Group #34181495 — subgroups

Subgroups — #34181495

Order 20224.

350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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	#23772334	C₂	1	1	yes	maximal, characteristic
2	#23762148	C₂	1	1	yes	maximal, characteristic
3	#23761963	C₂	1	2	yes	maximal
4	#23761258	C₂	1	2	yes	maximal
5	C₇₉×#1835	C₂	1	1	yes	maximal, characteristic
6	#19099120	C₂²	1	1	yes	characteristic
7	#19098693	—	2	1	no	—
8	#19098693	C₄	1	2	yes	complemented
9	C₈×Dic₁₅₈	—	2	1	no	—
10	C₈×Dic₁₅₈	C₄	1	2	yes	complemented
11	#19098616	C₂²	1	2	yes	—
12	#19098589	—	2	1	no	—
13	#19098587	C₂²	1	1	yes	characteristic
14	#19098518	—	2	1	no	—
15	#19098316	—	2	1	no	—
16	#19098314	—	2	1	no	—
17	#19098299	—	2	4	no	—
18	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
19	#382×C₇₉	C₂²	1	2	yes	—
20	#340×C₇₉	—	2	1	no	—
21	#340×C₇₉	—	2	1	no	—
22	C₂×#11929608	—	2	1	no	—
23	#14579161	Q₈	1	1	yes	characteristic
24	#14579161	Q₈	1	1	yes	characteristic
25	#14579153	—	2	1	no	—
26	#14579140	—	2	1	no	—
27	#14579140	D₄	1	2	yes	—
28	C₄×Dic₁₅₈	—	2	1	no	—
29	C₄×Dic₁₅₈	C₂×C₄	1	2	yes	—
30	#14579120	—	2	1	no	—
31	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
32	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
33	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
34	Dic₇₉⋊C₈	—	2	2	no	—
35	Dic₇₉⋊C₈	—	2	2	no	—
36	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
37	#14579071	—	2	2	no	—
38	C₄×C₇₉⋊C₈	—	2	2	no	—
39	C₈×Dic₇₉	—	2	2	no	—
40	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
43	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
44	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
47	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
48	#95×C₇₉	—	2	2	no	—
49	#95×C₇₉	—	2	2	no	—
50	C₂×Dic₁₅₈	—	2	1	no	—
51	C₂×Dic₁₅₈	C₄⋊C₄	1	2	yes	—
52	#11929608	—	4	2	no	—
53	C₂×C₇₉⋊C₈	—	2	2	no	—
54	C₂×C₇₉⋊C₈	—	4	2	no	—
55	C₄⋊Dic₇₉	—	2	1	no	—
56	C₄⋊Dic₇₉	—	2	1	no	—
57	C₄⋊Dic₇₉	—	2	1	no	—
58	C₄⋊Dic₇₉	C₄⋊C₄	1	2	yes	—
59	Dic₇₉⋊C₄	—	2	2	no	—
60	Dic₇₉⋊C₄	—	2	2	no	—
61	C₂²⋊Dic₇₉	—	2	2	no	—
62	C₄×Dic₇₉	—	2	2	no	—
63	C₂²×C₄×C₇₉	—	4	2	no	—
64	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
67	C₂×C₈×C₇₉	—	2	2	no	—
68	C₂×C₈×C₇₉	—	2	2	no	—
69	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₄⋊C₄×C₇₉	—	4	2	no	—
74	C₄⋊C₄×C₇₉	—	4	2	no	—
75	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
76	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
78	C₄²×C₇₉	#41	1	1	yes	characteristic
79	C₂³×C₇₉	#121	1	1	yes	characteristic
80	C₂×C₄×C₇₉	—	4	1	no	—
81	C₂×C₄×C₇₉	—	4	1	no	—
82	C₂×C₄×C₇₉	—	8	2	no	—
83	C₂×C₄×C₇₉	—	8	2	no	—
84	C₂×C₄×C₇₉	—	8	2	no	—
85	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₇₉	#117	1	1	yes	characteristic
88	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
89	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
90	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
91	C₂×C₄×C₇₉	#135	1	2	yes	—
92	C₂×C₄×C₇₉	#137	1	2	yes	—
93	C₂×Dic₇₉	—	2	2	no	—
94	C₂×Dic₇₉	—	2	2	no	—
95	Dic₁₅₈	—	4	2	no	—
96	Dic₁₅₈	—	4	2	no	—
97	C₈×C₇₉	—	2	1	no	—
98	C₈×C₇₉	—	2	1	no	—
99	C₈×C₇₉	—	2	1	no	—
100	C₈×C₇₉	—	2	1	no	—
101	C₇₉⋊C₈	—	4	2	no	—
102	C₇₉⋊C₈	—	8	2	no	—
103	C₂²×C₇₉	—	2	1	no	—
104	C₂²×C₇₉	—	2	1	no	—
105	C₂²×C₇₉	#380	1	1	yes	characteristic
106	C₂²×C₇₉	#464	1	2	yes	—
107	C₄×C₇₉	—	2	1	no	—
108	C₄×C₇₉	—	2	1	no	—
109	C₄×C₇₉	—	2	1	no	—
110	C₄×C₇₉	—	2	1	no	—
111	C₄×C₇₉	—	16	2	no	—
112	C₄×C₇₉	#416	1	1	yes	characteristic
113	C₄×C₇₉	#419	1	1	yes	characteristic
114	C₄×C₇₉	#479	1	2	yes	—
115	Dic₇₉	—	4	2	no	—
116	Dic₇₉	—	4	2	no	—
117	#8679	—	79	1	no	maximal, Sylow
118	C₂×C₇₉	—	2	2	no	—
119	C₂×C₇₉	#1805	1	1	yes	characteristic
