Group #18069863 — subgroups

Subgroups — #18069863

Order 4864.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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	#14563706	C₂	1	1	yes	maximal, characteristic
2	#14561969	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1464	C₂	1	1	yes	maximal, characteristic
4	#11926601	—	2	1	no	—
5	C₂×C₂²⋊(C₁₉⋊C₈)	C₄	1	1	yes	characteristic
6	C₂×C₂²⋊(C₁₉⋊C₈)	C₄	1	1	yes	characteristic
7	#11926299	—	2	1	no	—
8	#11926299	—	2	1	no	—
9	#11926270	C₄	1	2	yes	—
10	#11926268	—	2	1	no	—
11	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
12	C₁₉×#432	—	2	1	no	—
13	C₁₉×#324	C₄	1	2	yes	—
14	C₁₉×#323	—	2	1	no	—
15	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₁₉×#117	—	4	1	no	—
17	C₁₉×#117	—	4	1	no	—
18	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₂²⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
22	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
24	C₂²×C₁₉⋊C₈	—	2	1	no	—
25	C₂²×C₁₉⋊C₈	—	2	1	no	—
26	C₁₉×C₄⋊C₈	—	4	1	no	—
27	C₁₉×C₂²⋊C₈	—	2	2	no	—
28	C₁₉×#97	—	4	1	no	—
29	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
30	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
31	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
32	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
33	#10597260	—	4	1	no	—
34	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	—	2	1	no	—
36	C₂²×C₄×C₁₉	—	2	1	no	—
37	C₂²×C₄×C₁₉	—	4	1	no	—
38	C₂²×C₄×C₁₉	—	4	1	no	—
39	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₉	—	4	2	no	—
46	C₄⋊C₄×C₁₉	—	4	1	no	—
47	C₄⋊C₄×C₁₉	—	4	1	no	—
48	C₂²⋊C₄×C₁₉	—	4	1	no	—
49	C₂²⋊C₄×C₁₉	—	4	1	no	—
50	C₄²×C₁₉	—	2	1	no	—
51	C₄²×C₁₉	—	2	1	no	—
52	C₄²×C₁₉	—	2	1	no	—
53	C₄²×C₁₉	—	2	1	no	—
54	C₂×C₁₉⋊C₈	—	4	2	no	—
55	C₂×C₁₉⋊C₈	—	4	1	no	—
56	C₂×C₁₉⋊C₈	—	4	1	no	—
57	C₂×C₁₉⋊C₈	—	4	1	no	—
58	C₂×C₁₉⋊C₈	—	4	1	no	—
59	C₂×C₁₉⋊C₈	—	4	1	no	—
60	C₂×C₁₉⋊C₈	—	4	1	no	—
61	#7327	—	19	1	no	maximal, Sylow
62	C₂³×C₁₉	—	2	1	no	—
63	C₂³×C₁₉	—	2	1	no	—
64	C₂³×C₁₉	—	2	1	no	—
65	C₂³×C₁₉	—	4	1	no	—
66	C₂³×C₁₉	—	4	1	no	—
67	C₂³×C₁₉	#95	1	1	yes	characteristic
68	C₂×C₄×C₁₉	—	2	1	no	—
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	2	1	no	—
72	C₂×C₄×C₁₉	—	2	1	no	—
73	C₂×C₄×C₁₉	—	2	1	no	—
74	C₂×C₄×C₁₉	—	2	1	no	—
75	C₂×C₄×C₁₉	—	2	1	no	—
76	C₂×C₄×C₁₉	—	2	1	no	—
77	C₂×C₄×C₁₉	—	4	2	no	—
78	C₂×C₄×C₁₉	—	4	2	no	—
79	C₂×C₄×C₁₉	—	4	1	no	—
80	C₂×C₄×C₁₉	—	4	1	no	—
81	C₂×C₄×C₁₉	—	4	1	no	—
82	C₂×C₄×C₁₉	—	4	1	no	—
83	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
85	C₈×C₁₉	—	8	2	no	—
86	C₁₉⋊C₈	—	8	1	no	—
87	C₁₉⋊C₈	—	8	1	no	—
88	C₁₉⋊C₈	—	8	2	no	—
89	#1818	—	19	1	no	—
90	#1464	—	19	1	no	—
91	#1464	D₁₉	1	1	yes	characteristic
92	C₂²×C₁₉	—	2	1	no	—
93	C₂²×C₁₉	—	2	1	no	—
94	C₂²×C₁₉	—	4	1	no	—
95	C₂²×C₁₉	—	4	1	no	—
96	C₂²×C₁₉	—	4	1	no	—
97	C₂²×C₁₉	—	8	1	no	—
98	C₂²×C₁₉	—	8	1	no	—
99	C₂²×C₁₉	#342	1	1	yes	characteristic
100	C₂²×C₁₉	#344	1	1	yes	characteristic
101	C₂²×C₁₉	#344	1	1	yes	characteristic
102	C₄×C₁₉	—	2	1	no	—
103	C₄×C₁₉	—	2	1	no	—
104	C₄×C₁₉	—	4	1	no	—
105	C₄×C₁₉	—	4	1	no	—
106	C₄×C₁₉	—	4	1	no	—
107	C₄×C₁₉	—	4	1	no	—
108	C₄×C₁₉	—	4	1	no	—
109	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
110	#432	—	2	1	no	—
