Group #18087535 — subgroups

Subgroups — #18087535

Order 4864.

304 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 91 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	#14564576	C₂	1	1	yes	maximal, characteristic
2	#14563775	C₂	1	1	yes	maximal, characteristic
3	#14562410	C₂	1	1	yes	maximal, characteristic
4	#14562407	C₂	1	1	yes	maximal, characteristic
5	#14562064	C₂	1	1	yes	maximal, characteristic
6	#14561465	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1487	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	#11926568	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#10597260	C₂²	1	1	yes	characteristic
12	#11926308	—	2	2	no	—
13	#11926299	—	2	2	no	—
14	#11926297	—	2	2	no	—
15	#11926294	—	2	2	no	—
16	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
17	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#431	C₂²	1	1	yes	characteristic
19	C₁₉×#423	C₂²	1	1	yes	characteristic
20	C₁₉×Q₈⋊C₈	—	2	2	no	—
21	C₂²×Q₈×C₁₉	Q₈	1	1	yes	characteristic
22	C₂×M₁₆×C₁₉	—	2	1	no	—
23	C₄×Q₈×C₁₉	—	2	1	no	—
24	C₄×Q₈×C₁₉	—	2	1	no	—
25	C₄×Q₈×C₁₉	—	2	1	no	—
26	C₄×Q₈×C₁₉	—	2	1	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
29	C₂×C₄²×C₁₉	—	2	1	no	—
30	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×#64520	—	2	1	no	—
32	C₂²×C₁₉⋊C₈	—	2	1	no	—
33	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
34	C₁₉×C₄⋊C₈	—	2	1	no	—
35	C₁₉×C₄⋊C₈	—	2	1	no	—
36	C₁₉×C₄⋊C₈	—	2	1	no	—
37	C₁₉×C₂²⋊C₈	—	2	1	no	—
38	C₄×C₈×C₁₉	D₄	1	2	yes	—
39	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
40	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
41	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
45	#10597260	—	2	1	no	—
46	#10597260	—	2	1	no	—
47	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
48	C₂×Q₈×C₁₉	—	2	1	no	—
49	C₂×Q₈×C₁₉	—	2	1	no	—
50	C₂×Q₈×C₁₉	—	4	2	no	—
51	C₂²×C₄×C₁₉	—	2	1	no	—
52	C₂²×C₄×C₁₉	—	2	1	no	—
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
56	M₁₆×C₁₉	—	4	2	no	—
57	C₂×C₈×C₁₉	—	2	2	no	—
58	C₂×C₈×C₁₉	—	4	1	no	—
59	C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₄⋊C₄×C₁₉	—	4	1	no	—
62	C₄⋊C₄×C₁₉	—	4	1	no	—
63	C₄²×C₁₉	—	4	1	no	—
64	C₄²×C₁₉	—	4	1	no	—
65	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₁₉	#41	1	1	yes	characteristic
68	C₄²×C₁₉	#41	1	1	yes	characteristic
