Group #34188189 — subgroups

Subgroups — #34188189

Order 20224.

498 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 119 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	#23773979	C₂	1	1	yes	maximal, characteristic
2	#23764227	C₂	1	2	yes	maximal, complemented
3	#23763145	C₂	1	1	yes	maximal, characteristic, complemented
4	#23761850	C₂	1	2	yes	maximal, complemented
5	C₇₉×#1566	C₂	1	1	yes	maximal, characteristic, complemented
6	#19099113	C₂²	1	2	yes	—
7	#19098968	C₄	1	1	yes	characteristic, complemented
8	#19098940	C₄	1	1	yes	characteristic, complemented
9	#19098910	C₄	1	2	yes	complemented
10	#19098799	—	2	2	no	—
11	C₄×D₆₃₂	—	2	2	no	—
12	C₂×#14579087	—	2	4	no	—
13	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
14	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
15	#19098317	—	2	2	no	—
16	#19098290	—	2	4	no	—
17	#423×C₇₉	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
19	#334×C₇₉	—	2	2	no	—
20	C₂×#11929624	—	2	2	no	—
21	C₂×D₆₃₂	—	2	2	no	—
22	C₂²×C₇₉⋊C₈	—	2	1	no	—
23	#14579161	C₂×C₄	1	2	yes	—
24	#14579158	C₂×C₄	1	2	yes	—
25	#14579149	—	2	2	no	—
26	#14579135	—	2	2	no	—
27	#14579135	—	2	2	no	—
28	C₄×D₃₁₆	—	2	2	no	—
29	C₄×D₃₁₆	—	2	2	no	—
30	C₂×C₄×Dic₇₉	—	2	1	no	—
31	C₂×C₄×Dic₇₉	—	2	1	no	—
32	C₂×C₄×Dic₇₉	D₄	1	2	yes	—
33	#14579095	—	2	2	no	—
34	#14579087	—	4	8	no	—
35	#14579083	—	2	4	no	—
36	C₄×C₇₉⋊C₈	—	2	1	no	—
37	C₄×C₇₉⋊C₈	D₄	1	2	yes	—
38	C₂×M₁₆×C₇₉	—	2	2	no	—
39	C₂²×C₈×C₇₉	D₄	1	2	yes	—
40	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
41	C₄⋊C₈×C₇₉	—	2	2	no	—
42	C₄⋊C₈×C₇₉	—	2	2	no	—
43	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₇₉	D₄	1	2	yes	—
46	#11929624	—	4	4	no	—
47	#11929624	—	4	4	no	—
48	C₂×Dic₁₅₈	—	2	2	no	—
49	C₂×D₃₁₆	—	2	2	no	—
50	C₂×D₃₁₆	—	2	2	no	—
51	C₂×D₃₁₆	—	2	2	no	—
52	C₂×C₂²⋊D₇₉	—	4	2	no	—
53	C₂²×Dic₇₉	—	2	2	no	—
54	C₂×C₄×D₇₉	—	4	2	no	—
55	D₆₃₂	—	4	4	no	—
56	C₂×C₇₉⋊C₈	—	2	2	no	—
57	C₂×C₇₉⋊C₈	—	4	2	no	—
58	C₄⋊Dic₇₉	—	2	2	no	—
59	C₄⋊Dic₇₉	—	2	2	no	—
60	(C₂×D₇₉)⋊C₄	—	4	2	no	—
61	(C₂×D₇₉)⋊C₄	—	4	2	no	—
62	C₄×Dic₇₉	—	2	4	no	—
63	C₄×Dic₇₉	—	2	4	no	—
64	C₄×Dic₇₉	—	4	2	no	—
65	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
68	M₁₆×C₇₉	—	4	4	no	—
69	C₂×C₈×C₇₉	—	4	2	no	—
70	C₂×C₈×C₇₉	—	4	2	no	—
71	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
72	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
73	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
74	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₇₉	#41	1	1	yes	characteristic
