Group #34193255 — subgroups

Subgroups — #34193255

Order 20224.

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

normal subgroups only

This group has 320 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	#23764341	C₂	1	1	yes	maximal, characteristic
2	#23763574	C₂	1	1	yes	maximal, characteristic
3	#23762176	C₂	1	1	yes	maximal, characteristic
4	#23762175	C₂	1	1	yes	maximal, characteristic
5	#23761829	C₂	1	1	yes	maximal, characteristic
6	#23761230	C₂	1	1	yes	maximal, characteristic
7	C₇₉×#1487	C₂	1	1	yes	maximal, characteristic
8	#19098616	C₂²	1	1	yes	characteristic
9	C₂×#14579096	—	2	2	no	—
10	#19098587	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×#14579072	C₂²	1	1	yes	characteristic
13	#19098318	—	2	2	no	—
14	#19098316	—	2	2	no	—
15	#19098315	—	2	2	no	—
16	Q₈⋊(C₇₉⋊C₈)	—	2	2	no	—
17	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
18	#431×C₇₉	C₂²	1	1	yes	characteristic
19	#423×C₇₉	C₂²	1	1	yes	characteristic
20	Q₈⋊C₈×C₇₉	—	2	2	no	—
21	C₂×#11929608	—	2	1	no	—
22	C₂²×C₇₉⋊C₈	—	2	1	no	—
23	C₂²×C₇₉⋊C₈	D₄	1	2	yes	—
24	#14579096	—	4	4	no	—
25	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
26	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
27	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
28	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
29	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
30	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
31	#14579072	—	2	1	no	—
32	#14579072	—	2	1	no	—
33	C₄×C₇₉⋊C₈	D₄	1	2	yes	—
34	C₂²×Q₈×C₇₉	Q₈	1	1	yes	characteristic
35	C₂×M₁₆×C₇₉	—	2	1	no	—
36	C₄×Q₈×C₇₉	—	2	1	no	—
37	C₄×Q₈×C₇₉	—	2	1	no	—
38	C₄×Q₈×C₇₉	—	2	1	no	—
39	C₄×Q₈×C₇₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
41	C₂×C₄⋊C₄×C₇₉	Q₈	1	1	yes	characteristic
42	C₂×C₄²×C₇₉	—	2	1	no	—
43	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
44	C₄⋊C₈×C₇₉	—	2	1	no	—
45	C₄⋊C₈×C₇₉	—	2	1	no	—
46	C₄⋊C₈×C₇₉	—	2	1	no	—
47	C₂²⋊C₈×C₇₉	—	2	1	no	—
48	C₄×C₈×C₇₉	D₄	1	2	yes	—
49	#11929608	—	4	2	no	—
50	C₂×C₇₉⋊C₈	—	2	2	no	—
51	C₂×C₇₉⋊C₈	—	2	2	no	—
52	C₂×C₇₉⋊C₈	—	2	2	no	—
53	C₂×C₇₉⋊C₈	—	4	1	no	—
54	C₂×C₇₉⋊C₈	—	4	1	no	—
55	C₂×C₇₉⋊C₈	—	4	2	no	—
56	C₂×C₇₉⋊C₈	Q₁₆	1	4	yes	—
57	C₂×Q₈×C₇₉	—	2	1	no	—
58	C₂×Q₈×C₇₉	—	2	1	no	—
59	C₂×Q₈×C₇₉	—	4	2	no	—
60	C₂²×C₄×C₇₉	—	2	1	no	—
61	C₂²×C₄×C₇₉	—	2	1	no	—
62	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
64	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
65	M₁₆×C₇₉	—	4	2	no	—
66	C₂×C₈×C₇₉	—	2	2	no	—
67	C₂×C₈×C₇₉	—	4	1	no	—
68	C₄⋊C₄×C₇₉	—	2	1	no	—
69	C₄⋊C₄×C₇₉	—	2	1	no	—
70	C₄⋊C₄×C₇₉	—	4	1	no	—
71	C₄⋊C₄×C₇₉	—	4	1	no	—
72	C₄²×C₇₉	—	4	1	no	—
73	C₄²×C₇₉	—	4	1	no	—
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	C₄²×C₇₉	#41	1	1	yes	characteristic
78	C₂³×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
79	Q₈×C₇₉	—	2	2	no	—
80	Q₈×C₇₉	—	2	2	no	—
81	Q₈×C₇₉	—	4	1	no	—
82	Q₈×C₇₉	—	4	1	no	—
83	C₂×C₄×C₇₉	—	2	2	no	—
84	C₂×C₄×C₇₉	—	4	1	no	—
85	C₂×C₄×C₇₉	—	4	1	no	—
86	C₂×C₄×C₇₉	—	4	1	no	—
87	C₂×C₄×C₇₉	—	4	1	no	—
88	C₂×C₄×C₇₉	—	4	2	no	—
89	C₂×C₄×C₇₉	—	4	1	no	—
90	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
91	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
92	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
93	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
94	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
95	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
96	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
97	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
98	C₈×C₇₉	—	4	2	no	—
99	C₈×C₇₉	—	8	1	no	—
100	C₇₉⋊C₈	—	2	4	no	—
101	C₇₉⋊C₈	—	4	2	no	—
102	C₇₉⋊C₈	—	8	1	no	—
103	C₇₉⋊C₈	—	8	1	no	—
104	C₂²×C₇₉	—	2	1	no	—
105	C₂²×C₇₉	—	2	1	no	—
