Group #18075492 — subgroups

Subgroups — #18075492

Order 4864.

450 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 101 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	C₂×#11926609	C₂	1	1	yes	maximal, characteristic
2	#14562396	C₂	1	2	yes	maximal, complemented
3	#14561975	C₂	1	2	yes	maximal
4	#14561505	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1290	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₁₉	C₄	1	2	yes	—
7	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
8	#11926609	—	2	2	no	—
9	#11926609	—	2	2	no	—
10	#11926601	C₂²	1	2	yes	—
11	C₂×(C₂×D₁₉)⋊C₈	C₄	1	2	yes	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#11926296	—	2	2	no	—
14	#11926294	—	2	2	no	—
15	#11926267	—	2	4	no	—
16	C₁₉×#432	C₂²	1	2	yes	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂²×D₇₆	Q₈	1	1	yes	characteristic
19	C₂²×C₄×D₁₉	C₂×C₄	1	2	yes	—
20	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
21	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×(C₂×D₁₉)⋊C₄	D₄	1	2	yes	—
23	C₂×C₄⋊Dic₁₉	Q₈	1	1	yes	characteristic
24	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₂×C₈×D₁₉	—	2	2	no	—
27	C₂×C₈×D₁₉	—	2	2	no	—
28	C₂×C₈×D₁₉	—	4	4	no	—
29	C₄×D₇₆	—	2	2	no	—
30	C₄×D₇₆	—	2	2	no	—
31	C₁₉×C₄⋊C₈	—	2	2	no	—
32	C₁₉×C₄⋊C₈	—	2	2	no	—
33	C₁₉×C₂²⋊C₈	—	2	2	no	—
34	C₁₉×#97	—	2	2	no	—
35	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
36	(C₂×D₁₉)⋊C₈	—	2	4	no	—
37	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
38	#10597260	—	2	2	no	—
39	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
40	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
41	C₂³×D₁₉	C₄⋊C₄	1	2	yes	—
42	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
45	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
46	C₂×D₇₆	—	2	4	no	—
47	C₂×D₇₆	—	2	2	no	—
48	C₂×C₄×D₁₉	—	2	2	no	—
49	C₂×C₄×D₁₉	—	2	2	no	—
50	C₂×C₄×D₁₉	—	4	2	no	—
51	C₂×C₄×D₁₉	—	4	2	no	—
52	C₂×C₈×C₁₉	—	2	2	no	—
53	C₂×C₈×C₁₉	—	4	2	no	—
54	C₂×C₈×C₁₉	—	4	2	no	—
55	C₄²×C₁₉	C₂×D₄	1	2	yes	—
56	C₄²×C₁₉	#41	1	2	yes	—
57	(C₂×D₁₉)⋊C₄	—	2	4	no	—
58	C₄⋊Dic₁₉	—	2	2	no	—
59	C₂×C₁₉⋊C₈	—	2	2	no	—
60	C₂×C₁₉⋊C₈	—	4	1	no	—
61	C₂×C₁₉⋊C₈	—	4	2	no	—
62	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