77	C₂³×C₇₉	#121	1	1	yes	characteristic
78	C₂²×D₇₉	—	4	2	no	—
79	C₂×C₄×C₇₉	—	2	2	no	—
80	C₂×C₄×C₇₉	—	2	2	no	—
81	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
83	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
84	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
85	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
86	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
87	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	4	yes	—
88	C₂²⋊D₇₉	—	8	4	no	—
89	C₂×Dic₇₉	—	2	4	no	—
90	C₂×Dic₇₉	—	4	2	no	—
91	C₂×Dic₇₉	—	4	2	no	—
92	C₂×Dic₇₉	—	4	2	no	—
93	D₃₁₆	—	4	4	no	—
94	D₃₁₆	—	4	4	no	—
95	D₃₁₆	—	4	4	no	—
96	C₄×D₇₉	—	8	2	no	—
97	C₄×D₇₉	—	8	2	no	—
98	Dic₁₅₈	—	4	4	no	—
99	C₈×C₇₉	—	2	2	no	—
100	C₈×C₇₉	—	2	2	no	—
101	C₈×C₇₉	—	8	2	no	—
102	C₇₉⋊C₈	—	4	2	no	—
103	C₂²×C₇₉	—	2	1	no	—
104	C₂²×C₇₉	—	2	1	no	—
105	C₂²×C₇₉	#390	1	1	yes	characteristic
106	C₂²×C₇₉	#469	1	2	yes	—
107	C₂×D₇₉	—	8	2	no	—
108	C₂×D₇₉	—	8	2	no	—
109	C₂×D₇₉	—	8	2	no	—
110	C₄×C₇₉	—	2	1	no	—
111	C₄×C₇₉	—	2	1	no	—
112	C₄×C₇₉	#421	1	2	yes	—
113	C₄×C₇₉	#442	1	2	yes	—
114	C₄×C₇₉	#443	1	2	yes	—
115	C₄×C₇₉	#496	1	2	yes	—
116	Dic₇₉	—	4	4	no	—
117	Dic₇₉	—	8	2	no	—
118	#9852	—	79	1	no	maximal, Sylow
119	C₂×C₇₉	—	2	2	no	—
120	C₂×C₇₉	#1963	1	1	yes	characteristic
121	C₂×C₇₉	#1972	1	1	yes	characteristic
122	C₂×C₇₉	#1974	1	1	yes	characteristic
123	D₇₉	—	16	2	no	—
124	#3169	—	79	1	no	—
125	#1962	—	79	2	no	—
126	#1744	—	79	1	no	—
127	#1566	D₇₉	1	1	yes	characteristic, complemented
128	#1492	—	79	2	no	—
129	C₇₉	#9852	1	1	yes	characteristic, complemented, Sylow
130	#532	—	79	2	no	—
131	#500	—	79	1	no	—
132	#493	—	79	1	no	—
133	#486	—	79	2	no	—
134	#466	—	158	2	no	—
135	C₄×D₈	—	158	2	no	—
136	#423	C₂×D₇₉	1	2	yes	—
137	C₂×#104	—	158	4	no	—
138	C₂×C₄×C₈	—	79	1	no	—
139	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
140	C₄³	—	79	1	no	—
141	#336	—	158	2	no	—
142	#334	—	2	2	no	—
143	D₄⋊C₈	—	158	4	no	—
144	C₂×#41	—	158	2	no	—
145	C₂×D₈	—	158	2	no	—
146	C₂×M₁₆	—	2	2	no	—
147	C₂²×C₈	—	158	1	no	—
148	C₂²×C₈	D₃₁₆	1	2	yes	—
149	C₄⋊Q₈	—	79	2	no	—
150	#127	—	79	2	no	—
151	#124	—	158	2	no	—
152	#121	—	158	2	no	—
153	#121	—	158	2	no	—
154	C₄×D₄	—	158	2	no	—
155	C₄×D₄	—	158	2	no	—
156	C₂×C₄²	—	79	2	no	—
157	C₂×C₄²	—	158	1	no	—
158	C₂×C₄²	—	158	1	no	—
159	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
160	#107	—	158	2	no	—
161	C₄⋊C₈	—	2	2	no	—
162	C₄⋊C₈	—	2	2	no	—
163	#104	—	316	8	no	—
164	#102	—	158	4	no	—
