Group #18081734 — subgroups

Subgroups — #18081734

Order 4864.

400 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 111 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	#14574221	C₂	1	1	yes	maximal, characteristic
2	C₄×#10597276	C₂	1	1	yes	maximal, characteristic
3	#14562229	C₂	1	2	yes	maximal
4	#14562055	C₂	1	2	yes	maximal
5	C₈×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	2	yes	—
7	#11926949	C₄	1	1	yes	characteristic
8	#11926924	C₄	1	1	yes	characteristic
9	#11926895	C₄	1	2	yes	—
10	#11926785	—	2	1	no	—
11	#11926785	—	2	1	no	—
12	C₄×Dic₇₆	—	2	1	no	—
13	C₄×Dic₇₆	—	2	1	no	—
14	C₂×#10597276	—	2	1	no	—
15	C₄×#64520	C₂²	1	2	yes	—
16	#11926309	—	2	1	no	—
17	#11926285	—	2	4	no	—
18	#11926274	—	2	4	no	—
19	C₁₉×#431	C₂²	1	1	yes	characteristic
20	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#322	—	2	1	no	—
23	C₈²×C₁₉	—	2	1	no	—
24	C₂×M₁₆×C₁₉	—	2	1	no	—
25	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	#10597372	—	2	2	no	—
29	#10597370	—	2	2	no	—
30	#10597370	—	2	2	no	—
31	C₂×#64520	—	2	2	no	—
32	C₂×Dic₇₆	—	2	1	no	—
33	C₂×Dic₇₆	—	2	1	no	—
34	#10597316	—	2	2	no	—
35	#10597315	C₂×C₄	1	2	yes	—
36	#10597315	C₂×C₄	1	2	yes	—
37	C₄×Dic₃₈	—	2	2	no	—
38	C₄×Dic₃₈	—	2	2	no	—
39	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
40	C₁₉×C₂²⋊C₈	—	2	1	no	—
41	C₁₉×#97	D₄	1	2	yes	—
42	C₄×C₈×C₁₉	—	2	1	no	—
43	C₄×C₈×C₁₉	—	2	1	no	—
44	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
47	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
48	#10597276	—	2	4	no	—
49	#10597275	—	2	1	no	—
50	#10597275	—	2	1	no	—
51	#10597273	—	2	2	no	—
52	#10597273	—	2	2	no	—
53	#10597260	—	2	2	no	—
54	C₄×C₁₉⋊C₈	—	2	2	no	—
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
58	C₂×Dic₃₈	—	2	2	no	—
59	C₂×Dic₃₈	—	2	2	no	—
60	M₁₆×C₁₉	—	2	4	no	—
61	C₂×C₈×C₁₉	—	2	2	no	—
62	C₂×C₈×C₁₉	—	2	2	no	—
63	C₂×C₈×C₁₉	—	2	2	no	—
64	C₂×C₈×C₁₉	—	4	1	no	—
65	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
70	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₂²⋊Dic₁₉	—	4	2	no	—
74	C₄⋊Dic₁₉	—	2	2	no	—
75	C₄⋊Dic₁₉	—	2	2	no	—
76	C₄⋊Dic₁₉	—	2	2	no	—
77	C₄⋊Dic₁₉	—	2	2	no	—
78	Dic₁₉⋊C₄	—	4	2	no	—
79	Dic₁₉⋊C₄	—	4	2	no	—
80	C₄×Dic₁₉	—	4	2	no	—
81	#64520	—	2	4	no	—
82	#64520	—	4	2	no	—
83	C₂×C₁₉⋊C₈	—	4	2	no	—
84	Dic₇₆	—	4	2	no	—
85	Dic₇₆	—	4	2	no	—
86	#9725	—	19	1	no	maximal, Sylow
87	C₂³×C₁₉	#124	1	1	yes	characteristic