69	#64520	—	4	2	no	—
70	C₂×C₁₉⋊C₈	—	2	2	no	—
71	C₂×C₁₉⋊C₈	—	2	2	no	—
72	C₂×C₁₉⋊C₈	—	2	2	no	—
73	C₂×C₁₉⋊C₈	—	2	2	no	—
74	C₂×C₁₉⋊C₈	—	4	1	no	—
75	C₂×C₁₉⋊C₈	—	4	1	no	—
76	C₂×C₁₉⋊C₈	—	4	2	no	—
77	#10664	—	19	1	no	maximal, Sylow
78	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
79	Q₈×C₁₉	—	2	2	no	—
80	Q₈×C₁₉	—	2	2	no	—
81	Q₈×C₁₉	—	4	1	no	—
82	Q₈×C₁₉	—	4	1	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	4	1	no	—
85	C₂×C₄×C₁₉	—	4	1	no	—
86	C₂×C₄×C₁₉	—	4	1	no	—
87	C₂×C₄×C₁₉	—	4	1	no	—
88	C₂×C₄×C₁₉	—	4	2	no	—
89	C₂×C₄×C₁₉	—	4	1	no	—
90	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
91	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#135	1	2	yes	—
97	C₂×C₄×C₁₉	#137	1	2	yes	—
98	C₈×C₁₉	—	4	2	no	—
99	C₈×C₁₉	—	8	1	no	—
100	C₁₉⋊C₈	—	4	2	no	—
101	C₁₉⋊C₈	—	4	2	no	—
102	C₁₉⋊C₈	—	8	1	no	—
103	C₁₉⋊C₈	—	8	1	no	—
104	#1985	—	19	1	no	—
105	#1838	—	19	1	no	—
106	#1571	—	19	1	no	—
107	#1570	—	19	1	no	—
108	#1487	—	19	1	no	—
109	#1487	D₁₉	1	1	yes	characteristic
110	#1275	—	19	1	no	—
111	C₂²×C₁₉	—	2	1	no	—
112	C₂²×C₁₉	—	2	1	no	—
113	C₂²×C₁₉	#399	1	1	yes	characteristic
114	C₂²×C₁₉	#479	1	2	yes	—
115	C₄×C₁₉	—	2	1	no	—
116	C₄×C₁₉	—	2	1	no	—
117	C₄×C₁₉	—	2	1	no	—
118	C₄×C₁₉	—	2	1	no	—
119	C₄×C₁₉	—	4	2	no	—
120	C₄×C₁₉	—	8	1	no	—
121	C₄×C₁₉	#485	1	2	yes	—
122	C₄×C₁₉	#495	1	1	yes	characteristic
123	C₄×C₁₉	#497	1	1	yes	characteristic
124	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
125	#431	—	19	1	no	—
126	#431	C₂×D₁₉	1	1	yes	characteristic
127	#423	—	19	1	no	—
128	#423	C₂×D₁₉	1	1	yes	characteristic
129	C₂×C₄⋊C₈	—	19	1	no	—
130	C₂×#97	—	19	1	no	—
131	#341	—	38	2	no	—
132	#336	—	38	2	no	—
133	#335	—	38	2	no	—
134	#334	—	38	2	no	—
135	Q₈⋊C₈	—	2	2	no	—
136	Q₈⋊C₈	—	38	2	no	—
137	C₂×C₁₉	—	2	2	no	—
138	C₂×C₁₉	#2091	1	1	yes	characteristic
139	C₂×C₁₉	#2097	1	1	yes	characteristic
140	C₂×C₁₉	#2098	1	1	yes	characteristic
141	C₂²×Q₈	Dic₃₈	1	1	yes	characteristic
142	C₂×M₁₆	—	2	1	no	—
143	C₂×M₁₆	—	38	1	no	—
144	C₂²×C₈	—	19	2	no	—
145	C₂²×C₈	—	38	1	no	—
146	C₄×Q₈	—	2	1	no	—
147	C₄×Q₈	—	2	1	no	—
148	C₄×Q₈	—	2	1	no	—
149	C₄×Q₈	—	2	1	no	—
150	C₂×C₄⋊C₄	—	2	1	no	—
151	C₂×C₄⋊C₄	Dic₃₈	1	1	yes	characteristic
152	C₂×C₄²	—	2	1	no	—
153	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
154	C₄⋊C₈	—	2	1	no	—
