Group #23764498 — subgroups

Subgroups — #23764498

Order 10112.

370 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 95 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	C₂²×#11929614	C₂	1	1	yes	maximal, characteristic
2	C₂×#14579159	C₂	1	1	yes	maximal, characteristic
3	C₂×#14579086	C₂	1	1	yes	maximal, characteristic
4	C₂×#14579085	C₂	1	1	yes	maximal, characteristic
5	#19098470	C₂	1	1	yes	maximal, characteristic
6	#19098317	C₂	1	1	yes	maximal, characteristic
7	C₂²×Q₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₁₅₈	C₂²	1	1	yes	characteristic
9	C₂×#11929614	—	2	2	no	—
10	C₂×#11929614	—	2	2	no	—
11	C₂×#11929614	—	2	2	no	—
12	C₂²×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
13	#14579159	—	2	2	no	—
14	#14579159	—	2	2	no	—
15	C₂×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
16	C₂×Dic₇₉⋊C₄	—	2	2	no	—
17	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
18	#14579086	—	2	2	no	—
19	#14579085	—	2	2	no	—
20	C₇₉⋊#95	—	2	2	no	—
21	C₂²×Q₈×C₇₉	C₂²	1	1	yes	characteristic
22	C₂²×Q₈×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×Q₁₆×C₇₉	—	2	2	no	—
24	C₂×Q₁₆×C₇₉	—	2	2	no	—
25	C₂×Q₁₆×C₇₉	—	2	2	no	—
26	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×Dic₁₅₈	—	2	1	no	—
28	C₂×Dic₁₅₈	—	2	1	no	—
29	C₂×Dic₁₅₈	—	2	1	no	—
30	C₂×Dic₁₅₈	—	2	1	no	—
31	C₂×Dic₁₅₈	—	2	1	no	—
32	C₂×Dic₁₅₈	D₄	1	2	yes	—
33	C₂²×Dic₇₉	—	2	1	no	—
34	C₂²×Dic₇₉	—	2	1	no	—
35	C₂²×Dic₇₉	D₄	1	2	yes	—
36	#11929614	—	2	8	no	—
37	C₂×C₇₉⋊C₈	—	2	1	no	—
38	C₂×C₇₉⋊C₈	—	2	1	no	—
39	C₂×C₇₉⋊C₈	D₄	1	2	yes	—
40	C₄⋊Dic₇₉	—	2	1	no	—
41	C₄⋊Dic₇₉	—	2	1	no	—
42	Dic₇₉⋊C₄	—	2	8	no	—
43	C₄×Dic₇₉	—	2	1	no	—
44	C₄×Dic₇₉	—	2	1	no	—
45	C₂×Q₈×C₇₉	—	2	1	no	—
46	C₂×Q₈×C₇₉	—	2	1	no	—
47	C₂×Q₈×C₇₉	—	2	1	no	—
48	C₂×Q₈×C₇₉	—	2	1	no	—
49	C₂×Q₈×C₇₉	—	2	1	no	—
50	C₂×Q₈×C₇₉	—	2	1	no	—
51	C₂×Q₈×C₇₉	—	2	1	no	—
52	C₂×Q₈×C₇₉	—	2	1	no	—
53	C₂×Q₈×C₇₉	—	2	1	no	—
54	C₂×Q₈×C₇₉	—	2	1	no	—
55	C₂×Q₈×C₇₉	D₄	1	2	yes	—
56	C₂×Q₈×C₇₉	D₄	1	2	yes	—
57	C₂²×C₄×C₇₉	—	2	1	no	—
58	C₂²×C₄×C₇₉	—	2	1	no	—
59	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
60	Q₁₆×C₇₉	—	2	8	no	—
61	C₂×C₈×C₇₉	—	2	1	no	—
62	C₂×C₈×C₇₉	—	2	1	no	—
63	C₂×C₈×C₇₉	D₄	1	2	yes	—
64	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
65	Q₈×C₇₉	—	2	2	no	—
66	Q₈×C₇₉	—	2	2	no	—
67	Q₈×C₇₉	—	2	2	no	—
68	Q₈×C₇₉	—	2	2	no	—
69	Q₈×C₇₉	—	4	1	no	—
70	Q₈×C₇₉	—	4	1	no	—