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	2	1	no	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	2	2	no	—
92	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
94	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
98	C₂×Dic₁₉	—	4	2	no	—
99	C₂×Dic₁₉	—	4	2	no	—
100	Dic₃₈	—	4	2	no	—
101	Dic₃₈	—	4	2	no	—
102	Dic₃₈	—	4	4	no	—
103	C₈×C₁₉	—	2	4	no	—
104	C₈×C₁₉	—	2	1	no	—
105	C₈×C₁₉	—	2	1	no	—
106	C₈×C₁₉	—	2	1	no	—
107	C₈×C₁₉	—	4	2	no	—
108	C₈×C₁₉	#104	1	2	yes	—
109	C₁₉⋊C₈	—	4	4	no	—
110	#3170	—	19	1	no	—
111	C₄×#108	—	19	1	no	—
112	#1526	—	19	2	no	—
113	#1485	—	19	2	no	—
114	C₈×M₁₆	D₁₉	1	1	yes	characteristic
115	C₂²×C₁₉	—	2	1	no	—
116	C₂²×C₁₉	—	2	1	no	—
117	C₂²×C₁₉	—	2	1	no	—
118	C₂²×C₁₉	#390	1	1	yes	characteristic
119	C₄×C₁₉	—	2	1	no	—
120	C₄×C₁₉	—	2	1	no	—
121	C₄×C₁₉	—	2	1	no	—
122	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
123	C₄×C₁₉	#421	1	1	yes	characteristic
124	C₄×C₁₉	#443	1	2	yes	—
125	C₄×C₁₉	#473	1	2	yes	—
126	Dic₁₉	—	8	2	no	—
127	Dic₁₉	—	8	2	no	—
128	#533	—	19	2	no	—
129	#500	—	19	1	no	—
130	#494	—	19	1	no	—
131	#487	—	19	2	no	—
132	#467	—	38	1	no	—
133	#467	—	38	1	no	—
134	C₄×Q₁₆	—	38	1	no	—
135	C₄×Q₁₆	—	38	1	no	—
136	#431	C₂×D₁₉	1	1	yes	characteristic
137	C₂×#108	—	38	1	no	—
138	C₄×M₁₆	—	19	2	no	—
139	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
140	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
141	#341	—	38	1	no	—
142	#330	—	38	4	no	—
143	Q₈⋊C₈	—	38	4	no	—
144	#322	—	2	1	no	—
145	C₈²	—	2	1	no	—
146	C₂×C₁₉	—	4	1	no	—
147	C₂×C₁₉	#1974	1	1	yes	characteristic
148	C₂×C₁₉	#1979	1	1	yes	characteristic
149	C₂×C₁₉	#1980	1	1	yes	characteristic
150	C₂×Q₁₆	—	38	1	no	—
151	C₂×Q₁₆	—	38	1	no	—
152	C₂×M₁₆	—	2	1	no	—
153	C₂×M₁₆	—	38	2	no	—
154	C₂²×C₈	D₇₆	1	1	yes	characteristic
155	C₂²×C₈	D₇₆	1	1	yes	characteristic
156	C₄⋊Q₈	—	19	2	no	—
157	C₄⋊Q₈	—	19	2	no	—
158	#125	—	38	2	no	—
159	C₂²⋊Q₈	—	38	2	no	—
160	C₂²⋊Q₈	—	38	2	no	—
161	C₄×Q₈	—	38	2	no	—
162	C₄×Q₈	—	38	2	no	—
163	#117	—	38	2	no	—
164	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
165	#108	—	38	4	no	—
166	#107	—	38	1	no	—
167	#107	—	38	1	no	—
168	C₄⋊C₈	D₇₆	1	2	yes	—
169	#103	—	38	2	no	—
170	#103	—	38	2	no	—
171	C₂²⋊C₈	—	2	1	no	—
172	#97	—	38	2	no	—
173	#97	D₇₆	1	2	yes	—
174	C₄×C₈	—	2	1	no	—
175	C₄×C₈	—	2	1	no	—
176	C₄×C₈	—	38	2	no	—
177	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
