Group #34192703 — subgroups

Subgroups — #34192703

Order 20224.

494 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 145 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	#23764158	C₂	1	2	yes	maximal
2	#23763559	C₂	1	1	yes	maximal, characteristic
3	#23761283	C₂	1	1	yes	maximal, characteristic
4	#23761241	C₂	1	2	yes	maximal
5	C₇₉×#2551	C₂	1	1	yes	maximal, characteristic
6	C₂×#14579094	—	2	2	no	—
7	C₂×#14579094	—	2	2	no	—
8	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
9	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
10	#19098433	C₂²	1	1	yes	characteristic
11	#19098325	—	2	2	no	—
12	C₂×C₄⋊Q₈×C₇₉	—	2	2	no	—
13	#395×C₇₉	—	2	2	no	—
14	#389×C₇₉	—	2	2	no	—
15	#384×C₇₉	C₂²	1	1	yes	characteristic
16	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
17	C₂²×C₇₉⋊C₈	—	2	1	no	—
18	C₂²×C₇₉⋊C₈	—	2	2	no	—
19	C₂×C₄⋊Dic₇₉	—	2	2	no	—
20	C₂×C₄⋊Dic₇₉	—	2	1	no	—
21	#14579094	—	4	4	no	—
22	#14579094	—	4	4	no	—
23	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
24	C₄⋊(C₇₉⋊C₈)	Q₈	1	4	yes	complemented
25	C₄×C₇₉⋊C₈	—	2	1	no	—
26	C₄×C₇₉⋊C₈	Q₈	1	2	yes	complemented
27	C₂²×Q₈×C₇₉	—	2	2	no	—
28	C₄⋊Q₈×C₇₉	—	4	4	no	—
29	C₄⋊Q₈×C₇₉	—	4	4	no	—
30	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
31	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
32	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
33	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
34	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
35	C₂×C₄²×C₇₉	—	2	2	no	—
36	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
37	#95×C₇₉	—	2	2	no	—
38	#95×C₇₉	—	2	2	no	—
39	C₂²×Dic₇₉	—	4	1	no	—
40	C₂×C₇₉⋊C₈	—	2	2	no	—
41	C₂×C₇₉⋊C₈	—	2	2	no	—
42	C₂×C₇₉⋊C₈	—	2	2	no	—
43	C₂×C₇₉⋊C₈	—	2	4	no	—
44	C₂×C₇₉⋊C₈	—	4	2	no	—
45	C₂×C₇₉⋊C₈	—	4	2	no	—
46	C₄⋊Dic₇₉	—	4	2	no	—
47	C₄⋊Dic₇₉	—	4	2	no	—
48	C₄⋊Dic₇₉	—	4	2	no	—
49	C₂×Q₈×C₇₉	—	4	8	no	—
50	C₂×Q₈×C₇₉	—	8	2	no	—
51	C₂²×C₄×C₇₉	—	2	2	no	—
52	C₂²×C₄×C₇₉	—	2	2	no	—
53	C₂²×C₄×C₇₉	—	2	2	no	—
54	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
56	C₄⋊C₄×C₇₉	—	2	2	no	—
57	C₄⋊C₄×C₇₉	—	2	2	no	—
58	C₄⋊C₄×C₇₉	—	4	8	no	—
59	C₄⋊C₄×C₇₉	—	4	2	no	—
60	C₄⋊C₄×C₇₉	—	4	2	no	—
61	C₄⋊C₄×C₇₉	—	4	2	no	—
62	C₄⋊C₄×C₇₉	D₈	1	4	yes	—
63	C₄⋊C₄×C₇₉	Q₁₆	1	4	yes	—
64	C₄²×C₇₉	—	4	2	no	—
65	C₄²×C₇₉	—	4	2	no	—
66	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
67	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
68	C₄²×C₇₉	#41	1	1	yes	characteristic
69	C₂³×C₇₉	#120	1	1	yes	characteristic
70	Q₈×C₇₉	—	8	8	no	—
71	C₂×C₄×C₇₉	—	2	1	no	—
72	C₂×C₄×C₇₉	—	2	1	no	—
73	C₂×C₄×C₇₉	—	2	4	no	—
74	C₂×C₄×C₇₉	—	2	4	no	—
75	C₂×C₄×C₇₉	—	4	2	no	—
76	C₂×C₄×C₇₉	—	4	2	no	—
77	C₂×C₄×C₇₉	—	4	2	no	—
78	C₂×C₄×C₇₉	—	4	2	no	—
79	C₂×C₄×C₇₉	—	4	4	no	—
80	C₂×C₄×C₇₉	—	4	2	no	—
81	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
82	C₂×C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
83	C₂×C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
84	C₂×C₄×C₇₉	C₄⋊Q₈	1	2	yes	—
85	C₂×C₄×C₇₉	C₂×D₈	1	2	yes	—
86	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
87	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
88	C₂×C₄×C₇₉	#137	1	2	yes	—
89	C₂×Dic₇₉	—	8	2	no	—
90	C₂×Dic₇₉	—	8	1	no	—
91	C₇₉⋊C₈	—	2	4	no	—
92	C₇₉⋊C₈	—	4	4	no	—
93	C₂²×C₇₉	#395	1	1	yes	characteristic
94	C₂²×C₇₉	#447	1	2	yes	—
95	C₂²×C₇₉	#451	1	2	yes	—
96	C₂²×C₇₉	#453	1	1	yes	characteristic
97	C₂²×C₇₉	#456	1	1	yes	characteristic
98	C₄×C₇₉	—	2	1	no	—
99	C₄×C₇₉	—	2	1	no	—
100	C₄×C₇₉	—	4	4	no	—
101	C₄×C₇₉	—	4	4	no	—
102	C₄×C₇₉	—	8	2	no	—
103	C₄×C₇₉	#474	1	2	yes	—
104	C₄×C₇₉	#477	1	2	yes	—