155	C₄⋊C₈	—	2	1	no	—
156	C₄⋊C₈	—	2	1	no	—
157	C₄⋊C₈	—	38	1	no	—
158	C₄⋊C₈	—	38	1	no	—
159	C₄⋊C₈	—	38	1	no	—
160	C₄⋊C₈	—	38	1	no	—
161	C₄⋊C₈	—	38	1	no	—
162	C₂²⋊C₈	—	2	1	no	—
163	C₂²⋊C₈	—	38	1	no	—
164	#97	—	38	1	no	—
165	#97	—	38	1	no	—
166	C₄×C₈	—	19	2	no	—
167	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
168	C₁₉	#10664	1	1	yes	characteristic, complemented, Sylow
169	C₂×Q₈	—	2	1	no	—
170	C₂×Q₈	—	2	1	no	—
171	C₂×Q₈	—	4	2	no	—
172	C₂²×C₄	—	2	1	no	—
173	C₂²×C₄	—	2	1	no	—
174	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
175	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
176	C₂²×C₄	#64543	1	1	yes	characteristic
177	M₁₆	—	4	2	no	—
178	M₁₆	—	76	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	4	1	no	—
181	C₂×C₈	—	38	2	no	—
182	C₂×C₈	—	38	2	no	—
183	C₂×C₈	—	38	2	no	—
184	C₂×C₈	—	38	2	no	—
185	C₂×C₈	—	76	1	no	—
186	C₂×C₈	—	76	1	no	—
187	C₂×C₈	—	76	2	no	—
188	C₄⋊C₄	—	2	1	no	—
189	C₄⋊C₄	—	2	1	no	—
190	C₄⋊C₄	—	4	1	no	—
191	C₄⋊C₄	—	4	1	no	—
192	C₄²	—	4	1	no	—
193	C₄²	—	4	1	no	—
194	C₄²	#64541	1	1	yes	characteristic
195	C₄²	D₄×D₁₉	1	1	yes	characteristic
196	C₄²	#64543	1	1	yes	characteristic
197	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
198	C₂³	#10597324	1	1	yes	characteristic
199	Q₈	—	2	2	no	—
200	Q₈	—	2	2	no	—
201	Q₈	—	4	1	no	—
202	Q₈	—	4	1	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	#10597324	1	1	yes	characteristic
211	C₂×C₄	#10597329	1	1	yes	characteristic
212	C₂×C₄	#10597329	1	1	yes	characteristic
213	C₂×C₄	#10597361	1	2	yes	—
214	C₂×C₄	#10597365	1	2	yes	—
215	C₂×C₄	#10597370	1	1	yes	characteristic
216	C₂×C₄	#10597381	1	1	yes	characteristic
217	C₂×C₄	#10597386	1	1	yes	characteristic
218	C₈	—	4	2	no	—
219	C₈	—	8	1	no	—
220	C₈	—	76	2	no	—
221	C₈	—	76	2	no	—
222	C₈	—	152	1	no	—
223	C₈	—	152	1	no	—
224	C₂²	—	2	1	no	—
225	C₂²	—	2	1	no	—
226	C₂²	#11926480	1	1	yes	characteristic
227	C₂²	#11926853	1	2	yes	—
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	4	2	no	—
233	C₄	—	8	1	no	—
234	C₄	#11926884	1	2	yes	—
235	C₄	#11926929	1	1	yes	characteristic
236	C₄	#11926935	1	1	yes	characteristic
237	C₂	—	2	2	no	—
238	C₂	#14565151	1	1	yes	characteristic
239	C₂	#14565181	1	1	yes	characteristic
240	C₂	#14565190	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564576