178	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
179	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
180	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
181	C₁₉	#9725	1	1	yes	characteristic, complemented, Sylow
182	C₂×Q₈	—	38	2	no	—
183	C₂×Q₈	—	38	2	no	—
184	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
185	C₂²×C₄	#64541	1	1	yes	characteristic
186	C₂²×C₄	#64541	1	1	yes	characteristic
187	Q₁₆	—	76	2	no	—
188	Q₁₆	—	76	2	no	—
189	M₁₆	—	2	4	no	—
190	M₁₆	—	38	4	no	—
191	M₁₆	—	76	2	no	—
192	C₂×C₈	—	2	2	no	—
193	C₂×C₈	—	2	2	no	—
194	C₂×C₈	—	2	2	no	—
195	C₂×C₈	—	4	1	no	—
196	C₂×C₈	—	76	2	no	—
197	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
198	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
199	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
200	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
201	C₄⋊C₄	—	38	2	no	—
202	C₄⋊C₄	—	38	2	no	—
203	C₄⋊C₄	—	38	2	no	—
204	C₄⋊C₄	—	38	2	no	—
205	C₄⋊C₄	—	76	2	no	—
206	C₄⋊C₄	—	76	2	no	—
207	C₂²⋊C₄	—	76	2	no	—
208	C₄²	—	76	2	no	—
209	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
210	C₄²	C₂×D₇₆	1	1	yes	characteristic
211	C₄²	C₂×D₇₆	1	1	yes	characteristic
212	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
213	C₂³	#10597321	1	1	yes	characteristic
214	Q₈	—	76	2	no	—
215	Q₈	—	76	2	no	—
216	Q₈	—	76	4	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	76	2	no	—
222	C₂×C₄	—	76	2	no	—
223	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
224	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
225	C₂×C₄	#10597320	1	1	yes	characteristic
226	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
227	C₂×C₄	#10597376	1	1	yes	characteristic
228	C₂×C₄	#10597376	1	1	yes	characteristic
229	C₈	—	2	4	no	—
230	C₈	—	2	1	no	—
231	C₈	—	2	1	no	—
232	C₈	—	2	1	no	—
233	C₈	—	4	2	no	—
234	C₈	—	76	4	no	—
235	C₈	#10597282	1	2	yes	—
236	C₂²	—	2	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	1	no	—
239	C₂²	#11926446	1	1	yes	characteristic
240	C₄	—	2	1	no	—
241	C₄	—	2	1	no	—
242	C₄	—	2	1	no	—
243	C₄	—	152	2	no	—
244	C₄	—	152	2	no	—
245	C₄	C₂×#10597282	1	1	yes	characteristic
246	C₄	#11926560	1	1	yes	characteristic
247	C₄	#11926662	1	2	yes	—
248	C₄	#11926819	1	2	yes	—
249	C₂	—	4	1	no	—
250	C₂	#14564523	1	1	yes	characteristic
251	C₂	#14564550	1	1	yes	characteristic
252	C₂	#14564554	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574221

