Group #23763742 — subgroups

Subgroups — #23763742

Order 10112.

338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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	C₂²×Dic₃₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#14579126	C₂	1	1	yes	maximal, characteristic
3	C₂×#14579084	C₂	1	1	yes	maximal, characteristic
4	C₂×#14579084	C₂	1	1	yes	maximal, characteristic
5	#19098468	C₂	1	1	yes	maximal, characteristic
6	#19098317	C₂	1	1	yes	maximal, characteristic
7	#340×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₁₅₈	C₂²	1	1	yes	characteristic
9	C₂²×Dic₁₅₈	C₂²	1	1	yes	characteristic
10	C₂×Dic₃₁₆	—	2	2	no	—
11	C₂×Dic₃₁₆	—	2	2	no	—
12	C₂×Dic₃₁₆	C₄	1	4	yes	complemented
13	C₂²×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
14	#14579126	—	2	2	no	—
15	#14579126	—	2	2	no	—
16	C₂×Dic₇₉⋊C₄	—	2	1	no	—
17	C₂×C₄×Dic₇₉	—	2	1	no	—
18	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
19	#14579084	—	2	2	no	—
20	#14579084	—	2	2	no	—
21	C₇₉⋊#95	—	2	1	no	—
22	C₇₉⋊#95	—	2	1	no	—
23	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×Dic₁₅₈	—	2	1	no	—
27	C₂×Dic₁₅₈	—	2	1	no	—
28	C₂×Dic₁₅₈	—	2	1	no	—
29	C₂×Dic₁₅₈	—	2	1	no	—
30	C₂×Dic₁₅₈	—	2	1	no	—
31	C₂×Dic₁₅₈	—	2	1	no	—
32	C₂×Dic₁₅₈	—	2	1	no	—
33	C₂×Dic₁₅₈	—	2	1	no	—
34	C₂×Dic₁₅₈	C₂×C₄	1	2	yes	—
35	C₂×Dic₁₅₈	C₂×C₄	1	2	yes	—
36	C₂×Dic₁₅₈	D₄	1	2	yes	—
37	C₂×Dic₁₅₈	D₄	1	2	yes	—
38	C₂²×Dic₇₉	—	2	1	no	—
39	C₂²×Dic₇₉	—	2	1	no	—
40	C₂²×Dic₇₉	D₄	1	1	yes	characteristic
41	C₂²×Dic₇₉	D₄	1	1	yes	characteristic
42	Dic₃₁₆	—	2	8	no	—
43	C₂×C₇₉⋊C₈	—	2	1	no	—
44	C₂×C₇₉⋊C₈	—	2	1	no	—
45	C₂×C₇₉⋊C₈	—	2	1	no	—
46	Dic₇₉⋊C₄	—	2	4	no	—
47	C₄×Dic₇₉	—	2	4	no	—
48	C₄×Dic₇₉	—	2	1	no	—
49	C₄×Dic₇₉	—	2	1	no	—
50	C₂²×C₄×C₇₉	—	2	1	no	—
51	C₂²×C₄×C₇₉	—	2	1	no	—
52	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
53	C₂×C₈×C₇₉	—	2	1	no	—
54	C₂×C₈×C₇₉	—	2	1	no	—
55	C₂×C₈×C₇₉	C₂×C₄	1	2	yes	—
56	C₄⋊C₄×C₇₉	—	2	1	no	—
57	C₄⋊C₄×C₇₉	—	2	1	no	—
58	C₄⋊C₄×C₇₉	—	2	1	no	—
59	C₄⋊C₄×C₇₉	D₄	1	2	yes	—
60	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄×C₇₉	—	2	2	no	—
62	C₂×C₄×C₇₉	—	4	1	no	—
63	C₂×C₄×C₇₉	—	4	1	no	—
64	C₂×C₄×C₇₉	—	4	1	no	—
65	C₂×C₄×C₇₉	—	4	1	no	—
66	C₂×C₄×C₇₉	—	4	1	no	—
67	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
69	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
71	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
72	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
73	C₂×Dic₇₉	—	2	2	no	—
