Group #18075370 — subgroups

Subgroups — #18075370

Order 4864.

476 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 167 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	#14563752	C₂	1	2	yes	maximal
2	C₂×#11926293	C₂	1	2	yes	maximal
3	#14561518	C₂	1	2	yes	maximal
4	C₄×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
6	#11926299	—	2	2	no	—
7	#11926299	—	2	2	no	—
8	#11926293	—	2	4	no	—
9	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₉	C₄	1	2	yes	—
11	C₁₉×#391	C₄	1	2	yes	—
12	C₁₉×#389	—	2	2	no	—
13	C₁₉×#384	C₂²	1	1	yes	characteristic
14	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
15	C₄³×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
17	C₁₉×C₄⋊Q₈	—	2	2	no	—
18	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
19	C₁₉×C₄⋊Q₈	Q₈	1	2	yes	—
20	C₄×Q₈×C₁₉	—	4	4	no	—
21	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
22	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
24	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₁₉	—	2	2	no	—
26	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	D₄	1	2	yes	—
29	C₂×C₄²×C₁₉	D₄	1	2	yes	—
30	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×C₁₉⋊C₈	—	2	4	no	—
32	C₁₉×#95	—	2	4	no	—
33	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
34	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
35	C₂×Q₈×C₁₉	—	2	2	no	—
36	C₂×Q₈×C₁₉	—	4	2	no	—
37	C₂×Q₈×C₁₉	—	4	2	no	—
38	C₂×Q₈×C₁₉	C₄⋊C₄	1	4	yes	—
39	C₂²×C₄×C₁₉	—	2	2	no	—
40	C₂²×C₄×C₁₉	—	2	2	no	—
41	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
43	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
46	C₄⋊C₄×C₁₉	—	2	4	no	—
47	C₄⋊C₄×C₁₉	—	2	4	no	—
48	C₄⋊C₄×C₁₉	—	4	2	no	—
49	C₄⋊C₄×C₁₉	—	4	4	no	—
50	C₄⋊C₄×C₁₉	—	4	4	no	—
51	C₄²×C₁₉	—	2	2	no	—
52	C₄²×C₁₉	—	2	4	no	—
53	C₄²×C₁₉	—	2	4	no	—
54	C₄²×C₁₉	—	4	1	no	—
55	C₄²×C₁₉	—	4	4	no	—
56	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
58	C₄²×C₁₉	#41	1	2	yes	—
59	C₂×C₁₉⋊C₈	—	4	4	no	—
60	C₂×C₁₉⋊C₈	—	4	4	no	—
61	C₂×C₁₉⋊C₈	—	4	4	no	—
62	#8594	—	19	1	no	maximal, Sylow
63	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
64	Q₈×C₁₉	—	4	4	no	—
65	Q₈×C₁₉	—	4	4	no	—
66	C₂×C₄×C₁₉	—	2	1	no	—
67	C₂×C₄×C₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	—	2	2	no	—
69	C₂×C₄×C₁₉	—	2	4	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	—	2	2	no	—
74	C₂×C₄×C₁₉	—	2	2	no	—
75	C₂×C₄×C₁₉	—	4	2	no	—
76	C₂×C₄×C₁₉	—	4	2	no	—
77	C₂×C₄×C₁₉	—	4	2	no	—
78	C₂×C₄×C₁₉	—	4	4	no	—
79	C₂×C₄×C₁₉	#100	1	2	yes	—
80	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
82	C₂×C₄×C₁₉	#121	1	2	yes	—
83	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
84	C₂×C₄×C₁₉	#135	1	4	yes	—
85	C₂×C₄×C₁₉	#137	1	4	yes	—
86	C₁₉⋊C₈	—	8	4	no	—
87	C₄×C₄⋊Q₈	D₁₉	1	1	yes	characteristic
88	#1831	—	19	2	no	—
89	C₂×#333	—	19	2	no	—
90	#1296	—	19	2	no	—
91	C₂²×C₁₉	#380	1	1	yes	characteristic
92	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
93	C₂²×C₁₉	#413	1	1	yes	characteristic
94	C₂²×C₁₉	#416	1	2	yes	—
95	C₂²×C₁₉	#419	1	2	yes	—
96	C₄×C₁₉	—	2	1	no	—
97	C₄×C₁₉	—	2	1	no	—
98	C₄×C₁₉	—	2	2	no	—
99	C₄×C₁₉	—	4	1	no	—
100	C₄×C₁₉	—	4	4	no	—
101	C₄×C₁₉	—	4	2	no	—
102	C₄×C₁₉	—	8	2	no	—
103	C₄×C₁₉	#464	1	4	yes	—
104	C₄×C₁₉	#479	1	4	yes	—