165	C₄×C₈	—	79	2	no	—
166	C₄×C₈	—	158	1	no	—
167	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
168	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
169	C₄×C₈	C₂²⋊D₇₉	1	2	yes	—
170	#41	—	316	4	no	—
171	#41	—	316	4	no	—
172	C₂×Q₈	—	158	2	no	—
173	C₂×D₄	—	316	2	no	—
174	C₂×D₄	—	158	2	no	—
175	C₂×D₄	—	158	2	no	—
176	C₂×D₄	—	158	2	no	—
177	C₂²×C₄	—	316	2	no	—
178	C₂²×C₄	—	158	2	no	—
179	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
180	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
181	C₂²×C₄	#11929625	1	1	yes	characteristic
182	D₈	—	316	4	no	—
183	M₁₆	—	4	4	no	—
184	C₂×C₈	—	4	2	no	—
185	C₂×C₈	—	4	2	no	—
186	C₂×C₈	—	316	2	no	—
187	C₂×C₈	—	158	2	no	—
188	C₂×C₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
189	C₂×C₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
190	C₄⋊C₄	—	158	2	no	—
191	C₄⋊C₄	—	158	2	no	—
192	C₂²⋊C₄	—	316	2	no	—
193	C₂²⋊C₄	—	316	2	no	—
194	C₄²	—	316	2	no	—
195	C₄²	—	158	4	no	—
196	C₄²	—	158	4	no	—
197	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
198	C₄²	D₄×D₇₉	1	1	yes	characteristic
199	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
200	C₄²	#11929625	1	1	yes	characteristic
201	C₂³	—	316	2	no	—
202	C₂³	#14579136	1	1	yes	characteristic
203	Q₈	—	316	4	no	—
204	D₄	—	316	4	no	—
205	D₄	—	316	4	no	—
206	D₄	—	316	4	no	—
207	D₄	—	632	4	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	316	2	no	—
211	C₂×C₄	—	316	2	no	—
212	C₂×C₄	—	316	2	no	—
213	C₂×C₄	—	632	2	no	—
214	C₂×C₄	—	632	2	no	—
215	C₂×C₄	—	158	4	no	—
216	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
217	C₂×C₄	#14579123	1	1	yes	characteristic
218	C₂×C₄	#14579123	1	1	yes	characteristic
219	C₂×C₄	#14579136	1	1	yes	characteristic
220	C₂×C₄	#14579150	1	1	yes	characteristic
221	C₂×C₄	#14579157	1	1	yes	characteristic
222	C₂×C₄	#14579188	1	4	yes	—
223	C₈	—	2	2	no	—
224	C₈	—	2	2	no	—
225	C₈	—	8	2	no	—
226	C₈	—	316	2	no	—
227	C₂²	—	2	1	no	—
228	C₂²	—	2	1	no	—
229	C₂²	—	632	2	no	—
230	C₂²	—	632	2	no	—
231	C₂²	—	632	2	no	—
232	C₂²	#19098464	1	1	yes	characteristic
233	C₂²	#19098817	1	2	yes	—
234	C₄	—	2	1	no	—
235	C₄	—	2	1	no	—
236	C₄	—	316	4	no	—
237	C₄	—	632	2	no	—
238	C₄	#19098579	1	2	yes	—
239	C₄	#19098674	1	2	yes	—
240	C₄	#19098679	1	2	yes	—
241	C₄	#19098949	1	2	yes	—
242	C₂	—	2	2	no	—
243	C₂	—	1264	2	no	—
244	C₂	#23764231	1	1	yes	characteristic
245	C₂	#23764274	1	1	yes	characteristic
246	C₂	#23764286	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23773979

