Group #34191282 — subgroups

Subgroups — #34191282

Order 20224.

504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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	#23768429	C₂	1	1	yes	maximal, characteristic
2	#23764349	C₂	1	2	yes	maximal
3	#23761283	C₂	1	1	yes	maximal, characteristic
4	#23761240	C₂	1	2	yes	maximal
5	C₇₉×#1956	C₂	1	1	yes	maximal, characteristic
6	C₂×#14579160	—	2	2	no	—
7	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
8	#19098483	—	2	2	no	—
9	#19098459	—	2	2	no	—
10	C₄×C₄⋊Dic₇₉	C₂²	1	2	yes	—
11	#19098325	—	2	2	no	—
12	#19098325	—	2	2	no	—
13	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×#103×C₇₉	—	2	2	no	—
15	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
16	#384×C₇₉	C₂²	1	1	yes	characteristic
17	C₂²×Dic₁₅₈	—	2	2	no	—
18	C₂²×C₇₉⋊C₈	—	2	2	no	—
19	#14579160	—	4	4	no	—
20	#14579160	—	4	4	no	—
21	C₂×C₄⋊Dic₇₉	D₄	1	2	yes	—
22	C₂×C₄⋊Dic₇₉	D₄	1	2	yes	—
23	C₂×Dic₇₉⋊C₄	—	2	4	no	—
24	C₂×C₄×Dic₇₉	—	2	2	no	—
25	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
26	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
27	C₇₉⋊#95	—	2	2	no	—
28	C₇₉⋊#95	—	2	2	no	—
29	C₂²×Q₈×C₇₉	—	2	1	no	—
30	C₂²×C₈×C₇₉	—	2	1	no	—
31	C₄⋊Q₈×C₇₉	—	2	2	no	—
32	C₄⋊Q₈×C₇₉	—	2	1	no	—
33	C₄⋊Q₈×C₇₉	Q₈	1	2	yes	complemented
34	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
35	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
37	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
38	#103×C₇₉	—	4	4	no	—
39	C₄×C₈×C₇₉	—	2	2	no	—
40	C₂×Dic₁₅₈	—	4	8	no	—
41	C₂×Dic₁₅₈	—	8	2	no	—
42	C₂²×Dic₇₉	—	2	2	no	—
43	C₂²×Dic₇₉	—	2	2	no	—
44	C₂×C₇₉⋊C₈	—	4	2	no	—
45	C₂×C₇₉⋊C₈	—	4	2	no	—
46	C₂×C₇₉⋊C₈	—	4	2	no	—
47	C₄⋊Dic₇₉	—	2	2	no	—
48	C₄⋊Dic₇₉	—	2	2	no	—
49	C₄⋊Dic₇₉	SD₁₆	1	4	yes	—
50	C₄⋊Dic₇₉	Q₁₆	1	4	yes	—
51	Dic₇₉⋊C₄	—	4	8	no	—
52	C₄×Dic₇₉	—	4	2	no	—
53	C₄×Dic₇₉	—	4	2	no	—
54	C₂×Q₈×C₇₉	—	2	2	no	—
55	C₂×Q₈×C₇₉	—	4	2	no	—
56	C₂×Q₈×C₇₉	—	4	2	no	—
57	C₂×Q₈×C₇₉	—	4	1	no	—
58	C₂²×C₄×C₇₉	—	2	2	no	—
59	C₂²×C₄×C₇₉	—	4	1	no	—
60	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
62	C₂×C₈×C₇₉	—	2	2	no	—
63	C₂×C₈×C₇₉	—	4	1	no	—
64	C₂×C₈×C₇₉	—	4	1	no	—
65	C₄⋊C₄×C₇₉	—	2	4	no	—
66	C₄⋊C₄×C₇₉	—	4	2	no	—
67	C₄⋊C₄×C₇₉	—	4	2	no	—
68	C₄⋊C₄×C₇₉	—	4	2	no	—
69	C₄⋊C₄×C₇₉	—	4	2	no	—
70	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
71	C₄²×C₇₉	#41	1	2	yes	—
72	C₄²×C₇₉	#41	1	1	yes	characteristic
