Group #31914013 — subgroups

Subgroups — #31914013

Order 18176.

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

normal subgroups only

This group has 414 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	C₂×#17986037	C₂	1	1	yes	maximal, characteristic
2	C₂×#17985823	C₂	1	2	yes	maximal, complemented
3	#22589951	C₂	1	1	yes	maximal, characteristic
4	#22586440	C₂	1	2	yes	maximal, complemented
5	C₇₁×#1810	C₂	1	1	yes	maximal, characteristic
6	C₂×#14556087	—	2	1	no	—
7	C₂×#14556068	C₂²	1	2	yes	—
8	#17986037	—	2	4	no	—
9	C₂×#14556062	—	2	1	no	—
10	C₂×#14556060	C₂²	1	2	yes	—
11	#17985823	—	2	4	no	—
12	C₂²⋊(C₇₁⋊C₁₆)	C₄	1	4	yes	complemented
13	C₂³×C₈×C₇₁	C₂²	1	1	yes	characteristic
14	C₂×#108×C₇₁	C₂²	1	1	yes	characteristic
15	C₂×#108×C₇₁	C₂²	1	1	yes	characteristic
16	#407×C₇₁	—	2	1	no	—
17	#341×C₇₁	—	2	1	no	—
18	#14556087	—	2	4	no	—
19	#14556087	—	4	2	no	—
20	C₂×C₄⋊Dic₇₁	—	2	2	no	—
21	C₂×C₂²⋊Dic₇₁	—	4	1	no	—
22	C₂×C₄×Dic₇₁	—	4	1	no	—
23	#14556068	—	2	2	no	—
24	#14556068	—	2	2	no	—
25	C₂×C₇₁⋊C₁₆	C₂×C₄	1	4	yes	—
26	#14556062	—	2	4	no	—
27	#14556060	—	2	2	no	—
28	#14556060	D₄	1	4	yes	—
29	C₂³×C₄×C₇₁	D₄	1	1	yes	characteristic
30	C₂×M₁₆×C₇₁	—	2	1	no	—
31	C₂×M₁₆×C₇₁	—	2	1	no	—
32	C₂²×C₈×C₇₁	—	2	2	no	—
33	C₂²×C₈×C₇₁	—	2	2	no	—
34	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
35	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₇₁	Q₈	1	2	yes	—
37	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
38	#108×C₇₁	—	2	2	no	—
39	#108×C₇₁	—	2	2	no	—
40	C₂²⋊C₈×C₇₁	—	4	2	no	—
41	C₂²×Dic₇₁	—	4	2	no	—
42	C₄⋊Dic₇₁	—	2	4	no	—
43	C₄⋊Dic₇₁	—	4	2	no	—
44	C₂²⋊Dic₇₁	—	4	4	no	—
45	C₄×Dic₇₁	—	4	4	no	—
46	C₇₁⋊C₁₆	—	2	4	no	—
47	C₂⁴×C₇₁	SD₁₆	1	1	yes	characteristic
48	C₂²×C₄×C₇₁	—	2	1	no	—
49	C₂²×C₄×C₇₁	—	2	1	no	—
50	C₂²×C₄×C₇₁	—	2	1	no	—
51	C₂²×C₄×C₇₁	—	2	1	no	—
52	C₂²×C₄×C₇₁	C₄⋊C₄	1	2	yes	—
53	C₂²×C₄×C₇₁	SD₁₆	1	1	yes	characteristic
54	C₂²×C₄×C₇₁	SD₁₆	1	2	yes	—
55	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
56	M₁₆×C₇₁	—	4	1	no	—
57	M₁₆×C₇₁	—	4	1	no	—
58	M₁₆×C₇₁	—	4	1	no	—
59	M₁₆×C₇₁	—	4	1	no	—
60	C₂×C₈×C₇₁	—	2	1	no	—
61	C₂×C₈×C₇₁	—	2	1	no	—
62	C₂×C₈×C₇₁	—	2	4	no	—
63	C₂×C₈×C₇₁	—	2	4	no	—
64	C₂×C₈×C₇₁	—	4	1	no	—
65	C₂×C₈×C₇₁	—	4	1	no	—
66	C₂×C₈×C₇₁	C₄⋊C₄	1	2	yes	—
67	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
69	C₂×C₈×C₇₁	C₂×Q₈	1	1	yes	characteristic
