Group #34181223 — subgroups

Subgroups — #34181223

Order 20224.

450 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 131 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	#23762163	C₂	1	2	yes	maximal, complemented
2	#23761741	C₂	1	2	yes	maximal
3	#23761270	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×D₄×C₇₉	C₂	1	1	yes	maximal, characteristic
5	#19098620	C₂²	1	4	yes	—
6	#19098316	—	2	2	no	—
7	#19098314	—	2	2	no	—
8	#19098287	—	2	4	no	—
9	C₂³×C₈×C₇₉	C₄	1	2	yes	—
10	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
11	C₈×D₄×C₇₉	—	2	2	no	—
12	C₈×D₄×C₇₉	—	2	2	no	—
13	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊C₈×C₇₉	C₄	1	2	yes	—
15	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
17	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
18	#14579072	—	2	4	no	—
19	C₂²×D₄×C₇₉	Q₈	1	1	yes	characteristic
20	C₂³×C₄×C₇₉	C₂×C₄	1	2	yes	—
21	C₂²×C₈×C₇₉	—	2	2	no	—
22	C₂²×C₈×C₇₉	—	2	2	no	—
23	C₂²×C₈×C₇₉	—	4	4	no	—
24	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₇₉	C₂×C₄	1	2	yes	—
26	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
27	C₄×D₄×C₇₉	—	2	2	no	—
28	C₄×D₄×C₇₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₇₉	Q₈	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₇₉	D₄	1	2	yes	—
31	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
32	C₄⋊C₈×C₇₉	—	2	2	no	—
33	C₂²⋊C₈×C₇₉	—	2	4	no	—
34	C₄×C₈×C₇₉	D₄	1	2	yes	—
35	C₄×C₈×C₇₉	D₄	1	2	yes	—
36	C₂×C₇₉⋊C₈	—	4	4	no	—
37	C₂⁴×C₇₉	C₄⋊C₄	1	2	yes	—
38	C₂×D₄×C₇₉	—	2	4	no	—
39	C₂×D₄×C₇₉	—	2	2	no	—
40	C₂²×C₄×C₇₉	—	2	2	no	—
41	C₂²×C₄×C₇₉	—	2	2	no	—
42	C₂²×C₄×C₇₉	—	4	2	no	—
43	C₂²×C₄×C₇₉	—	4	2	no	—
44	C₂²×C₄×C₇₉	C₄⋊C₄	1	2	yes	—
45	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
46	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₈×C₇₉	—	2	2	no	—
49	C₂×C₈×C₇₉	—	2	2	no	—
50	C₂×C₈×C₇₉	—	4	1	no	—
51	C₂×C₈×C₇₉	—	4	2	no	—
52	C₂×C₈×C₇₉	—	4	4	no	—
53	C₂×C₈×C₇₉	—	4	4	no	—
54	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
55	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₄⋊C₄×C₇₉	—	2	2	no	—
58	C₂²⋊C₄×C₇₉	—	2	4	no	—
59	C₄²×C₇₉	C₂×D₄	1	2	yes	—
60	C₄²×C₇₉	#41	1	2	yes	—
61	C₂³×C₇₉	—	2	2	no	—
62	C₂³×C₇₉	—	2	2	no	—
63	C₂³×C₇₉	—	4	2	no	—
64	C₂³×C₇₉	—	4	2	no	—
65	C₂³×C₇₉	#108	1	4	yes	—
66	C₂³×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
67	D₄×C₇₉	—	2	8	no	—
68	C₂×C₄×C₇₉	—	2	2	no	—
69	C₂×C₄×C₇₉	—	2	1	no	—
70	C₂×C₄×C₇₉	—	2	1	no	—
71	C₂×C₄×C₇₉	—	2	2	no	—
72	C₂×C₄×C₇₉	—	4	1	no	—
73	C₂×C₄×C₇₉	—	4	4	no	—
74	C₂×C₄×C₇₉	—	4	2	no	—
75	C₂×C₄×C₇₉	—	4	2	no	—
76	C₂×C₄×C₇₉	—	4	2	no	—
77	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₄×C₇₉	#117	1	1	yes	characteristic
79	C₂×C₄×C₇₉	#121	1	2	yes	—
80	C₂×C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
81	C₈×C₇₉	—	2	1	no	—
82	C₈×C₇₉	—	2	2	no	—
83	C₈×C₇₉	—	4	2	no	—
84	C₈×C₇₉	#100	1	2	yes	—
85	C₇₉⋊C₈	—	8	4	no	—
86	C₂²×C₇₉	—	2	1	no	—
87	C₂²×C₇₉	—	2	1	no	—
88	C₂²×C₇₉	—	2	4	no	—
89	C₂²×C₇₉	—	4	4	no	—
90	C₂²×C₇₉	—	4	4	no	—
91	C₂²×C₇₉	—	4	2	no	—
92	C₂²×C₇₉	—	4	2	no	—
93	C₂²×C₇₉	#380	1	1	yes	characteristic
94	C₂²×C₇₉	C₂×#108	1	2	yes	—
95	C₄×C₇₉	—	2	1	no	—
96	C₄×C₇₉	—	2	2	no	—
97	C₄×C₇₉	—	2	2	no	—
98	C₄×C₇₉	—	4	2	no	—
99	C₄×C₇₉	C₂×#100	1	1	yes	characteristic
100	C₄×C₇₉	#413	1	1	yes	characteristic
101	#8622	—	79	1	no	maximal, Sylow
102	C₂×C₇₉	—	2	2	no	—
103	C₂×C₇₉	—	4	4	no	—