C₂

yes

maximal, characteristic

#23764227

C₂

yes

maximal, complemented

#23763145

C₂

yes

maximal, characteristic, complemented

#23761850

C₂

yes

maximal, complemented

C₇₉×#1566

C₂

yes

maximal, characteristic, complemented

#19099113

C₂²

yes

—

#19098968

C₄

yes

characteristic, complemented

#19098940

C₄

yes

characteristic, complemented

#19098910

C₄

yes

complemented

#19098799

—

C₄×D₆₃₂

—

C₂×#14579087

—

C₂×C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₄²×Dic₇₉

C₂²

yes

characteristic

#19098317

—

#19098290

—

#423×C₇₉

C₂²

yes

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

#334×C₇₉

—

C₂×#11929624

—

C₂×D₆₃₂

—

C₂²×C₇₉⋊C₈

—

#14579161

C₂×C₄

yes

—

#14579158

C₂×C₄

yes

—

#14579149

—

#14579135

—

#14579135

—

C₄×D₃₁₆

—

C₄×D₃₁₆

—

C₂×C₄×Dic₇₉

—

C₂×C₄×Dic₇₉

—

C₂×C₄×Dic₇₉

D₄

yes

—

#14579095

—

#14579087

—

#14579083

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

D₄

yes

—

C₂×M₁₆×C₇₉

—

C₂²×C₈×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

D₄

yes

—

#11929624

—

#11929624

—

C₂×Dic₁₅₈

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×C₂²⋊D₇₉

—

C₂²×Dic₇₉

—

C₂×C₄×D₇₉

—

D₆₃₂

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₄²×C₇₉

C₂²×C₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

C₄²×C₇₉

yes

C₂³×C₇₉

yes

C₂²×D₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄×D₄

yes

characteristic

C₂×C₄×C₇₉

C₄×D₄

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

—

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

C₄×D₇₉

—

C₄×D₇₉

—

Dic₁₅₈

—

C₈×C₇₉

—

100

C₈×C₇₉

—

101

C₈×C₇₉

—

102

C₇₉⋊C₈

—

103

C₂²×C₇₉

—

104

C₂²×C₇₉

—

105

C₂²×C₇₉

#390

yes

characteristic

106

C₂²×C₇₉

#469

yes

—

107

C₂×D₇₉

—

108

C₂×D₇₉

—

109

C₂×D₇₉

—

110

C₄×C₇₉

—

111

C₄×C₇₉

—

112

C₄×C₇₉

#421

yes

—

113

C₄×C₇₉

#442

yes

—

114

C₄×C₇₉

#443

yes

—

115

C₄×C₇₉

#496

yes

—

116

Dic₇₉

—

117

Dic₇₉

—

118

#9852

—

maximal, Sylow

119

C₂×C₇₉

—

120

C₂×C₇₉

#1963

yes

characteristic

121

C₂×C₇₉

#1972

yes

characteristic

122

C₂×C₇₉

#1974

yes

characteristic

123

D₇₉

—

124

#3169

—

125

#1962

—

126

#1744

—

127

#1566

D₇₉

yes

characteristic, complemented

128

#1492

—

129

C₇₉

#9852

yes

characteristic, complemented, Sylow

130

#532

—

131

#500

—

132

#493

—

133

#486

—

134

#466

—

158

—

135

C₄×D₈

—

158

—

136

#423

C₂×D₇₉

yes

—

137

C₂×#104

—

158

—

138

C₂×C₄×C₈

—

139

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

140

C₄³

—

141

#336

—

158

—

142

#334

—

143

D₄⋊C₈

—

158

—

144

C₂×#41

—

158

—

145

C₂×D₈

—

158

—

146

C₂×M₁₆

—

147

C₂²×C₈

—

158

—

148

C₂²×C₈

D₃₁₆

yes

—

149

C₄⋊Q₈

—

150

#127

—

151

#124

—

158

—

152

#121

—

158

—

153

#121

—

158

—

154

C₄×D₄

—

158

—

155

C₄×D₄

—

158

—

156

C₂×C₄²

—

157

C₂×C₄²

—

158

—

158

C₂×C₄²

—

158

—

159

C₂×C₄²

C₂²×D₇₉

yes

characteristic

160

#107

—

158

—

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

#104

—

316

—

164

#102

—

158

—

165

C₄×C₈

—

166

C₄×C₈

—

158

—

167

C₄×C₈

C₄×D₇₉

yes

characteristic

168

C₄×C₈

C₄×D₇₉

yes

characteristic

169

C₄×C₈

C₂²⋊D₇₉

yes

—

170

#41

—

316

—

171

#41

—

316

—

172

C₂×Q₈

—

158

—

173

C₂×D₄