120	C₂×C₇₉	#1812	1	1	yes	characteristic
121	C₂×C₇₉	#1814	1	1	yes	characteristic
122	#2960	—	79	1	no	—
123	#1835	D₇₉	1	1	yes	characteristic
124	#1564	—	79	1	no	—
125	#1518	—	79	2	no	—
126	#1286	—	79	2	no	—
127	C₇₉	#8679	1	1	yes	characteristic, complemented, Sylow
128	#533	—	79	1	no	—
129	#446	—	79	2	no	—
130	#446	—	158	1	no	—
131	C₈×Q₈	—	79	2	no	—
132	C₈×Q₈	—	158	1	no	—
133	#431	—	79	2	no	—
134	#424	—	158	1	no	—
135	#423	—	79	1	no	—
136	#405	—	158	1	no	—
137	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
138	#382	C₂×D₇₉	1	2	yes	—
139	#340	—	2	1	no	—
140	#340	—	2	1	no	—
141	#335	—	158	1	no	—
142	#334	—	158	1	no	—
143	#328	—	158	4	no	—
144	C₂×M₁₆	—	158	1	no	—
145	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
146	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
147	C₄⋊Q₈	—	79	1	no	—
148	C₄⋊Q₈	—	79	1	no	—
149	#125	—	158	1	no	—
150	C₂²⋊Q₈	—	79	2	no	—
151	C₂²⋊Q₈	—	158	1	no	—
152	C₄×Q₈	—	79	2	no	—
153	C₄×Q₈	—	158	1	no	—
154	#117	—	158	1	no	—
155	C₂×C₄⋊C₄	—	2	2	no	—
156	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
157	C₄⋊C₈	—	79	2	no	—
158	C₄⋊C₈	—	158	2	no	—
159	C₄⋊C₈	—	158	2	no	—
160	C₄⋊C₈	—	158	2	no	—
161	C₄⋊C₈	—	158	1	no	—
162	C₂²⋊C₈	—	158	2	no	—
163	#97	—	158	2	no	—
164	C₄×C₈	—	158	2	no	—
165	C₄×C₈	—	158	2	no	—
166	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
167	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
168	C₄×C₈	D₃₁₆	1	1	yes	characteristic
169	C₄×C₈	D₃₁₆	1	1	yes	characteristic
170	#95	—	2	2	no	—
171	#95	—	2	2	no	—
172	C₂×Q₈	—	79	2	no	—
173	C₂×Q₈	—	158	1	no	—
174	C₂²×C₄	—	4	2	no	—
175	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
176	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
177	C₂²×C₄	#11929623	1	1	yes	characteristic
178	M₁₆	—	316	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	316	2	no	—
182	C₂×C₈	—	158	2	no	—
183	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
184	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
185	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
186	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄⋊C₄	—	79	2	no	—
190	C₄⋊C₄	—	158	2	no	—
191	C₄⋊C₄	—	158	2	no	—
192	C₄⋊C₄	—	158	1	no	—
193	C₄⋊C₄	—	158	1	no	—
194	C₄⋊C₄	—	158	1	no	—
195	C₂²⋊C₄	—	158	2	no	—
196	C₄²	—	158	2	no	—
197	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
198	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
199	C₄²	Q₈×D₇₉	1	1	yes	characteristic
200	C₄²	#11929625	1	1	yes	characteristic
201	C₂³	#14579132	1	1	yes	characteristic
202	Q₈	—	316	2	no	—
203	Q₈	—	316	2	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	8	2	no	—
207	C₂×C₄	—	8	2	no	—
208	C₂×C₄	—	8	2	no	—
209	C₂×C₄	—	158	2	no	—
210	C₂×C₄	—	158	2	no	—
211	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
212	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
213	C₂×C₄	#14579119	1	1	yes	characteristic
214	C₂×C₄	#14579136	1	1	yes	characteristic
215	C₂×C₄	#14579137	1	1	yes	characteristic
216	C₂×C₄	#14579141	1	1	yes	characteristic
217	C₂×C₄	#14579181	1	2	yes	—
218	C₂×C₄	#14579191	1	2	yes	—
219	C₈	—	2	1	no	—
220	C₈	—	2	1	no	—
221	C₈	—	2	1	no	—
222	C₈	—	2	1	no	—
223	C₈	—	316	2	no	—
224	C₈	—	632	2	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	2	1	no	—
227	C₂²	#19098420	1	1	yes	characteristic
228	C₂²	#19098782	1	2	yes	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	16	2	no	—
234	C₄	—	316	2	no	—
235	C₄	—	316	2	no	—
236	C₄	#19098557	1	1	yes	characteristic
237	C₄	#19098571	1	1	yes	characteristic
238	C₄	#19098867	1	2	yes	—
239	C₂	—	2	2	no	—
240	C₂	#23763412	1	1	yes	characteristic
241	C₂	#23763443	1	1	yes	characteristic
242	C₂	#23763451	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23772334

