Group #23776310 — subgroups

Subgroups — #23776310

Order 10112.

340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 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	Q₈×Dic₁₅₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098973	C₂	1	2	yes	maximal, complemented
3	#19098966	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098867	C₂	1	2	yes	maximal, complemented
5	#19098855	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098853	C₂	1	1	yes	maximal, characteristic
7	#19098843	C₂	1	2	yes	maximal
8	#19098694	C₂	1	1	yes	maximal, characteristic, complemented
9	#19098663	C₂	1	2	yes	maximal
10	C₄×#11929612	C₂	1	1	yes	maximal, characteristic
11	#554×C₇₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#11929612	C₂²	1	1	yes	characteristic
13	#14579161	C₂²	1	1	yes	characteristic
14	#14579161	C₂²	1	2	yes	—
15	#14579160	—	2	1	no	—
16	#14579160	—	2	2	no	—
17	Q₈×Dic₇₉	—	2	1	no	—
18	C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
19	C₄×Dic₁₅₈	C₂²	1	2	yes	—
20	#14579094	C₂²	1	2	yes	—
21	#14579094	C₂²	1	2	yes	—
22	#14579094	C₂²	1	2	yes	—
23	#14579092	C₂²	1	1	yes	characteristic
24	#14579092	C₂²	1	2	yes	—
25	C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
26	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
27	#14579084	C₂²	1	1	yes	characteristic
28	#14579084	C₂²	1	2	yes	—
29	#14579082	C₂²	1	1	yes	characteristic
30	#14579082	C₂²	1	2	yes	—
31	#14579072	C₂²	1	2	yes	—
32	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
33	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
34	#125×C₇₉	C₂²	1	2	yes	—
35	C₂²⋊Q₈×C₇₉	—	2	1	no	—
36	C₂²⋊Q₈×C₇₉	—	2	2	no	—
37	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
38	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₇₉	C₂²	1	2	yes	—
40	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
41	C₂×Dic₁₅₈	—	2	1	no	—
42	C₂×Dic₁₅₈	—	2	2	no	—
43	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
44	#11929612	Q₈	1	4	yes	complemented
45	C₂×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
46	C₂×C₇₉⋊C₈	C₂³	1	2	yes	—
47	C₂×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
48	C₄⋊Dic₇₉	—	2	2	no	—
49	C₄⋊Dic₇₉	—	2	1	no	—
50	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
51	C₄⋊Dic₇₉	C₂³	1	2	yes	—
52	Dic₇₉⋊C₄	—	2	1	no	—
53	Dic₇₉⋊C₄	—	2	2	no	—
54	C₄×Dic₇₉	—	2	2	no	—
55	C₄×Dic₇₉	—	2	1	no	—
56	C₂×Q₈×C₇₉	—	2	1	no	—
57	C₂×Q₈×C₇₉	D₄	1	1	yes	characteristic
58	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₇₉	—	2	1	no	—
60	C₂²×C₄×C₇₉	—	2	2	no	—
61	C₄⋊C₄×C₇₉	—	2	2	no	—
62	C₄⋊C₄×C₇₉	—	2	1	no	—
63	C₄⋊C₄×C₇₉	—	2	2	no	—
64	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
65	C₄⋊C₄×C₇₉	D₄	1	2	yes	—
66	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
67	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
68	C₂²⋊C₄×C₇₉	—	2	1	no	—
69	C₂²⋊C₄×C₇₉	—	2	2	no	—
70	C₄²×C₇₉	C₂³	1	2	yes	—
71	C₄²×C₇₉	C₂³	1	1	yes	characteristic
72	C₂³×C₇₉	—	2	1	no	—
73	Q₈×C₇₉	—	2	2	no	—
74	Q₈×C₇₉	—	8	1	no	—
75	D₄×C₇₉	—	2	1	no	—
76	D₄×C₇₉	C₂×Q₈	1	2	yes	—
77	C₂×C₄×C₇₉	—	2	1	no	—
78	C₂×C₄×C₇₉	—	2	2	no	—
79	C₂×C₄×C₇₉	—	4	2	no	—
80	C₂×C₄×C₇₉	—	8	2	no	—
81	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
82	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
83	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
84	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
86	C₂×Dic₇₉	—	2	1	no	—
87	C₂×Dic₇₉	—	2	2	no	—
88	C₂×Dic₇₉	—	2	1	no	—
89	Dic₁₅₈	—	2	1	no	—
90	Dic₁₅₈	—	8	2	no	—
91	Dic₁₅₈	—	8	1	no	—
92	Dic₁₅₈	C₂×Q₈	1	2	yes	—
93	C₇₉⋊C₈	—	2	1	no	—
94	C₇₉⋊C₈	—	2	2	no	—
95	C₇₉⋊C₈	C₂×Q₈	1	2	yes	—
96	C₂²×C₇₉	—	2	2	no	—
97	C₂²×C₇₉	—	4	1	no	—
98	C₂²×C₇₉	—	4	1	no	—
99	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
100	C₄×C₇₉	—	2	2	no	—