70	C₂×C₈×C₇₁	#41	1	2	yes	—
71	C₂³×C₇₁	—	2	1	no	—
72	C₂³×C₇₁	—	2	1	no	—
73	C₂³×C₇₁	—	4	2	no	—
74	C₂³×C₇₁	#106	1	2	yes	—
75	C₂³×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
76	C₂×C₄×C₇₁	—	2	1	no	—
77	C₂×C₄×C₇₁	—	2	1	no	—
78	C₂×C₄×C₇₁	—	2	2	no	—
79	C₂×C₄×C₇₁	—	2	2	no	—
80	C₂×C₄×C₇₁	—	2	2	no	—
81	C₂×C₄×C₇₁	—	2	2	no	—
82	C₂×C₄×C₇₁	#106	1	2	yes	—
83	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₇₁	#120	1	1	yes	characteristic
85	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
86	C₂×C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
87	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
88	C₂×C₄×C₇₁	#137	1	1	yes	characteristic
89	C₂×Dic₇₁	—	4	4	no	—
90	C₂×Dic₇₁	—	8	4	no	—
91	C₈×C₇₁	—	2	2	no	—
92	C₈×C₇₁	—	8	1	no	—
93	C₈×C₇₁	—	8	1	no	—
94	C₈×C₇₁	C₄×D₄	1	2	yes	—
95	C₈×C₇₁	C₂²⋊Q₈	1	2	yes	—
96	C₂²×C₇₁	—	2	2	no	—
97	C₂²×C₇₁	—	2	2	no	—
98	C₂²×C₇₁	—	2	4	no	—
99	C₂²×C₇₁	—	4	2	no	—
100	C₂²×C₇₁	—	4	2	no	—
101	C₂²×C₇₁	C₂×#106	1	1	yes	characteristic
102	C₂²×C₇₁	#450	1	1	yes	characteristic
103	C₂²×C₇₁	#483	1	1	yes	characteristic
104	C₄×C₇₁	—	2	2	no	—
105	C₄×C₇₁	#385	1	1	yes	characteristic
106	C₄×C₇₁	#428	1	1	yes	characteristic
107	C₄×C₇₁	#448	1	1	yes	characteristic
108	C₄×C₇₁	#481	1	1	yes	characteristic
109	Dic₇₁	—	8	4	no	—
110	#12930	—	71	1	no	maximal, Sylow
111	C₂×C₇₁	—	2	1	no	—
112	C₂×C₇₁	—	2	1	no	—
113	C₂×C₇₁	—	4	2	no	—
114	C₂×C₇₁	#1853	1	1	yes	characteristic
115	C₂×C₇₁	#2155	1	2	yes	—
116	C₂×#427	—	71	1	no	—
117	C₂×#365	—	71	2	no	—
118	#2112	—	71	1	no	—
119	#1810	D₇₁	1	1	yes	characteristic
120	#1383	—	71	2	no	—
121	C₇₁	#12930	1	1	yes	characteristic, complemented, Sylow
122	C₂³×C₈	C₂×D₇₁	1	1	yes	characteristic
123	C₂×#117	—	142	1	no	—
124	C₂×M₃₂	—	71	2	no	—
125	C₂×#108	C₂×D₇₁	1	1	yes	characteristic
126	C₂×#108	C₂×D₇₁	1	1	yes	characteristic
127	#427	—	142	4	no	—
128	C₂×#107	—	142	1	no	—
129	C₂×#106	—	71	2	no	—
130	#407	—	2	1	no	—
131	#365	—	142	4	no	—
132	C₂²⋊C₁₆	—	71	4	no	—
133	#341	—	2	1	no	—
134	C₂³×C₄	C₂²⋊D₇₁	1	1	yes	characteristic
135	C₂×M₁₆	—	2	1	no	—
136	C₂×M₁₆	—	2	1	no	—
137	C₂²×C₈	—	2	2	no	—
138	C₂²×C₈	—	2	2	no	—
139	C₂²×C₈	Dic₁₄₂	1	2	yes	—
140	C₂²×C₈	C₄×D₇₁	1	2	yes	—
141	C₂²×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
142	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
143	#117	—	284	2	no	—
144	#117	—	142	4	no	—
145	C₂×C₄⋊C₄	—	142	2	no	—
