65	#9647	—	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	—	2	2	no	—
73	C₂×C₄×C₁₉	#104	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×M₁₆	1	2	yes	—
79	C₂×C₄×C₁₉	#131	1	2	yes	—
80	C₂×C₄×C₁₉	#137	1	4	yes	—
81	C₂×Dic₁₉	—	2	4	no	—
82	C₂×Dic₁₉	—	4	2	no	—
83	C₂×Dic₁₉	—	4	2	no	—
84	C₂×Dic₁₉	—	4	2	no	—
85	C₂×Dic₁₉	—	4	4	no	—
86	Dic₃₈	—	2	8	no	—
87	Dic₃₈	—	4	4	no	—
88	C₈×C₁₉	—	2	8	no	—
89	C₁₉⋊C₈	—	8	2	no	—
90	C₄×C₄⋊Q₈	—	19	1	no	—
91	#1831	—	19	1	no	—
92	C₄×#97	D₁₉	1	1	yes	characteristic
93	C₂×Q₈⋊C₈	—	19	4	no	—
94	C₂²×C₁₉	#390	1	1	yes	characteristic
95	C₂²×C₁₉	#407	1	1	yes	characteristic
96	C₂²×C₁₉	#408	1	1	yes	characteristic
97	C₂²×C₁₉	#419	1	2	yes	—
98	C₂²×C₁₉	C₂×#104	1	2	yes	—
99	C₄×C₁₉	—	2	2	no	—
100	C₄×C₁₉	—	2	4	no	—
101	C₄×C₁₉	—	4	2	no	—
102	C₄×C₁₉	#435	1	4	yes	—
103	C₄×C₁₉	#491	1	2	yes	—
104	C₄×C₁₉	#497	1	2	yes	—
105	Dic₁₉	—	4	4	no	—
106	Dic₁₉	—	8	2	no	—
107	C₂×C₄⋊Q₈	—	19	1	no	—
108	C₂×C₄×Q₈	—	19	2	no	—
109	C₂×C₄⋊C₈	—	19	2	no	—
110	C₂×#97	—	2	2	no	—
111	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
112	#391	—	19	2	no	—
113	#389	—	38	2	no	—
114	#384	—	19	1	no	—
115	C₄×C₄⋊C₄	—	38	2	no	—
116	C₄³	C₂×D₁₉	1	1	yes	characteristic
117	#336	—	38	2	no	—
118	Q₈⋊C₈	—	38	8	no	—
119	C₂×C₁₉	#1485	1	2	yes	—
120	C₂×C₁₉	#1491	1	2	yes	—
121	C₂×C₁₉	#1955	1	1	yes	characteristic
122	C₂×C₁₉	#1960	1	1	yes	characteristic
123	C₂×C₁₉	#1962	1	1	yes	characteristic
124	C₂²×Q₈	—	19	2	no	—
125	C₂²×C₈	—	2	2	no	—
126	C₂²×C₈	—	38	2	no	—
127	C₄⋊Q₈	—	38	4	no	—
128	C₄×Q₈	—	38	4	no	—
129	C₄×Q₈	—	38	4	no	—
130	C₂×C₄⋊C₄	—	19	2	no	—
131	C₂×C₄⋊C₄	—	38	2	no	—
132	C₂×C₄⋊C₄	—	38	2	no	—
133	C₂×C₄⋊C₄	—	38	2	no	—
134	C₂×C₄²	—	38	2	no	—
135	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
136	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
137	C₂×C₄²	D₇₆	1	2	yes	—
138	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
139	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
140	C₄⋊C₈	—	38	4	no	—
141	#97	—	2	8	no	—
142	C₄×C₈	—	2	2	no	—
143	C₄×C₈	D₇₆	1	4	yes	—
144	#95	—	38	4	no	—
