Group #23763668 — subgroups

Subgroups — #23763668

Order 10112.

298 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 113 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	C₂×#14579092	C₂	1	1	yes	maximal, characteristic
2	C₂×#14579085	C₂	1	1	yes	maximal, characteristic
3	C₂×#14579085	C₂	1	1	yes	maximal, characteristic
4	#19098461	C₂	1	1	yes	maximal, characteristic
5	#19098325	C₂	1	1	yes	maximal, characteristic
6	#19098318	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄×Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂²×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
12	C₂×Dic₇₉⋊C₄	—	2	1	no	—
13	#14579092	—	2	2	no	—
14	#14579085	—	2	2	no	—
15	#14579085	C₄	1	4	yes	complemented
16	C₇₉⋊#95	—	2	1	no	—
17	C₂²×Q₈×C₇₉	C₂²	1	1	yes	characteristic
18	C₄×Q₈×C₇₉	—	2	2	no	—
19	C₄×Q₈×C₇₉	—	2	2	no	—
20	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
21	C₂×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
22	C₂×C₄²×C₇₉	—	2	1	no	—
23	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
24	C₂²×Dic₇₉	—	2	1	no	—
25	C₂²×Dic₇₉	—	2	1	no	—
26	C₂×C₇₉⋊C₈	—	2	1	no	—
27	C₂×C₇₉⋊C₈	—	2	1	no	—
28	C₂×C₇₉⋊C₈	—	2	1	no	—
29	C₂×C₇₉⋊C₈	—	2	1	no	—
30	C₂×C₇₉⋊C₈	—	2	1	no	—
31	C₂×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
32	C₄⋊Dic₇₉	—	2	1	no	—
33	C₄⋊Dic₇₉	—	2	1	no	—
34	C₄⋊Dic₇₉	—	2	1	no	—
35	C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
36	Dic₇₉⋊C₄	—	4	2	no	—
37	C₂×Q₈×C₇₉	—	2	1	no	—
38	C₂×Q₈×C₇₉	—	2	1	no	—
39	C₂×Q₈×C₇₉	—	2	1	no	—
40	C₂×Q₈×C₇₉	C₂×C₄	1	2	yes	—
41	C₂×Q₈×C₇₉	D₄	1	2	yes	—
42	C₂×Q₈×C₇₉	Q₈	1	2	yes	—
43	C₂²×C₄×C₇₉	—	2	1	no	—
44	C₂²×C₄×C₇₉	—	2	1	no	—
45	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
46	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
47	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
48	C₄⋊C₄×C₇₉	—	2	4	no	—
49	C₄⋊C₄×C₇₉	—	2	1	no	—
50	C₄⋊C₄×C₇₉	D₄	1	2	yes	—
51	C₄²×C₇₉	—	2	4	no	—
52	C₄²×C₇₉	—	2	1	no	—
53	C₄²×C₇₉	—	2	1	no	—
54	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
55	Q₈×C₇₉	—	2	2	no	—
56	Q₈×C₇₉	—	2	2	no	—
57	Q₈×C₇₉	—	2	2	no	—
58	Q₈×C₇₉	C₄⋊C₄	1	4	yes	complemented
59	C₂×C₄×C₇₉	—	2	2	no	—
60	C₂×C₄×C₇₉	—	2	1	no	—
61	C₂×C₄×C₇₉	—	2	2	no	—
62	C₂×C₄×C₇₉	—	2	2	no	—
63	C₂×C₄×C₇₉	—	2	1	no	—
64	C₂×C₄×C₇₉	—	2	1	no	—
65	C₂×C₄×C₇₉	—	2	2	no	—
66	C₂×C₄×C₇₉	—	2	1	no	—
67	C₂×C₄×C₇₉	—	2	1	no	—
68	C₂×C₄×C₇₉	—	4	1	no	—
69	C₂×C₄×C₇₉	—	4	1	no	—
70	C₂×C₄×C₇₉	SD₁₆	1	2	yes	—
71	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
73	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
74	C₂×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
75	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
76	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
77	C₂×Dic₇₉	—	2	2	no	—
78	C₂×Dic₇₉	—	4	1	no	—
79	C₂×Dic₇₉	—	4	1	no	—
80	C₂×Dic₇₉	—	4	1	no	—
81	C₂×Dic₇₉	—	4	1	no	—
82	C₂×Dic₇₉	—	4	1	no	—
83	C₇₉⋊C₈	—	2	2	no	—
84	C₇₉⋊C₈	—	4	1	no	—
85	C₂²×C₇₉	C₄×D₄	1	1	yes	characteristic
86	C₂²×C₇₉	#120	1	1	yes	characteristic
87	C₂²×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
88	C₂²×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
89	C₂²×C₇₉	#135	1	1	yes	characteristic
90	C₂²×C₇₉	#137	1	1	yes	characteristic
91	C₂²×C₇₉	#137	1	1	yes	characteristic
92	C₄×C₇₉	—	2	4	no	—
93	C₄×C₇₉	—	2	2	no	—
94	C₄×C₇₉	—	4	1	no	—
95	C₄×C₇₉	—	4	2	no	—
96	C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
97	C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
98	C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
99	C₄×C₇₉	#123	1	1	yes	characteristic
100	Dic₇₉	—	4	2	no	—
101	Dic₇₉	—	8	1	no	—
102	C₂×C₇₉	#385	1	1	yes	characteristic
103	C₂×C₇₉	C₄×SD₁₆	1	1	yes	characteristic