104	C₂×C₇₉	#1800	1	1	yes	characteristic
105	C₂×C₇₉	#1810	1	1	yes	characteristic
106	C₂×C₇₉	#1812	1	1	yes	characteristic
107	C₂×C₈×D₄	D₇₉	1	1	yes	characteristic
108	#1568	—	79	2	no	—
109	#1466	—	79	2	no	—
110	#1290	—	79	2	no	—
111	C₇₉	#8622	1	1	yes	characteristic, complemented, Sylow
112	C₂³×C₈	Dic₇₉	1	2	yes	—
113	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
114	C₈×D₄	—	2	2	no	—
115	C₈×D₄	—	2	2	no	—
116	#432	—	79	4	no	—
117	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
118	C₂×C₂²⋊C₈	Dic₇₉	1	2	yes	—
119	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
120	#335	—	158	2	no	—
121	#334	—	158	2	no	—
122	#323	—	158	4	no	—
123	C₂²×D₄	Dic₁₅₈	1	1	yes	characteristic
124	C₂³×C₄	C₂×Dic₇₉	1	2	yes	—
125	C₂²×C₈	—	2	2	no	—
126	C₂²×C₈	—	2	2	no	—
127	C₂²×C₈	—	4	4	no	—
128	C₂²×C₈	C₂×Dic₇₉	1	1	yes	characteristic
129	C₂²×C₈	C₂×Dic₇₉	1	2	yes	—
130	C₂²×C₈	C₂×Dic₇₉	1	1	yes	characteristic
131	C₄×D₄	—	2	2	no	—
132	C₄×D₄	—	2	2	no	—
133	C₂×C₄⋊C₄	Dic₁₅₈	1	1	yes	characteristic
134	C₂×C₂²⋊C₄	D₃₁₆	1	2	yes	—
135	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
136	C₄⋊C₈	—	2	2	no	—
137	C₄⋊C₈	—	158	4	no	—
138	C₂²⋊C₈	—	2	4	no	—
139	C₂²⋊C₈	—	158	4	no	—
140	#97	—	158	4	no	—
141	C₄×C₈	C₂²⋊D₇₉	1	2	yes	—
142	C₄×C₈	C₂²⋊D₇₉	1	2	yes	—
143	C₂⁴	C₄⋊Dic₇₉	1	2	yes	—
144	C₂×D₄	—	2	4	no	—
145	C₂×D₄	—	2	2	no	—
146	C₂²×C₄	—	2	2	no	—
147	C₂²×C₄	—	2	2	no	—
148	C₂²×C₄	—	4	2	no	—
149	C₂²×C₄	—	4	2	no	—
150	C₂²×C₄	C₄⋊Dic₇₉	1	2	yes	—
151	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
152	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
153	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
154	C₂×C₈	—	2	2	no	—
155	C₂×C₈	—	2	2	no	—
156	C₂×C₈	—	4	1	no	—
157	C₂×C₈	—	4	4	no	—
158	C₂×C₈	—	4	4	no	—
159	C₂×C₈	—	4	2	no	—
160	C₂×C₈	—	316	4	no	—
161	C₂×C₈	C₂²⋊Dic₇₉	1	2	yes	—
162	C₂×C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
163	C₂×C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
164	C₄⋊C₄	—	2	2	no	—
165	C₂²⋊C₄	—	2	4	no	—
166	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
167	C₄²	#11929624	1	2	yes	—
168	C₂³	—	2	2	no	—
169	C₂³	—	2	2	no	—
170	C₂³	—	4	2	no	—
171	C₂³	—	4	2	no	—
172	C₂³	#14579097	1	4	yes	—
173	C₂³	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
174	D₄	—	2	8	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	1	no	—
177	C₂×C₄	—	2	1	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	4	1	no	—
180	C₂×C₄	—	4	4	no	—
181	C₂×C₄	—	4	2	no	—
182	C₂×C₄	—	4	2	no	—
183	C₂×C₄	—	4	2	no	—
184	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
185	C₂×C₄	#14579120	1	1	yes	characteristic
186	C₂×C₄	#14579135	1	2	yes	—
187	C₂×C₄	#14579140	1	2	yes	—
188	C₈	—	2	1	no	—
189	C₈	—	2	2	no	—
190	C₈	—	4	2	no	—
191	C₈	—	632	4	no	—
192	C₈	#14579078	1	2	yes	—
193	C₂²	—	2	1	no	—
194	C₂²	—	2	1	no	—
195	C₂²	—	2	4	no	—
196	C₂²	—	4	4	no	—
197	C₂²	—	4	4	no	—
198	C₂²	—	4	2	no	—
199	C₂²	—	4	2	no	—
200	C₂²	#19098423	1	1	yes	characteristic
201	C₂²	C₂×#14579097	1	2	yes	—
202	C₄	—	2	1	no	—
203	C₄	—	2	2	no	—
204	C₄	—	2	2	no	—
205	C₄	—	4	2	no	—
206	C₄	C₂×#14579078	1	1	yes	characteristic
207	C₄	#19098547	1	1	yes	characteristic
208	C₂	—	2	2	no	—
209	C₂	—	4	4	no	—
210	C₂	#23763392	1	1	yes	characteristic
211	C₂	#23763438	1	1	yes	characteristic
212	C₂	#23763446	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23762163