101	C₄×C₇₉	—	2	2	no	—
102	C₄×C₇₉	—	2	1	no	—
103	C₄×C₇₉	—	4	1	no	—
104	C₄×C₇₉	—	4	2	no	—
105	C₄×C₇₉	#137	1	2	yes	—
106	C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
107	C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
108	Dic₇₉	—	2	2	no	—
109	Dic₇₉	—	4	1	no	—
110	Dic₇₉	—	4	2	no	—
111	C₂×C₇₉	—	4	2	no	—
112	C₂×C₇₉	D₄×Q₈	1	1	yes	characteristic
113	C₂×C₇₉	C₂×#137	1	1	yes	characteristic
114	C₂×C₇₉	#576	1	1	yes	characteristic
115	#3385	—	79	1	no	maximal, Sylow
116	C₇₉	#3385	1	1	yes	characteristic, complemented, Sylow
117	Q₈²	—	79	1	no	—
118	#554	D₇₉	1	1	yes	characteristic
119	#501	—	79	2	no	—
120	#500	—	79	1	no	—
121	#479	—	79	2	no	—
122	#477	—	79	1	no	—
123	#476	—	79	1	no	—
124	#474	—	79	2	no	—
125	#446	—	79	1	no	—
126	#440	—	79	2	no	—
127	C₄×SD₁₆	—	79	1	no	—
128	C₂×SD₁₆	—	79	1	no	—
129	C₄⋊Q₈	—	79	2	no	—
130	C₄⋊Q₈	—	79	1	no	—
131	C₄⋊Q₈	—	158	1	no	—
132	C₄⋊Q₈	—	158	2	no	—
133	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
134	#125	C₂×D₇₉	1	2	yes	—
135	C₂²⋊Q₈	—	2	1	no	—
136	C₂²⋊Q₈	—	2	2	no	—
137	C₄×Q₈	—	79	1	no	—
138	C₄×Q₈	—	79	2	no	—
139	C₄×Q₈	—	158	1	no	—
140	C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
141	C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
142	C₄×D₄	C₂×D₇₉	1	2	yes	—
143	C₂×C₄⋊C₄	—	2	1	no	—
144	#107	—	79	2	no	—
145	#107	—	79	2	no	—
146	#107	—	79	2	no	—
147	#106	—	79	1	no	—
148	#106	—	79	2	no	—
149	C₄⋊C₈	—	79	2	no	—
150	C₄⋊C₈	—	79	1	no	—
151	#103	—	79	1	no	—
152	#103	—	79	2	no	—
153	#102	—	79	1	no	—
154	#102	—	79	2	no	—
155	#97	—	79	2	no	—
156	C₄×C₈	—	79	1	no	—
157	C₂×Q₈	—	2	1	no	—
158	C₂×Q₈	—	79	1	no	—
159	C₂×Q₈	—	158	1	no	—
160	C₂×Q₈	—	158	2	no	—
161	C₂×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
162	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
163	C₂²×C₄	—	2	1	no	—
164	C₂²×C₄	—	2	2	no	—
165	SD₁₆	—	79	4	no	—
166	C₂×C₈	—	79	1	no	—
167	C₂×C₈	—	79	1	no	—
168	C₂×C₈	—	79	2	no	—
169	C₄⋊C₄	—	2	2	no	—
170	C₄⋊C₄	—	2	1	no	—
171	C₄⋊C₄	—	2	2	no	—
172	C₄⋊C₄	—	79	1	no	—
173	C₄⋊C₄	—	79	2	no	—
174	C₄⋊C₄	—	158	1	no	—
175	C₄⋊C₄	—	158	2	no	—
176	C₄⋊C₄	—	158	2	no	—
177	C₄⋊C₄	—	158	1	no	—
178	C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
179	C₄⋊C₄	C₂²⋊D₇₉	1	2	yes	—
180	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
181	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
182	C₂²⋊C₄	—	2	1	no	—
183	C₂²⋊C₄	—	2	2	no	—
184	C₄²	—	158	2	no	—
185	C₄²	—	158	1	no	—
186	C₄²	C₂²×D₇₉	1	1	yes	characteristic
187	C₄²	C₂²×D₇₉	1	2	yes	—
188	C₂³	—	2	1	no	—
189	Q₈	—	2	2	no	—
190	Q₈	—	8	1	no	—
191	Q₈	—	79	2	no	—
192	Q₈	—	632	2	no	—
193	Q₈	—	632	1	no	—
194	Q₈	—	158	1	no	—
195	D₄	—	2	1	no	—
196	D₄	Q₈×D₇₉	1	2	yes	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	8	2	no	—
201	C₂×C₄	—	158	2	no	—
202	C₂×C₄	—	158	1	no	—
203	C₂×C₄	—	158	1	no	—
204	C₂×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
205	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
206	C₂×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
207	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
208	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
209	C₈	—	79	2	no	—
210	C₈	—	158	1	no	—
211	C₈	—	158	2	no	—
212	C₂²	—	2	2	no	—
213	C₂²	—	4	1	no	—
214	C₂²	—	4	1	no	—
215	C₂²	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
216	C₄	—	2	2	no	—
217	C₄	—	2	2	no	—
218	C₄	—	2	1	no	—
219	C₄	—	4	1	no	—
220	C₄	—	4	2	no	—
221	C₄	—	316	1	no	—
222	C₄	—	316	2	no	—
223	C₄	—	158	2	no	—
224	C₄	#14579191	1	2	yes	—
225	C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
226	C₄	#14579209	1	1	yes	characteristic
227	C₂	—	4	2	no	—
228	C₂	Q₈×C₂²⋊D₇₉	1	1	yes	characteristic
229	C₂	C₂×#14579191	1	1	yes	characteristic
230	C₂	#19099366	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₈×Dic₁₅₈