73	C₂³×C₇₉	#120	1	1	yes	characteristic
74	Q₈×C₇₉	—	4	4	no	—
75	Q₈×C₇₉	—	8	2	no	—
76	C₂×C₄×C₇₉	—	2	1	no	—
77	C₂×C₄×C₇₉	—	2	1	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	—	8	1	no	—
82	C₂×C₄×C₇₉	—	8	1	no	—
83	C₂×C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
84	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
85	C₂×C₄×C₇₉	#124	1	2	yes	—
86	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
87	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
88	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
89	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
90	C₂×C₄×C₇₉	#137	1	2	yes	—
91	C₂×Dic₇₉	—	2	4	no	—
92	C₂×Dic₇₉	—	2	4	no	—
93	C₂×Dic₇₉	—	4	2	no	—
94	C₂×Dic₇₉	—	4	2	no	—
95	C₂×Dic₇₉	—	4	2	no	—
96	C₂×Dic₇₉	—	4	2	no	—
97	Dic₁₅₈	—	8	8	no	—
98	C₈×C₇₉	—	4	2	no	—
99	C₇₉⋊C₈	—	8	2	no	—
100	C₂²×C₇₉	#393	1	1	yes	characteristic
101	C₂²×C₇₉	#450	1	2	yes	—
102	C₂²×C₇₉	#451	1	2	yes	—
103	C₂²×C₇₉	#453	1	1	yes	characteristic
104	C₂²×C₇₉	#454	1	1	yes	characteristic
105	C₄×C₇₉	—	2	1	no	—
106	C₄×C₇₉	—	2	1	no	—
107	C₄×C₇₉	—	8	2	no	—
108	C₄×C₇₉	—	8	2	no	—
109	C₄×C₇₉	#475	1	2	yes	—
110	C₄×C₇₉	#477	1	2	yes	—
111	C₄×C₇₉	#487	1	2	yes	—
112	C₄×C₇₉	#489	1	2	yes	—
113	Dic₇₉	—	4	4	no	—
114	Dic₇₉	—	4	4	no	—
115	#10349	—	79	1	no	maximal, Sylow
116	C₂×C₇₉	#1629	1	1	yes	characteristic
117	C₂×C₇₉	#1633	1	1	yes	characteristic
118	C₂×C₇₉	#1637	1	2	yes	—
119	C₂×C₇₉	#2024	1	2	yes	—
120	C₂×C₇₉	#2027	1	1	yes	characteristic
121	#2551	—	79	1	no	—
122	#1987	—	79	2	no	—
123	#1956	D₇₉	1	1	yes	characteristic
124	#1296	—	79	1	no	—
125	#1279	—	79	2	no	—
126	C₇₉	#10349	1	1	yes	characteristic, complemented, Sylow
127	C₂×C₄⋊Q₈	—	158	2	no	—
128	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
129	C₂×C₄⋊C₈	—	79	2	no	—
130	C₂×#103	—	2	2	no	—
131	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
132	#395	—	158	2	no	—
133	#389	—	158	2	no	—
134	#384	C₂×D₇₉	1	1	yes	characteristic
135	C₄×C₄⋊C₄	—	79	2	no	—
136	#340	—	158	2	no	—
137	#340	—	158	2	no	—
138	C₂²×Q₈	—	2	1	no	—
139	C₂²×Q₈	—	158	2	no	—
140	C₂²×C₈	—	2	1	no	—
141	C₂²×C₈	—	158	2	no	—
142	C₄⋊Q₈	—	2	2	no	—
143	C₄⋊Q₈	—	2	1	no	—
144	C₄⋊Q₈	—	316	4	no	—
145	C₄⋊Q₈	—	316	4	no	—
146	C₄⋊Q₈	Dic₁₅₈	1	2	yes	complemented
147	C₂×C₄⋊C₄	—	2	2	no	—
148	C₂×C₄⋊C₄	—	2	2	no	—
149	C₂×C₄⋊C₄	—	79	2	no	—
150	C₂×C₄⋊C₄	—	79	2	no	—
151	C₂×C₄⋊C₄	—	158	4	no	—
