Group #34188172 — subgroups

Subgroups — #34188172

Order 20224.

530 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 127 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	#23773979	C₂	1	1	yes	maximal, characteristic
2	#23764227	C₂	1	2	yes	maximal, complemented
3	C₄×#14579071	C₂	1	1	yes	maximal, characteristic, complemented
4	#23761850	C₂	1	2	yes	maximal, complemented
5	C₇₉×#1566	C₂	1	1	yes	maximal, characteristic, complemented
6	#19099113	C₂²	1	2	yes	—
7	#19098968	C₄	1	1	yes	characteristic, complemented
8	#19098940	C₄	1	1	yes	characteristic, complemented
9	#19098910	C₄	1	2	yes	complemented
10	#19098799	—	2	2	no	—
11	C₄×D₆₃₂	—	2	2	no	—
12	C₂×#14579087	—	2	4	no	—
13	C₂×#14579071	—	2	2	no	—
14	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
16	#19098290	—	2	4	no	—
17	#423×C₇₉	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
19	#334×C₇₉	—	2	2	no	—
20	C₂×#11929624	—	2	2	no	—
21	C₂×D₆₃₂	—	2	2	no	—
22	C₂²×C₇₉⋊C₈	—	2	1	no	—
23	#14579161	C₂×C₄	1	2	yes	—
24	#14579158	C₂×C₄	1	2	yes	—
25	#14579149	—	2	2	no	—
26	#14579135	—	2	2	no	—
27	#14579135	—	2	2	no	—
28	C₄×D₃₁₆	—	2	2	no	—
29	C₄×D₃₁₆	—	2	2	no	—
30	C₂×C₄×Dic₇₉	—	2	1	no	—
31	C₂×C₄×Dic₇₉	—	2	1	no	—
32	C₂×C₄×Dic₇₉	D₄	1	2	yes	—
33	#14579095	—	2	2	no	—
34	#14579087	—	4	8	no	—
35	#14579083	—	2	4	no	—
36	#14579071	—	2	8	no	—
37	C₄×C₇₉⋊C₈	—	2	1	no	—
38	C₄×C₇₉⋊C₈	D₄	1	2	yes	—
39	C₂×M₁₆×C₇₉	—	2	2	no	—
40	C₂²×C₈×C₇₉	D₄	1	2	yes	—
41	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₇₉	—	2	2	no	—
43	C₄⋊C₈×C₇₉	—	2	2	no	—
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	2	yes	—
47	#11929624	—	4	4	no	—
48	#11929624	—	4	4	no	—
49	C₂×Dic₁₅₈	—	2	2	no	—
50	C₂×D₃₁₆	—	2	2	no	—
51	C₂×D₃₁₆	—	2	2	no	—
52	C₂×D₃₁₆	—	2	2	no	—
53	C₂×C₂²⋊D₇₉	—	4	2	no	—
54	C₂²×Dic₇₉	—	2	2	no	—
55	C₂×C₄×D₇₉	—	4	2	no	—
56	D₆₃₂	—	4	4	no	—
57	C₂×C₇₉⋊C₈	—	2	4	no	—
58	C₂×C₇₉⋊C₈	—	2	2	no	—
59	C₄⋊Dic₇₉	—	2	2	no	—
60	C₄⋊Dic₇₉	—	2	2	no	—
61	(C₂×D₇₉)⋊C₄	—	4	2	no	—
62	(C₂×D₇₉)⋊C₄	—	4	2	no	—
63	C₄×Dic₇₉	—	2	4	no	—
64	C₄×Dic₇₉	—	2	4	no	—
65	C₄×Dic₇₉	—	4	2	no	—
66	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
69	M₁₆×C₇₉	—	4	4	no	—
70	C₂×C₈×C₇₉	—	2	4	no	—
71	C₂×C₈×C₇₉	—	4	2	no	—
72	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
73	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
74	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
75	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₇₉	#41	1	1	yes	characteristic
78	C₂³×C₇₉	#121	1	1	yes	characteristic