106	C₂²×C₇₉	#399	1	1	yes	characteristic
107	C₂²×C₇₉	#477	1	2	yes	—
108	C₄×C₇₉	—	2	1	no	—
109	C₄×C₇₉	—	2	1	no	—
110	C₄×C₇₉	—	2	1	no	—
111	C₄×C₇₉	—	2	1	no	—
112	C₄×C₇₉	—	4	2	no	—
113	C₄×C₇₉	—	8	1	no	—
114	C₄×C₇₉	#484	1	2	yes	—
115	C₄×C₇₉	#494	1	1	yes	characteristic
116	C₄×C₇₉	#496	1	1	yes	characteristic
117	#10662	—	79	1	no	maximal, Sylow
118	C₂×C₇₉	—	2	2	no	—
119	C₂×C₇₉	#2091	1	1	yes	characteristic
120	C₂×C₇₉	#2095	1	1	yes	characteristic
121	C₂×C₇₉	#2098	1	1	yes	characteristic
122	#1985	—	79	1	no	—
123	#1849	—	79	1	no	—
124	#1571	—	79	1	no	—
125	#1571	—	79	1	no	—
126	#1487	—	79	1	no	—
127	#1487	D₇₉	1	1	yes	characteristic
128	#1275	—	79	1	no	—
129	C₇₉	#10662	1	1	yes	characteristic, complemented, Sylow
130	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
131	#431	—	79	1	no	—
132	#431	C₂×D₇₉	1	1	yes	characteristic
133	C₂×#108	—	158	2	no	—
134	#423	—	79	1	no	—
135	#423	C₂×D₇₉	1	1	yes	characteristic
136	C₂×C₄⋊C₈	—	79	1	no	—
137	C₂×#97	—	79	1	no	—
138	#336	—	158	2	no	—
139	#335	—	158	2	no	—
140	#335	—	158	2	no	—
141	Q₈⋊C₈	—	2	2	no	—
142	Q₈⋊C₈	—	158	2	no	—
143	C₂²×Q₈	Dic₁₅₈	1	1	yes	characteristic
144	C₂×M₁₆	—	2	1	no	—
145	C₂×M₁₆	—	158	1	no	—
146	C₂²×C₈	—	79	2	no	—
147	C₂²×C₈	—	158	1	no	—
148	C₄×Q₈	—	2	1	no	—
149	C₄×Q₈	—	2	1	no	—
150	C₄×Q₈	—	2	1	no	—
151	C₄×Q₈	—	2	1	no	—
152	C₂×C₄⋊C₄	—	2	1	no	—
153	C₂×C₄⋊C₄	Dic₁₅₈	1	1	yes	characteristic
154	C₂×C₄²	—	2	1	no	—
155	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
156	#108	—	316	4	no	—
157	C₄⋊C₈	—	2	1	no	—
158	C₄⋊C₈	—	2	1	no	—
159	C₄⋊C₈	—	2	1	no	—
160	C₄⋊C₈	—	158	1	no	—
161	C₄⋊C₈	—	158	1	no	—
162	C₄⋊C₈	—	158	1	no	—
163	C₄⋊C₈	—	158	1	no	—
164	C₄⋊C₈	—	158	1	no	—
165	C₂²⋊C₈	—	2	1	no	—
166	C₂²⋊C₈	—	158	1	no	—
167	#97	—	158	1	no	—
168	#97	—	158	1	no	—
169	C₄×C₈	—	79	2	no	—
170	C₄×C₈	C₂²⋊D₇₉	1	2	yes	—
171	C₂×Q₈	—	2	1	no	—
172	C₂×Q₈	—	2	1	no	—
173	C₂×Q₈	—	4	2	no	—
174	C₂²×C₄	—	2	1	no	—
175	C₂²×C₄	—	2	1	no	—
176	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
177	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
178	C₂²×C₄	#11929623	1	1	yes	characteristic
179	M₁₆	—	4	2	no	—
180	M₁₆	—	316	2	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	4	1	no	—
183	C₂×C₈	—	316	1	no	—
184	C₂×C₈	—	316	1	no	—
185	C₂×C₈	—	316	2	no	—
186	C₂×C₈	—	79	4	no	—
187	C₂×C₈	—	158	2	no	—
188	C₂×C₈	—	158	2	no	—
189	C₂×C₈	—	158	2	no	—
190	C₄⋊C₄	—	2	1	no	—
191	C₄⋊C₄	—	2	1	no	—
192	C₄⋊C₄	—	4	1	no	—
193	C₄⋊C₄	—	4	1	no	—
194	C₄²	—	4	1	no	—
195	C₄²	—	4	1	no	—
196	C₄²	D₄×D₇₉	1	1	yes	characteristic
197	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
198	C₄²	#11929623	1	1	yes	characteristic
199	C₄²	#11929624	1	1	yes	characteristic
200	C₂³	#14579138	1	1	yes	characteristic
201	Q₈	—	2	2	no	—
202	Q₈	—	2	2	no	—
203	Q₈	—	4	1	no	—
204	Q₈	—	4	1	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	#14579138	1	1	yes	characteristic
213	C₂×C₄	#14579140	1	1	yes	characteristic
214	C₂×C₄	#14579142	1	1	yes	characteristic
215	C₂×C₄	#14579143	1	1	yes	characteristic
216	C₂×C₄	#14579143	1	1	yes	characteristic
217	C₂×C₄	#14579157	1	1	yes	characteristic
218	C₂×C₄	Q₁₆×D₇₉	1	2	yes	—
219	C₂×C₄	#14579188	1	2	yes	—
220	C₈	—	4	2	no	—
221	C₈	—	8	1	no	—
222	C₈	—	316	2	no	—
223	C₈	—	632	1	no	—
224	C₈	—	632	1	no	—
225	C₈	—	158	4	no	—
226	C₂²	—	2	1	no	—
227	C₂²	—	2	1	no	—
228	C₂²	#19098499	1	1	yes	characteristic
229	C₂²	#19098856	1	2	yes	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	4	2	no	—
235	C₄	—	8	1	no	—
236	C₄	#19098897	1	2	yes	—
237	C₄	#19098941	1	1	yes	characteristic
238	C₄	#19098949	1	1	yes	characteristic
239	C₂	—	2	2	no	—
240	C₂	#23764916	1	1	yes	characteristic
241	C₂	#23764936	1	1	yes	characteristic
242	C₂	#23764955	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23764341

