Group #18081652 — subgroups

Subgroups — #18081652

Order 4864.

466 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 147 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	#14572013	C₂	1	1	yes	maximal, characteristic
2	#14563752	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926292	C₂	1	2	yes	maximal
4	C₂×#11926291	C₂	1	2	yes	maximal
5	C₁₉×#1767	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	C₂×#10597315	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
9	#11926450	—	2	1	no	—
10	#11926450	—	2	1	no	—
11	#11926450	C₄	1	4	yes	—
12	#11926410	—	2	2	no	—
13	#11926299	—	2	2	no	—
14	#11926292	—	2	4	no	—
15	#11926291	—	2	4	no	—
16	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₉×#97	—	2	1	no	—
18	C₄³×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#336	—	2	1	no	—
20	C₂²×Dic₃₈	—	2	1	no	—
21	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
22	C₂²×C₈×C₁₉	—	2	2	no	—
23	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₉	D₄	1	2	yes	—
25	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₉	—	2	1	no	—
29	C₂×C₄⋊Dic₁₉	—	2	1	no	—
30	C₂×C₄⋊Dic₁₉	—	2	1	no	—
31	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
32	C₂²×C₁₉⋊C₈	—	2	2	no	—
33	#10597315	—	2	2	no	—
34	#10597315	—	2	2	no	—
35	#10597315	—	2	2	no	—
36	#10597315	—	2	2	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉×C₄⋊C₈	D₄	1	4	yes	—
39	C₁₉×#97	—	4	2	no	—
40	C₁₉⋊#95	—	2	4	no	—
41	C₁₉⋊#95	—	2	4	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
45	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
46	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×Dic₁₉	—	2	2	no	—
50	C₂²×Dic₁₉	—	2	2	no	—
51	C₂×Dic₃₈	—	2	4	no	—
52	C₂×Dic₃₈	—	4	2	no	—
53	C₂×Dic₃₈	—	4	2	no	—
54	C₂×Dic₃₈	—	4	1	no	—
55	C₂×Dic₃₈	—	4	1	no	—
56	C₂×Dic₃₈	—	4	4	no	—
57	C₂×C₈×C₁₉	—	2	4	no	—
58	C₂×C₈×C₁₉	—	4	2	no	—
59	C₂×C₈×C₁₉	—	4	2	no	—
60	C₄²×C₁₉	—	2	2	no	—
61	C₄²×C₁₉	—	2	1	no	—
62	C₄²×C₁₉	—	2	1	no	—
63	C₄²×C₁₉	—	2	4	no	—
64	C₄²×C₁₉	—	4	2	no	—
65	C₄²×C₁₉	C₂×D₄	1	2	yes	—
66	C₄²×C₁₉	#41	1	2	yes	—
67	C₄⋊Dic₁₉	—	2	4	no	—
68	C₄⋊Dic₁₉	—	4	2	no	—
69	C₄⋊Dic₁₉	—	4	1	no	—
70	C₄⋊Dic₁₉	—	4	1	no	—
71	C₄⋊Dic₁₉	—	4	1	no	—
72	C₄⋊Dic₁₉	—	4	1	no	—
73	C₂×C₁₉⋊C₈	—	4	2	no	—
74	C₂×C₁₉⋊C₈	—	4	4	no	—
75	#9709	—	19	1	no	maximal, Sylow
76	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
85	C₂×C₄×C₁₉	#121	1	2	yes	—
86	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#135	1	2	yes	—
89	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#137	1	4	yes	—
92	C₂×Dic₁₉	—	4	2	no	—
93	C₂×Dic₁₉	—	4	2	no	—
94	C₂×Dic₁₉	—	4	4	no	—
95	C₂×Dic₁₉	—	4	2	no	—
96	C₂×Dic₁₉	—	4	2	no	—
97	Dic₃₈	—	8	2	no	—
98	Dic₃₈	—	8	2	no	—
99	Dic₃₈	—	8	4	no	—
100	C₈×C₁₉	—	4	4	no	—
101	C₁₉⋊C₈	—	8	2	no	—
102	#2862	—	19	1	no	—
103	#1831	—	19	1	no	—
104	#1767	D₁₉	1	1	yes	characteristic
105	C₂×#333	—	19	2	no	—
106	C₂×#332	—	19	2	no	—
107	C₂²×C₁₉	#390	1	1	yes	characteristic
108	C₂²×C₁₉	#413	1	2	yes	—
109	C₂²×C₁₉	#416	1	1	yes	characteristic
110	C₂²×C₁₉	#417	1	1	yes	characteristic
111	C₂²×C₁₉	#419	1	2	yes	—
112	C₄×C₁₉	—	2	2	no	—
113	C₄×C₁₉	—	4	2	no	—
114	C₄×C₁₉	—	4	2	no	—
115	C₄×C₁₉	#463	1	2	yes	—
116	C₄×C₁₉	#464	1	2	yes	—
117	C₄×C₁₉	#491	1	2	yes	—
118	C₄×C₁₉	#497	1	2	yes	—
119	Dic₁₉	—	8	2	no	—
120	Dic₁₉	—	8	2	no	—
121	C₂×C₄⋊Q₈	—	19	1	no	—
122	C₂×C₄⋊Q₈	—	19	1	no	—