79	C₂²×D₇₉	—	4	2	no	—
80	C₂×C₄×C₇₉	—	2	2	no	—
81	C₂×C₄×C₇₉	—	2	2	no	—
82	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
84	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
86	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
87	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
88	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	4	yes	—
89	C₂²⋊D₇₉	—	8	4	no	—
90	C₂×Dic₇₉	—	2	4	no	—
91	C₂×Dic₇₉	—	4	2	no	—
92	C₂×Dic₇₉	—	4	2	no	—
93	C₂×Dic₇₉	—	4	2	no	—
94	D₃₁₆	—	4	4	no	—
95	D₃₁₆	—	4	4	no	—
96	D₃₁₆	—	4	4	no	—
97	C₄×D₇₉	—	8	2	no	—
98	C₄×D₇₉	—	8	2	no	—
99	Dic₁₅₈	—	4	4	no	—
100	C₈×C₇₉	—	2	2	no	—
101	C₈×C₇₉	—	8	2	no	—
102	C₈×C₇₉	#104	1	4	yes	complemented
103	C₇₉⋊C₈	—	2	4	no	—
104	C₂²×C₇₉	—	2	1	no	—
105	C₂²×C₇₉	—	2	1	no	—
106	C₂²×C₇₉	#390	1	1	yes	characteristic
107	C₂²×C₇₉	#469	1	2	yes	—
108	C₂×D₇₉	—	8	2	no	—
109	C₂×D₇₉	—	8	2	no	—
110	C₂×D₇₉	—	8	2	no	—
111	C₄×C₇₉	—	2	1	no	—
112	C₄×C₇₉	—	2	1	no	—
113	C₄×C₇₉	C₂×#104	1	2	yes	—
114	C₄×C₇₉	#442	1	2	yes	—
115	C₄×C₇₉	#444	1	2	yes	—
116	C₄×C₇₉	#496	1	2	yes	—
117	Dic₇₉	—	4	4	no	—
118	Dic₇₉	—	8	2	no	—
119	#9849	—	79	1	no	maximal, Sylow
120	C₂×C₇₉	—	2	2	no	—
121	C₂×C₇₉	#1962	1	1	yes	characteristic
122	C₂×C₇₉	#1972	1	1	yes	characteristic
123	C₂×C₇₉	#1975	1	1	yes	characteristic
124	D₇₉	—	16	2	no	—
125	#3169	—	79	1	no	—
126	#1962	—	79	2	no	—
127	C₄×#97	—	79	1	no	—
128	#1566	D₇₉	1	1	yes	characteristic, complemented
129	#1492	—	79	2	no	—
130	C₇₉	#9849	1	1	yes	characteristic, complemented, Sylow
131	#532	—	79	2	no	—
132	#500	—	79	1	no	—
133	#493	—	79	1	no	—
134	#486	—	79	2	no	—
135	#466	—	158	2	no	—
136	C₄×D₈	—	158	2	no	—
137	#423	C₂×D₇₉	1	2	yes	—
138	C₂×#104	—	158	4	no	—
139	C₂×#97	—	158	2	no	—
140	C₂×C₄×C₈	—	79	1	no	—
141	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
142	C₄³	—	79	1	no	—
143	#334	—	2	2	no	—
144	D₄⋊C₈	—	158	4	no	—
145	C₂×#41	—	158	2	no	—
146	C₂×D₈	—	158	2	no	—
147	C₂×M₁₆	—	2	2	no	—
148	C₂²×C₈	—	158	1	no	—
149	C₂²×C₈	D₃₁₆	1	2	yes	—
150	C₄⋊Q₈	—	79	2	no	—
151	#127	—	79	2	no	—
152	#124	—	158	2	no	—
153	#121	—	158	2	no	—
154	#121	—	158	2	no	—
155	C₄×D₄	—	158	2	no	—
156	C₄×D₄	—	158	2	no	—
157	C₂×C₄²	—	79	2	no	—
158	C₂×C₄²	—	158	1	no	—
159	C₂×C₄²	—	158	1	no	—
160	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
161	#107	—	158	2	no	—
162	C₄⋊C₈	—	2	2	no	—
163	C₄⋊C₈	—	2	2	no	—
164	#104	—	316	8	no	—
165	#102	—	158	4	no	—
166	#97	—	158	8	no	—
167	C₄×C₈	—	79	2	no	—
168	C₄×C₈	—	158	1	no	—