71	Q₈×C₇₉	—	4	1	no	—
72	Q₈×C₇₉	—	4	1	no	—
73	C₂×C₄×C₇₉	—	2	2	no	—
74	C₂×C₄×C₇₉	—	2	2	no	—
75	C₂×C₄×C₇₉	—	4	1	no	—
76	C₂×C₄×C₇₉	—	4	1	no	—
77	C₂×C₄×C₇₉	—	4	1	no	—
78	C₂×C₄×C₇₉	—	4	1	no	—
79	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
80	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
83	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
84	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
85	C₂×Dic₇₉	—	2	2	no	—
86	C₂×Dic₇₉	—	2	2	no	—
87	C₂×Dic₇₉	—	2	2	no	—
88	C₂×Dic₇₉	—	4	1	no	—
89	C₂×Dic₇₉	—	4	1	no	—
90	C₂×Dic₇₉	—	4	1	no	—
91	C₂×Dic₇₉	—	4	2	no	—
92	C₂×Dic₇₉	Q₁₆	1	4	yes	complemented
93	Dic₁₅₈	—	2	2	no	—
94	Dic₁₅₈	—	2	2	no	—
95	Dic₁₅₈	—	4	1	no	—
96	Dic₁₅₈	—	4	1	no	—
97	C₈×C₇₉	—	2	2	no	—
98	C₇₉⋊C₈	—	2	2	no	—
99	C₂²×C₇₉	#120	1	1	yes	characteristic
100	C₂²×C₇₉	#121	1	1	yes	characteristic
101	C₂²×C₇₉	#127	1	1	yes	characteristic
102	C₂²×C₇₉	C₂×Q₁₆	1	2	yes	—
103	C₂²×C₇₉	#137	1	2	yes	—
104	C₄×C₇₉	—	4	2	no	—
105	C₄×C₇₉	—	4	2	no	—
106	C₄×C₇₉	#120	1	1	yes	characteristic
107	C₄×C₇₉	#120	1	1	yes	characteristic
108	C₄×C₇₉	#121	1	1	yes	characteristic
109	C₄×C₇₉	#121	1	1	yes	characteristic
110	Dic₇₉	—	2	4	no	—
111	Dic₇₉	—	4	2	no	—
112	Dic₇₉	—	8	1	no	—
113	C₂×C₇₉	#392	1	1	yes	characteristic
114	C₂×C₇₉	#451	1	2	yes	—
115	C₂×C₇₉	#462	1	2	yes	—
116	C₂×C₇₉	#494	1	1	yes	characteristic
117	C₂×C₇₉	#497	1	1	yes	characteristic
118	#2016	—	79	1	no	maximal, Sylow
119	C₇₉	#2016	1	1	yes	characteristic, complemented, Sylow
120	C₂²×Q₁₆	—	79	1	no	—
121	C₂²×Q₁₆	D₇₉	1	1	yes	characteristic
122	C₂×C₄⋊Q₈	—	79	1	no	—
123	C₂×#103	—	79	1	no	—
124	C₂×#103	—	79	1	no	—
125	#391	—	79	1	no	—
126	#336	—	79	1	no	—
127	C₂²×Q₈	—	79	1	no	—
128	C₂²×Q₈	C₂×D₇₉	1	1	yes	characteristic
129	C₂²×Q₈	C₂×D₇₉	1	1	yes	characteristic
130	C₂×Q₁₆	—	2	2	no	—
131	C₂×Q₁₆	—	2	2	no	—
132	C₂×Q₁₆	—	2	2	no	—
133	C₂×Q₁₆	—	158	2	no	—
134	C₂×Q₁₆	—	158	2	no	—
135	C₂×Q₁₆	—	158	2	no	—
136	C₂²×C₈	—	79	1	no	—
137	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
138	C₄⋊Q₈	—	158	2	no	—
139	C₄⋊Q₈	—	158	2	no	—
140	C₂×C₄⋊C₄	—	79	1	no	—
141	C₂×C₄⋊C₄	—	158	2	no	—
142	C₂×C₄²	—	79	1	no	—
143	#103	—	158	2	no	—
144	#103	—	158	2	no	—
145	#95	—	158	2	no	—
146	C₂×Q₈	—	2	1	no	—
147	C₂×Q₈	—	2	1	no	—
148	C₂×Q₈	—	2	1	no	—
149	C₂×Q₈	—	2	1	no	—
150	C₂×Q₈	—	2	1	no	—
151	C₂×Q₈	—	2	1	no	—
152	C₂×Q₈	—	2	1	no	—
153	C₂×Q₈	—	2	1	no	—