C₂

yes

maximal, characteristic

#23762148

C₂

yes

maximal, characteristic

#23761963

C₂

yes

maximal

#23761258

C₂

yes

maximal

C₇₉×#1835

C₂

yes

maximal, characteristic

#19099120

C₂²

yes

characteristic

#19098693

—

#19098693

C₄

yes

complemented

C₈×Dic₁₅₈

—

C₈×Dic₁₅₈

C₄

yes

complemented

#19098616

C₂²

yes

—

#19098589

—

#19098587

C₂²

yes

—

—

—

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

#382×C₇₉

C₂²

yes

—

#340×C₇₉

—

#340×C₇₉

—

C₂×#11929608

—

#14579161

Q₈

yes

characteristic

#14579161

Q₈

yes

—

—

D₄

yes

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

C₂×C₄

yes

—

#14579120

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

C₂×C₄

yes

—

Dic₇₉⋊C₈

—

Dic₇₉⋊C₈

—

C₂²⋊(C₇₉⋊C₈)

—

#14579071

—

C₄×C₇₉⋊C₈

—

C₈×Dic₇₉

—

C₂²×C₈×C₇₉

D₄

yes

characteristic

C₂²×C₈×C₇₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

D₄

yes

characteristic

C₄×C₈×C₇₉

D₄

yes

characteristic

#95×C₇₉

—

#95×C₇₉

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

C₄⋊C₄

yes

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₄⋊C₄

yes

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂²×C₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×Q₈