C₂

yes

maximal, complemented

#23761741

C₂

yes

maximal

#23761270

C₂

yes

maximal, complemented

C₂×C₈×D₄×C₇₉

C₂

yes

maximal, characteristic

#19098620

C₂²

yes

—

#19098316

—

#19098314

—

#19098287

—

C₂³×C₈×C₇₉

C₄

yes

—

C₂×C₄×D₄×C₇₉

C₂²

yes

characteristic

C₈×D₄×C₇₉

—

C₈×D₄×C₇₉

—

C₂×C₄⋊C₈×C₇₉

C₂²

yes

characteristic

C₂×C₂²⋊C₈×C₇₉

C₄

yes

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

#14579072

—

C₂²×D₄×C₇₉

Q₈

yes

characteristic

C₂³×C₄×C₇₉

C₂×C₄

yes

—

C₂²×C₈×C₇₉

—

C₂²×C₈×C₇₉

—

C₂²×C₈×C₇₉

—

C₂²×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₉

C₂×C₄

yes

—

C₂²×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×D₄×C₇₉

—

C₄×D₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

Q₈

yes

characteristic

C₂×C₂²⋊C₄×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₂²⋊C₈×C₇₉

—

C₄×C₈×C₇₉

D₄

yes

—

C₄×C₈×C₇₉

D₄

yes

—

C₂×C₇₉⋊C₈

—

C₂⁴×C₇₉

C₄⋊C₄

yes

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₄⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×Q₈