104	C₂×C₇₉	#441	1	1	yes	characteristic
105	C₂×C₇₉	#448	1	1	yes	characteristic
106	C₂×C₇₉	#452	1	1	yes	characteristic
107	C₂×C₇₉	#475	1	1	yes	characteristic
108	C₂×C₇₉	#479	1	1	yes	characteristic
109	#1865	—	79	1	no	maximal, Sylow
110	C₇₉	#1865	1	1	yes	characteristic, complemented, Sylow
111	C₂×C₄×Q₈	D₇₉	1	1	yes	characteristic
112	C₂×#106	—	79	1	no	—
113	C₂×#103	—	79	1	no	—
114	C₂×#103	—	79	1	no	—
115	#389	—	79	1	no	—
116	#340	—	79	1	no	—
117	#336	—	79	1	no	—
118	C₂²×Q₈	C₂×D₇₉	1	1	yes	characteristic
119	C₂²×C₈	—	79	1	no	—
120	C₂²×C₈	—	79	1	no	—
121	C₄×Q₈	—	2	2	no	—
122	C₄×Q₈	—	2	2	no	—
123	C₂×C₄⋊C₄	—	2	1	no	—
124	C₂×C₄⋊C₄	—	79	1	no	—
125	C₂×C₄⋊C₄	—	79	1	no	—
126	C₂×C₄⋊C₄	—	158	1	no	—
127	C₂×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
128	C₂×C₄²	—	2	1	no	—
129	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
130	#106	—	158	2	no	—
131	#103	—	79	4	no	—
132	#103	—	158	2	no	—
133	#95	—	158	1	no	—
134	C₂×Q₈	—	2	1	no	—
135	C₂×Q₈	—	2	1	no	—
136	C₂×Q₈	—	2	1	no	—
137	C₂×Q₈	Dic₁₅₈	1	2	yes	—
138	C₂×Q₈	C₄×D₇₉	1	2	yes	—
139	C₂×Q₈	C₂²⋊D₇₉	1	2	yes	—
140	C₂²×C₄	—	2	1	no	—
141	C₂²×C₄	—	2	1	no	—
142	C₂²×C₄	—	158	1	no	—
143	C₂²×C₄	—	158	1	no	—
144	C₂²×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
145	C₂²×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
146	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
147	C₂×C₈	—	79	2	no	—
148	C₂×C₈	—	158	1	no	—
149	C₂×C₈	—	158	1	no	—
150	C₂×C₈	—	158	1	no	—
151	C₂×C₈	—	158	1	no	—
152	C₂×C₈	—	158	1	no	—
153	C₄⋊C₄	—	2	4	no	—
154	C₄⋊C₄	—	2	1	no	—
155	C₄⋊C₄	—	316	2	no	—
156	C₄⋊C₄	—	79	2	no	—
157	C₄⋊C₄	—	158	1	no	—
158	C₄⋊C₄	—	158	1	no	—
159	C₄⋊C₄	—	158	1	no	—
160	C₄⋊C₄	C₂²⋊D₇₉	1	2	yes	—
161	C₄²	—	2	4	no	—
162	C₄²	—	2	1	no	—
163	C₄²	—	2	1	no	—
164	C₂³	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
165	Q₈	—	2	2	no	—
166	Q₈	—	2	2	no	—
167	Q₈	—	2	2	no	—
168	Q₈	Dic₇₉⋊C₄	1	4	yes	complemented
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	1	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	1	no	—
174	C₂×C₄	—	2	1	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	1	no	—
177	C₂×C₄	—	2	1	no	—
178	C₂×C₄	—	4	1	no	—
179	C₂×C₄	—	4	1	no	—
180	C₂×C₄	—	316	1	no	—
181	C₂×C₄	—	316	1	no	—
182	C₂×C₄	—	316	1	no	—
183	C₂×C₄	—	316	1	no	—
184	C₂×C₄	—	316	1	no	—
185	C₂×C₄	—	158	2	no	—
186	C₂×C₄	#11929611	1	2	yes	—
187	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
188	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
189	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
190	C₂×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
191	C₂×C₄	#11929624	1	1	yes	characteristic
192	C₂×C₄	#11929624	1	1	yes	characteristic
193	C₈	—	316	1	no	—
194	C₈	—	158	2	no	—
195	C₂²	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
196	C₂²	#14579130	1	1	yes	characteristic
197	C₂²	#14579140	1	1	yes	characteristic
198	C₂²	C₂×#11929611	1	1	yes	characteristic
199	C₂²	#14579181	1	1	yes	characteristic
200	C₂²	#14579191	1	1	yes	characteristic
201	C₂²	#14579192	1	1	yes	characteristic
202	C₄	—	2	4	no	—
203	C₄	—	2	2	no	—
204	C₄	—	4	1	no	—
205	C₄	—	4	2	no	—
206	C₄	—	316	2	no	—
207	C₄	—	632	1	no	—
208	C₄	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
209	C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
210	C₄	#14579140	1	1	yes	characteristic
211	C₄	#14579144	1	1	yes	characteristic
212	C₂	#19098436	1	1	yes	characteristic
213	C₂	C₄×#11929611	1	1	yes	characteristic
214	C₂	#19098668	1	1	yes	characteristic
215	C₂	#19098702	1	1	yes	characteristic
216	C₂	#19098725	1	1	yes	characteristic
217	C₂	#19098848	1	1	yes	characteristic
218	C₂	#19098870	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579092