C₂

yes

maximal, characteristic

#23763574

C₂

yes

maximal, characteristic

#23762176

C₂

yes

maximal, characteristic

#23762175

C₂

yes

maximal, characteristic

#23761829

C₂

yes

maximal, characteristic

#23761230

C₂

yes

maximal, characteristic

C₇₉×#1487

C₂

yes

maximal, characteristic

#19098616

C₂²

yes

characteristic

C₂×#14579096

—

#19098587

C₂²

yes

characteristic

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₂×#14579072

C₂²

yes

—

—

—

Q₈⋊(C₇₉⋊C₈)

—

C₂×C₄×Q₈×C₇₉

C₂²

yes

characteristic

#431×C₇₉

C₂²

yes

characteristic

#423×C₇₉

C₂²

yes

characteristic

Q₈⋊C₈×C₇₉

—

C₂×#11929608

—

C₂²×C₇₉⋊C₈

—

C₂²×C₇₉⋊C₈

D₄

yes

—

#14579096

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

#14579072

—

#14579072

—

C₄×C₇₉⋊C₈

D₄

yes

—

C₂²×Q₈×C₇₉

Q₈

yes

characteristic

C₂×M₁₆×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

Q₈

yes

characteristic

C₂×C₄²×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₂²⋊C₈×C₇₉

—

C₄×C₈×C₇₉

D₄

yes

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

Q₁₆

yes

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

C₄²×C₇₉

yes

C₄²×C₇₉

yes

C₂³×C₇₉

C₂²⋊Q₈

yes

characteristic

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×C₄×C₇₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

C₂×Q₁₆

yes

—

C₂×C₄×C₇₉

AGL(1,ℤ/8)