154	C₂×Q₈	—	2	1	no	—
155	C₂×Q₈	—	2	1	no	—
156	C₂×Q₈	—	79	2	no	—
157	C₂×Q₈	—	158	1	no	—
158	C₂×Q₈	—	158	1	no	—
159	C₂×Q₈	—	158	1	no	—
160	C₂×Q₈	—	158	1	no	—
161	C₂×Q₈	—	158	1	no	—
162	C₂×Q₈	C₂²⋊D₇₉	1	2	yes	—
163	C₂×Q₈	C₂²⋊D₇₉	1	2	yes	—
164	C₂²×C₄	—	2	1	no	—
165	C₂²×C₄	—	2	1	no	—
166	C₂²×C₄	—	79	2	no	—
167	C₂²×C₄	—	158	1	no	—
168	C₂²×C₄	—	158	1	no	—
169	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
170	Q₁₆	—	2	8	no	—
171	Q₁₆	—	158	8	no	—
172	C₂×C₈	—	2	1	no	—
173	C₂×C₈	—	2	1	no	—
174	C₂×C₈	—	79	2	no	—
175	C₂×C₈	—	158	1	no	—
176	C₂×C₈	—	158	1	no	—
177	C₂×C₈	C₂²⋊D₇₉	1	2	yes	—
178	C₄⋊C₄	—	158	8	no	—
179	C₄⋊C₄	—	158	1	no	—
180	C₄⋊C₄	—	158	1	no	—
181	C₄²	—	158	1	no	—
182	C₄²	—	158	1	no	—
183	C₂³	D₄×D₇₉	1	1	yes	characteristic
184	Q₈	—	2	2	no	—
185	Q₈	—	2	2	no	—
186	Q₈	—	2	2	no	—
187	Q₈	—	2	2	no	—
188	Q₈	—	4	1	no	—
189	Q₈	—	4	1	no	—
190	Q₈	—	4	1	no	—
191	Q₈	—	4	1	no	—
192	Q₈	—	316	1	no	—
193	Q₈	—	316	1	no	—
194	Q₈	—	158	2	no	—
195	Q₈	—	158	2	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	4	1	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	4	1	no	—
201	C₂×C₄	—	4	1	no	—
202	C₂×C₄	—	316	1	no	—
203	C₂×C₄	—	316	1	no	—
204	C₂×C₄	—	316	1	no	—
205	C₂×C₄	—	316	2	no	—
206	C₂×C₄	—	79	4	no	—
207	C₂×C₄	—	158	2	no	—
208	C₂×C₄	—	158	2	no	—
209	C₂×C₄	—	158	2	no	—
210	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
211	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
212	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
213	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
214	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
215	C₂×C₄	#11929623	1	1	yes	characteristic
216	C₈	—	2	2	no	—
217	C₈	—	158	2	no	—
218	C₂²	#14579129	1	1	yes	characteristic
219	C₂²	#14579133	1	1	yes	characteristic
220	C₂²	#14579157	1	1	yes	characteristic
221	C₂²	Q₁₆×D₇₉	1	2	yes	—
222	C₂²	#14579193	1	2	yes	—
223	C₄	—	4	2	no	—
224	C₄	—	4	2	no	—
225	C₄	—	316	2	no	—
226	C₄	—	632	1	no	—
227	C₄	—	158	4	no	—
228	C₄	#14579129	1	1	yes	characteristic
229	C₄	#14579130	1	1	yes	characteristic
230	C₄	#14579132	1	1	yes	characteristic
231	C₄	#14579133	1	1	yes	characteristic
232	C₂	#19098471	1	1	yes	characteristic
233	C₂	#19098717	1	2	yes	—
234	C₂	#19098771	1	2	yes	—
235	C₂	#19098941	1	1	yes	characteristic
236	C₂	#19098956	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11929614