123	C₂×C₄⋊C₈	—	19	2	no	—
124	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
125	C₂×#97	—	2	1	no	—
126	#391	—	19	4	no	—
127	#391	—	38	1	no	—
128	#391	—	38	1	no	—
129	#382	—	38	2	no	—
130	C₄³	C₂×D₁₉	1	1	yes	characteristic
131	#336	—	2	1	no	—
132	#336	—	38	2	no	—
133	#333	—	38	4	no	—
134	#332	—	38	4	no	—
135	C₂×C₁₉	#1554	1	2	yes	—
136	C₂×C₁₉	#1559	1	2	yes	—
137	C₂×C₁₉	#1960	1	1	yes	characteristic
138	C₂×C₁₉	#1967	1	1	yes	characteristic
139	C₂×C₁₉	#1983	1	1	yes	characteristic
140	C₂²×Q₈	—	19	2	no	—
141	C₂²×Q₈	—	38	1	no	—
142	C₂²×C₈	—	2	2	no	—
143	C₂²×C₈	—	38	2	no	—
144	C₄⋊Q₈	—	38	2	no	—
145	C₄⋊Q₈	—	38	2	no	—
146	C₄⋊Q₈	—	38	2	no	—
147	C₄⋊Q₈	—	38	2	no	—
148	C₂×C₄⋊C₄	—	19	2	no	—
149	C₂×C₄⋊C₄	—	38	1	no	—
150	C₂×C₄⋊C₄	—	38	1	no	—
151	C₂×C₄⋊C₄	—	38	1	no	—
152	C₂×C₄²	C₄×D₁₉	1	2	yes	—
153	C₂×C₄²	D₇₆	1	2	yes	—
154	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
155	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
156	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	38	2	no	—
159	C₄⋊C₈	—	38	2	no	—
160	C₄⋊C₈	D₇₆	1	4	yes	—
161	#97	—	4	2	no	—
162	#95	—	38	4	no	—
163	#95	—	38	4	no	—
164	C₁₉	#9709	1	1	yes	characteristic, complemented, Sylow
165	C₂×Q₈	—	38	4	no	—
166	C₂×Q₈	—	76	4	no	—
167	C₂×Q₈	—	76	2	no	—
168	C₂×Q₈	—	76	1	no	—
169	C₂×Q₈	—	76	1	no	—
170	C₂×Q₈	—	76	2	no	—
171	C₂²×C₄	—	38	2	no	—
172	C₂²×C₄	—	38	2	no	—
173	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
174	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
175	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
176	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
177	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
178	C₂×C₈	—	2	4	no	—
179	C₂×C₈	—	4	2	no	—
180	C₂×C₈	—	4	2	no	—
181	C₂×C₈	—	76	2	no	—
182	C₂×C₈	—	76	4	no	—
183	C₄⋊C₄	—	38	4	no	—
184	C₄⋊C₄	—	76	2	no	—
185	C₄⋊C₄	—	76	1	no	—
186	C₄⋊C₄	—	76	1	no	—
187	C₄⋊C₄	—	76	1	no	—
188	C₄⋊C₄	—	76	1	no	—
189	C₄²	—	2	1	no	—
190	C₄²	—	2	1	no	—
191	C₄²	—	2	2	no	—
192	C₄²	—	2	4	no	—
193	C₄²	—	4	2	no	—
194	C₄²	C₂×D₇₆	1	2	yes	—
195	C₄²	#64541	1	2	yes	—
196	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
197	Q₈	—	152	4	no	—
198	Q₈	—	152	2	no	—
199	Q₈	—	152	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	76	2	no	—
208	C₂×C₄	—	76	2	no	—
209	C₂×C₄	—	76	2	no	—
210	C₂×C₄	—	76	2	no	—
211	C₂×C₄	—	76	4	no	—
212	C₂×C₄	C₄×D₇₆	1	2	yes	—
213	C₂×C₄	#10597320	1	1	yes	characteristic
214	C₂×C₄	#10597321	1	1	yes	characteristic
215	C₂×C₄	#10597355	1	4	yes	—
216	C₂×C₄	#10597376	1	2	yes	—
217	C₂×C₄	#10597378	1	1	yes	characteristic
218	C₂×C₄	#10597388	1	1	yes	characteristic
219	C₂×C₄	#10597396	1	2	yes	—
220	C₈	—	4	4	no	—
221	C₈	—	152	2	no	—
222	C₂²	#11926446	1	1	yes	characteristic
223	C₂²	#11926526	1	2	yes	—
224	C₂²	#11926538	1	1	yes	characteristic
225	C₂²	#11926543	1	1	yes	characteristic
226	C₂²	#11926554	1	2	yes	—
227	C₄	—	2	2	no	—
228	C₄	—	4	2	no	—
229	C₄	—	4	2	no	—
230	C₄	—	152	2	no	—
231	C₄	—	152	2	no	—
232	C₄	#11926759	1	2	yes	—
233	C₄	#11926766	1	2	yes	—
234	C₄	#11926913	1	2	yes	—
235	C₄	#11926938	1	2	yes	—
236	C₂	#14562346	1	2	yes	—
237	C₂	#14562363	1	2	yes	—
238	C₂	#14564455	1	1	yes	characteristic
239	C₂	#14564484	1	1	yes	characteristic
240	C₂	#14564567	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572013