C₂

yes

maximal, characteristic, complemented

#19098973

C₂

yes

maximal, complemented

#19098966

C₂

yes

maximal, characteristic, complemented

#19098867

C₂

yes

maximal, complemented

#19098855

C₂

yes

maximal, characteristic, complemented

#19098853

C₂

yes

maximal, characteristic

#19098843

C₂

yes

maximal

#19098694

C₂

yes

maximal, characteristic, complemented

#19098663

C₂

yes

maximal

C₄×#11929612

C₂

yes

maximal, characteristic

#554×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929612

C₂²

yes

characteristic

#14579161

C₂²

yes

characteristic

#14579161

C₂²

yes

—

#14579160

—

#14579160

—

Q₈×Dic₇₉

—

C₄×Dic₁₅₈

C₂²

yes

characteristic

C₄×Dic₁₅₈

C₂²

yes

—

#14579094

C₂²

yes

—

#14579094

C₂²

yes

—

#14579094

C₂²

yes

—

#14579092

C₂²

yes

characteristic

#14579092

C₂²

yes

—

C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

#14579084

C₂²

yes

characteristic

#14579084

C₂²

yes

—

#14579082

C₂²

yes

characteristic

#14579082

C₂²

yes

—

#14579072

C₂²

yes

—

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

#125×C₇₉

C₂²

yes

—

C₂²⋊Q₈×C₇₉

—

C₂²⋊Q₈×C₇₉

—

C₄×Q₈×C₇₉

C₂²

yes

characteristic

C₄×D₄×C₇₉

C₂²

yes

characteristic

C₄×D₄×C₇₉

C₂²

yes

—

C₂×C₄⋊C₄×C₇₉

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

C₂³

yes

characteristic

#11929612

Q₈

yes

complemented

C₂×C₇₉⋊C₈

C₂³

yes

characteristic

C₂×C₇₉⋊C₈

C₂³

yes

—

C₂×C₇₉⋊C₈

C₂³

yes

characteristic

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₂³

yes

characteristic

C₄⋊Dic₇₉

C₂³

yes

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

D₄

yes

characteristic

C₂×D₄×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₄⋊C₄×C₇₉

D₄

yes

—

C₄⋊C₄×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

C₂³

yes

—

C₂²⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

C₂³

yes

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂⁴

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

C₂×Q₈

yes

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

C₂×Q₈

yes

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂²×D₄

yes

characteristic

100

C₄×C₇₉

—

101

C₄×C₇₉

—

102

C₄×C₇₉

—

103

C₄×C₇₉

—

104

C₄×C₇₉

—

105

C₄×C₇₉

#137

yes

—

106

C₄×C₇₉

C₂²×Q₈

yes

characteristic

107

C₄×C₇₉

2₋¹⁺⁴

yes

characteristic

108

Dic₇₉

—

109

Dic₇₉

—

110

Dic₇₉

—

111

C₂×C₇₉

—

112

C₂×C₇₉

D₄×Q₈

yes

characteristic

113

C₂×C₇₉

C₂×#137

yes

characteristic

114

C₂×C₇₉

yes

115

—

116

C₇₉

#3385

yes

characteristic, complemented, Sylow

117

Q₈²

—

118

#554

D₇₉

yes

characteristic

119

#501

—

120

#500

—

121

#479

—

122

#477

—

123

#476

—

124

#474

—

125

#446

—

126

#440

—

127

C₄×SD₁₆

—

128

C₂×SD₁₆

—

129

C₄⋊Q₈

—

130

C₄⋊Q₈

—

131

C₄⋊Q₈

—

158

—

132

C₄⋊Q₈

—

158

—

133

C₄⋊Q₈

C₂×D₇₉

yes

characteristic

134

#125

C₂×D₇₉

yes

—

135

C₂²⋊Q₈

—

136

C₂²⋊Q₈

—

137

C₄×Q₈

—

138