105	C₄×C₇₉	#500	1	2	yes	—
106	C₄×C₇₉	#501	1	2	yes	—
107	Dic₇₉	—	16	1	no	—
108	#10573	—	79	1	no	maximal, Sylow
109	C₂×C₇₉	#1619	1	1	yes	characteristic
110	C₂×C₇₉	#1633	1	1	yes	characteristic
111	C₂×C₇₉	#1649	1	2	yes	—
112	C₂×C₇₉	#2057	1	2	yes	—
113	C₂×C₇₉	#2060	1	1	yes	characteristic
114	#2551	D₇₉	1	1	yes	characteristic
115	#1947	—	79	2	no	—
116	#1845	—	79	1	no	—
117	#1296	—	79	1	no	—
118	#1279	—	79	2	no	—
119	C₇₉	#10573	1	1	yes	characteristic, complemented, Sylow
120	C₂×C₄⋊Q₈	—	2	2	no	—
121	C₂×#107	—	158	2	no	—
122	C₂×#107	—	158	2	no	—
123	C₂×C₄⋊C₈	—	79	2	no	—
124	C₂×C₄×C₈	—	79	1	no	—
125	#395	—	2	2	no	—
126	#389	—	2	2	no	—
127	#384	—	79	1	no	—
128	#384	C₂×D₇₉	1	1	yes	characteristic
129	C₄×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
130	#340	—	158	2	no	—
131	C₂²×Q₈	—	2	2	no	—
132	C₂²×C₈	—	158	2	no	—
133	C₂²×C₈	—	158	1	no	—
134	C₄⋊Q₈	—	4	4	no	—
135	C₄⋊Q₈	—	4	4	no	—
136	C₂×C₄⋊C₄	—	2	4	no	—
137	C₂×C₄⋊C₄	—	2	2	no	—
138	C₂×C₄⋊C₄	—	158	2	no	—
139	C₂×C₄⋊C₄	—	158	1	no	—
140	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	2	yes	—
141	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	2	yes	—
142	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	2	yes	—
143	C₂×C₄²	—	2	2	no	—
144	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
145	#107	—	316	4	no	—
146	#107	—	316	4	no	—
147	C₄⋊C₈	—	79	4	no	—
148	C₄⋊C₈	—	158	2	no	—
149	C₄×C₈	—	79	2	no	—
150	C₄×C₈	—	158	1	no	—
151	#95	—	2	2	no	—
152	#95	—	2	2	no	—
153	C₂×Q₈	—	4	8	no	—
154	C₂×Q₈	—	8	2	no	—
155	C₂²×C₄	—	2	2	no	—
156	C₂²×C₄	—	2	2	no	—
157	C₂²×C₄	—	2	2	no	—
158	C₂²×C₄	—	316	1	no	—
159	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
160	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
161	C₂×C₈	—	316	2	no	—
162	C₂×C₈	—	316	2	no	—
163	C₂×C₈	—	158	4	no	—
164	C₂×C₈	—	158	2	no	—
165	C₂×C₈	—	158	2	no	—
166	C₂×C₈	—	158	2	no	—
167	C₄⋊C₄	—	2	2	no	—
168	C₄⋊C₄	—	2	2	no	—
169	C₄⋊C₄	—	4	2	no	—
170	C₄⋊C₄	—	4	8	no	—
171	C₄⋊C₄	—	4	2	no	—
172	C₄⋊C₄	—	4	2	no	—
173	C₄⋊C₄	—	316	2	no	—
174	C₄⋊C₄	—	316	2	no	—
175	C₄⋊C₄	—	316	2	no	—
176	C₄⋊C₄	#11929609	1	4	yes	—
177	C₄⋊C₄	#11929614	1	4	yes	—
178	C₄²	—	4	2	no	—
179	C₄²	—	4	2	no	—
180	C₄²	Q₈×D₇₉	1	1	yes	characteristic
181	C₄²	Q₈×D₇₉	1	2	yes	—
182	C₄²	#11929625	1	1	yes	characteristic
183	C₂³	#14579130	1	1	yes	characteristic
184	Q₈	—	8	8	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	—	2	4	no	—
188	C₂×C₄	—	2	4	no	—
189	C₂×C₄	—	4	2	no	—
190	C₂×C₄	—	4	2	no	—
191	C₂×C₄	—	4	2	no	—
192	C₂×C₄	—	4	2	no	—
193	C₂×C₄	—	4	4	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	632	2	no	—
196	C₂×C₄	—	632	1	no	—
197	C₂×C₄	#14579137	1	1	yes	characteristic
198	C₂×C₄	#14579137	1	2	yes	—
199	C₂×C₄	#14579159	1	1	yes	characteristic
200	C₂×C₄	#14579159	1	2	yes	—
201	C₂×C₄	C₂×#11929609	1	2	yes	—
202	C₂×C₄	C₂×#11929614	1	2	yes	—
203	C₂×C₄	#14579187	1	2	yes	—
204	C₂×C₄	#14579192	1	2	yes	—
205	C₈	—	316	4	no	—
206	C₈	—	158	4	no	—
207	C₂²	#19098482	1	1	yes	characteristic
208	C₂²	#19098697	1	2	yes	—
209	C₂²	#19098719	1	2	yes	—
210	C₂²	#19098731	1	1	yes	characteristic
211	C₂²	#19098746	1	1	yes	characteristic
212	C₄	—	2	1	no	—
213	C₄	—	2	1	no	—
214	C₄	—	4	4	no	—
215	C₄	—	4	4	no	—
216	C₄	—	8	2	no	—
217	C₄	—	1264	1	no	—
218	C₄	#19098840	1	2	yes	—
219	C₄	#19098855	1	2	yes	—
220	C₄	#19098966	1	2	yes	—
221	C₄	#19098969	1	2	yes	—
222	C₂	#23762454	1	1	yes	characteristic
223	C₂	#23762540	1	1	yes	characteristic
224	C₂	#23762649	1	2	yes	—
225	C₂	#23764725	1	2	yes	—
226	C₂	#23764742	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23764158