152	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	2	yes	—
153	C₂×C₄²	—	158	2	no	—
154	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
155	C₄⋊C₈	—	158	2	no	—
156	C₄⋊C₈	—	158	2	no	—
157	#103	—	4	4	no	—
158	C₄×C₈	—	2	2	no	—
159	#95	—	158	2	no	—
160	#95	—	158	2	no	—
161	C₂×Q₈	—	2	2	no	—
162	C₂×Q₈	—	4	2	no	—
163	C₂×Q₈	—	4	2	no	—
164	C₂×Q₈	—	4	1	no	—
165	C₂×Q₈	—	316	8	no	—
166	C₂×Q₈	—	632	2	no	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	—	4	1	no	—
169	C₂²×C₄	—	158	2	no	—
170	C₂²×C₄	—	158	2	no	—
171	C₂²×C₄	D₄×D₇₉	1	2	yes	—
172	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	4	1	no	—
176	C₂×C₈	—	316	2	no	—
177	C₂×C₈	—	316	2	no	—
178	C₂×C₈	—	316	2	no	—
179	C₄⋊C₄	—	2	4	no	—
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	4	2	no	—
183	C₄⋊C₄	—	4	2	no	—
184	C₄⋊C₄	—	316	8	no	—
185	C₄⋊C₄	—	79	4	no	—
186	C₄⋊C₄	—	79	4	no	—
187	C₄⋊C₄	—	158	2	no	—
188	C₄⋊C₄	—	158	2	no	—
189	C₄²	—	316	2	no	—
190	C₄²	—	316	2	no	—
191	C₄²	C₂×Dic₁₅₈	1	1	yes	characteristic
192	C₄²	#11929623	1	2	yes	—
193	C₄²	#11929624	1	1	yes	characteristic
194	C₂³	#14579129	1	1	yes	characteristic
195	Q₈	—	4	4	no	—
196	Q₈	—	8	2	no	—
197	Q₈	—	632	8	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	4	4	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	8	1	no	—
204	C₂×C₄	—	8	1	no	—
205	C₂×C₄	—	316	2	no	—
206	C₂×C₄	—	316	2	no	—
207	C₂×C₄	—	316	2	no	—
208	C₂×C₄	—	316	2	no	—
209	C₂×C₄	—	158	4	no	—
210	C₂×C₄	—	158	4	no	—
211	C₂×C₄	#14579138	1	2	yes	—
212	C₂×C₄	#14579140	1	1	yes	characteristic
213	C₂×C₄	#14579147	1	2	yes	—
214	C₂×C₄	#14579148	1	1	yes	characteristic
215	C₂×C₄	SD₁₆×D₇₉	1	2	yes	—
216	C₂×C₄	Q₁₆×D₇₉	1	2	yes	—
217	C₂×C₄	#14579188	1	2	yes	—
218	C₂×C₄	#14579193	1	2	yes	—
219	C₈	—	4	2	no	—
220	C₈	—	632	2	no	—
221	C₂²	#19098475	1	1	yes	characteristic
222	C₂²	#19098712	1	2	yes	—
223	C₂²	#19098717	1	2	yes	—
224	C₂²	#19098730	1	1	yes	characteristic
225	C₂²	#19098735	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	8	2	no	—
229	C₄	—	8	2	no	—
230	C₄	—	316	4	no	—
231	C₄	—	316	4	no	—
232	C₄	#19098846	1	2	yes	—
233	C₄	#19098856	1	2	yes	—
234	C₄	#19098912	1	2	yes	—
235	C₄	#19098924	1	2	yes	—
236	C₂	#23762514	1	1	yes	characteristic
237	C₂	#23762538	1	1	yes	characteristic
238	C₂	#23762562	1	2	yes	—
239	C₂	#23764539	1	2	yes	—
240	C₂	#23764556	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23768429

