Group #18087307 — subgroups

Subgroups — #18087307

Order 4864.

330 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 95 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	#14563789	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562284	C₂	1	2	yes	maximal
3	#14561530	C₂	1	2	yes	maximal, complemented
4	#14561464	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1963	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
8	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
10	#11926290	—	2	2	no	—
11	#11926288	—	2	2	no	—
12	C₁₉×#532	C₂²	1	1	yes	characteristic
13	C₁₉×#423	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#104	—	2	1	no	—
15	C₂×C₁₉×#104	—	2	1	no	—
16	C₁₉×#376	C₂²	1	1	yes	characteristic
17	C₂×#41×C₁₉	—	2	1	no	—
18	C₂×M₁₆×C₁₉	—	2	1	no	—
19	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
20	C₁₉×#127	D₄	1	1	yes	characteristic
21	C₁₉×#124	—	2	1	no	—
22	C₁₉×#121	—	2	2	no	—
23	C₄×D₄×C₁₉	—	2	2	no	—
24	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂²×C₁₉⋊C₈	—	2	2	no	—
28	C₁₉×C₄⋊C₈	—	2	2	no	—
29	C₁₉×#104	—	4	2	no	—
30	C₁₉×#104	—	4	2	no	—
31	C₁₉×#95	—	2	2	no	—
32	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
33	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
34	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
35	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
36	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
37	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
38	C₄×C₁₉⋊C₈	—	2	2	no	—
39	#41×C₁₉	—	4	1	no	—
40	#41×C₁₉	—	4	1	no	—
41	#41×C₁₉	—	4	1	no	—
42	#41×C₁₉	—	4	1	no	—
43	C₂×Q₈×C₁₉	—	2	1	no	—
44	C₂×D₄×C₁₉	—	2	1	no	—
45	C₂×D₄×C₁₉	—	2	2	no	—
46	C₂×D₄×C₁₉	—	4	1	no	—
47	C₂²×C₄×C₁₉	—	2	1	no	—
48	C₂²×C₄×C₁₉	—	2	1	no	—
49	C₂²×C₄×C₁₉	—	4	1	no	—
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	#41	1	2	yes	—
52	M₁₆×C₁₉	—	4	1	no	—
53	M₁₆×C₁₉	—	4	1	no	—
54	C₂×C₈×C₁₉	—	4	1	no	—
55	C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂²⋊C₄×C₁₉	—	4	2	no	—
57	C₄²×C₁₉	—	2	1	no	—
58	C₄²×C₁₉	—	2	1	no	—
59	C₄²×C₁₉	D₈	1	2	yes	—
60	C₄²×C₁₉	SD₁₆	1	2	yes	—
61	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₄²×C₁₉	#41	1	1	yes	characteristic
63	C₄²×C₁₉	#41	1	2	yes	—
64	C₂×C₁₉⋊C₈	—	4	2	no	—
65	C₂×C₁₉⋊C₈	—	4	2	no	—
66	C₂×C₁₉⋊C₈	—	4	2	no	—