yes

C₄²×C₇₉

yes

C₂³×C₇₉

yes

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₉

#135

yes

—

C₂×C₄×C₇₉

#137

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

100

C₈×C₇₉

—

101

C₇₉⋊C₈

—

102

C₇₉⋊C₈

—

103

C₂²×C₇₉

—

104

C₂²×C₇₉

—

105

C₂²×C₇₉

#380

yes

characteristic

106

C₂²×C₇₉

#464

yes

—

107

C₄×C₇₉

—

108

C₄×C₇₉

—

109

C₄×C₇₉

—

110

C₄×C₇₉

—

111

C₄×C₇₉

—

112

C₄×C₇₉

#416

yes

characteristic

113

C₄×C₇₉

#419

yes

characteristic

114

C₄×C₇₉

#479

yes

—

115

Dic₇₉

—

116

Dic₇₉

—

117

#8679

—

maximal, Sylow

118

C₂×C₇₉

—

119

C₂×C₇₉

#1805

yes

characteristic

120

C₂×C₇₉

#1812

yes

characteristic

121

C₂×C₇₉

#1814

yes

characteristic

122

#2960

—

123

#1835

D₇₉

yes

characteristic

124

#1564

—

125

#1518

—

126

#1286

—

127

C₇₉

#8679

yes

characteristic, complemented, Sylow

128

#533

—

129

#446

—

130

#446

—

158

—

131

C₈×Q₈

—

132

C₈×Q₈

—

158

—

133

#431

—

134

#424

—

158

—

135

#423

—

136

#405

—

158

—

137

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

138

#382

C₂×D₇₉

yes

—

139

#340

—

140

#340

—

141

#335

—

158

—

142

#334

—

158

—

143

#328

—

158

—

144

C₂×M₁₆

—

158

—

145

C₂²×C₈

C₂²⋊D₇₉

yes

characteristic

146

C₂²×C₈

C₂²⋊D₇₉

yes

characteristic

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

149

#125

—

158

—

150

C₂²⋊Q₈

—

151

C₂²⋊Q₈

—

158

—

152

C₄×Q₈

—

153

C₄×Q₈

—

158

—

154

#117

—

158

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄²

C₂²×D₇₉

yes

characteristic

157

C₄⋊C₈

—

158

C₄⋊C₈

—

158

—

159

C₄⋊C₈

—

158

—

160

C₄⋊C₈

—

158

—

161

C₄⋊C₈

—

158

—

162

C₂²⋊C₈

—

158

—

163

#97

—

158

—

164

C₄×C₈

—

158

—

165

C₄×C₈

—

158

—

166

C₄×C₈

C₄×D₇₉

yes

characteristic

167

C₄×C₈

C₄×D₇₉

yes

characteristic

168

C₄×C₈

D₃₁₆

yes

characteristic

169

C₄×C₈

D₃₁₆

yes

characteristic

170

#95

—

171

#95

—

172

C₂×Q₈

—

173

C₂×Q₈

—

158

—

174

C₂²×C₄

—

175

C₂²×C₄

D₄×D₇₉

yes

characteristic

176

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

177

C₂²×C₄

#11929623

yes

characteristic

178

M₁₆

—

316

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

316

—

182

C₂×C₈

—

158

—

183

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

184

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

185

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

186

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

158

—

191

C₄⋊C₄

—

158

—

192

C₄⋊C₄

—

158

—

193

C₄⋊C₄

—

158

—

194

C₄⋊C₄

—

158

—

195

C₂²⋊C₄

—

158

—

196

C₄²

—

158

—

197

C₄²

C₂×C₄×D₇₉

yes

characteristic

198

C₄²

C₂×D₃₁₆

yes

characteristic

199

C₄²

Q₈×D₇₉

yes

characteristic

200

C₄²

#11929625

yes

characteristic

201

C₂³

#14579132

yes

characteristic

202

Q₈

—

316

—

203

Q₈

—

316

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

158

—

210

C₂×C₄

—

158

—

211

C₂×C₄

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

212

C₂×C₄

C₄⋊C₄×D₇₉

yes

characteristic

213

C₂×C₄

#14579119

yes

characteristic

214

C₂×C₄

#14579136

yes

characteristic

215

C₂×C₄

#14579137

yes

characteristic

216

C₂×C₄

#14579141

yes

characteristic

217

C₂×C₄

#14579181

yes

—

218

C₂×C₄

#14579191

yes

—

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

316

—

224

C₈

—

632

—

225

C₂²

—

226

C₂²

—

227

C₂²

#19098420

yes

characteristic

228

C₂²

#19098782

yes

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

316

—

235

C₄

—

316

—

236

C₄

#19098557

yes

characteristic

237

C₄

#19098571

yes

characteristic

238

C₄

#19098867

yes

—

239

C₂

—

240

C₂

#23763412

yes

characteristic

241

C₂

#23763443

yes

characteristic

242

C₂

#23763451

yes

characteristic

	subgroup	G/H
center	C₂²	#19098420
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1835	C₂
socle	C₂²×C₇₉	#380
prime radical	C₂³×C₇₉	#121
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1835	D₇₉
hypocenter	C₇₉	#8679
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1835

subgroup

G/H

center

C₂²

#19098420

commutator

C₄²×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1835

C₂

C₂²×C₇₉

C₂³×C₇₉

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1835

N	H ≅ G/N	type
8. #19098693	C₄	semidirect
10. C₈×Dic₁₅₈	C₄	semidirect
127. C₇₉	#8679	semidirect

H ≅ G/N

type

8. #19098693

C₄

semidirect

10. C₈×Dic₁₅₈

C₄

semidirect

127. C₇₉

#8679

semidirect

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

subgroup	index
#23772334	2
#23762148	2
#23761963	2
#23761258	2
C₇₉×#1835	2
#8679	79

subgroup

index

C₇₉×#1835

Subgroups — #34181495

Conjugacy classes of subgroups

Complements

Maximal subgroups