C₂

yes

maximal, characteristic

#23764349

C₂

yes

maximal

#23761283

C₂

yes

maximal, characteristic

#23761240

C₂

yes

maximal

C₇₉×#1956

C₂

yes

maximal, characteristic

C₂×#14579160

—

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

#19098483

—

#19098459

—

C₄×C₄⋊Dic₇₉

C₂²

yes

—

#19098325

—

#19098325

—

C₂×C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

C₂×#103×C₇₉

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

#384×C₇₉

C₂²

yes

characteristic

C₂²×Dic₁₅₈

—

C₂²×C₇₉⋊C₈

—

#14579160

—

#14579160

—

C₂×C₄⋊Dic₇₉

D₄

yes

—

C₂×C₄⋊Dic₇₉

D₄

yes

—

C₂×Dic₇₉⋊C₄

—

C₂×C₄×Dic₇₉

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₇₉⋊#95

—

C₇₉⋊#95

—

C₂²×Q₈×C₇₉

—

C₂²×C₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

Q₈

yes

complemented

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#103×C₇₉

—

C₄×C₈×C₇₉

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

SD₁₆

yes

—

C₄⋊Dic₇₉

Q₁₆

yes

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

—

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×D₄

yes

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂×Q₈

yes

characteristic

C₄²×C₇₉

#41

yes

—

C₄²×C₇₉

yes

C₂³×C₇₉

yes

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

—

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₉

#124

yes

—

C₂×C₄×C₇₉

#124

yes

characteristic

C₂×C₄×C₇₉

C₂×SD₁₆

yes

—

C₂×C₄×C₇₉

C₂×Q₁₆

yes

—

C₂×C₄×C₇₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₇₉

#137

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

C₈×C₇₉

—

C₇₉⋊C₈

—

100

C₂²×C₇₉

#393

yes

characteristic

101

C₂²×C₇₉

#450

yes

—

102

C₂²×C₇₉

#451

yes

—

103

C₂²×C₇₉

#453

yes

characteristic

104

C₂²×C₇₉

#454

yes

characteristic

105

C₄×C₇₉

—

106

C₄×C₇₉

—

107

C₄×C₇₉

—

108

C₄×C₇₉

—

109

C₄×C₇₉

#475

yes

—

110

C₄×C₇₉

#477

yes

—

111

C₄×C₇₉

#487

yes

—

112

C₄×C₇₉

#489

yes

—

113

Dic₇₉

—

114

Dic₇₉

—

115

#10349

—

maximal, Sylow

116

C₂×C₇₉

#1629

yes

characteristic

117

C₂×C₇₉

#1633

yes

characteristic

118

C₂×C₇₉

#1637

yes

—

119

C₂×C₇₉

#2024

yes

—

120

C₂×C₇₉

#2027

yes

characteristic

121

#2551

—

122

#1987

—

123

#1956

D₇₉

yes

characteristic

124

#1296

—

125

#1279

—

126

C₇₉

#10349

yes

characteristic, complemented, Sylow

127

C₂×C₄⋊Q₈

—

158

—

128

C₂×C₄⋊Q₈

C₂×D₇₉

yes

characteristic

129

C₂×C₄⋊C₈

—

130

C₂×#103

—

131

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

132

#395

—

158

—

133

#389

—

158

—

134

#384

C₂×D₇₉

yes

characteristic

135

C₄×C₄⋊C₄

—

136

#340

—

158

—

137

#340

—

158

—

138

C₂²×Q₈

—

139

C₂²×Q₈

—

158

—

140

C₂²×C₈

—

141

C₂²×C₈

—

158

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

316

—

145

C₄⋊Q₈

—

316

—

146

C₄⋊Q₈

Dic₁₅₈

yes

complemented