74	C₂×Dic₇₉	—	2	1	no	—
75	C₂×Dic₇₉	—	2	2	no	—
76	C₂×Dic₇₉	—	2	2	no	—
77	C₂×Dic₇₉	—	2	1	no	—
78	C₂×Dic₇₉	—	2	2	no	—
79	C₂×Dic₇₉	—	2	1	no	—
80	C₂×Dic₇₉	—	2	1	no	—
81	C₂×Dic₇₉	—	2	1	no	—
82	C₂×Dic₇₉	—	4	1	no	—
83	C₂×Dic₇₉	—	4	1	no	—
84	C₂×Dic₇₉	Q₁₆	1	2	yes	complemented
85	Dic₁₅₈	—	2	2	no	—
86	Dic₁₅₈	—	2	2	no	—
87	Dic₁₅₈	—	2	2	no	—
88	Dic₁₅₈	—	2	2	no	—
89	Dic₁₅₈	—	2	2	no	—
90	Dic₁₅₈	—	4	1	no	—
91	Dic₁₅₈	—	4	1	no	—
92	Dic₁₅₈	C₂²⋊C₄	1	4	yes	—
93	C₈×C₇₉	—	2	2	no	—
94	C₇₉⋊C₈	—	4	1	no	—
95	C₂²×C₇₉	C₄×D₄	1	1	yes	characteristic
96	C₂²×C₇₉	#120	1	1	yes	characteristic
97	C₂²×C₇₉	#121	1	1	yes	characteristic
98	C₂²×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
99	C₂²×C₇₉	#135	1	1	yes	characteristic
100	C₂²×C₇₉	#137	1	1	yes	characteristic
101	C₂²×C₇₉	#137	1	1	yes	characteristic
102	C₄×C₇₉	—	4	2	no	—
103	C₄×C₇₉	—	8	1	no	—
104	C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
106	C₄×C₇₉	#121	1	1	yes	characteristic
107	C₄×C₇₉	#123	1	1	yes	characteristic
108	Dic₇₉	—	2	4	no	—
109	Dic₇₉	—	2	2	no	—
110	Dic₇₉	—	4	2	no	—
111	Dic₇₉	—	4	1	no	—
112	C₂×C₇₉	#386	1	1	yes	characteristic
113	C₂×C₇₉	C₄×Q₁₆	1	1	yes	characteristic
114	C₂×C₇₉	#441	1	1	yes	characteristic
115	C₂×C₇₉	#451	1	1	yes	characteristic
116	C₂×C₇₉	#452	1	1	yes	characteristic
117	C₂×C₇₉	#462	1	1	yes	characteristic
118	C₂×C₇₉	#464	1	1	yes	characteristic
119	#1878	—	79	1	no	maximal, Sylow
120	C₇₉	#1878	1	1	yes	characteristic, complemented, Sylow
121	C₂²×Q₁₆	—	79	1	no	—
122	C₂×C₄×Q₈	—	79	1	no	—
123	C₂×#103	—	79	1	no	—
124	C₂×#103	—	79	1	no	—
125	#391	—	79	1	no	—
126	#340	D₇₉	1	1	yes	characteristic
127	#336	—	79	1	no	—
128	C₂²×Q₈	—	79	1	no	—
129	C₂²×Q₈	—	79	1	no	—
130	C₂×Q₁₆	—	79	4	no	—
131	C₂×Q₁₆	—	158	2	no	—
132	C₂×Q₁₆	—	158	2	no	—
133	C₂²×C₈	—	79	1	no	—
134	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
135	C₄×Q₈	—	158	2	no	—
136	C₄×Q₈	—	158	2	no	—
137	C₂×C₄⋊C₄	—	158	1	no	—
138	C₂×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
139	C₂×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
140	C₂×C₄²	—	79	1	no	—
141	C₂×C₄²	—	158	1	no	—
142	#103	—	158	2	no	—
143	#103	—	158	2	no	—
144	#95	—	158	1	no	—
145	#95	—	158	1	no	—
146	C₂×Q₈	—	79	2	no	—
147	C₂×Q₈	—	79	2	no	—
148	C₂×Q₈	—	79	2	no	—
149	C₂×Q₈	—	79	2	no	—
150	C₂×Q₈	—	158	1	no	—
151	C₂×Q₈	—	158	1	no	—
152	C₂×Q₈	—	158	1	no	—
153	C₂×Q₈	—	158	1	no	—
154	C₂×Q₈	—	158	1	no	—
155	C₂×Q₈	—	158	1	no	—
156	C₂×Q₈	—	158	1	no	—
157	C₂×Q₈	—	158	1	no	—