C₂

yes

maximal, characteristic

C₂×#14579159

C₂

yes

maximal, characteristic

C₂×#14579086

C₂

yes

maximal, characteristic

C₂×#14579085

C₂

yes

maximal, characteristic

#19098470

C₂

yes

maximal, characteristic

#19098317

C₂

yes

maximal, characteristic

C₂²×Q₁₆×C₇₉

C₂

yes

maximal, characteristic

C₂²×Dic₁₅₈

C₂²

yes

—

—

—

C₂²×C₇₉⋊C₈

C₂²

yes

characteristic

#14579159

—

#14579159

—

C₂×C₄⋊Dic₇₉

C₂²

yes

characteristic

C₂×Dic₇₉⋊C₄

—

C₂×C₄×Dic₇₉

C₂²

yes

characteristic

#14579086

—

#14579085

—

C₇₉⋊#95

—

C₂²×Q₈×C₇₉

C₂²

yes

characteristic

C₂²×Q₈×C₇₉

C₂²

yes

characteristic

C₂×Q₁₆×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂²×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

D₄

yes

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

D₄

yes

—

#11929614

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

D₄

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

D₄

yes

—

C₂×Q₈×C₇₉

D₄

yes

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

Q₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

Q₁₆

yes

complemented

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

#120

yes

characteristic

100

C₂²×C₇₉

#121

yes

characteristic

101

C₂²×C₇₉

#127

yes

characteristic

102

C₂²×C₇₉

C₂×Q₁₆

yes

—

103

C₂²×C₇₉

#137

yes

—

104

C₄×C₇₉

—

105

C₄×C₇₉

—

106

C₄×C₇₉

#120

yes

characteristic

107

C₄×C₇₉

#120

yes

characteristic

108

C₄×C₇₉

#121

yes

characteristic

109

C₄×C₇₉

#121

yes

characteristic

110

Dic₇₉

—

111

Dic₇₉

—

112

Dic₇₉

—

113

C₂×C₇₉

#392

yes

characteristic

114

C₂×C₇₉

#451

yes

—

115

C₂×C₇₉

#462

yes

—

116

C₂×C₇₉

#494

yes

characteristic

117

C₂×C₇₉

yes

118

—

119

C₇₉

#2016

yes

characteristic, complemented, Sylow

120

C₂²×Q₁₆

—

121

C₂²×Q₁₆

D₇₉

yes

characteristic

122

C₂×C₄⋊Q₈

—

123

C₂×#103

—

124

C₂×#103

—

125

#391

—

126

#336

—

127

C₂²×Q₈

—

128

C₂²×Q₈

C₂×D₇₉

yes

characteristic

129

C₂²×Q₈

C₂×D₇₉

yes

characteristic

130

C₂×Q₁₆

—

131

C₂×Q₁₆

—

132

C₂×Q₁₆

—

133

C₂×Q₁₆

—

158

—

134

C₂×Q₁₆

—

158

—

135

C₂×Q₁₆

—

158

—

136

C₂²×C₈

—

137

C₂²×C₈

C₂×D₇₉

yes

characteristic

138

C₄⋊Q₈

—

158

—

139

C₄⋊Q₈

—

158

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄⋊C₄

—

158

—

142

C₂×C₄²

—

143

#103

—

158

—

144

#103

—

158

—

145

#95

—

158

—

146

C₂×Q₈

—

147

C₂×Q₈

—

148

C₂×Q₈

—

149

C₂×Q₈

—

150

C₂×Q₈

—

151

C₂×Q₈

—

152

C₂×Q₈

—

153

C₂×Q₈

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

—

158

C₂×Q₈

—

158

—

159

C₂×Q₈

—

158

—

160

C₂×Q₈

—

158

—

161

C₂×Q₈

—