C₂

yes

maximal, characteristic

#14563775

C₂

yes

maximal, characteristic

#14562410

C₂

yes

maximal, characteristic

#14562407

C₂

yes

maximal, characteristic

#14562064

C₂

yes

maximal, characteristic

#14561465

C₂

yes

maximal, characteristic

C₁₉×#1487

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

characteristic

#11926568

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×#10597260

C₂²

yes

—

—

—

—

Q₈⋊(C₁₉⋊C₈)

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₁₉×Q₈⋊C₈

—

C₂²×Q₈×C₁₉

Q₈

yes

characteristic

C₂×M₁₆×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#10664

—

maximal, Sylow

C₂³×C₁₉

C₂²⋊Q₈

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×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

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

100

C₁₉⋊C₈

—

101

C₁₉⋊C₈

—

102

C₁₉⋊C₈

—

103

C₁₉⋊C₈

—

104

#1985

—

105

#1838

—

106

#1571

—

107

#1570

—

108

#1487

—

109

#1487

D₁₉

yes

characteristic

110

#1275

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

#399

yes

characteristic

114

C₂²×C₁₉

#479

yes

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

#485

yes

—

122

C₄×C₁₉

#495

yes

characteristic

123

C₄×C₁₉

#497

yes

characteristic

124

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

125

#431

—

126

#431

C₂×D₁₉

yes

characteristic

127

#423

—

128

#423

C₂×D₁₉

yes

characteristic

129

C₂×C₄⋊C₈

—

130

C₂×#97

—

131

#341

—

132

#336

—

133

#335

—

134

#334

—

135

Q₈⋊C₈

—

136

Q₈⋊C₈

—

137

C₂×C₁₉

—

138

C₂×C₁₉

#2091

yes

characteristic

139

C₂×C₁₉

#2097

yes

characteristic

140

C₂×C₁₉

#2098

yes

characteristic

141

C₂²×Q₈

Dic₃₈

yes

characteristic

142

C₂×M₁₆

—

143

C₂×M₁₆

—

144

C₂²×C₈

—

145

C₂²×C₈

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

C₄×Q₈

—

149

C₄×Q₈

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

Dic₃₈

yes

characteristic

152

C₂×C₄²

—

153

C₂×C₄²

C₂²×D₁₉

yes

characteristic

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₂²⋊C₈

—

163

C₂²⋊C₈

—

164

#97

—

165

#97

—

166

C₄×C₈

—

167

C₄×C₈

C₂²⋊D₁₉

yes

—

168

C₁₉

#10664

yes

characteristic, complemented, Sylow

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

175

C₂²×C₄

D₄×D₁₉

yes

characteristic

176

C₂²×C₄

#64543

yes

characteristic

177

M₁₆

—

178

M₁₆

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄²

—

193

C₄²

—

194

C₄²

#64541

yes

characteristic

195

C₄²

D₄×D₁₉

yes

characteristic

196

C₄²

#64543

yes

characteristic

197

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

198

C₂³

#10597324

yes

characteristic

199

Q₈

—

200

Q₈

—

201

Q₈

—

202

Q₈

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

#10597324

yes

characteristic

211

C₂×C₄

#10597329

yes

characteristic

212

C₂×C₄

#10597329

yes

characteristic

213

C₂×C₄

#10597361

yes

—

214

C₂×C₄

#10597365

yes

—

215

C₂×C₄

#10597370

yes

characteristic

216

C₂×C₄

#10597381

yes

characteristic

217

C₂×C₄

#10597386

yes

characteristic

218

C₈

—

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

152

—

223

C₈

—

152

—

224

C₂²

—

225

C₂²

—

226

C₂²

#11926480

yes

characteristic

227

C₂²

#11926853

yes

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

#11926884

yes

—

235

C₄

#11926929

yes

characteristic

236

C₄

#11926935

yes

characteristic

237

C₂

—

238

C₂

#14565151

yes

characteristic

239

C₂

#14565181

yes

characteristic

240

C₂

#14565190

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1487	C₂
socle	C₂²×C₁₉	#399
prime radical	C₂³×C₁₉	C₂²⋊Q₈
hypercenter	#1487	D₁₉
hypocenter	C₁₉	#10664
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1487

subgroup

G/H

center

C₂×C₄

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1487

C₂

socle

C₂²×C₁₉

#399

prime radical

C₂³×C₁₉

C₂²⋊Q₈

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1487

N	H ≅ G/N	type
168. C₁₉	#10664	semidirect

H ≅ G/N

type

168. C₁₉

#10664

semidirect

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

subgroup	index
#14564576	2
#14563775	2
#14562410	2
#14562407	2
#14562064	2
#14561465	2
C₁₉×#1487	2
#10664	19

subgroup

index

C₁₉×#1487

Subgroups — #18087535

Conjugacy classes of subgroups

Complements

Maximal subgroups