Group #34181282 — subgroups

Subgroups — #34181282

Order 20224.

320 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 119 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	#23762163	C₂	1	1	yes	maximal, characteristic
2	#23762163	C₂	1	1	yes	maximal, characteristic
3	#23762038	C₂	1	2	yes	maximal
4	#23761311	C₂	1	2	yes	maximal
5	C₇₉×#2960	C₂	1	1	yes	maximal, characteristic
6	#19098620	C₂²	1	2	yes	—
7	#19098620	C₂²	1	2	yes	—
8	#19098316	—	2	1	no	—
9	#19098316	—	2	1	no	—
10	#19098314	—	2	1	no	—
11	#19098314	—	2	1	no	—
12	#19098305	—	2	4	no	—
13	#533×C₇₉	C₂²	1	1	yes	characteristic
14	#446×C₇₉	—	2	1	no	—
15	#446×C₇₉	—	2	1	no	—
16	C₈×Q₈×C₇₉	—	2	1	no	—
17	C₈×Q₈×C₇₉	—	2	1	no	—
18	#424×C₇₉	C₄	1	2	yes	—
19	#423×C₇₉	C₂²	1	1	yes	characteristic
20	#405×C₇₉	C₄	1	2	yes	—
21	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
22	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
23	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
24	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
25	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
26	#14579072	—	2	2	no	—
27	#14579072	—	2	2	no	—
28	C₂×M₁₆×C₇₉	C₂×C₄	1	2	yes	—
29	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
31	C₄⋊Q₈×C₇₉	Q₈	1	1	yes	characteristic
32	C₄⋊Q₈×C₇₉	Q₈	1	1	yes	characteristic
33	#125×C₇₉	D₄	1	2	yes	—
34	C₂²⋊Q₈×C₇₉	—	2	1	no	—
35	C₂²⋊Q₈×C₇₉	—	2	1	no	—
36	C₄×Q₈×C₇₉	—	2	1	no	—
37	C₄×Q₈×C₇₉	—	2	1	no	—
38	#117×C₇₉	C₂×C₄	1	2	yes	—
39	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
40	C₄⋊C₈×C₇₉	—	2	2	no	—
41	C₄⋊C₈×C₇₉	—	2	2	no	—
42	C₄⋊C₈×C₇₉	—	2	1	no	—
43	C₄⋊C₈×C₇₉	—	2	1	no	—
44	#97×C₇₉	—	2	2	no	—
45	C₄×C₈×C₇₉	—	2	2	no	—
46	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
47	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
48	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
49	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
50	C₂×C₇₉⋊C₈	—	4	2	no	—
51	C₂×C₇₉⋊C₈	—	4	2	no	—
52	C₂×Q₈×C₇₉	—	2	1	no	—
53	C₂×Q₈×C₇₉	—	2	1	no	—
54	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
56	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
57	M₁₆×C₇₉	—	4	2	no	—
58	C₂×C₈×C₇₉	—	2	2	no	—
59	C₂×C₈×C₇₉	—	2	2	no	—
60	C₂×C₈×C₇₉	—	4	1	no	—
61	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₄⋊C₄×C₇₉	—	2	2	no	—
66	C₄⋊C₄×C₇₉	—	2	2	no	—
67	C₄⋊C₄×C₇₉	—	2	1	no	—
68	C₄⋊C₄×C₇₉	—	2	1	no	—
69	C₄⋊C₄×C₇₉	C₄⋊C₄	1	2	yes	—
70	C₄⋊C₄×C₇₉	C₄⋊C₄	1	2	yes	—
71	C₂²⋊C₄×C₇₉	—	2	2	no	—
72	C₄²×C₇₉	—	2	2	no	—
73	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
77	C₂³×C₇₉	#117	1	1	yes	characteristic
78	Q₈×C₇₉	—	4	2	no	—
79	Q₈×C₇₉	—	4	2	no	—
80	C₂×C₄×C₇₉	—	2	1	no	—
81	C₂×C₄×C₇₉	—	2	1	no	—
82	C₂×C₄×C₇₉	—	2	2	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	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
88	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
89	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
90	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
91	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
92	C₈×C₇₉	—	2	1	no	—
93	C₈×C₇₉	—	2	1	no	—
94	C₈×C₇₉	—	2	1	no	—
95	C₈×C₇₉	—	4	2	no	—
96	C₈×C₇₉	#101	1	2	yes	—
97	C₇₉⋊C₈	—	8	2	no	—
98	C₇₉⋊C₈	—	8	2	no	—
99	C₂²×C₇₉	—	2	1	no	—
100	C₂²×C₇₉	—	2	1	no	—
101	C₂²×C₇₉	—	2	1	no	—
102	C₂²×C₇₉	#380	1	1	yes	characteristic
103	C₄×C₇₉	—	2	1	no	—
104	C₄×C₇₉	—	2	1	no	—
105	C₄×C₇₉	—	2	1	no	—
106	C₄×C₇₉	—	2	1	no	—
107	C₄×C₇₉	—	2	1	no	—
108	C₄×C₇₉	—	4	2	no	—
109	C₄×C₇₉	—	4	2	no	—
110	C₄×C₇₉	C₂×#101	1	1	yes	characteristic
111	C₄×C₇₉	#413	1	1	yes	characteristic
112	#8635	—	79	1	no	maximal, Sylow
113	C₂×C₇₉	—	4	1	no	—
114	C₂×C₇₉	#1801	1	1	yes	characteristic
115	C₂×C₇₉	#1814	1	1	yes	characteristic