63	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
65	C₈×D₁₉	—	4	4	no	—
66	C₈×D₁₉	—	4	4	no	—
67	#8622	—	19	1	no	maximal, Sylow
68	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
69	C₂²×D₁₉	—	2	2	no	—
70	C₂²×D₁₉	—	2	2	no	—
71	C₂²×D₁₉	—	4	2	no	—
72	C₂²×D₁₉	—	4	2	no	—
73	C₂²×D₁₉	#108	1	4	yes	—
74	C₂×C₄×C₁₉	—	2	2	no	—
75	C₂×C₄×C₁₉	—	2	1	no	—
76	C₂×C₄×C₁₉	—	2	1	no	—
77	C₂×C₄×C₁₉	—	4	1	no	—
78	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
80	C₂×C₄×C₁₉	#121	1	2	yes	—
81	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
82	C₂×Dic₁₉	—	2	2	no	—
83	C₂×Dic₁₉	—	4	2	no	—
84	D₇₆	—	2	8	no	—
85	C₄×D₁₉	—	4	4	no	—
86	C₄×D₁₉	—	4	2	no	—
87	C₄×D₁₉	—	4	2	no	—
88	C₈×C₁₉	—	4	2	no	—
89	C₈×C₁₉	—	8	2	no	—
90	C₁₉⋊C₈	—	2	1	no	—
91	C₁₉⋊C₈	—	2	2	no	—
92	C₁₉⋊C₈	—	8	2	no	—
93	C₁₉⋊C₈	#100	1	2	yes	—
94	C₂×C₈×D₄	—	19	1	no	—
95	#1568	—	19	2	no	—
96	#1466	—	19	2	no	—
97	#1290	—	19	1	no	—
98	#1290	D₁₉	1	1	yes	characteristic, complemented
99	C₂²×C₁₉	—	2	1	no	—
100	C₂²×C₁₉	—	2	1	no	—
101	C₂²×C₁₉	#380	1	1	yes	characteristic
102	C₂²×C₁₉	C₂×#108	1	2	yes	—
103	C₂×D₁₉	—	2	4	no	—
104	C₂×D₁₉	—	4	4	no	—
105	C₂×D₁₉	—	4	2	no	—
106	C₂×D₁₉	—	4	2	no	—
107	C₂×D₁₉	—	4	4	no	—
108	C₄×C₁₉	—	2	1	no	—
109	C₄×C₁₉	—	2	2	no	—
110	C₄×C₁₉	—	2	2	no	—
111	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
112	C₄×C₁₉	#413	1	1	yes	characteristic
113	Dic₁₉	—	4	2	no	—
114	C₂³×C₈	—	19	2	no	—
115	C₂×C₄×D₄	—	19	1	no	—
116	C₈×D₄	—	38	2	no	—
117	C₈×D₄	—	38	2	no	—
118	#432	—	19	2	no	—
119	#432	C₂×D₁₉	1	2	yes	—
120	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
121	C₂×C₂²⋊C₈	—	19	2	no	—
122	C₂×C₄×C₈	—	19	1	no	—
123	#335	—	38	2	no	—
124	#334	—	38	2	no	—
125	#323	—	38	4	no	—
126	C₂×C₁₉	—	2	2	no	—
127	C₂×C₁₉	#1800	1	1	yes	characteristic
128	C₂×C₁₉	#1810	1	1	yes	characteristic
129	C₂×C₁₉	#1812	1	1	yes	characteristic
130	D₁₉	—	4	4	no	—
131	C₂²×D₄	—	19	1	no	—
132	C₂³×C₄	—	19	2	no	—
133	C₂²×C₈	—	19	1	no	—
134	C₂²×C₈	—	19	1	no	—
135	C₂²×C₈	—	38	2	no	—
136	C₂²×C₈	—	38	2	no	—
137	C₂²×C₈	—	76	4	no	—
138	C₂²×C₈	C₄×D₁₉	1	2	yes	—
139	C₄×D₄	—	38	2	no	—
140	C₄×D₄	—	38	2	no	—
141	C₂×C₄⋊C₄	—	19	1	no	—
142	C₂×C₂²⋊C₄	—	19	2	no	—
143	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