105	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
106	C₂×C₄×Q₈	Dic₁₉	1	2	yes	—
107	C₂×C₄⋊C₈	—	19	4	no	—
108	#391	Dic₁₉	1	2	yes	—
109	#389	—	2	2	no	—
110	#384	C₂×D₁₉	1	1	yes	characteristic
111	C₄×C₄⋊C₄	—	2	2	no	—
112	C₄³	C₂×D₁₉	1	1	yes	characteristic
113	#336	—	38	2	no	—
114	#336	—	38	2	no	—
115	#333	—	38	4	no	—
116	C₂×C₁₉	#1543	1	1	yes	characteristic
117	C₂×C₁₉	#1554	1	2	yes	—
118	C₂×C₁₉	#1558	1	1	yes	characteristic
119	C₂×C₁₉	#1800	1	1	yes	characteristic
120	C₂×C₁₉	#1805	1	2	yes	—
121	C₂²×Q₈	C₂×Dic₁₉	1	2	yes	—
122	C₂²×C₈	—	38	4	no	—
123	C₄⋊Q₈	—	2	2	no	—
124	C₄⋊Q₈	Dic₃₈	1	2	yes	—
125	C₄⋊Q₈	D₇₆	1	2	yes	—
126	C₄×Q₈	—	4	4	no	—
127	C₂×C₄⋊C₄	—	2	2	no	—
128	C₂×C₄⋊C₄	—	2	2	no	—
129	C₂×C₄⋊C₄	—	2	2	no	—
130	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
131	C₂×C₄²	—	2	2	no	—
132	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
133	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
134	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
135	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
136	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
137	C₄⋊C₈	—	38	4	no	—
138	C₄⋊C₈	—	38	4	no	—
139	#95	—	2	4	no	—
140	C₁₉	#8594	1	1	yes	characteristic, complemented, Sylow
141	C₂×Q₈	—	2	2	no	—
142	C₂×Q₈	—	4	2	no	—
143	C₂×Q₈	—	4	2	no	—
144	C₂×Q₈	C₄⋊Dic₁₉	1	4	yes	—
145	C₂²×C₄	—	2	2	no	—
146	C₂²×C₄	—	2	2	no	—
147	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
148	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
149	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
150	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
151	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
152	C₂×C₈	—	76	4	no	—
153	C₂×C₈	—	76	4	no	—
154	C₂×C₈	—	76	4	no	—
155	C₄⋊C₄	—	2	4	no	—
156	C₄⋊C₄	—	2	4	no	—
157	C₄⋊C₄	—	4	2	no	—
158	C₄⋊C₄	—	4	4	no	—
159	C₄⋊C₄	—	4	4	no	—
160	C₄²	—	2	4	no	—
161	C₄²	—	2	4	no	—
162	C₄²	—	2	2	no	—
163	C₄²	—	4	1	no	—
164	C₄²	—	4	4	no	—
165	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
166	C₄²	C₂×D₇₆	1	1	yes	characteristic
167	C₄²	#64541	1	2	yes	—
168	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
169	Q₈	—	4	4	no	—
170	Q₈	—	4	4	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	1	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	4	no	—
179	C₂×C₄	—	2	1	no	—
180	C₂×C₄	—	4	2	no	—
181	C₂×C₄	—	4	2	no	—
182	C₂×C₄	—	4	4	no	—
183	C₂×C₄	—	4	2	no	—
184	C₂×C₄	#10597290	1	2	yes	—
185	C₂×C₄	#10597370	1	2	yes	—
186	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
187	C₂×C₄	#10597372	1	1	yes	characteristic
188	C₂×C₄	#10597376	1	2	yes	—
189	C₂×C₄	#10597388	1	4	yes	—
190	C₂×C₄	#10597396	1	4	yes	—
191	C₈	—	152	4	no	—
192	C₂²	#11926404	1	1	yes	characteristic
193	C₂²	C₂×#10597290	1	1	yes	characteristic
194	C₂²	#11926528	1	1	yes	characteristic
195	C₂²	#11926540	1	2	yes	—
196	C₂²	#11926553	1	2	yes	—
197	C₄	—	2	1	no	—
198	C₄	—	2	1	no	—
199	C₄	—	2	2	no	—
200	C₄	—	4	2	no	—
201	C₄	—	4	4	no	—
202	C₄	—	4	1	no	—
203	C₄	—	8	2	no	—
204	C₄	#11926766	1	4	yes	—
205	C₄	#11926851	1	4	yes	—
206	C₂	#14562297	1	1	yes	characteristic
207	C₂	#14562345	1	2	yes	—
208	C₂	#14562361	1	1	yes	characteristic
209	C₂	#14563627	1	1	yes	characteristic
210	C₂	#14563650	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563752