C₂

yes

maximal, characteristic

C₂×#14579085

C₂

yes

maximal, characteristic

C₂×#14579085

C₂

yes

maximal, characteristic

#19098461

C₂

yes

maximal, characteristic

#19098325

C₂

yes

maximal, characteristic

#19098318

C₂

yes

maximal, characteristic

C₂×C₄×Q₈×C₇₉

C₂

yes

maximal, characteristic

C₂²×C₇₉⋊C₈

C₂²

yes

characteristic

C₂²×C₇₉⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

characteristic

C₂×Dic₇₉⋊C₄

—

#14579092

—

#14579085

—

#14579085

C₄

yes

complemented

C₇₉⋊#95

—

C₂²×Q₈×C₇₉

C₂²

yes

characteristic

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

C₂²

yes

characteristic

C₂×C₄²×C₇₉

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₂×C₄

yes

—

Dic₇₉⋊C₄

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

C₂×C₄

yes

—

C₂×Q₈×C₇₉

D₄

yes

—

C₂×Q₈×C₇₉

Q₈

yes

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

D₄

yes

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

C₄⋊C₄

yes

complemented

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×C₄×C₇₉

—

C₂×C₄×C₇₉

SD₁₆

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₈

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

C₄×D₄

yes

characteristic

C₂²×C₇₉

#120

yes

characteristic

C₂²×C₇₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₇₉

C₂×SD₁₆

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₉

C₄×D₄

yes

characteristic

C₄×C₇₉

C₂²⋊Q₈

yes

characteristic

C₄×C₇₉

#123

yes

characteristic

100

Dic₇₉

—

101

Dic₇₉

—

102

C₂×C₇₉

#385

yes

characteristic

103

C₂×C₇₉

C₄×SD₁₆

yes

characteristic

104

C₂×C₇₉

#441

yes

characteristic

105

C₂×C₇₉

#448

yes

characteristic

106

C₂×C₇₉

#452

yes

characteristic

107

C₂×C₇₉

#475

yes

characteristic

108

C₂×C₇₉

yes

109

—

110

C₇₉

#1865

yes

characteristic, complemented, Sylow

111

C₂×C₄×Q₈

D₇₉

yes

characteristic

112

C₂×#106

—

113

C₂×#103

—

114

C₂×#103

—

115

#389

—

116

#340

—

117

#336

—

118

C₂²×Q₈

C₂×D₇₉

yes

characteristic

119

C₂²×C₈

—

120

C₂²×C₈

—

121

C₄×Q₈

—

122

C₄×Q₈

—

123

C₂×C₄⋊C₄

—

124

C₂×C₄⋊C₄

—

125

C₂×C₄⋊C₄

—

126

C₂×C₄⋊C₄

—

158

—

127

C₂×C₄⋊C₄

C₂×D₇₉

yes

characteristic

128

C₂×C₄²

—

129

C₂×C₄²

C₂×D₇₉

yes

characteristic

130

#106

—

158

—

131

#103

—

132

#103

—

158

—

133

#95

—

158

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂×Q₈

—

137

C₂×Q₈

Dic₁₅₈

yes

—

138

C₂×Q₈

C₄×D₇₉

yes

—

139

C₂×Q₈

C₂²⋊D₇₉

yes

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

158

—

143

C₂²×C₄

—

158

—

144

C₂²×C₄

C₂²⋊D₇₉

yes

characteristic

145

C₂²×C₄

C₂²⋊D₇₉

yes

characteristic

146

C₂²×C₄

C₂²×D₇₉

yes

characteristic

147

C₂×C₈

—

148

C₂×C₈

—

158