146	C₂×C₂²⋊C₄	—	284	1	no	—
147	C₂×C₄²	—	284	1	no	—
148	M₃₂	—	142	2	no	—
149	M₃₂	—	142	2	no	—
150	C₂×C₁₆	—	71	4	no	—
151	#108	—	2	2	no	—
152	#108	—	2	2	no	—
153	#107	—	142	4	no	—
154	#106	—	71	4	no	—
155	#106	—	142	2	no	—
156	C₂²⋊C₈	—	4	2	no	—
157	C₂⁴	#11765852	1	1	yes	characteristic
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	2	1	no	—
160	C₂²×C₄	—	2	1	no	—
161	C₂²×C₄	—	2	1	no	—
162	C₂²×C₄	—	284	2	no	—
163	C₂²×C₄	Dic₇₁⋊C₄	1	2	yes	—
164	C₂²×C₄	#11765852	1	1	yes	characteristic
165	C₂²×C₄	#11765853	1	2	yes	—
166	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
167	M₁₆	—	4	1	no	—
168	M₁₆	—	4	1	no	—
169	M₁₆	—	4	1	no	—
170	M₁₆	—	4	1	no	—
171	C₂×C₈	—	2	1	no	—
172	C₂×C₈	—	2	1	no	—
173	C₂×C₈	—	2	4	no	—
174	C₂×C₈	—	2	4	no	—
175	C₂×C₈	—	4	1	no	—
176	C₂×C₈	—	4	1	no	—
177	C₂×C₈	Dic₇₁⋊C₄	1	2	yes	—
178	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
179	C₂×C₈	D₄×D₇₁	1	2	yes	—
180	C₂×C₈	C₂×Dic₁₄₂	1	1	yes	characteristic
181	C₂×C₈	#11765864	1	2	yes	—
182	C₄⋊C₄	—	284	2	no	—
183	C₄⋊C₄	—	142	4	no	—
184	C₂²⋊C₄	—	284	4	no	—
185	C₄²	—	284	4	no	—
186	C₁₆	—	142	4	no	—
187	C₂³	—	2	1	no	—
188	C₂³	—	2	1	no	—
189	C₂³	—	4	2	no	—
190	C₂³	#14556059	1	2	yes	—
191	C₂³	C₂×#11765852	1	1	yes	characteristic
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	284	4	no	—
199	C₂×C₄	—	568	4	no	—
200	C₂×C₄	#14556059	1	2	yes	—
201	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
202	C₂×C₄	#14556096	1	1	yes	characteristic
203	C₂×C₄	#14556109	1	1	yes	characteristic
204	C₂×C₄	C₂×#11765853	1	1	yes	characteristic
205	C₂×C₄	#14556153	1	1	yes	characteristic
206	C₂×C₄	#14556158	1	1	yes	characteristic
207	C₈	—	2	2	no	—
208	C₈	—	8	1	no	—
209	C₈	—	8	1	no	—
210	C₈	(C₂²⋊D₇₁)⋊C₄	1	2	yes	—
211	C₈	#14556105	1	2	yes	—
212	C₂²	—	2	2	no	—
213	C₂²	—	2	2	no	—
214	C₂²	—	2	4	no	—
215	C₂²	—	4	2	no	—
216	C₂²	—	4	2	no	—
217	C₂²	C₂×#14556059	1	1	yes	characteristic
218	C₂²	#17986149	1	1	yes	characteristic
219	C₂²	#17986327	1	1	yes	characteristic
220	C₄	—	2	2	no	—
221	C₄	—	568	4	no	—
222	C₄	#17985871	1	1	yes	characteristic
223	C₄	#17986042	1	1	yes	characteristic
224	C₄	#17986137	1	1	yes	characteristic
225	C₄	#17986315	1	1	yes	characteristic
226	C₂	—	2	1	no	—
227	C₂	—	2	1	no	—
228	C₂	—	4	2	no	—
229	C₂	#22588532	1	1	yes	characteristic
230	C₂	#22590114	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17986037