116	C₂×C₇₉	#1814	1	1	yes	characteristic
117	#2960	D₇₉	1	1	yes	characteristic
118	#1568	—	79	1	no	—
119	#1568	—	79	1	no	—
120	#1537	—	79	2	no	—
121	#1307	—	79	2	no	—
122	C₇₉	#8635	1	1	yes	characteristic, complemented, Sylow
123	#533	C₂×D₇₉	1	1	yes	characteristic
124	#446	—	2	1	no	—
125	#446	—	2	1	no	—
126	C₈×Q₈	—	2	1	no	—
127	C₈×Q₈	—	2	1	no	—
128	#432	—	79	2	no	—
129	#432	—	79	2	no	—
130	#424	Dic₇₉	1	2	yes	—
131	#423	C₂×D₇₉	1	1	yes	characteristic
132	#405	Dic₇₉	1	2	yes	—
133	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
134	#335	—	158	1	no	—
135	#335	—	158	1	no	—
136	#334	—	158	1	no	—
137	#334	—	158	1	no	—
138	#330	—	158	4	no	—
139	C₂×M₁₆	C₂×Dic₇₉	1	2	yes	—
140	C₂²×C₈	C₂×Dic₇₉	1	1	yes	characteristic
141	C₂²×C₈	C₂×Dic₇₉	1	1	yes	characteristic
142	C₄⋊Q₈	Dic₁₅₈	1	1	yes	characteristic
143	C₄⋊Q₈	Dic₁₅₈	1	1	yes	characteristic
144	#125	D₃₁₆	1	2	yes	—
145	C₂²⋊Q₈	—	2	1	no	—
146	C₂²⋊Q₈	—	2	1	no	—
147	C₄×Q₈	—	2	1	no	—
148	C₄×Q₈	—	2	1	no	—
149	#117	C₂×Dic₇₉	1	2	yes	—
150	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
151	C₄⋊C₈	—	2	2	no	—
152	C₄⋊C₈	—	2	2	no	—
153	C₄⋊C₈	—	2	1	no	—
154	C₄⋊C₈	—	2	1	no	—
155	C₄⋊C₈	—	158	2	no	—
156	C₄⋊C₈	—	158	2	no	—
157	C₂²⋊C₈	—	158	2	no	—
158	C₂²⋊C₈	—	158	2	no	—
159	#97	—	2	2	no	—
160	#97	—	158	2	no	—
161	#97	—	158	2	no	—
162	C₄×C₈	—	2	2	no	—
163	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
164	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
165	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
166	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
167	C₂×Q₈	—	2	1	no	—
168	C₂×Q₈	—	2	1	no	—
169	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
170	C₂²×C₄	#11929624	1	1	yes	characteristic
171	C₂²×C₄	#11929624	1	1	yes	characteristic
172	M₁₆	—	4	2	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	2	2	no	—
175	C₂×C₈	—	4	1	no	—
176	C₂×C₈	—	316	2	no	—
177	C₂×C₈	—	316	2	no	—
178	C₂×C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
179	C₂×C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
180	C₂×C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
181	C₂×C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
182	C₄⋊C₄	—	2	2	no	—
183	C₄⋊C₄	—	2	2	no	—
184	C₄⋊C₄	—	2	1	no	—
185	C₄⋊C₄	—	2	1	no	—
186	C₄⋊C₄	C₄⋊Dic₇₉	1	2	yes	—
187	C₄⋊C₄	C₄⋊Dic₇₉	1	2	yes	—
188	C₂²⋊C₄	—	2	2	no	—
189	C₄²	—	2	2	no	—
190	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
191	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
192	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
193	C₄²	C₂×Dic₁₅₈	1	1	yes	characteristic
194	C₂³	#14579120	1	1	yes	characteristic
195	Q₈	—	4	2	no	—
196	Q₈	—	4	2	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	4	1	no	—
202	C₂×C₄	—	4	1	no	—
203	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
204	C₂×C₄	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
205	C₂×C₄	#14579135	1	1	yes	characteristic
206	C₂×C₄	#14579135	1	1	yes	characteristic
207	C₂×C₄	#14579140	1	1	yes	characteristic
208	C₂×C₄	#14579140	1	1	yes	characteristic
209	C₈	—	2	1	no	—
210	C₈	—	2	1	no	—
211	C₈	—	2	1	no	—
212	C₈	—	4	2	no	—
213	C₈	—	632	2	no	—
214	C₈	—	632	2	no	—
215	C₈	#14579080	1	2	yes	—
216	C₂²	—	2	1	no	—
217	C₂²	—	2	1	no	—
218	C₂²	—	2	1	no	—
219	C₂²	#19098423	1	1	yes	characteristic
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	2	1	no	—
225	C₄	—	4	2	no	—
226	C₄	—	4	2	no	—
227	C₄	C₂×#14579080	1	1	yes	characteristic
228	C₄	#19098547	1	1	yes	characteristic
229	C₂	—	4	1	no	—
230	C₂	#23763396	1	1	yes	characteristic
231	C₂	#23763454	1	1	yes	characteristic
232	C₂	#23763454	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23762163