158

—

162

C₂×Q₈

C₂²⋊D₇₉

yes

—

163

C₂×Q₈

C₂²⋊D₇₉

yes

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

—

158

—

168

C₂²×C₄

—

158

—

169

C₂²×C₄

C₂²×D₇₉

yes

characteristic

170

Q₁₆

—

171

Q₁₆

—

158

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

158

—

176

C₂×C₈

—

158

—

177

C₂×C₈

C₂²⋊D₇₉

yes

—

178

C₄⋊C₄

—

158

—

179

C₄⋊C₄

—

158

—

180

C₄⋊C₄

—

158

—

181

C₄²

—

158

—

182

C₄²

—

158

—

183

C₂³

D₄×D₇₉

yes

characteristic

184

Q₈

—

185

Q₈

—

186

Q₈

—

187

Q₈

—

188

Q₈

—

189

Q₈

—

190

Q₈

—

191

Q₈

—

192

Q₈

—

316

—

193

Q₈

—

316

—

194

Q₈

—

158

—

195

Q₈

—

158

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

316

—

203

C₂×C₄

—

316

—

204

C₂×C₄

—

316

—

205

C₂×C₄

—

316

—

206

C₂×C₄

—

207

C₂×C₄

—

158

—

208

C₂×C₄

—

158

—

209

C₂×C₄

—

158

—

210

C₂×C₄

D₄×D₇₉

yes

characteristic

211

C₂×C₄

D₄×D₇₉

yes

characteristic

212

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

213

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

214

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

215

C₂×C₄

#11929623

yes

characteristic

216

C₈

—

217

C₈

—

158

—

218

C₂²

#14579129

yes

characteristic

219

C₂²

#14579133

yes

characteristic

220

C₂²

#14579157

yes

characteristic

221

C₂²

Q₁₆×D₇₉

yes

—

222

C₂²

#14579193

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

316

—

226

C₄

—

632

—

227

C₄

—

158

—

228

C₄

#14579129

yes

characteristic

229

C₄

#14579130

yes

characteristic

230

C₄

#14579132

yes

characteristic

231

C₄

#14579133

yes

characteristic

232

C₂

#19098471

yes

characteristic

233

C₂

#19098717

yes

—

234

C₂

#19098771

yes

—

235

C₂

#19098941

yes

characteristic

236

C₂

#19098956

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₇₉
commutator, cosocle	C₂²×C₄×C₇₉	C₂³
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	C₂²×Q₁₆×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂×D₄
hypercenter	C₂²×Q₁₆	D₇₉
hypocenter	C₇₉	#2016
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₁₆

subgroup

G/H

center

C₂³

D₄×D₇₉

commutator, cosocle

C₂²×C₄×C₇₉

C₂³

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

C₂²×Q₁₆×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

C₂×D₄

hypercenter

C₂²×Q₁₆

D₇₉

hypocenter

C₇₉

#2016

LCS

G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₁₆

N	H ≅ G/N	type
92. C₂×Dic₇₉	Q₁₆	semidirect
119. C₇₉	#2016	semidirect

H ≅ G/N

type

92. C₂×Dic₇₉

Q₁₆

semidirect

119. C₇₉

#2016

semidirect

Subgroups — #23764498

Conjugacy classes of subgroups

Complements