67	C₂×C₁₉⋊C₈	—	4	2	no	—
68	#10627	—	19	1	no	maximal, Sylow
69	C₂³×C₁₉	—	4	1	no	—
70	C₂³×C₁₉	#123	1	1	yes	characteristic
71	Q₈×C₁₉	—	4	1	no	—
72	Q₈×C₁₉	—	4	1	no	—
73	D₄×C₁₉	—	4	1	no	—
74	D₄×C₁₉	—	4	1	no	—
75	D₄×C₁₉	—	8	2	no	—
76	D₄×C₁₉	—	8	1	no	—
77	D₄×C₁₉	—	8	1	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	4	2	no	—
81	C₂×C₄×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	—	4	1	no	—
84	C₂×C₄×C₁₉	—	8	1	no	—
85	C₂×C₄×C₁₉	—	8	1	no	—
86	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#123	1	2	yes	—
88	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
89	C₂×C₄×C₁₉	#126	1	2	yes	—
90	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
91	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
92	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
94	C₈×C₁₉	—	8	1	no	—
95	C₁₉⋊C₈	—	8	2	no	—
96	C₁₉⋊C₈	—	8	2	no	—
97	#1963	D₁₉	1	1	yes	characteristic
98	#1843	—	19	1	no	—
99	#1540	—	19	2	no	—
100	#1301	—	19	2	no	—
101	#1274	—	19	1	no	—
102	C₂²×C₁₉	—	2	2	no	—
103	C₂²×C₁₉	—	8	1	no	—
104	C₂²×C₁₉	—	8	2	no	—
105	C₂²×C₁₉	#397	1	1	yes	characteristic
106	C₂²×C₁₉	#480	1	1	yes	characteristic
107	C₂²×C₁₉	#481	1	1	yes	characteristic
108	C₄×C₁₉	—	2	2	no	—
109	C₄×C₁₉	—	2	2	no	—
110	C₄×C₁₉	—	4	2	no	—
111	C₄×C₁₉	—	4	2	no	—
112	C₄×C₁₉	—	8	1	no	—
113	C₄×C₁₉	#459	1	1	yes	characteristic
114	C₄×C₁₉	#461	1	1	yes	characteristic
115	C₄×C₁₉	#486	1	1	yes	characteristic
116	C₄×C₁₉	#489	1	1	yes	characteristic
117	#532	C₂×D₁₉	1	1	yes	characteristic
118	#431	—	19	2	no	—
119	#423	C₂×D₁₉	1	1	yes	characteristic
120	C₂×C₄⋊C₈	—	19	2	no	—
121	C₂×C₄⋊C₈	—	38	1	no	—
122	C₂×C₄⋊C₈	—	38	1	no	—
123	C₂×#104	—	2	1	no	—
124	C₂×#104	—	2	1	no	—
125	#376	C₂×D₁₉	1	1	yes	characteristic
126	#332	—	38	2	no	—
127	#331	—	38	2	no	—
128	C₂×C₁₉	—	2	1	no	—
129	C₂×C₁₉	—	2	1	no	—
130	C₂×C₁₉	—	16	1	no	—
131	C₂×C₁₉	#2071	1	1	yes	characteristic
132	C₂×C₁₉	#2080	1	2	yes	—
133	C₂×#41	—	2	1	no	—
134	C₂×M₁₆	—	2	1	no	—
135	C₂²×C₈	—	38	2	no	—
136	C₄⋊Q₈	D₇₆	1	1	yes	characteristic
137	#127	D₇₆	1	1	yes	characteristic
138	#124	—	2	1	no	—
139	#121	—	2	2	no	—
140	C₄×D₄	—	2	2	no	—
141	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
142	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
143	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