C₂

yes

maximal, characteristic

#23762163

C₂

yes

maximal, characteristic

#23762038

C₂

yes

maximal

#23761311

C₂

yes

maximal

C₇₉×#2960

C₂

yes

maximal, characteristic

#19098620

C₂²

yes

—

#19098620

C₂²

yes

—

—

—

—

—

—

#533×C₇₉

C₂²

yes

characteristic

#446×C₇₉

—

#446×C₇₉

—

C₈×Q₈×C₇₉

—

C₈×Q₈×C₇₉

—

#424×C₇₉

C₄

yes

—

#423×C₇₉

C₂²

yes

characteristic

#405×C₇₉

C₄

yes

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

#14579072

—

#14579072

—

C₂×M₁₆×C₇₉

C₂×C₄

yes

—

C₂²×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄⋊Q₈×C₇₉

Q₈

yes

characteristic

C₄⋊Q₈×C₇₉

Q₈

yes

characteristic

#125×C₇₉

D₄

yes

—

C₂²⋊Q₈×C₇₉

—

C₂²⋊Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

#117×C₇₉

C₂×C₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

#97×C₇₉

—

C₄×C₈×C₇₉

—

C₄×C₈×C₇₉

D₄

yes

characteristic

C₄×C₈×C₇₉

D₄

yes

characteristic

C₄×C₈×C₇₉

D₄

yes

characteristic

C₄×C₈×C₇₉

D₄

yes

characteristic

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

C₂²×C₄×C₇₉

yes

C₂²×C₄×C₇₉

yes

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

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

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

C₄⋊C₄

yes

—

C₄⋊C₄×C₇₉

C₄⋊C₄

yes

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×Q₈

yes

characteristic

C₂³×C₇₉

#117

yes

characteristic

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×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