145	C₁₉	#9647	1	1	yes	characteristic, complemented, Sylow
146	C₂×Q₈	—	19	4	no	—
147	C₂×Q₈	—	38	2	no	—
148	C₂×Q₈	—	38	4	no	—
149	C₂×Q₈	—	38	4	no	—
150	C₂²×C₄	—	38	2	no	—
151	C₂²×C₄	—	38	2	no	—
152	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
153	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
154	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
155	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
156	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
157	C₂×C₈	—	2	8	no	—
158	C₂×C₈	—	2	4	no	—
159	C₂×C₈	—	76	2	no	—
160	C₂×C₈	—	76	4	no	—
161	C₄⋊C₄	—	38	8	no	—
162	C₄⋊C₄	—	38	4	no	—
163	C₄⋊C₄	—	76	4	no	—
164	C₄⋊C₄	—	76	4	no	—
165	C₄²	—	2	4	no	—
166	C₄²	—	2	2	no	—
167	C₄²	—	2	2	no	—
168	C₄²	—	2	4	no	—
169	C₄²	—	76	2	no	—
170	C₄²	—	76	2	no	—
171	C₄²	C₂×D₇₆	1	2	yes	—
172	C₄²	#64541	1	2	yes	—
173	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
174	Q₈	—	38	8	no	—
175	Q₈	—	76	4	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	—	2	2	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	38	4	no	—
183	C₂×C₄	—	76	2	no	—
184	C₂×C₄	—	76	2	no	—
185	C₂×C₄	—	76	4	no	—
186	C₂×C₄	—	76	2	no	—
187	C₂×C₄	#10597262	1	4	yes	—
188	C₂×C₄	C₄×D₇₆	1	2	yes	—
189	C₂×C₄	#10597320	1	1	yes	characteristic
190	C₂×C₄	#10597321	1	1	yes	characteristic
191	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
192	C₂×C₄	#10597353	1	2	yes	—
193	C₂×C₄	#10597355	1	4	yes	—
194	C₂×C₄	#10597376	1	2	yes	—
195	C₈	—	2	8	no	—
196	C₈	—	152	2	no	—
197	C₂²	#11926446	1	1	yes	characteristic
198	C₂²	#11926507	1	1	yes	characteristic
199	C₂²	#11926512	1	1	yes	characteristic
200	C₂²	#11926554	1	2	yes	—
201	C₂²	C₂×#10597262	1	2	yes	—
202	C₄	—	2	4	no	—
203	C₄	—	2	2	no	—
204	C₄	—	4	2	no	—
205	C₄	—	76	4	no	—
206	C₄	—	152	2	no	—
207	C₄	#11926617	1	4	yes	—
208	C₄	#11926913	1	2	yes	—
209	C₄	#11926938	1	2	yes	—
210	C₂	#14562057	1	2	yes	—
211	C₂	#14562083	1	2	yes	—
212	C₂	#14564433	1	1	yes	characteristic
213	C₂	#14564455	1	1	yes	characteristic
214	C₂	#14564463	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10597315