144	C₄⋊C₈	—	2	2	no	—
145	C₄⋊C₈	—	38	2	no	—
146	C₄⋊C₈	—	38	2	no	—
147	C₄⋊C₈	—	38	2	no	—
148	C₄⋊C₈	—	76	2	no	—
149	C₄⋊C₈	—	76	2	no	—
150	#104	—	4	2	no	—
151	#104	—	4	2	no	—
152	C₂²⋊C₈	—	38	2	no	—
153	C₄×C₈	—	38	2	no	—
154	#95	—	2	2	no	—
155	C₁₉	#10627	1	1	yes	characteristic, complemented, Sylow
156	#41	—	4	1	no	—
157	#41	—	4	1	no	—
158	#41	—	4	1	no	—
159	#41	—	4	1	no	—
160	C₂×Q₈	—	2	1	no	—
161	C₂×D₄	—	2	1	no	—
162	C₂×D₄	—	2	2	no	—
163	C₂×D₄	—	4	1	no	—
164	C₂²×C₄	—	2	1	no	—
165	C₂²×C₄	—	2	1	no	—
166	C₂²×C₄	—	4	1	no	—
167	C₂²×C₄	#64543	1	2	yes	—
168	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
169	M₁₆	—	4	1	no	—
170	M₁₆	—	4	1	no	—
171	C₂×C₈	—	4	1	no	—
172	C₂×C₈	—	76	2	no	—
173	C₂×C₈	—	76	2	no	—
174	C₂×C₈	—	76	2	no	—
175	C₂×C₈	—	76	2	no	—
176	C₄⋊C₄	—	2	2	no	—
177	C₂²⋊C₄	—	4	2	no	—
178	C₄²	—	2	1	no	—
179	C₄²	—	2	1	no	—
180	C₄²	#64525	1	2	yes	—
181	C₄²	#64526	1	2	yes	—
182	C₄²	C₂×D₇₆	1	1	yes	characteristic
183	C₄²	#64541	1	1	yes	characteristic
184	C₄²	#64543	1	2	yes	—
185	C₂³	—	4	1	no	—
186	C₂³	#10597381	1	1	yes	characteristic
187	Q₈	—	4	1	no	—
188	Q₈	—	4	1	no	—
189	D₄	—	4	1	no	—
190	D₄	—	4	1	no	—
191	D₄	—	8	2	no	—
192	D₄	—	8	1	no	—
193	D₄	—	8	1	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	8	1	no	—
201	C₂×C₄	—	8	1	no	—
202	C₂×C₄	#10597325	1	2	yes	—
203	C₂×C₄	#10597332	1	2	yes	—
204	C₂×C₄	#10597376	1	1	yes	characteristic
205	C₂×C₄	C₂×#64525	1	1	yes	characteristic
206	C₂×C₄	C₂×#64526	1	1	yes	characteristic
207	C₂×C₄	#10597382	1	1	yes	characteristic
208	C₂×C₄	#10597395	1	1	yes	characteristic
209	C₂×C₄	#10597397	1	1	yes	characteristic
210	C₈	—	8	1	no	—
211	C₈	—	152	2	no	—
212	C₈	—	152	2	no	—
213	C₂²	—	2	2	no	—
214	C₂²	—	8	1	no	—
215	C₂²	—	8	2	no	—
216	C₂²	#11926469	1	1	yes	characteristic
217	C₂²	#11926855	1	1	yes	characteristic
218	C₂²	#11926860	1	1	yes	characteristic
219	C₄	—	2	2	no	—
220	C₄	—	2	2	no	—
221	C₄	—	4	2	no	—
222	C₄	—	4	2	no	—
223	C₄	—	8	1	no	—
224	C₄	#11926739	1	1	yes	characteristic
225	C₄	#11926749	1	1	yes	characteristic
226	C₄	#11926890	1	1	yes	characteristic
227	C₄	#11926903	1	1	yes	characteristic
228	C₂	—	2	1	no	—
229	C₂	—	2	1	no	—
230	C₂	—	16	1	no	—
231	C₂	#14565038	1	1	yes	characteristic
232	C₂	#14565085	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563789