144	C₄⋊C₈	—	2	2	no	—
145	C₄⋊C₈	—	2	2	no	—
146	C₄⋊C₈	—	38	2	no	—
147	C₂²⋊C₈	—	2	2	no	—
148	C₂²⋊C₈	—	38	4	no	—
149	C₂²⋊C₈	—	38	2	no	—
150	#97	—	2	2	no	—
151	#97	—	38	2	no	—
152	C₄×C₈	—	19	2	no	—
153	C₄×C₈	—	19	2	no	—
154	C₁₉	#8622	1	1	yes	characteristic, complemented, Sylow
155	C₂⁴	—	19	2	no	—
156	C₂×D₄	—	38	4	no	—
157	C₂×D₄	—	38	2	no	—
158	C₂²×C₄	—	19	2	no	—
159	C₂²×C₄	—	38	2	no	—
160	C₂²×C₄	—	38	2	no	—
161	C₂²×C₄	—	76	2	no	—
162	C₂²×C₄	—	76	2	no	—
163	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
164	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
165	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
166	C₂×C₈	—	2	2	no	—
167	C₂×C₈	—	4	2	no	—
168	C₂×C₈	—	4	2	no	—
169	C₂×C₈	—	19	1	no	—
170	C₂×C₈	—	19	2	no	—
171	C₂×C₈	—	19	1	no	—
172	C₂×C₈	—	38	2	no	—
173	C₂×C₈	—	76	4	no	—
174	C₂×C₈	—	76	4	no	—
175	C₂×C₈	—	76	1	no	—
176	C₂×C₈	—	76	2	no	—
177	C₄⋊C₄	—	38	2	no	—
178	C₂²⋊C₄	—	38	4	no	—
179	C₄²	#64541	1	2	yes	—
180	C₄²	D₄×D₁₉	1	2	yes	—
181	C₂³	—	19	4	no	—
182	C₂³	—	38	2	no	—
183	C₂³	—	38	2	no	—
184	C₂³	—	76	2	no	—
185	C₂³	—	76	2	no	—
186	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
187	D₄	—	38	8	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	4	1	no	—
192	C₂×C₄	—	38	2	no	—
193	C₂×C₄	—	76	4	no	—
194	C₂×C₄	—	76	2	no	—
195	C₂×C₄	—	76	2	no	—
196	C₂×C₄	—	76	2	no	—
197	C₂×C₄	#10597318	1	1	yes	characteristic
198	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
199	C₂×C₄	#10597330	1	2	yes	—
200	C₂×C₄	#10597342	1	2	yes	—
201	C₈	—	4	2	no	—
202	C₈	—	8	2	no	—
203	C₈	—	19	2	no	—
204	C₈	—	38	1	no	—
205	C₈	—	38	2	no	—
206	C₈	—	152	2	no	—
207	C₂²	—	2	1	no	—
208	C₂²	—	2	1	no	—
209	C₂²	—	38	4	no	—
210	C₂²	—	76	4	no	—
211	C₂²	—	76	4	no	—
212	C₂²	—	76	2	no	—
213	C₂²	—	76	2	no	—
214	C₂²	#11926403	1	1	yes	characteristic
215	C₂²	#108×D₁₉	1	2	yes	—
216	C₄	—	2	1	no	—
217	C₄	—	2	2	no	—
218	C₄	—	2	2	no	—
219	C₄	—	76	2	no	—
220	C₄	#100×D₁₉	1	1	yes	characteristic
221	C₄	#11926527	1	1	yes	characteristic
222	C₂	—	2	2	no	—
223	C₂	—	76	4	no	—
224	C₂	#14563626	1	1	yes	characteristic
225	C₂	#14563672	1	1	yes	characteristic
226	C₂	#14563680	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926609