169	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
170	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
171	C₄×C₈	C₂²⋊D₇₉	1	2	yes	—
172	#41	—	316	4	no	—
173	#41	—	316	4	no	—
174	C₂×Q₈	—	158	2	no	—
175	C₂×D₄	—	316	2	no	—
176	C₂×D₄	—	158	2	no	—
177	C₂×D₄	—	158	2	no	—
178	C₂×D₄	—	158	2	no	—
179	C₂²×C₄	—	316	2	no	—
180	C₂²×C₄	—	158	2	no	—
181	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
182	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
183	C₂²×C₄	#11929625	1	1	yes	characteristic
184	D₈	—	316	4	no	—
185	M₁₆	—	4	4	no	—
186	C₂×C₈	—	2	4	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	—	158	4	no	—
189	C₂×C₈	—	158	2	no	—
190	C₂×C₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
191	C₂×C₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
192	C₄⋊C₄	—	158	2	no	—
193	C₄⋊C₄	—	158	2	no	—
194	C₂²⋊C₄	—	316	2	no	—
195	C₂²⋊C₄	—	316	2	no	—
196	C₄²	—	316	2	no	—
197	C₄²	—	158	4	no	—
198	C₄²	—	158	4	no	—
199	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
200	C₄²	D₄×D₇₉	1	1	yes	characteristic
201	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
202	C₄²	#11929625	1	1	yes	characteristic
203	C₂³	—	316	2	no	—
204	C₂³	#14579136	1	1	yes	characteristic
205	Q₈	—	316	4	no	—
206	D₄	—	316	4	no	—
207	D₄	—	316	4	no	—
208	D₄	—	316	4	no	—
209	D₄	—	632	4	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	316	2	no	—
213	C₂×C₄	—	316	2	no	—
214	C₂×C₄	—	316	2	no	—
215	C₂×C₄	—	632	2	no	—
216	C₂×C₄	—	632	2	no	—
217	C₂×C₄	—	158	4	no	—
218	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
219	C₂×C₄	#14579123	1	1	yes	characteristic
220	C₂×C₄	#14579123	1	1	yes	characteristic
221	C₂×C₄	#14579136	1	1	yes	characteristic
222	C₂×C₄	#14579150	1	1	yes	characteristic
223	C₂×C₄	#14579157	1	1	yes	characteristic
224	C₂×C₄	#14579188	1	4	yes	—
225	C₈	—	2	2	no	—
226	C₈	—	8	2	no	—
227	C₈	—	158	4	no	—
228	C₈	#14579087	1	4	yes	complemented
229	C₂²	—	2	1	no	—
230	C₂²	—	2	1	no	—
231	C₂²	—	632	2	no	—
232	C₂²	—	632	2	no	—
233	C₂²	—	632	2	no	—
234	C₂²	#19098464	1	1	yes	characteristic
235	C₂²	#19098817	1	2	yes	—
236	C₄	—	2	1	no	—
237	C₄	—	2	1	no	—
238	C₄	—	316	4	no	—
239	C₄	—	632	2	no	—
240	C₄	C₂×#14579087	1	2	yes	—
241	C₄	#19098674	1	2	yes	—
242	C₄	#19098684	1	2	yes	—
243	C₄	#19098949	1	2	yes	—
244	C₂	—	2	2	no	—
245	C₂	—	1264	2	no	—
246	C₂	#23764227	1	1	yes	characteristic
247	C₂	#23764274	1	1	yes	characteristic
248	C₂	#23764291	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23773979