C₂

yes

maximal, characteristic

#14563752

C₂

yes

maximal, characteristic

C₂×#11926292

C₂

yes

maximal

C₂×#11926291

C₂

yes

maximal

C₁₉×#1767

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

characteristic

C₂×#10597315

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#11926450

—

#11926450

—

#11926450

C₄

yes

—

—

—

—

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₂×C₁₉×#97

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₂²×Dic₃₈

—

C₂²×Dic₃₈

C₂×C₄

yes

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

—

—

—

—

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×#97

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9709

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

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

C₄×D₄

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

100

C₈×C₁₉

—

101

C₁₉⋊C₈

—

102

#2862

—

103

#1831

—

104

#1767

D₁₉

yes

characteristic

105

C₂×#333

—

106

C₂×#332

—

107

C₂²×C₁₉

#390

yes

characteristic

108

C₂²×C₁₉

#413

yes

—

109

C₂²×C₁₉

#416

yes

characteristic

110

C₂²×C₁₉

#417

yes

characteristic

111

C₂²×C₁₉

#419

yes

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

#463

yes

—

116

C₄×C₁₉

#464

yes

—

117

C₄×C₁₉

#491

yes

—

118

C₄×C₁₉

#497

yes

—

119

Dic₁₉

—

120

Dic₁₉

—

121

C₂×C₄⋊Q₈

—

122

C₂×C₄⋊Q₈

—

123

C₂×C₄⋊C₈

—

124

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

125

C₂×#97

—

126

#391

—

127

#391

—

128

#391

—

129

#382

—

130

C₄³

C₂×D₁₉

yes

characteristic

131

#336

—

132

#336

—

133

#333

—

134

#332

—

135

C₂×C₁₉

#1554

yes

—

136

C₂×C₁₉

#1559

yes

—

137

C₂×C₁₉

#1960

yes

characteristic

138

C₂×C₁₉

#1967

yes

characteristic

139

C₂×C₁₉

#1983

yes

characteristic

140

C₂²×Q₈

—

141

C₂²×Q₈

—

142

C₂²×C₈

—

143

C₂²×C₈

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄²

C₄×D₁₉

yes

—

153

C₂×C₄²

D₇₆

yes

—

154

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

155

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

156

C₂×C₄²

C₂²×D₁₉

yes

characteristic

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

D₇₆

yes

—

161

#97

—

162

#95

—

163

#95

—

164

C₁₉

#9709

yes

characteristic, complemented, Sylow

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

174

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

175

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

176

C₂²×C₄

C₂×D₇₆

yes

characteristic

177

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

193

C₄²

—

194

C₄²

C₂×D₇₆

yes

—

195

C₄²

#64541

yes

—

196

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

197

Q₈

—

152

—

198

Q₈

—

152

—

199

Q₈

—

152

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

C₄×D₇₆

yes

—

213

C₂×C₄

#10597320

yes

characteristic

214

C₂×C₄

#10597321

yes

characteristic

215

C₂×C₄

#10597355

yes

—

216

C₂×C₄

#10597376

yes

—

217

C₂×C₄

#10597378

yes

characteristic

218

C₂×C₄

#10597388

yes

characteristic

219

C₂×C₄

#10597396

yes

—

220

C₈

—

221

C₈

—

152

—

222

C₂²

#11926446

yes

characteristic

223

C₂²

#11926526

yes

—

224

C₂²

#11926538

yes

characteristic

225

C₂²

#11926543

yes

characteristic

226

C₂²

#11926554

yes

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

152

—

231

C₄

—

152

—

232

C₄

#11926759

yes

—

233

C₄

#11926766

yes

—

234

C₄

#11926913

yes

—

235

C₄

#11926938

yes

—

236

C₂

#14562346

yes

—

237

C₂

#14562363

yes

—

238

C₂

#14564455

yes

characteristic

239

C₂

#14564484

yes

characteristic

240

C₂

#14564567

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1767	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1767	D₁₉
hypocenter	C₁₉	#9709
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1767

subgroup

G/H

center

C₂³

C₂×(C₂×D₁₉)⋊C₄

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1767

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1767

N	H ≅ G/N	type
164. C₁₉	#9709	semidirect

H ≅ G/N

type

164. C₁₉

#9709

semidirect

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

subgroup	index
#14572013	2
#14563752	2
C₂×#11926292	2
C₂×#11926291	2
C₁₉×#1767	2
#9709	19

subgroup

index

C₁₉×#1767

Subgroups — #18081652

Conjugacy classes of subgroups

Complements

Maximal subgroups