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	2	1	no	—
160	C₂²×C₄	—	79	1	no	—
161	C₂²×C₄	—	79	1	no	—
162	C₂²×C₄	—	158	1	no	—
163	C₂²×C₄	—	158	1	no	—
164	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
165	Q₁₆	—	158	8	no	—
166	C₂×C₈	—	2	1	no	—
167	C₂×C₈	—	2	1	no	—
168	C₂×C₈	—	158	1	no	—
169	C₂×C₈	—	158	1	no	—
170	C₂×C₈	—	158	1	no	—
171	C₂×C₈	C₄×D₇₉	1	2	yes	—
172	C₄⋊C₄	—	2	1	no	—
173	C₄⋊C₄	—	2	1	no	—
174	C₄⋊C₄	—	2	1	no	—
175	C₄⋊C₄	—	158	4	no	—
176	C₄⋊C₄	D₃₁₆	1	2	yes	—
177	C₄²	—	158	4	no	—
178	C₄²	—	158	1	no	—
179	C₄²	—	158	1	no	—
180	C₂³	D₄×D₇₉	1	1	yes	characteristic
181	Q₈	—	316	1	no	—
182	Q₈	—	316	1	no	—
183	Q₈	—	79	4	no	—
184	Q₈	—	158	2	no	—
185	Q₈	—	158	2	no	—
186	Q₈	—	158	2	no	—
187	Q₈	—	158	2	no	—
188	Q₈	—	158	2	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	4	1	no	—
191	C₂×C₄	—	4	1	no	—
192	C₂×C₄	—	4	1	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	4	1	no	—
195	C₂×C₄	—	316	1	no	—
196	C₂×C₄	—	316	1	no	—
197	C₂×C₄	—	79	2	no	—
198	C₂×C₄	—	158	2	no	—
199	C₂×C₄	—	158	1	no	—
200	C₂×C₄	—	158	1	no	—
201	C₂×C₄	—	158	1	no	—
202	C₂×C₄	—	158	2	no	—
203	C₂×C₄	—	158	1	no	—
204	C₂×C₄	—	158	2	no	—
205	C₂×C₄	—	158	2	no	—
206	C₂×C₄	—	158	1	no	—
207	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
208	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
209	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
210	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
211	C₂×C₄	#11929624	1	1	yes	characteristic
212	C₂×C₄	#11929625	1	1	yes	characteristic
213	C₈	—	2	2	no	—
214	C₈	—	316	1	no	—
215	C₂²	#14579123	1	1	yes	characteristic
216	C₂²	#14579131	1	1	yes	characteristic
217	C₂²	#14579134	1	1	yes	characteristic
218	C₂²	Q₁₆×D₇₉	1	1	yes	characteristic
219	C₂²	#14579180	1	1	yes	characteristic
220	C₂²	#14579190	1	1	yes	characteristic
221	C₂²	#14579190	1	1	yes	characteristic
222	C₄	—	4	2	no	—
223	C₄	—	8	1	no	—
224	C₄	—	316	2	no	—
225	C₄	—	316	1	no	—
226	C₄	—	158	4	no	—
227	C₄	—	158	2	no	—
228	C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
229	C₄	C₄×D₃₁₆	1	1	yes	characteristic
230	C₄	#14579136	1	1	yes	characteristic
231	C₄	#14579146	1	1	yes	characteristic
232	C₂	#19098441	1	1	yes	characteristic
233	C₂	#19098657	1	1	yes	characteristic
234	C₂	#19098669	1	1	yes	characteristic
235	C₂	#19098720	1	1	yes	characteristic
236	C₂	#19098726	1	1	yes	characteristic
237	C₂	#19098772	1	1	yes	characteristic
238	C₂	#19098784	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₃₁₆