C₂

yes

maximal, characteristic

#23764227

C₂

yes

maximal, complemented

C₄×#14579071

C₂

yes

maximal, characteristic, complemented

#23761850

C₂

yes

maximal, complemented

C₇₉×#1566

C₂

yes

maximal, characteristic, complemented

#19099113

C₂²

yes

—

#19098968

C₄

yes

characteristic, complemented

#19098940

C₄

yes

characteristic, complemented

#19098910

C₄

yes

complemented

#19098799

—

C₄×D₆₃₂

—

C₂×#14579087

—

C₂×#14579071

—

C₂×C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₄²×Dic₇₉

C₂²

yes

characteristic

#19098290

—

#423×C₇₉

C₂²

yes

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

#334×C₇₉

—

C₂×#11929624

—

C₂×D₆₃₂

—

C₂²×C₇₉⋊C₈

—

#14579161

C₂×C₄

yes

—

#14579158

C₂×C₄

yes

—

#14579149

—

#14579135

—

#14579135

—

C₄×D₃₁₆

—

C₄×D₃₁₆

—

C₂×C₄×Dic₇₉

—

C₂×C₄×Dic₇₉

—

C₂×C₄×Dic₇₉

D₄

yes

—

—

—

—

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

D₄

yes

—

C₂×M₁₆×C₇₉

—

C₂²×C₈×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

D₄

yes

—

#11929624

—

#11929624

—

C₂×Dic₁₅₈

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×C₂²⋊D₇₉

—

C₂²×Dic₇₉

—

C₂×C₄×D₇₉

—

D₆₃₂

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₄²×C₇₉

C₂²×C₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

C₄²×C₇₉

yes

C₂³×C₇₉

yes

C₂²×D₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄×D₄

yes

characteristic

C₂×C₄×C₇₉

C₄×D₄

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

—

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

C₄×D₇₉

—

C₄×D₇₉

—

Dic₁₅₈

—

100

C₈×C₇₉

—

101

C₈×C₇₉

—

102

C₈×C₇₉

#104

yes

complemented

103

C₇₉⋊C₈

—

104

C₂²×C₇₉

—

105

C₂²×C₇₉

—

106

C₂²×C₇₉

#390

yes

characteristic

107

C₂²×C₇₉

#469

yes

—

108

C₂×D₇₉

—

109

C₂×D₇₉

—

110

C₂×D₇₉

—

111

C₄×C₇₉

—

112

C₄×C₇₉

—

113

C₄×C₇₉

C₂×#104

yes

—

114

C₄×C₇₉

#442

yes

—

115

C₄×C₇₉

#444

yes

—

116

C₄×C₇₉

#496

yes

—

117

Dic₇₉

—

118

Dic₇₉

—

119

#9849

—

maximal, Sylow

120

C₂×C₇₉

—

121

C₂×C₇₉

#1962

yes

characteristic

122

C₂×C₇₉

#1972

yes

characteristic

123

C₂×C₇₉

#1975

yes

characteristic

124

D₇₉

—

125

#3169

—

126

#1962

—

127

C₄×#97

—

128

#1566

D₇₉

yes

characteristic, complemented

129

#1492

—

130

C₇₉

#9849

yes

characteristic, complemented, Sylow

131

#532

—

132

#500

—

133

#493

—

134

#486

—

135

#466

—

158

—

136

C₄×D₈

—

158

—

137

#423

C₂×D₇₉

yes

—

138

C₂×#104

—

158

—

139

C₂×#97

—

158

—

140

C₂×C₄×C₈

—

141

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

142

C₄³

—

143

#334

—

144

D₄⋊C₈

—

158

—

145

C₂×#41

—

158

—

146

C₂×D₈

—

158

—

147

C₂×M₁₆

—

148

C₂²×C₈

—

158

—

149

C₂²×C₈

D₃₁₆

yes

—

150

C₄⋊Q₈

—

151

#127

—

152

#124

—

158

—

153

#121

—

158

—

154

#121

—

158

—

155

C₄×D₄

—

158

—

156

C₄×D₄

—

158

—

157

C₂×C₄²

—

158

C₂×C₄²

—

158

—

159

C₂×C₄²

—

158

—

160

C₂×C₄²

C₂²×D₇₉

yes

characteristic

161

#107

—

158

—

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

#104

—

316

—

165

#102

—

158

—

166

#97

—

158

—

167

C₄×C₈

—

168

C₄×C₈

—

158

—

169

C₄×C₈

C₄×D₇₉

yes

characteristic

170

C₄×C₈

C₄×D₇₉

yes

characteristic

171

C₄×C₈

C₂²⋊D₇₉

yes

—

172

#41

—

316

—

173

#41

—

316

—

174

C₂×Q₈

—

158

—

175

C₂×D₄

—

316

—

176

C₂×D₄

—

158

—

177

C₂×D₄

—

158

—

178