111	#432	—	38	1	no	—
112	C₂×C₂²⋊C₈	—	19	1	no	—
113	C₂×C₂²⋊C₈	—	19	1	no	—
114	#336	—	38	1	no	—
115	#336	—	38	1	no	—
116	#324	—	19	2	no	—
117	#324	Dic₁₉	1	2	yes	—
118	#323	—	2	1	no	—
119	#323	—	38	1	no	—
120	C₂×C₁₉	—	2	1	no	—
121	C₂×C₁₉	—	2	1	no	—
122	C₂×C₁₉	—	8	1	no	—
123	C₂×C₁₉	#1306	1	1	yes	characteristic
124	C₂×C₁₉	#1395	1	1	yes	characteristic
125	C₂×C₁₉	#1395	1	1	yes	characteristic
126	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
127	C₂²×C₈	—	38	1	no	—
128	C₂²×C₈	—	38	1	no	—
129	#117	—	4	1	no	—
130	#117	—	4	1	no	—
131	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
132	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
133	C₂×C₂²⋊C₄	Dic₃₈	1	1	yes	characteristic
134	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
135	C₂×C₄²	D₇₆	1	1	yes	characteristic
136	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
137	C₄⋊C₈	—	4	1	no	—
138	C₄⋊C₈	—	76	1	no	—
139	C₂²⋊C₈	—	2	2	no	—
140	C₂²⋊C₈	—	38	2	no	—
141	C₂²⋊C₈	—	76	1	no	—
142	C₂²⋊C₈	—	76	1	no	—
143	#97	—	4	1	no	—
144	#97	—	76	1	no	—
145	C₁₉	#7327	1	1	yes	characteristic, complemented, Sylow
146	C₂⁴	Dic₁₉⋊C₄	1	1	yes	characteristic
147	C₂²×C₄	—	2	1	no	—
148	C₂²×C₄	—	2	1	no	—
149	C₂²×C₄	—	4	1	no	—
150	C₂²×C₄	—	4	1	no	—
151	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
152	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
153	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
154	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
155	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
156	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
157	C₂×C₈	—	4	2	no	—
158	C₂×C₈	—	76	2	no	—
159	C₂×C₈	—	76	1	no	—
160	C₂×C₈	—	76	1	no	—
161	C₂×C₈	—	76	1	no	—
162	C₂×C₈	—	76	1	no	—
163	C₂×C₈	—	76	1	no	—
164	C₂×C₈	—	76	1	no	—
165	C₄⋊C₄	—	4	1	no	—
166	C₄⋊C₄	—	4	1	no	—
167	C₂²⋊C₄	—	4	1	no	—
168	C₂²⋊C₄	—	4	1	no	—
169	C₄²	—	2	1	no	—
170	C₄²	—	2	1	no	—
171	C₄²	—	2	1	no	—
172	C₄²	—	2	1	no	—
173	C₂³	—	2	1	no	—
174	C₂³	—	2	1	no	—
175	C₂³	—	2	1	no	—
176	C₂³	—	4	1	no	—
177	C₂³	—	4	1	no	—
178	C₂³	C₁₉⋊#95	1	1	yes	characteristic
179	C₂×C₄	—	2	1	no	—
180	C₂×C₄	—	2	1	no	—
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	1	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	—	2	1	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	—	4	2	no	—
190	C₂×C₄	—	4	1	no	—
191	C₂×C₄	—	4	1	no	—
192	C₂×C₄	—	4	1	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	#10597263	1	1	yes	characteristic
195	C₂×C₄	#10597263	1	1	yes	characteristic
196	C₈	—	8	2	no	—
197	C₈	—	152	1	no	—
198	C₈	—	152	1	no	—
199	C₈	—	152	2	no	—
200	C₂²	—	2	1	no	—
201	C₂²	—	2	1	no	—
202	C₂²	—	4	1	no	—
203	C₂²	—	4	1	no	—
204	C₂²	—	4	1	no	—
205	C₂²	—	8	1	no	—
206	C₂²	—	8	1	no	—
207	C₂²	#11926310	1	1	yes	characteristic
208	C₂²	#11926315	1	1	yes	characteristic
209	C₂²	#11926316	1	1	yes	characteristic
210	C₄	—	2	1	no	—
211	C₄	—	2	1	no	—
212	C₄	—	4	1	no	—
213	C₄	—	4	1	no	—
214	C₄	—	4	1	no	—
215	C₄	—	4	1	no	—
216	C₄	—	4	1	no	—
217	C₂	—	2	1	no	—
218	C₂	—	2	1	no	—
219	C₂	—	8	1	no	—
220	C₂	#14561544	1	1	yes	characteristic
221	C₂	#14561763	1	1	yes	characteristic
222	C₂	#14561765	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563706