C₂

yes

maximal, characteristic, complemented

#14562284

C₂

yes

maximal

#14561530

C₂

yes

maximal, complemented

#14561464

C₂

yes

maximal, characteristic, complemented

C₁₉×#1963

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

—

C₂×C₄⋊(C₁₉⋊C₈)

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#11926290

—

#11926288

—

C₁₉×#532

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₂×C₁₉×#104

—

C₂×C₁₉×#104

—

C₁₉×#376

C₂²

yes

characteristic

C₂×#41×C₁₉

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

D₄

yes

characteristic

C₁₉×#127

D₄

yes

characteristic

C₁₉×#124

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#104

—

C₁₉×#104

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

#41×C₁₉

—

#41×C₁₉

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₈

yes

—

C₄²×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#10627

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#123

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×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

#121

yes

characteristic

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

#126

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1963

D₁₉

yes

characteristic

#1843

—

#1540

—

100

#1301

—

101

#1274

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

#397

yes

characteristic

106

C₂²×C₁₉

#480

yes

characteristic

107

C₂²×C₁₉

#481

yes

characteristic

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

#459

yes

characteristic

114

C₄×C₁₉

#461

yes

characteristic

115

C₄×C₁₉

#486

yes

characteristic

116

C₄×C₁₉

#489

yes

characteristic

117

#532

C₂×D₁₉

yes

characteristic

118

#431

—

119

#423

C₂×D₁₉

yes

characteristic

120

C₂×C₄⋊C₈

—

121

C₂×C₄⋊C₈

—

122

C₂×C₄⋊C₈

—

123

C₂×#104

—

124

C₂×#104

—

125

#376

C₂×D₁₉

yes

characteristic

126

#332

—

127

#331

—

128

C₂×C₁₉

—

129

C₂×C₁₉

—

130

C₂×C₁₉

—

131

C₂×C₁₉

#2071

yes

characteristic

132

C₂×C₁₉

#2080

yes

—

133

C₂×#41

—

134

C₂×M₁₆

—

135

C₂²×C₈

—

136

C₄⋊Q₈

D₇₆

yes

characteristic

137

#127

D₇₆

yes

characteristic

138

#124

—

139

#121

—

140

C₄×D₄

—

141

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

142

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

143

C₂×C₄²

C₂²×D₁₉

yes

characteristic

144

C₄⋊C₈

—

145

C₄⋊C₈

—

146

C₄⋊C₈

—

147

C₄⋊C₈

—

148

C₄⋊C₈

—

149

C₄⋊C₈

—

150

#104

—

151

#104

—

152

C₂²⋊C₈

—

153

C₄×C₈

—

154

#95

—

155

C₁₉

#10627

yes

characteristic, complemented, Sylow

156

#41

—

157

#41

—

158

#41

—

159

#41

—

160

C₂×Q₈

—

161

C₂×D₄

—

162

C₂×D₄

—

163

C₂×D₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

#64543

yes

—

168

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

169

M₁₆

—

170

M₁₆

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₄⋊C₄

—

177

C₂²⋊C₄

—

178

C₄²

—

179

C₄²

—

180

C₄²

#64525

yes

—

181

C₄²

#64526

yes

—

182

C₄²

C₂×D₇₆

yes

characteristic

183

C₄²

#64541

yes

characteristic

184

C₄²

#64543

yes

—

185

C₂³

—

186

C₂³

#10597381

yes

characteristic

187

Q₈

—

188

Q₈

—

189

D₄

—

190

D₄

—

191

D₄

—

192

D₄

—

193

D₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

#10597325

yes

—

203

C₂×C₄

#10597332

yes

—

204

C₂×C₄

#10597376

yes

characteristic

205

C₂×C₄

C₂×#64525

yes

characteristic

206

C₂×C₄

C₂×#64526

yes

characteristic

207

C₂×C₄

#10597382

yes

characteristic

208

C₂×C₄

#10597395

yes

characteristic

209

C₂×C₄

#10597397

yes

characteristic

210

C₈

—

211

C₈

—

152

—

212

C₈

—

152

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

#11926469

yes

characteristic

217

C₂²

#11926855

yes

characteristic

218

C₂²

#11926860

yes

characteristic

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

#11926739

yes

characteristic

225

C₄

#11926749

yes

characteristic

226

C₄

#11926890

yes

characteristic

227

C₄

#11926903

yes

characteristic

228

C₂

—

229

C₂

—

230

C₂

—

231

C₂

#14565038

yes

characteristic

232

C₂

#14565085

yes

—

	subgroup	G/H
center	C₂×C₄	#10597382
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1963	C₂
socle	C₂²×C₁₉	#397
prime radical	C₁₉×#532	C₂²
hypercenter	#1963	D₁₉
hypocenter	C₁₉	#10627
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1963

subgroup

G/H

center

C₂×C₄

#10597382

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1963

C₂

socle

C₂²×C₁₉

#397

prime radical

C₁₉×#532

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1963

N	H ≅ G/N	type
1. #14563789	C₂	semidirect
3. #14561530	C₂	semidirect
4. #14561464	C₂	semidirect
155. C₁₉	#10627	semidirect

H ≅ G/N

type

1. #14563789

C₂

semidirect

3. #14561530

C₂

semidirect

4. #14561464

C₂

semidirect

155. C₁₉

#10627

semidirect

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

subgroup	index
#14563789	2
#14562284	2
#14561530	2
#14561464	2
C₁₉×#1963	2
#10627	19

subgroup

index

C₁₉×#1963

Subgroups — #18087307

Conjugacy classes of subgroups

Complements

Maximal subgroups