C₄×Q₈

—

139

C₄×Q₈

—

158

—

140

C₄×Q₈

C₂×D₇₉

yes

characteristic

141

C₄×D₄

C₂×D₇₉

yes

characteristic

142

C₄×D₄

C₂×D₇₉

yes

—

143

C₂×C₄⋊C₄

—

144

#107

—

145

#107

—

146

#107

—

147

#106

—

148

#106

—

149

C₄⋊C₈

—

150

C₄⋊C₈

—

151

#103

—

152

#103

—

153

#102

—

154

#102

—

155

#97

—

156

C₄×C₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

158

—

160

C₂×Q₈

—

158

—

161

C₂×Q₈

C₂²⋊D₇₉

yes

characteristic

162

C₂×D₄

C₂²×D₇₉

yes

characteristic

163

C₂²×C₄

—

164

C₂²×C₄

—

165

SD₁₆

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

158

—

175

C₄⋊C₄

—

158

—

176

C₄⋊C₄

—

158

—

177

C₄⋊C₄

—

158

—

178

C₄⋊C₄

C₂²⋊D₇₉

yes

characteristic

179

C₄⋊C₄

C₂²⋊D₇₉

yes

—

180

C₄⋊C₄

C₂²×D₇₉

yes

characteristic

181

C₄⋊C₄

C₂²×D₇₉

yes

—

182

C₂²⋊C₄

—

183

C₂²⋊C₄

—

184

C₄²

—

158

—

185

C₄²

—

158

—

186

C₄²

C₂²×D₇₉

yes

characteristic

187

C₄²

C₂²×D₇₉

yes

—

188

C₂³

—

189

Q₈

—

190

Q₈

—

191

Q₈

—

192

Q₈

—

632

—

193

Q₈

—

632

—

194

Q₈

—

158

—

195

D₄

—

196

D₄

Q₈×D₇₉

yes

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

158

—

202

C₂×C₄

—

158

—

203

C₂×C₄

—

158

—

204

C₂×C₄

C₂×C₂²⋊D₇₉

yes

—

205

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

206

C₂×C₄

C₂×C₂²⋊D₇₉

yes

—

207

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

208

C₂×C₄

C₂³×D₇₉

yes

characteristic

209

C₈

—

210

C₈

—

158

—

211

C₈

—

158

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

C₂²×C₂²⋊D₇₉

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

316

—

222

C₄

—

316

—

223

C₄

—

158

—

224

C₄

#14579191

yes

—

225

C₄

C₂×Q₈×D₇₉

yes

characteristic

226

C₄

#14579209

yes

characteristic

227

C₂

—

228

C₂

Q₈×C₂²⋊D₇₉

yes

characteristic

229

C₂

C₂×#14579191

yes

characteristic

230

C₂

#19099366

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₉
Fitting	#554×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₄
prime radical	C₂×D₄×C₇₉	C₂³
hypercenter	#554	D₇₉
hypocenter	C₇₉	#3385
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #554

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₇₉

commutator, cosocle

C₂×C₄×C₇₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₉

Fitting

#554×C₇₉

C₂

socle

C₂²×C₇₉

C₂²×D₄

prime radical

C₂×D₄×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #554

N	H ≅ G/N	type
1. Q₈×Dic₁₅₈	C₂	semidirect
2. #19098973	C₂	semidirect
3. #19098966	C₂	semidirect
4. #19098867	C₂	semidirect
5. #19098855	C₂	semidirect
8. #19098694	C₂	semidirect
44. #11929612	Q₈	semidirect
116. C₇₉	#3385	semidirect

H ≅ G/N

type

1. Q₈×Dic₁₅₈

C₂

semidirect

2. #19098973

C₂

semidirect

3. #19098966

C₂

semidirect

4. #19098867

C₂

semidirect

5. #19098855

C₂

semidirect

8. #19098694

C₂

semidirect

44. #11929612

Q₈

semidirect

116. C₇₉

#3385

semidirect

Subgroups — #23776310

Conjugacy classes of subgroups

Complements