C₂

yes

maximal, characteristic

#14561969

C₂

yes

maximal, characteristic

C₁₉×#1464

C₂

yes

maximal, characteristic

#11926601

—

C₂×C₂²⋊(C₁₉⋊C₈)

C₄

yes

characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

C₄

yes

—

—

C₄

yes

—

#11926268

—

C₂×C₁₉×#117

C₂²

yes

characteristic

C₁₉×#432

—

C₁₉×#324

C₄

yes

—

C₁₉×#323

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂⁴×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7327

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#95

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1818

—

#1464

—

#1464

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#342

yes

characteristic

100

C₂²×C₁₉

#344

yes

characteristic

101

C₂²×C₁₉

#344

yes

characteristic

102

C₄×C₁₉

—

103

C₄×C₁₉

—

104

C₄×C₁₉

—

105

C₄×C₁₉

—

106

C₄×C₁₉

—

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₂×#117

C₂×D₁₉

yes

characteristic

110

#432

—

111

#432

—

112

C₂×C₂²⋊C₈

—

113

C₂×C₂²⋊C₈

—

114

#336

—

115

#336

—

116

#324

—

117

#324

Dic₁₉

yes

—

118

#323

—

119

#323

—

120

C₂×C₁₉

—

121

C₂×C₁₉

—

122

C₂×C₁₉

—

123

C₂×C₁₉

#1306

yes

characteristic

124

C₂×C₁₉

#1395

yes

characteristic

125

C₂×C₁₉

#1395

yes

characteristic

126

C₂³×C₄

C₄×D₁₉

yes

characteristic

127

C₂²×C₈

—

128

C₂²×C₈

—

129

#117

—

130

#117

—

131

C₂×C₄⋊C₄

C₄×D₁₉

yes

characteristic

132

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

133

C₂×C₂²⋊C₄

Dic₃₈

yes

characteristic

134

C₂×C₂²⋊C₄

C₂²⋊D₁₉

yes

characteristic

135

C₂×C₄²

D₇₆

yes

characteristic

136

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

137

C₄⋊C₈

—

138

C₄⋊C₈

—

139

C₂²⋊C₈

—

140

C₂²⋊C₈

—

141

C₂²⋊C₈

—

142

C₂²⋊C₈

—

143

#97

—

144

#97

—

145

C₁₉

#7327

yes

characteristic, complemented, Sylow

146

C₂⁴

Dic₁₉⋊C₄

yes

characteristic

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

—

151

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

152

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

153

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

154

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

155

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

156

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₂²⋊C₄

—

168

C₂²⋊C₄

—

169

C₄²

—

170

C₄²

—

171

C₄²

—

172

C₄²

—

173

C₂³

—

174

C₂³

—

175

C₂³

—

176

C₂³

—

177

C₂³

—

178

C₂³

C₁₉⋊#95

yes

characteristic

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

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

#10597263

yes

characteristic

195

C₂×C₄

#10597263

yes

characteristic

196

C₈

—

197

C₈

—

152

—

198

C₈

—

152

—

199

C₈

—

152

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

—

204

C₂²

—

205

C₂²

—

206

C₂²

—

207

C₂²

#11926310

yes

characteristic

208

C₂²

#11926315

yes

characteristic

209

C₂²

#11926316

yes

characteristic

210

C₄

—

211

C₄

—

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₂

—

218

C₂

—

219

C₂

—

220

C₂

#14561544

yes

characteristic

221

C₂

#14561763

yes

characteristic

222

C₂

#14561765

yes

characteristic

	subgroup	G/H
center	C₂²	#11926310
commutator	C₂²×C₄×C₁₉	C₄²
Frattini	C₂×#117	C₂×D₁₉
Fitting	C₁₉×#1464	C₂
socle	C₂²×C₁₉	#342
prime radical	C₂⁴×C₁₉	C₄⋊C₄
cosocle	C₂×C₁₉×#117	C₂²
hypercenter	#1464	D₁₉
hypocenter	C₁₉	#7327
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#117 ◁ #1464

subgroup

G/H

center

C₂²

#11926310

commutator

C₂²×C₄×C₁₉

C₄²

Frattini

C₂×#117

C₂×D₁₉

Fitting

C₁₉×#1464

C₂

socle

C₂²×C₁₉

#342

prime radical

C₂⁴×C₁₉

C₄⋊C₄

cosocle

C₂×C₁₉×#117

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#117 ◁ #1464

N	H ≅ G/N	type
145. C₁₉	#7327	semidirect

H ≅ G/N

type

145. C₁₉

#7327

semidirect

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

subgroup	index
#14563706	2
#14561969	2
C₁₉×#1464	2
#7327	19

subgroup

index

#14563706

#14561969

C₁₉×#1464

#7327

Subgroups — #18069863

Conjugacy classes of subgroups

Complements

Maximal subgroups