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

#101

yes

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

100

C₂²×C₇₉

—

101

C₂²×C₇₉

—

102

C₂²×C₇₉

#380

yes

characteristic

103

C₄×C₇₉

—

104

C₄×C₇₉

—

105

C₄×C₇₉

—

106

C₄×C₇₉

—

107

C₄×C₇₉

—

108

C₄×C₇₉

—

109

C₄×C₇₉

—

110

C₄×C₇₉

C₂×#101

yes

characteristic

111

C₄×C₇₉

yes

112

—

113

C₂×C₇₉

—

114

C₂×C₇₉

#1801

yes

characteristic

115

C₂×C₇₉

#1814

yes

characteristic

116

C₂×C₇₉

#1814

yes

characteristic

117

#2960

D₇₉

yes

characteristic

118

#1568

—

119

#1568

—

120

#1537

—

121

#1307

—

122

C₇₉

#8635

yes

characteristic, complemented, Sylow

123

#533

C₂×D₇₉

yes

characteristic

124

#446

—

125

#446

—

126

C₈×Q₈

—

127

C₈×Q₈

—

128

#432

—

129

#432

—

130

#424

Dic₇₉

yes

—

131

#423

C₂×D₇₉

yes

characteristic

132

#405

Dic₇₉

yes

—

133

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

134

#335

—

158

—

135

#335

—

158

—

136

#334

—

158

—

137

#334

—

158

—

138

#330

—

158

—

139

C₂×M₁₆

C₂×Dic₇₉

yes

—

140

C₂²×C₈

C₂×Dic₇₉

yes

characteristic

141

C₂²×C₈

C₂×Dic₇₉

yes

characteristic

142

C₄⋊Q₈

Dic₁₅₈

yes

characteristic

143

C₄⋊Q₈

Dic₁₅₈

yes

characteristic

144

#125

D₃₁₆

yes

—

145

C₂²⋊Q₈

—

146

C₂²⋊Q₈

—

147

C₄×Q₈

—

148

C₄×Q₈

—

149

#117

C₂×Dic₇₉

yes

—

150

C₂×C₄²

C₂²×D₇₉

yes

characteristic

151

C₄⋊C₈

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

158

—

156

C₄⋊C₈

—

158

—

157

C₂²⋊C₈

—

158

—

158

C₂²⋊C₈

—

158

—

159

#97

—

160

#97

—

158

—

161

#97

—

158

—

162

C₄×C₈

—

163

C₄×C₈

C₂²⋊D₇₉

yes

characteristic

164

C₄×C₈

C₂²⋊D₇₉

yes

characteristic

165

C₄×C₈

C₂²⋊D₇₉

yes

characteristic

166

C₄×C₈

C₂²⋊D₇₉

yes

characteristic

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂²×C₄

C₂²×Dic₇₉

yes

characteristic

170

C₂²×C₄

#11929624

yes

characteristic

171

C₂²×C₄

#11929624

yes

characteristic

172

M₁₆

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

316

—

177

C₂×C₈

—

316

—

178

C₂×C₈

C₂²⋊Dic₇₉

yes

characteristic

179

C₂×C₈

C₂²⋊Dic₇₉

yes

characteristic

180

C₂×C₈

C₂²⋊Dic₇₉

yes

characteristic

181

C₂×C₈

C₂²⋊Dic₇₉

yes

characteristic

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

C₄⋊Dic₇₉

yes

—

187

C₄⋊C₄

C₄⋊Dic₇₉

yes

—

188

C₂²⋊C₄

—

189

C₄²

—

190

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

191

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

192

C₄²

C₂×D₃₁₆

yes

characteristic

193

C₄²

C₂×Dic₁₅₈

yes

characteristic

194

C₂³

#14579120

yes

characteristic

195

Q₈

—

196

Q₈

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

C₂×C₂²⋊Dic₇₉

yes

characteristic

204

C₂×C₄

C₂×C₄⋊Dic₇₉

yes

characteristic

205

C₂×C₄

#14579135

yes

characteristic

206

C₂×C₄

#14579135

yes

characteristic

207

C₂×C₄

#14579140

yes

characteristic

208

C₂×C₄

#14579140

yes

characteristic

209

C₈

—

210

C₈

—

211

C₈

—

212

C₈

—

213

C₈

—

632

—

214

C₈

—

632

—

215

C₈

#14579080

yes

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

219

C₂²

#19098423

yes

characteristic

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

C₂×#14579080

yes

characteristic

228

C₄

#19098547

yes

characteristic

229

C₂

—

230

C₂

#23763396

yes

characteristic

231

C₂

#23763454

yes

characteristic

232

C₂

#23763454

yes

characteristic

	subgroup	G/H
center	C₂²	#19098423
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#2960	C₂
socle	C₂²×C₇₉	#380
prime radical	C₂³×C₇₉	#117
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#2960	D₇₉
hypocenter	C₇₉	#8635
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2960

subgroup

G/H

center

C₂²

#19098423

commutator

C₂²×C₄×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#2960

C₂

C₂²×C₇₉

C₂³×C₇₉

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2960

N	H ≅ G/N	type
122. C₇₉	#8635	semidirect

H ≅ G/N

type

122. C₇₉

#8635

semidirect

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

subgroup	index
#23762163	2
#23762038	2
#23761311	2
C₇₉×#2960	2
#8635	79

subgroup

index

C₇₉×#2960

Subgroups — #34181282

Conjugacy classes of subgroups

Complements

Maximal subgroups