C₂×D₄

—

158

—

179

C₂²×C₄

—

316

—

180

C₂²×C₄

—

158

—

181

C₂²×C₄

D₄×D₇₉

yes

characteristic

182

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

183

C₂²×C₄

#11929625

yes

characteristic

184

D₈

—

316

—

185

M₁₆

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

158

—

189

C₂×C₈

—

158

—

190

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

—

191

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

—

192

C₄⋊C₄

—

158

—

193

C₄⋊C₄

—

158

—

194

C₂²⋊C₄

—

316

—

195

C₂²⋊C₄

—

316

—

196

C₄²

—

316

—

197

C₄²

—

158

—

198

C₄²

—

158

—

199

C₄²

C₂×C₄×D₇₉

yes

characteristic

200

C₄²

D₄×D₇₉

yes

characteristic

201

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

202

C₄²

#11929625

yes

characteristic

203

C₂³

—

316

—

204

C₂³

#14579136

yes

characteristic

205

Q₈

—

316

—

206

D₄

—

316

—

207

D₄

—

316

—

208

D₄

—

316

—

209

D₄

—

632

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

316

—

213

C₂×C₄

—

316

—

214

C₂×C₄

—

316

—

215

C₂×C₄

—

632

—

216

C₂×C₄

—

632

—

217

C₂×C₄

—

158

—

218

C₂×C₄

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

219

C₂×C₄

#14579123

yes

characteristic

220

C₂×C₄

#14579123

yes

characteristic

221

C₂×C₄

#14579136

yes

characteristic

222

C₂×C₄

#14579150

yes

characteristic

223

C₂×C₄

#14579157

yes

characteristic

224

C₂×C₄

#14579188

yes

—

225

C₈

—

226

C₈

—

227

C₈

—

158

—

228

C₈

#14579087

yes

complemented

229

C₂²

—

230

C₂²

—

231

C₂²

—

632

—

232

C₂²

—

632

—

233

C₂²

—

632

—

234

C₂²

#19098464

yes

characteristic

235

C₂²

#19098817

yes

—

236

C₄

—

237

C₄

—

238

C₄

—

316

—

239

C₄

—

632

—

240

C₄

C₂×#14579087

yes

—

241

C₄

#19098674

yes

—

242

C₄

#19098684

yes

—

243

C₄

#19098949

yes

—

244

C₂

—

245

C₂

—

1264

—

246

C₂

#23764227

yes

characteristic

247

C₂

#23764274

yes

characteristic

248

C₂

#23764291

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14579157
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1566	C₂
socle	C₂²×C₇₉	#390
prime radical	#23773979	C₂
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1566	D₇₉
hypocenter	C₇₉	#9849
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1566

subgroup

G/H

center

C₂×C₄

#14579157

commutator

C₄²×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1566

C₂

C₂²×C₇₉

C₂

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1566

N	H ≅ G/N	type
2. #23764227	C₂	semidirect
3. C₄×#14579071	C₂	semidirect
4. #23761850	C₂	semidirect
5. C₇₉×#1566	C₂	semidirect
7. #19098968	C₄	semidirect
8. #19098940	C₄	semidirect
9. #19098910	C₄	semidirect
102. C₈×C₇₉	#104	semidirect
128. #1566	D₇₉	semidirect
130. C₇₉	#9849	semidirect
228. C₈	#14579087	semidirect

H ≅ G/N

type

2. #23764227

C₂

semidirect

3. C₄×#14579071

C₂

semidirect

4. #23761850

C₂

semidirect

5. C₇₉×#1566

C₂

semidirect

7. #19098968

C₄

semidirect

8. #19098940

C₄

semidirect

9. #19098910

C₄

semidirect

102. C₈×C₇₉

#104

semidirect

128. #1566

D₇₉

semidirect

130. C₇₉

#9849

semidirect

228. C₈

#14579087

semidirect

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

subgroup	index
#23773979	2
#23764227	2
C₄×#14579071	2
#23761850	2
C₇₉×#1566	2
#9849	79

subgroup

index

C₇₉×#1566

Subgroups — #34188172

Conjugacy classes of subgroups

Complements

Maximal subgroups