C₂

yes

maximal, characteristic

C₂×#14579126

C₂

yes

maximal, characteristic

C₂×#14579084

C₂

yes

maximal, characteristic

C₂×#14579084

C₂

yes

maximal, characteristic

#19098468

C₂

yes

maximal, characteristic

#19098317

C₂

yes

maximal, characteristic

#340×C₇₉

C₂

yes

maximal, characteristic

C₂²×Dic₁₅₈

C₂²

yes

characteristic

C₂²×Dic₁₅₈

C₂²

yes

characteristic

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

C₄

yes

complemented

C₂²×C₇₉⋊C₈

C₂²

yes

characteristic

#14579126

—

#14579126

—

C₂×Dic₇₉⋊C₄

—

C₂×C₄×Dic₇₉

—

C₂×C₄×Dic₇₉

C₂²

yes

characteristic

#14579084

—

#14579084

—

C₇₉⋊#95

—

C₇₉⋊#95

—

C₂²×C₈×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

C₂×C₄

yes

—

C₂×Dic₁₅₈

C₂×C₄

yes

—

C₂×Dic₁₅₈

D₄

yes

—

C₂×Dic₁₅₈

D₄

yes

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

D₄

yes

characteristic

C₂²×Dic₇₉

D₄

yes

characteristic

Dic₃₁₆

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

D₄

yes

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

Q₁₆

yes

complemented

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

C₂²⋊C₄

yes

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

C₄×D₄

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

C₂×Q₁₆

yes

characteristic

C₂²×C₇₉

#135

yes

characteristic

100

C₂²×C₇₉

#137

yes

characteristic

101

C₂²×C₇₉

#137

yes

characteristic

102

C₄×C₇₉

—

103

C₄×C₇₉

—

104

C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

105

C₄×C₇₉

C₄×D₄

yes

characteristic

106

C₄×C₇₉

#121

yes

characteristic

107

C₄×C₇₉

#123

yes

characteristic

108

Dic₇₉

—

109

Dic₇₉

—

110

Dic₇₉

—

111

Dic₇₉

—

112

C₂×C₇₉

#386

yes

characteristic

113

C₂×C₇₉

C₄×Q₁₆

yes

characteristic

114

C₂×C₇₉

#441

yes

characteristic

115

C₂×C₇₉

#451

yes

characteristic

116

C₂×C₇₉

#452

yes

characteristic

117

C₂×C₇₉

#462

yes

characteristic

118

C₂×C₇₉

yes

119

—

120

C₇₉

#1878

yes

characteristic, complemented, Sylow

121

C₂²×Q₁₆

—

122

C₂×C₄×Q₈

—

123

C₂×#103

—

124

C₂×#103

—

125

#391

—

126

#340

D₇₉

yes

characteristic

127

#336

—

128

C₂²×Q₈

—

129

C₂²×Q₈

—

130

C₂×Q₁₆

—

131

C₂×Q₁₆

—

158

—

132

C₂×Q₁₆

—

158

—

133

C₂²×C₈

—

134

C₂²×C₈

C₂×D₇₉

yes

characteristic

135

C₄×Q₈

—

158

—

136

C₄×Q₈

—

158

—

137

C₂×C₄⋊C₄

—

158

—

138

C₂×C₄⋊C₄

C₂×D₇₉

yes

characteristic

139

C₂×C₄⋊C₄

C₂×D₇₉

yes

characteristic

140

C₂×C₄²

—

141

C₂×C₄²

—

158

—

142

#103

—

158

—

143

#103

—

158

—

144

#95

—

158

—

145

#95

—

158

—

146

C₂×Q₈

—

147

C₂×Q₈

—

148

C₂×Q₈

—

149

C₂×Q₈

—

150

C₂×Q₈

—

158

—

151

C₂×Q₈

—

158

—

152

C₂×Q₈

—

158

—

153

C₂×Q₈

—

158

—

154

C₂×Q₈

—

158

—

155

C₂×Q₈

—

158

—

156

C₂×Q₈

—