C₂

yes

maximal, characteristic

#14562396

C₂

yes

maximal, complemented

#14561975

C₂

yes

maximal

#14561505

C₂

yes

maximal, characteristic, complemented

C₁₉×#1290

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₁₉

C₄

yes

—

C₂×C₄×D₇₆

C₂²

yes

—

—

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₈

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

C₁₉×#432

C₂²

yes

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂²×D₇₆

Q₈

yes

characteristic

C₂²×C₄×D₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

D₄

yes

—

C₂×C₄⋊Dic₁₉

Q₈

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₈×D₁₉

—

C₂×C₈×D₁₉

—

C₂×C₈×D₁₉

—

C₄×D₇₆

—

C₄×D₇₆

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₂²⋊(C₁₉⋊C₈)

—

(C₂×D₁₉)⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂³×D₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×Dic₁₉

C₄⋊C₄

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₈×D₁₉

—

C₈×D₁₉

—

#8622

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

#108

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

#100

yes

—

C₂×C₈×D₄

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

#380

yes

characteristic

102

C₂²×C₁₉

C₂×#108

yes

—

103

C₂×D₁₉

—

104

C₂×D₁₉

—

105

C₂×D₁₉

—

106

C₂×D₁₉

—

107

C₂×D₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

C₂×#100

yes

characteristic

112

C₄×C₁₉

#413

yes

characteristic

113

Dic₁₉

—

114

C₂³×C₈

—

115

C₂×C₄×D₄

—

116

C₈×D₄

—

117

C₈×D₄

—

118

#432

—

119

#432

C₂×D₁₉

yes

—

120

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

121

C₂×C₂²⋊C₈

—

122

C₂×C₄×C₈

—

123

#335

—

124

#334

—

125

#323

—

126

C₂×C₁₉

—

127

C₂×C₁₉

#1800

yes

characteristic

128

C₂×C₁₉

#1810

yes

characteristic

129

C₂×C₁₉

#1812

yes

characteristic

130

D₁₉

—

131

C₂²×D₄

—

132

C₂³×C₄

—

133

C₂²×C₈

—

134

C₂²×C₈

—

135

C₂²×C₈

—

136

C₂²×C₈

—

137

C₂²×C₈

—

138

C₂²×C₈

C₄×D₁₉

yes

—

139

C₄×D₄

—

140

C₄×D₄

—

141

C₂×C₄⋊C₄

—

142

C₂×C₂²⋊C₄

—

143

C₂×C₄²

C₂²×D₁₉

yes

characteristic

144

C₄⋊C₈

—

145

C₄⋊C₈

—

146

C₄⋊C₈

—

147

C₂²⋊C₈

—

148

C₂²⋊C₈

—

149

C₂²⋊C₈

—

150

#97

—

151

#97

—

152

C₄×C₈

—

153

C₄×C₈

—

154

C₁₉

#8622

yes

characteristic, complemented, Sylow

155

C₂⁴

—

156

C₂×D₄

—

157

C₂×D₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

164

C₂²×C₄

D₄×D₁₉

yes

characteristic

165

C₂²×C₄

Q₈×D₁₉

yes

characteristic

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₄⋊C₄

—

178

C₂²⋊C₄

—

179

C₄²

#64541

yes

—

180

C₄²

D₄×D₁₉

yes

—

181

C₂³

—

182

C₂³

—

183

C₂³

—

184

C₂³

—

185

C₂³

—

186

C₂³

C₄⋊C₄×D₁₉

yes

characteristic

187

D₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

#10597318

yes

characteristic

198

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

199

C₂×C₄

#10597330

yes

—

200

C₂×C₄

#10597342

yes

—

201

C₈

—

202

C₈

—

203

C₈

—

204

C₈

—

205

C₈

—

206

C₈

—

152

—

207

C₂²

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

#11926403

yes

characteristic

215

C₂²

#108×D₁₉

yes

—

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

#100×D₁₉

yes

characteristic

221

C₄

#11926527

yes

characteristic

222

C₂

—

223

C₂

—

224

C₂

#14563626

yes

characteristic

225

C₂

#14563672

yes

characteristic

226

C₂

#14563680

yes

characteristic

	subgroup	G/H
center	C₂²	#11926403
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1290	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂²×D₇₆	Q₈
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1290	D₁₉
hypocenter	C₁₉	#8622
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1290

subgroup

G/H

center

C₂²

#11926403

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1290

C₂

socle

C₂²×C₁₉

#380

prime radical

C₂²×D₇₆

Q₈

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1290

N	H ≅ G/N	type
2. #14562396	C₂	semidirect
4. #14561505	C₂	semidirect
5. C₁₉×#1290	C₂	semidirect
98. #1290	D₁₉	semidirect
154. C₁₉	#8622	semidirect

H ≅ G/N

type

2. #14562396

C₂

semidirect

4. #14561505

C₂

semidirect

5. C₁₉×#1290

C₂

semidirect

98. #1290

D₁₉

semidirect

154. C₁₉

#8622

semidirect

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

subgroup	index
C₂×#11926609	2
#14562396	2
#14561975	2
#14561505	2
C₁₉×#1290	2
#8622	19

subgroup

index

C₁₉×#1290

Subgroups — #18075492

Conjugacy classes of subgroups

Complements

Maximal subgroups