C₂

yes

maximal

#23763559

C₂

yes

maximal, characteristic

#23761283

C₂

yes

maximal, characteristic

#23761241

C₂

yes

maximal

C₇₉×#2551

C₂

yes

maximal, characteristic

C₂×#14579094

—

C₂×#14579094

—

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

C₂×C₄×C₇₉⋊C₈

C₂²

yes

characteristic

#19098433

C₂²

yes

characteristic

#19098325

—

C₂×C₄⋊Q₈×C₇₉

—

#395×C₇₉

—

#389×C₇₉

—

#384×C₇₉

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₇₉

C₂²

yes

—

C₂²×C₇₉⋊C₈

—

C₂²×C₇₉⋊C₈

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

#14579094

—

#14579094

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

Q₈

yes

complemented

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

Q₈

yes

complemented

C₂²×Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

D₄

yes

—

C₂×C₄⋊C₄×C₇₉

D₄

yes

—

C₂×C₄⋊C₄×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#95×C₇₉

—

#95×C₇₉

—

C₂²×Dic₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

D₈

yes

—

C₄⋊C₄×C₇₉

Q₁₆

yes

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂×Q₈

yes

characteristic

C₄²×C₇₉

C₂×Q₈

yes

—

C₄²×C₇₉

yes

C₂³×C₇₉

yes

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

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₇₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₇₉