—

149

C₂×C₈

—

158

—

150

C₂×C₈

—

158

—

151

C₂×C₈

—

158

—

152

C₂×C₈

—

158

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

316

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

—

158

C₄⋊C₄

—

158

—

159

C₄⋊C₄

—

158

—

160

C₄⋊C₄

C₂²⋊D₇₉

yes

—

161

C₄²

—

162

C₄²

—

163

C₄²

—

164

C₂³

C₂×C₂²⋊D₇₉

yes

characteristic

165

Q₈

—

166

Q₈

—

167

Q₈

—

168

Q₈

Dic₇₉⋊C₄

yes

complemented

169

C₂×C₄

—

170

C₂×C₄

—

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

—

316

—

181

C₂×C₄

—

316

—

182

C₂×C₄

—

316

—

183

C₂×C₄

—

316

—

184

C₂×C₄

—

316

—

185

C₂×C₄

—

158

—

186

C₂×C₄

#11929611

yes

—

187

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

188

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

189

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

190

C₂×C₄

C₂×Dic₁₅₈

yes

characteristic

191

C₂×C₄

#11929624

yes

characteristic

192

C₂×C₄

#11929624

yes

characteristic

193

C₈

—

316

—

194

C₈

—

158

—

195

C₂²

C₄×C₂²⋊D₇₉

yes

characteristic

196

C₂²

#14579130

yes

characteristic

197

C₂²

#14579140

yes

characteristic

198

C₂²

C₂×#11929611

yes

characteristic

199

C₂²

#14579181

yes

characteristic

200

C₂²

#14579191

yes

characteristic

201

C₂²

#14579192

yes

characteristic

202

C₄

—

203

C₄

—

204

C₄

—

205

C₄

—

206

C₄

—

316

—

207

C₄

—

632

—

208

C₄

C₂×Dic₇₉⋊C₄

yes

characteristic

209

C₄

C₄×C₂²⋊D₇₉

yes

characteristic

210

C₄

#14579140

yes

characteristic

211

C₄

#14579144

yes

characteristic

212

C₂

#19098436

yes

characteristic

213

C₂

C₄×#11929611

yes

characteristic

214

C₂

#19098668

yes

characteristic

215

C₂

#19098702

yes

characteristic

216

C₂

#19098725

yes

characteristic

217

C₂

#19098848

yes

characteristic

218

C₂

#19098870

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	C₂×C₄×Q₈×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂×D₄
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	C₂×C₄×Q₈	D₇₉
hypocenter	C₇₉	#1865
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₇₉

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

C₂×C₄×Q₈×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

C₂×D₄

cosocle

C₂²×C₄×C₇₉

C₂³

hypercenter

C₂×C₄×Q₈

D₇₉

hypocenter

C₇₉

#1865

LCS

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×Q₈

N	H ≅ G/N	type
15. #14579085	C₄	semidirect
58. Q₈×C₇₉	C₄⋊C₄	semidirect
110. C₇₉	#1865	semidirect
168. Q₈	Dic₇₉⋊C₄	semidirect

H ≅ G/N

type

15. #14579085

C₄

semidirect

58. Q₈×C₇₉

C₄⋊C₄

semidirect

110. C₇₉

#1865

semidirect

168. Q₈

Dic₇₉⋊C₄

semidirect

Subgroups — #23763668

Conjugacy classes of subgroups

Complements