C₂

yes

maximal

C₂×#11926293

C₂

yes

maximal

#14561518

C₂

yes

maximal

C₄×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#11926299

—

#11926299

—

#11926293

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₄

yes

—

C₁₉×#391

C₄

yes

—

C₁₉×#389

—

C₁₉×#384

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₁₉

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

Q₈

yes

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8594

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#100

yes

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₁₉⋊C₈

—

C₄×C₄⋊Q₈

D₁₉

yes

—

—

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#419

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

100

C₄×C₁₉

—

101

C₄×C₁₉

—

102

C₄×C₁₉

—

103

C₄×C₁₉

#464

yes

—

104

C₄×C₁₉

#479

yes

—

105

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

106

C₂×C₄×Q₈

Dic₁₉

yes

—

107

C₂×C₄⋊C₈

—

108

#391

Dic₁₉

yes

—

109

#389

—

110

#384

C₂×D₁₉

yes

characteristic

111

C₄×C₄⋊C₄

—

112

C₄³

C₂×D₁₉

yes

characteristic

113

#336

—

114

#336

—

115

#333

—

116

C₂×C₁₉

#1543

yes

characteristic

117

C₂×C₁₉

#1554

yes

—

118

C₂×C₁₉

#1558

yes

characteristic

119

C₂×C₁₉

#1800

yes

characteristic

120

C₂×C₁₉

#1805

yes

—

121

C₂²×Q₈

C₂×Dic₁₉

yes

—

122

C₂²×C₈

—

123

C₄⋊Q₈

—

124

C₄⋊Q₈

Dic₃₈

yes

—

125

C₄⋊Q₈

D₇₆

yes

—

126

C₄×Q₈

—

127

C₂×C₄⋊C₄

—

128

C₂×C₄⋊C₄

—

129

C₂×C₄⋊C₄

—

130

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

131

C₂×C₄²

—

132

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

133

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

134

C₂×C₄²

C₂²⋊D₁₉

yes

—

135

C₂×C₄²

C₂²⋊D₁₉

yes

—

136

C₂×C₄²

C₂²×D₁₉

yes

characteristic

137

C₄⋊C₈

—

138

C₄⋊C₈

—

139

#95

—

140

C₁₉

#8594

yes

characteristic, complemented, Sylow

141

C₂×Q₈

—

142

C₂×Q₈

—

143

C₂×Q₈

—

144

C₂×Q₈

C₄⋊Dic₁₉

yes

—

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

148

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

149

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

150

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

151

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄²

—

161

C₄²

—

162

C₄²

—

163

C₄²

—

164

C₄²

—

165

C₄²

C₂×Dic₃₈

yes

characteristic

166

C₄²

C₂×D₇₆

yes

characteristic

167

C₄²

#64541

yes

—

168

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

169

Q₈

—

170

Q₈

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

#10597290

yes

—

185

C₂×C₄

#10597370

yes

—

186

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

187

C₂×C₄

#10597372

yes

characteristic

188

C₂×C₄

#10597376

yes

—

189

C₂×C₄

#10597388

yes

—

190

C₂×C₄

#10597396

yes

—

191

C₈

—

152

—

192

C₂²

#11926404

yes

characteristic

193

C₂²

C₂×#10597290

yes

characteristic

194

C₂²

#11926528

yes

characteristic

195

C₂²

#11926540

yes

—

196

C₂²

#11926553

yes

—

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

—

201

C₄

—

202

C₄

—

203

C₄

—

204

C₄

#11926766

yes

—

205

C₄

#11926851

yes

—

206

C₂

#14562297

yes

characteristic

207

C₂

#14562345

yes

—

208

C₂

#14562361

yes

characteristic

209

C₂

#14563627

yes

characteristic

210

C₂

#14563650

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×C₄⋊Q₈	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×C₄⋊Q₈	D₁₉
hypocenter	C₁₉	#8594
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×C₄⋊Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×C₄⋊Q₈

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

hypercenter

C₄×C₄⋊Q₈

D₁₉

hypocenter

C₁₉

#8594

LCS

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×C₄⋊Q₈

N	H ≅ G/N	type
140. C₁₉	#8594	semidirect

H ≅ G/N

type

140. C₁₉

#8594

semidirect

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

subgroup	index
#14563752	2
C₂×#11926293	2
#14561518	2
C₄×C₁₉×C₄⋊Q₈	2
#8594	19

subgroup

index

C₄×C₁₉×C₄⋊Q₈

Subgroups — #18075370

Conjugacy classes of subgroups

Complements

Maximal subgroups