yes

—

C₈×C₇₉

—

C₈×C₇₉

—

100

C₇₉⋊C₈

—

101

C₇₉⋊C₈

—

102

C₇₉⋊C₈

—

103

C₇₉⋊C₈

—

104

C₂²×C₇₉

—

105

C₂²×C₇₉

—

106

C₂²×C₇₉

#399

yes

characteristic

107

C₂²×C₇₉

#477

yes

—

108

C₄×C₇₉

—

109

C₄×C₇₉

—

110

C₄×C₇₉

—

111

C₄×C₇₉

—

112

C₄×C₇₉

—

113

C₄×C₇₉

—

114

C₄×C₇₉

#484

yes

—

115

C₄×C₇₉

#494

yes

characteristic

116

C₄×C₇₉

yes

117

—

118

C₂×C₇₉

—

119

C₂×C₇₉

#2091

yes

characteristic

120

C₂×C₇₉

#2095

yes

characteristic

121

C₂×C₇₉

#2098

yes

characteristic

122

#1985

—

123

#1849

—

124

#1571

—

125

#1571

—

126

#1487

—

127

#1487

D₇₉

yes

characteristic

128

#1275

—

129

C₇₉

#10662

yes

characteristic, complemented, Sylow

130

C₂×C₄×Q₈

C₂×D₇₉

yes

characteristic

131

#431

—

132

#431

C₂×D₇₉

yes

characteristic

133

C₂×#108

—

158

—

134

#423

—

135

#423

C₂×D₇₉

yes

characteristic

136

C₂×C₄⋊C₈

—

137

C₂×#97

—

138

#336

—

158

—

139

#335

—

158

—

140

#335

—

158

—

141

Q₈⋊C₈

—

142

Q₈⋊C₈

—

158

—

143

C₂²×Q₈

Dic₁₅₈

yes

characteristic

144

C₂×M₁₆

—

145

C₂×M₁₆

—

158

—

146

C₂²×C₈

—

147

C₂²×C₈

—

158

—

148

C₄×Q₈

—

149

C₄×Q₈

—

150

C₄×Q₈

—

151

C₄×Q₈

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄⋊C₄

Dic₁₅₈

yes

characteristic

154

C₂×C₄²

—

155

C₂×C₄²

C₂²×D₇₉

yes

characteristic

156

#108

—

316

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

158

—

161

C₄⋊C₈

—

158

—

162

C₄⋊C₈

—

158

—

163

C₄⋊C₈

—

158

—

164

C₄⋊C₈

—

158

—

165

C₂²⋊C₈

—

166

C₂²⋊C₈

—

158

—

167

#97

—

158

—

168

#97

—

158

—

169

C₄×C₈

—

170

C₄×C₈

C₂²⋊D₇₉

yes

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

D₄×D₇₉

yes

characteristic

177

C₂²×C₄

C₂×Dic₁₅₈

yes

characteristic

178

C₂²×C₄

#11929623

yes

characteristic

179

M₁₆

—

180

M₁₆

—

316

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

316

—

184

C₂×C₈

—

316

—

185

C₂×C₈

—

316

—

186

C₂×C₈

—

187

C₂×C₈

—

158

—

188

C₂×C₈

—

158

—

189

C₂×C₈

—

158

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄²

—

195

C₄²

—

196

C₄²

D₄×D₇₉

yes

characteristic

197

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

198

C₄²

#11929623

yes

characteristic

199

C₄²

#11929624

yes

characteristic

200

C₂³

#14579138

yes

characteristic

201

Q₈

—

202

Q₈

—

203

Q₈

—

204

Q₈

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

#14579138

yes

characteristic

213

C₂×C₄

#14579140

yes

characteristic

214

C₂×C₄

#14579142

yes

characteristic

215

C₂×C₄

#14579143

yes

characteristic

216

C₂×C₄

#14579143

yes

characteristic

217

C₂×C₄

#14579157

yes

characteristic

218

C₂×C₄

Q₁₆×D₇₉

yes

—

219

C₂×C₄

#14579188

yes

—

220

C₈

—

221

C₈

—

222

C₈

—

316

—

223

C₈

—

632

—

224

C₈

—

632

—

225

C₈

—

158

—

226

C₂²

—

227

C₂²

—

228

C₂²

#19098499

yes

characteristic

229

C₂²

#19098856

yes

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

#19098897

yes

—

237

C₄

#19098941

yes

characteristic

238

C₄

#19098949

yes

characteristic

239

C₂

—

240

C₂

#23764916

yes

characteristic

241

C₂

#23764936

yes

characteristic

242

C₂

#23764955

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14579157
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1487	C₂
socle	C₂²×C₇₉	#399
prime radical	C₂³×C₇₉	C₂²⋊Q₈
hypercenter	#1487	D₇₉
hypocenter	C₇₉	#10662
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1487

subgroup

G/H

center

C₂×C₄

#14579157

commutator, cosocle

C₂×C₄²×C₇₉

C₂³

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1487

C₂

socle

C₂²×C₇₉

#399

prime radical

C₂³×C₇₉

C₂²⋊Q₈

D₇₉

C₇₉

G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1487

N	H ≅ G/N	type
129. C₇₉	#10662	semidirect

H ≅ G/N

type

129. C₇₉

#10662

semidirect

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

subgroup	index
#23764341	2
#23763574	2
#23762176	2
#23762175	2
#23761829	2
#23761230	2
C₇₉×#1487	2
#10662	79

subgroup

index

C₇₉×#1487

Subgroups — #34193255

Conjugacy classes of subgroups

Complements

Maximal subgroups