—

316

—

174

C₂×D₄

—

158

—

175

C₂×D₄

—

158

—

176

C₂×D₄

—

158

—

177

C₂²×C₄

—

316

—

178

C₂²×C₄

—

158

—

179

C₂²×C₄

D₄×D₇₉

yes

characteristic

180

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

181

C₂²×C₄

#11929625

yes

characteristic

182

D₈

—

316

—

183

M₁₆

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

316

—

187

C₂×C₈

—

158

—

188

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

—

189

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

—

190

C₄⋊C₄

—

158

—

191

C₄⋊C₄

—

158

—

192

C₂²⋊C₄

—

316

—

193

C₂²⋊C₄

—

316

—

194

C₄²

—

316

—

195

C₄²

—

158

—

196

C₄²

—

158

—

197

C₄²

C₂×C₄×D₇₉

yes

characteristic

198

C₄²

D₄×D₇₉

yes

characteristic

199

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

200

C₄²

#11929625

yes

characteristic

201

C₂³

—

316

—

202

C₂³

#14579136

yes

characteristic

203

Q₈

—

316

—

204

D₄

—

316

—

205

D₄

—

316

—

206

D₄

—

316

—

207

D₄

—

632

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

316

—

211

C₂×C₄

—

316

—

212

C₂×C₄

—

316

—

213

C₂×C₄

—

632

—

214

C₂×C₄

—

632

—

215

C₂×C₄

—

158

—

216

C₂×C₄

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

217

C₂×C₄

#14579123

yes

characteristic

218

C₂×C₄

#14579123

yes

characteristic

219

C₂×C₄

#14579136

yes

characteristic

220

C₂×C₄

#14579150

yes

characteristic

221

C₂×C₄

#14579157

yes

characteristic

222

C₂×C₄

#14579188

yes

—

223

C₈

—

224

C₈

—

225

C₈

—

226

C₈

—

316

—

227

C₂²

—

228

C₂²

—

229

C₂²

—

632

—

230

C₂²

—

632

—

231

C₂²

—

632

—

232

C₂²

#19098464

yes

characteristic

233

C₂²

#19098817

yes

—

234

C₄

—

235

C₄

—

236

C₄

—

316

—

237

C₄

—

632

—

238

C₄

#19098579

yes

—

239

C₄

#19098674

yes

—

240

C₄

#19098679

yes

—

241

C₄

#19098949

yes

—

242

C₂

—

243

C₂

—

1264

—

244

C₂

#23764231

yes

characteristic

245

C₂

#23764274

yes

characteristic

246

C₂

#23764286

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14579157
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1566	C₂
socle	C₂²×C₇₉	#390
prime radical	#23773979	C₂
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1566	D₇₉
hypocenter	C₇₉	#9852
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1566

subgroup

G/H

center

C₂×C₄

#14579157

commutator

C₄²×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1566

C₂

C₂²×C₇₉

C₂

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1566

N	H ≅ G/N	type
2. #23764227	C₂	semidirect
3. #23763145	C₂	semidirect
4. #23761850	C₂	semidirect
5. C₇₉×#1566	C₂	semidirect
7. #19098968	C₄	semidirect
8. #19098940	C₄	semidirect
9. #19098910	C₄	semidirect
127. #1566	D₇₉	semidirect
129. C₇₉	#9852	semidirect

H ≅ G/N

type

2. #23764227

C₂

semidirect

3. #23763145

C₂

semidirect

4. #23761850

C₂

semidirect

5. C₇₉×#1566

C₂

semidirect

7. #19098968

C₄

semidirect

8. #19098940

C₄

semidirect

9. #19098910

C₄

semidirect

127. #1566

D₇₉

semidirect

129. C₇₉

#9852

semidirect

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

subgroup	index
#23773979	2
#23764227	2
#23763145	2
#23761850	2
C₇₉×#1566	2
#9852	79

subgroup

index

C₇₉×#1566

Subgroups — #34188189

Conjugacy classes of subgroups

Complements

Maximal subgroups