C₂

yes

maximal, characteristic

C₄×#10597276

C₂

yes

maximal, characteristic

#14562229

C₂

yes

maximal

#14562055

C₂

yes

maximal

C₈×M₁₆×C₁₉

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

—

#11926949

C₄

yes

characteristic

#11926924

C₄

yes

characteristic

#11926895

C₄

yes

—

#11926785

—

#11926785

—

C₄×Dic₇₆

—

C₄×Dic₇₆

—

C₂×#10597276

—

C₄×#64520

C₂²

yes

—

#11926309

—

#11926285

—

#11926274

—

C₁₉×#431

C₂²

yes

characteristic

C₄×M₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#322

—

C₈²×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

#10597316

—

#10597315

C₂×C₄

yes

—

#10597315

C₂×C₄

yes

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

D₄

yes

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

—

—

—

—

—

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂×D₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

Dic₇₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

100

Dic₃₈

—

101

Dic₃₈

—

102

Dic₃₈

—

103

C₈×C₁₉

—

104

C₈×C₁₉

—

105

C₈×C₁₉

—

106

C₈×C₁₉

—

107

C₈×C₁₉

—

108

C₈×C₁₉

#104

yes

—

109

C₁₉⋊C₈

—

110

#3170

—

111

C₄×#108

—

112

#1526

—

113

#1485

—

114

C₈×M₁₆

D₁₉

yes

characteristic

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

#390

yes

characteristic

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

—

122

C₄×C₁₉

C₂×#104

yes

characteristic

123

C₄×C₁₉

#421

yes

characteristic

124

C₄×C₁₉

#443

yes

—

125

C₄×C₁₉

#473

yes

—

126

Dic₁₉

—

127

Dic₁₉

—

128

#533

—

129

#500

—

130

#494

—

131

#487

—

132

#467

—

133

#467

—

134

C₄×Q₁₆

—

135

C₄×Q₁₆

—

136

#431

C₂×D₁₉

yes

characteristic

137

C₂×#108

—

138

C₄×M₁₆

—

139

C₄×M₁₆

C₂×D₁₉

yes

characteristic

140

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

141

#341

—

142

#330

—

143

Q₈⋊C₈

—

144

#322

—

145

C₈²

—

146

C₂×C₁₉

—

147

C₂×C₁₉

#1974

yes

characteristic

148

C₂×C₁₉

#1979

yes

characteristic

149

C₂×C₁₉

#1980

yes

characteristic

150

C₂×Q₁₆

—

151

C₂×Q₁₆

—

152

C₂×M₁₆

—

153

C₂×M₁₆

—

154

C₂²×C₈

D₇₆

yes

characteristic

155

C₂²×C₈

D₇₆

yes

characteristic

156

C₄⋊Q₈

—

157

C₄⋊Q₈

—

158

#125

—

159

C₂²⋊Q₈

—

160

C₂²⋊Q₈

—

161

C₄×Q₈

—

162

C₄×Q₈

—

163

#117

—

164

C₂×C₄²

C₂²×D₁₉

yes

characteristic

165

#108

—

166

#107

—

167

#107

—

168

C₄⋊C₈

D₇₆

yes

—

169

#103

—

170

#103

—

171

C₂²⋊C₈

—

172

#97

—

173

#97

D₇₆

yes

—

174

C₄×C₈

—

175

C₄×C₈

—

176

C₄×C₈

—

177

C₄×C₈

C₄×D₁₉

yes

characteristic

178

C₄×C₈

C₄×D₁₉

yes

characteristic

179

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

180

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

181

C₁₉

#9725

yes

characteristic, complemented, Sylow

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂²×C₄

C₂×D₇₆

yes

characteristic

185

C₂²×C₄

#64541

yes

characteristic

186

C₂²×C₄

#64541

yes

characteristic

187

Q₁₆

—

188

Q₁₆

—

189

M₁₆

—

190

M₁₆

—

191

M₁₆

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

198

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

199

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

200

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₂²⋊C₄

—

208

C₄²

—

209

C₄²

C₂×C₄×D₁₉

yes

characteristic

210

C₄²

C₂×D₇₆

yes

characteristic

211

C₄²

C₂×D₇₆

yes

characteristic

212

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

213

C₂³

#10597321

yes

characteristic

214

Q₈

—

215

Q₈

—

216

Q₈

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

C₄×D₇₆

yes

characteristic

224

C₂×C₄

C₄×D₇₆

yes

characteristic

225

C₂×C₄

#10597320

yes

characteristic

226

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

227

C₂×C₄

#10597376

yes

characteristic

228

C₂×C₄

#10597376

yes

characteristic

229

C₈

—

230

C₈

—

231

C₈

—

232

C₈

—

233

C₈

—

234

C₈

—

235

C₈

#10597282

yes

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

#11926446

yes

characteristic

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

152

—

244

C₄

—

152

—

245

C₄

C₂×#10597282

yes

characteristic

246

C₄

#11926560

yes

characteristic

247

C₄

#11926662

yes

—

248

C₄

#11926819

yes

—

249

C₂

—

250

C₂

#14564523

yes

characteristic

251

C₂

#14564550

yes

characteristic

252

C₂

#14564554

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597376
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₈×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂³×C₁₉	#124
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₈×M₁₆	D₁₉
hypocenter	C₁₉	#9725
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₈×M₁₆

subgroup

G/H

center

C₂×C₄

#10597376

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₈×M₁₆×C₁₉

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

hypercenter

C₈×M₁₆

D₁₉

hypocenter

C₁₉

#9725

LCS

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₈×M₁₆

N	H ≅ G/N	type
181. C₁₉	#9725	semidirect

H ≅ G/N

type

181. C₁₉

#9725

semidirect

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

subgroup	index
#14574221	2
C₄×#10597276	2
#14562229	2
#14562055	2
C₈×M₁₆×C₁₉	2
#9725	19

subgroup

index

C₈×M₁₆×C₁₉

Subgroups — #18081734

Conjugacy classes of subgroups

Complements

Maximal subgroups