C₄⋊Q₈

yes

—

C₂×C₄×C₇₉

C₂×D₈

yes

—

C₂×C₄×C₇₉

C₂×Q₁₆

yes

—

C₂×C₄×C₇₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₇₉

#137

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

#395

yes

characteristic

C₂²×C₇₉

#447

yes

—

C₂²×C₇₉

#451

yes

—

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₄×C₇₉

—

C₄×C₇₉

—

100

C₄×C₇₉

—

101

C₄×C₇₉

—

102

C₄×C₇₉

—

103

C₄×C₇₉

#474

yes

—

104

C₄×C₇₉

#477

yes

—

105

C₄×C₇₉

#500

yes

—

106

C₄×C₇₉

#501

yes

—

107

Dic₇₉

—

108

#10573

—

maximal, Sylow

109

C₂×C₇₉

#1619

yes

characteristic

110

C₂×C₇₉

#1633

yes

characteristic

111

C₂×C₇₉

#1649

yes

—

112

C₂×C₇₉

#2057

yes

—

113

C₂×C₇₉

#2060

yes

characteristic

114

#2551

D₇₉

yes

characteristic

115

#1947

—

116

#1845

—

117

#1296

—

118

#1279

—

119

C₇₉

#10573

yes

characteristic, complemented, Sylow

120

C₂×C₄⋊Q₈

—

121

C₂×#107

—

158

—

122

C₂×#107

—

158

—

123

C₂×C₄⋊C₈

—

124

C₂×C₄×C₈

—

125

#395

—

126

#389

—

127

#384

—

128

#384

C₂×D₇₉

yes

characteristic

129

C₄×C₄⋊C₄

C₂×D₇₉

yes

—

130

#340

—

158

—

131

C₂²×Q₈

—

132

C₂²×C₈

—

158

—

133

C₂²×C₈

—

158

—

134

C₄⋊Q₈

—

135

C₄⋊Q₈

—

136

C₂×C₄⋊C₄

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

—

158

—

139

C₂×C₄⋊C₄

—

158

—

140

C₂×C₄⋊C₄

C₂²⋊D₇₉

yes

—

141

C₂×C₄⋊C₄

C₂²⋊D₇₉

yes

—

142

C₂×C₄⋊C₄

C₂²⋊D₇₉

yes

—

143

C₂×C₄²

—

144

C₂×C₄²

C₂²×D₇₉

yes

characteristic

145

#107

—

316

—

146

#107

—

316

—

147

C₄⋊C₈

—

148

C₄⋊C₈

—

158

—

149

C₄×C₈

—

150

C₄×C₈

—

158

—

151

#95

—

152

#95

—

153

C₂×Q₈

—

154

C₂×Q₈

—

155

C₂²×C₄

—

156

C₂²×C₄

—

157

C₂²×C₄

—

158

C₂²×C₄

—

316

—

159

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

160

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

—

161

C₂×C₈

—

316

—

162

C₂×C₈

—

316

—

163

C₂×C₈

—

158

—

164

C₂×C₈

—

158

—

165

C₂×C₈

—

158

—

166

C₂×C₈

—

158

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

316

—

174

C₄⋊C₄

—

316

—

175

C₄⋊C₄

—

316

—

176

C₄⋊C₄

#11929609

yes

—

177

C₄⋊C₄

#11929614

yes

—

178

C₄²

—

179

C₄²

—

180

C₄²

Q₈×D₇₉

yes

characteristic

181

C₄²

Q₈×D₇₉

yes

—

182

C₄²

#11929625

yes

characteristic

183

C₂³

#14579130

yes

characteristic

184

Q₈

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

632

—

196

C₂×C₄

—

632

—

197

C₂×C₄

#14579137

yes

characteristic

198

C₂×C₄

#14579137

yes

—

199

C₂×C₄

#14579159

yes

characteristic

200

C₂×C₄

#14579159

yes

—

201

C₂×C₄

C₂×#11929609

yes

—

202

C₂×C₄

C₂×#11929614

yes

—

203

C₂×C₄

#14579187

yes

—

204

C₂×C₄

#14579192

yes

—

205

C₈

—

316

—

206

C₈

—

158

—

207

C₂²

#19098482

yes

characteristic

208

C₂²

#19098697

yes

—

209

C₂²

#19098719

yes

—

210

C₂²

#19098731

yes

characteristic

211

C₂²

#19098746

yes

characteristic

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

1264

—

218

C₄

#19098840

yes

—

219

C₄

#19098855

yes

—

220

C₄

#19098966

yes

—

221

C₄

#19098969

yes

—

222

C₂

#23762454

yes

characteristic

223

C₂

#23762540

yes

characteristic

224

C₂

#23762649

yes

—

225

C₂

#23764725

yes

—

226

C₂

#23764742

yes

characteristic

	subgroup	G/H
center	C₂³	#14579130
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#2551	C₂
socle, prime radical	C₂³×C₇₉	#120
hypercenter	#2551	D₇₉
hypocenter	C₇₉	#10573
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2551

subgroup

G/H

center

C₂³

#14579130

commutator, cosocle

C₂×C₄²×C₇₉

C₂³

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#2551

C₂

C₂³×C₇₉

D₇₉

C₇₉

G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2551

N	H ≅ G/N	type
24. C₄⋊(C₇₉⋊C₈)	Q₈	semidirect
26. C₄×C₇₉⋊C₈	Q₈	semidirect
119. C₇₉	#10573	semidirect

H ≅ G/N

type

24. C₄⋊(C₇₉⋊C₈)

Q₈

semidirect

26. C₄×C₇₉⋊C₈

Q₈

semidirect

119. C₇₉

#10573

semidirect

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

subgroup	index
#23764158	2
#23763559	2
#23761283	2
#23761241	2
C₇₉×#2551	2
#10573	79

subgroup

index

C₇₉×#2551

Subgroups — #34192703

Conjugacy classes of subgroups

Complements

Maximal subgroups