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

—

C₄²×C₇₉

#41

yes

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

#108

yes

—

C₂³×C₇₉

C₂×C₄⋊C₄

yes

characteristic

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

—

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

#100

yes

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#380

yes

characteristic

C₂²×C₇₉

C₂×#108

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×#100

yes

characteristic

100

C₄×C₇₉

yes

101

—

102

C₂×C₇₉

—

103

C₂×C₇₉

—

104

C₂×C₇₉

#1800

yes

characteristic

105

C₂×C₇₉

#1810

yes

characteristic

106

C₂×C₇₉

#1812

yes

characteristic

107

C₂×C₈×D₄

D₇₉

yes

characteristic

108

#1568

—

109

#1466

—

110

#1290

—

111

C₇₉

#8622

yes

characteristic, complemented, Sylow

112

C₂³×C₈

Dic₇₉

yes

—

113

C₂×C₄×D₄

C₂×D₇₉

yes

characteristic

114

C₈×D₄

—

115

C₈×D₄

—

116

#432

—

117

C₂×C₄⋊C₈

C₂×D₇₉

yes

characteristic

118

C₂×C₂²⋊C₈

Dic₇₉

yes

—

119

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

120

#335

—

158

—

121

#334

—

158

—

122

#323

—

158

—

123

C₂²×D₄

Dic₁₅₈

yes

characteristic

124

C₂³×C₄

C₂×Dic₇₉

yes

—

125

C₂²×C₈

—

126

C₂²×C₈

—

127

C₂²×C₈

—

128

C₂²×C₈

C₂×Dic₇₉

yes

characteristic

129

C₂²×C₈

C₂×Dic₇₉

yes

—

130

C₂²×C₈

C₂×Dic₇₉

yes

characteristic

131

C₄×D₄

—

132

C₄×D₄

—

133

C₂×C₄⋊C₄

Dic₁₅₈

yes

characteristic

134

C₂×C₂²⋊C₄

D₃₁₆

yes

—

135

C₂×C₄²

C₂²×D₇₉

yes

characteristic

136

C₄⋊C₈

—

137

C₄⋊C₈

—

158

—

138

C₂²⋊C₈

—

139

C₂²⋊C₈

—

158

—

140

#97

—

158

—

141

C₄×C₈

C₂²⋊D₇₉

yes

—

142

C₄×C₈

C₂²⋊D₇₉

yes

—

143

C₂⁴

C₄⋊Dic₇₉

yes

—

144

C₂×D₄

—

145

C₂×D₄

—

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

C₄⋊Dic₇₉

yes

—

151

C₂²×C₄

C₂²×Dic₇₉

yes

characteristic

152

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

153

C₂²×C₄

C₂×Dic₁₅₈

yes

characteristic

154

C₂×C₈

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

316

—

161

C₂×C₈

C₂²⋊Dic₇₉

yes

—

162

C₂×C₈

C₂²⋊Dic₇₉

yes

characteristic

163

C₂×C₈

C₂²⋊Dic₇₉

yes

characteristic

164

C₄⋊C₄

—

165

C₂²⋊C₄

—

166

C₄²

C₂×C₂²⋊D₇₉

yes

—

167

C₄²

#11929624

yes

—

168

C₂³

—

169

C₂³

—

170

C₂³

—

171

C₂³

—

172

C₂³

#14579097

yes

—

173

C₂³

C₂×C₄⋊Dic₇₉

yes

characteristic

174

D₄

—

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

C₂×C₂²⋊Dic₇₉

yes

characteristic

185

C₂×C₄

#14579120

yes

characteristic

186

C₂×C₄

#14579135

yes

—

187

C₂×C₄

#14579140

yes

—

188

C₈

—

189

C₈

—

190

C₈

—

191

C₈

—

632

—

192

C₈

#14579078

yes

—

193

C₂²

—

194

C₂²

—

195

C₂²

—

196

C₂²

—

197

C₂²

—

198

C₂²

—

199

C₂²

—

200

C₂²

#19098423

yes

characteristic

201

C₂²

C₂×#14579097

yes

—

202

C₄

—

203

C₄

—

204

C₄

—

205

C₄

—

206

C₄

C₂×#14579078

yes

characteristic

207

C₄

#19098547

yes

characteristic

208

C₂

—

209

C₂

—

210

C₂

#23763392

yes

characteristic

211

C₂

#23763438

yes

characteristic

212

C₂

#23763446

yes

characteristic

	subgroup	G/H
center	C₂²	#19098423
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₂×C₈×D₄×C₇₉	C₂
socle	C₂²×C₇₉	#380
prime radical	C₂²×D₄×C₇₉	Q₈
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	C₂×C₈×D₄	D₇₉
hypocenter	C₇₉	#8622
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₈×D₄

subgroup

G/H

center

C₂²

#19098423

commutator

C₂²×C₄×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₂×C₈×D₄×C₇₉

C₂

socle

C₂²×C₇₉

#380

prime radical

C₂²×D₄×C₇₉

Q₈

cosocle

C₂×C₄²×C₇₉

C₂³

hypercenter

C₂×C₈×D₄

D₇₉

hypocenter

C₇₉

#8622

LCS

G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₈×D₄

N	H ≅ G/N	type
1. #23762163	C₂	semidirect
3. #23761270	C₂	semidirect
111. C₇₉	#8622	semidirect

H ≅ G/N

type

1. #23762163

C₂

semidirect

3. #23761270

C₂

semidirect

111. C₇₉

#8622

semidirect

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

subgroup	index
#23762163	2
#23761741	2
#23761270	2
C₂×C₈×D₄×C₇₉	2
#8622	79

subgroup

index

C₂×C₈×D₄×C₇₉

Subgroups — #34181223

Conjugacy classes of subgroups

Complements

Maximal subgroups