158

—

157

C₂×Q₈

—

158

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

158

—

163

C₂²×C₄

—

158

—

164

C₂²×C₄

C₂²×D₇₉

yes

characteristic

165

Q₁₆

—

158

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

158

—

169

C₂×C₈

—

158

—

170

C₂×C₈

—

158

—

171

C₂×C₈

C₄×D₇₉

yes

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

158

—

176

C₄⋊C₄

D₃₁₆

yes

—

177

C₄²

—

158

—

178

C₄²

—

158

—

179

C₄²

—

158

—

180

C₂³

D₄×D₇₉

yes

characteristic

181

Q₈

—

316

—

182

Q₈

—

316

—

183

Q₈

—

184

Q₈

—

158

—

185

Q₈

—

158

—

186

Q₈

—

158

—

187

Q₈

—

158

—

188

Q₈

—

158

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

316

—

196

C₂×C₄

—

316

—

197

C₂×C₄

—

198

C₂×C₄

—

158

—

199

C₂×C₄

—

158

—

200

C₂×C₄

—

158

—

201

C₂×C₄

—

158

—

202

C₂×C₄

—

158

—

203

C₂×C₄

—

158

—

204

C₂×C₄

—

158

—

205

C₂×C₄

—

158

—

206

C₂×C₄

—

158

—

207

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

208

C₂×C₄

D₄×D₇₉

yes

characteristic

209

C₂×C₄

D₄×D₇₉

yes

characteristic

210

C₂×C₄

C₂×D₃₁₆

yes

characteristic

211

C₂×C₄

#11929624

yes

characteristic

212

C₂×C₄

#11929625

yes

characteristic

213

C₈

—

214

C₈

—

316

—

215

C₂²

#14579123

yes

characteristic

216

C₂²

#14579131

yes

characteristic

217

C₂²

#14579134

yes

characteristic

218

C₂²

Q₁₆×D₇₉

yes

characteristic

219

C₂²

#14579180

yes

characteristic

220

C₂²

#14579190

yes

characteristic

221

C₂²

#14579190

yes

characteristic

222

C₄

—

223

C₄

—

224

C₄

—

316

—

225

C₄

—

316

—

226

C₄

—

158

—

227

C₄

—

158

—

228

C₄

C₂²⋊C₄×D₇₉

yes

characteristic

229

C₄

C₄×D₃₁₆

yes

characteristic

230

C₄

#14579136

yes

characteristic

231

C₄

#14579146

yes

characteristic

232

C₂

#19098441

yes

characteristic

233

C₂

#19098657

yes

characteristic

234

C₂

#19098669

yes

characteristic

235

C₂

#19098720

yes

characteristic

236

C₂

#19098726

yes

characteristic

237

C₂

#19098772

yes

characteristic

238

C₂

#19098784

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#340×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂×D₄
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	#340	D₇₉
hypocenter	C₇₉	#1878
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₇₉

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

#340×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

C₂×D₄

cosocle

C₂²×C₄×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
12. C₂×Dic₃₁₆	C₄	semidirect
84. C₂×Dic₇₉	Q₁₆	semidirect
120. C₇₉	#1878	semidirect

H ≅ G/N

type

12. C₂×Dic₃₁₆

C₄

semidirect

84. C₂×Dic₇₉

Q₁₆

semidirect

120. C₇₉

#1878

semidirect

Subgroups — #23763742

Conjugacy classes of subgroups

Complements