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

158

—

152

C₂×C₄⋊C₄

C₂²⋊D₇₉

yes

—

153

C₂×C₄²

—

158

—

154

C₂×C₄²

C₂²×D₇₉

yes

characteristic

155

C₄⋊C₈

—

158

—

156

C₄⋊C₈

—

158

—

157

#103

—

158

C₄×C₈

—

159

#95

—

158

—

160

#95

—

158

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

316

—

166

C₂×Q₈

—

632

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

158

—

170

C₂²×C₄

—

158

—

171

C₂²×C₄

D₄×D₇₉

yes

—

172

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

316

—

177

C₂×C₈

—

316

—

178

C₂×C₈

—

316

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

316

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

158

—

188

C₄⋊C₄

—

158

—

189

C₄²

—

316

—

190

C₄²

—

316

—

191

C₄²

C₂×Dic₁₅₈

yes

characteristic

192

C₄²

#11929623

yes

—

193

C₄²

#11929624

yes

characteristic

194

C₂³

#14579129

yes

characteristic

195

Q₈

—

196

Q₈

—

197

Q₈

—

632

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

316

—

206

C₂×C₄

—

316

—

207

C₂×C₄

—

316

—

208

C₂×C₄

—

316

—

209

C₂×C₄

—

158

—

210

C₂×C₄

—

158

—

211

C₂×C₄

#14579138

yes

—

212

C₂×C₄

#14579140

yes

characteristic

213

C₂×C₄

#14579147

yes

—

214

C₂×C₄

#14579148

yes

characteristic

215

C₂×C₄

SD₁₆×D₇₉

yes

—

216

C₂×C₄

Q₁₆×D₇₉

yes

—

217

C₂×C₄

#14579188

yes

—

218

C₂×C₄

#14579193

yes

—

219

C₈

—

220

C₈

—

632

—

221

C₂²

#19098475

yes

characteristic

222

C₂²

#19098712

yes

—

223

C₂²

#19098717

yes

—

224

C₂²

#19098730

yes

characteristic

225

C₂²

#19098735

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

316

—

231

C₄

—

316

—

232

C₄

#19098846

yes

—

233

C₄

#19098856

yes

—

234

C₄

#19098912

yes

—

235

C₄

#19098924

yes

—

236

C₂

#23762514

yes

characteristic

237

C₂

#23762538

yes

characteristic

238

C₂

#23762562

yes

—

239

C₂

#23764539

yes

—

240

C₂

#23764556

yes

characteristic

	subgroup	G/H
center	C₂³	#14579129
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1956	C₂
socle, prime radical	C₂³×C₇₉	#120
hypercenter	#1956	D₇₉
hypocenter	C₇₉	#10349
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

subgroup

G/H

center

C₂³

#14579129

commutator, cosocle

C₂×C₄²×C₇₉

C₂³

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1956

C₂

C₂³×C₇₉

D₇₉

C₇₉

G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

N	H ≅ G/N	type
33. C₄⋊Q₈×C₇₉	Q₈	semidirect
126. C₇₉	#10349	semidirect
146. C₄⋊Q₈	Dic₁₅₈	semidirect

H ≅ G/N

type

33. C₄⋊Q₈×C₇₉

Q₈

semidirect

126. C₇₉

#10349

semidirect

146. C₄⋊Q₈

Dic₁₅₈

semidirect

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

subgroup	index
#23768429	2
#23764349	2
#23761283	2
#23761240	2
C₇₉×#1956	2
#10349	79

subgroup

index

C₇₉×#1956

Subgroups — #34191282

Conjugacy classes of subgroups

Complements

Maximal subgroups