C₂

yes

maximal, characteristic

#14563752

C₂

yes

maximal, characteristic

C₂×#11926276

C₂

yes

maximal

C₄×C₁₉×#97

C₂

yes

maximal, characteristic

C₂×#10597315

C₄

yes

characteristic

C₂×C₄×Dic₃₈

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#11926450

C₄

yes

—

#11926442

—

#11926414

C₄

yes

characteristic

C₄×C₄⋊Dic₁₉

—

#11926299

—

#11926276

—

C₂×C₁₉×#97

—

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂×C₄

yes

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

#10597315

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

D₄

yes

—

C₁₉⋊#95

—

C₄⋊(C₁₉⋊C₈)

—

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

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

M₁₆

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9647

—

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

—

C₂×C₄×C₁₉

#104

yes

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₄×C₄⋊Q₈

—

#1831

—

C₄×#97

D₁₉

yes

characteristic

C₂×Q₈⋊C₈

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

C₂×#104

yes

—

C₄×C₁₉

—

100

C₄×C₁₉

—

101

C₄×C₁₉

—

102

C₄×C₁₉

#435

yes

—

103

C₄×C₁₉

#491

yes

—

104

C₄×C₁₉

#497

yes

—

105

Dic₁₉

—

106

Dic₁₉

—

107

C₂×C₄⋊Q₈

—

108

C₂×C₄×Q₈

—

109

C₂×C₄⋊C₈

—

110

C₂×#97

—

111

C₂×C₄×C₈

C₂×D₁₉

yes

—

112

#391

—

113

#389

—

114

#384

—

115

C₄×C₄⋊C₄

—

116

C₄³

C₂×D₁₉

yes

characteristic

117

#336

—

118

Q₈⋊C₈

—

119

C₂×C₁₉

#1485

yes

—

120

C₂×C₁₉

#1491

yes

—

121

C₂×C₁₉

#1955

yes

characteristic

122

C₂×C₁₉

#1960

yes

characteristic

123

C₂×C₁₉

#1962

yes

characteristic

124

C₂²×Q₈

—

125

C₂²×C₈

—

126

C₂²×C₈

—

127

C₄⋊Q₈

—

128

C₄×Q₈

—

129

C₄×Q₈

—

130

C₂×C₄⋊C₄

—

131

C₂×C₄⋊C₄

—

132

C₂×C₄⋊C₄

—

133

C₂×C₄⋊C₄

—

134

C₂×C₄²

—

135

C₂×C₄²

C₄×D₁₉

yes

characteristic

136

C₂×C₄²

C₄×D₁₉

yes

characteristic

137

C₂×C₄²

D₇₆

yes

—

138

C₂×C₄²

C₂²⋊D₁₉

yes

—

139

C₂×C₄²

C₂²×D₁₉

yes

characteristic

140

C₄⋊C₈

—

141

#97

—

142

C₄×C₈

—

143

C₄×C₈

D₇₆

yes

—

144

#95

—

145

C₁₉

#9647

yes

characteristic, complemented, Sylow

146

C₂×Q₈

—

147

C₂×Q₈

—

148

C₂×Q₈

—

149

C₂×Q₈

—

150

C₂²×C₄

—

151

C₂²×C₄

—

152

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

153

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

154

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

155

C₂²×C₄

C₂×D₇₆

yes

characteristic

156

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄²

—

166

C₄²

—

167

C₄²

—

168

C₄²

—

169

C₄²

—

170

C₄²

—

171

C₄²

C₂×D₇₆

yes

—

172

C₄²

#64541

yes

—

173

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

174

Q₈

—

175

Q₈

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

#10597262

yes

—

188

C₂×C₄

C₄×D₇₆

yes

—

189

C₂×C₄

#10597320

yes

characteristic

190

C₂×C₄

#10597321

yes

characteristic

191

C₂×C₄

M₁₆×D₁₉

yes

—

192

C₂×C₄

#10597353

yes

—

193

C₂×C₄

#10597355

yes

—

194

C₂×C₄

#10597376

yes

—

195

C₈

—

196

C₈

—

152

—

197

C₂²

#11926446

yes

characteristic

198

C₂²

#11926507

yes

characteristic

199

C₂²

#11926512

yes

characteristic

200

C₂²

#11926554

yes

—

201

C₂²

C₂×#10597262

yes

—

202

C₄

—

203

C₄

—

204

C₄

—

205

C₄

—

206

C₄

—

152

—

207

C₄

#11926617

yes

—

208

C₄

#11926913

yes

—

209

C₄

#11926938

yes

—

210

C₂

#14562057

yes

—

211

C₂

#14562083

yes

—

212

C₂

#14564433

yes

characteristic

213

C₂

#14564455

yes

characteristic

214

C₂

#14564463

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₇₆
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#97	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#97	D₁₉
hypocenter	C₁₉	#9647
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×#97

subgroup

G/H

center

C₂²×C₄

C₂×D₇₆

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×#97

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

hypercenter

C₄×#97

D₁₉

hypocenter

C₁₉

#9647

LCS

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×#97

N	H ≅ G/N	type
145. C₁₉	#9647	semidirect

H ≅ G/N

type

145. C₁₉

#9647

semidirect

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

subgroup	index
C₄×#10597315	2
#14563752	2
C₂×#11926276	2
C₄×C₁₉×#97	2
#9647	19

subgroup

index

C₄×C₁₉×#97

Subgroups — #18081355

Conjugacy classes of subgroups

Complements

Maximal subgroups