C₂

yes

maximal, characteristic

C₂×#17985823

C₂

yes

maximal, complemented

#22589951

C₂

yes

maximal, characteristic

#22586440

C₂

yes

maximal, complemented

C₇₁×#1810

C₂

yes

maximal, characteristic

C₂×#14556087

—

C₂×#14556068

C₂²

yes

—

#17986037

—

C₂×#14556062

—

C₂×#14556060

C₂²

yes

—

#17985823

—

C₂²⋊(C₇₁⋊C₁₆)

C₄

yes

complemented

C₂³×C₈×C₇₁

C₂²

yes

characteristic

C₂×#108×C₇₁

C₂²

yes

characteristic

C₂×#108×C₇₁

C₂²

yes

characteristic

#407×C₇₁

—

#341×C₇₁

—

#14556087

—

#14556087

—

C₂×C₄⋊Dic₇₁

—

C₂×C₂²⋊Dic₇₁

—

C₂×C₄×Dic₇₁

—

#14556068

—

#14556068

—

C₂×C₇₁⋊C₁₆

C₂×C₄

yes

—

#14556062

—

#14556060

—

#14556060

D₄

yes

—

C₂³×C₄×C₇₁

D₄

yes

characteristic

C₂×M₁₆×C₇₁

—

C₂×M₁₆×C₇₁

—

C₂²×C₈×C₇₁

—

C₂²×C₈×C₇₁

—

C₂²×C₈×C₇₁

C₂×C₄

yes

—

C₂²×C₈×C₇₁

D₄

yes

characteristic

C₂²×C₈×C₇₁

Q₈

yes

—

C₂²×C₈×C₇₁

C₂³

yes

characteristic

#108×C₇₁

—

#108×C₇₁

—

C₂²⋊C₈×C₇₁

—

C₂²×Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₂²⋊Dic₇₁

—

C₄×Dic₇₁

—

C₇₁⋊C₁₆

—

C₂⁴×C₇₁

SD₁₆

yes

characteristic

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

C₄⋊C₄

yes

—

C₂²×C₄×C₇₁

SD₁₆

yes

characteristic

C₂²×C₄×C₇₁

SD₁₆

yes

—

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

M₁₆×C₇₁

—

M₁₆×C₇₁

—

M₁₆×C₇₁

—

M₁₆×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

C₄⋊C₄

yes

—

C₂×C₈×C₇₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

—

C₂×C₈×C₇₁

C₂×Q₈

yes

characteristic

C₂×C₈×C₇₁

#41

yes

—

C₂³×C₇₁

—

C₂³×C₇₁

—

C₂³×C₇₁

—

C₂³×C₇₁

#106

yes

—

C₂³×C₇₁

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

#106

yes

—

C₂×C₄×C₇₁

C₂×C₄⋊C₄

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

C₂×SD₁₆

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

C₄×D₄

yes

—

C₈×C₇₁

C₂²⋊Q₈

yes

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

—

100

C₂²×C₇₁

—

101

C₂²×C₇₁

C₂×#106

yes

characteristic

102

C₂²×C₇₁

#450

yes

characteristic

103

C₂²×C₇₁

#483

yes

characteristic

104

C₄×C₇₁

—

105

C₄×C₇₁

#385

yes

characteristic

106

C₄×C₇₁

#428

yes

characteristic

107

C₄×C₇₁

#448

yes

characteristic

108

C₄×C₇₁

#481

yes

characteristic

109

Dic₇₁

—

110

#12930

—

maximal, Sylow

111

C₂×C₇₁

—

112

C₂×C₇₁

—

113

C₂×C₇₁

—

114

C₂×C₇₁

#1853

yes

characteristic

115

C₂×C₇₁

#2155

yes

—

116

C₂×#427

—

117

C₂×#365

—

118

#2112

—

119

#1810

D₇₁

yes

characteristic

120

#1383

—

121

C₇₁

#12930

yes

characteristic, complemented, Sylow

122

C₂³×C₈

C₂×D₇₁

yes

characteristic

123

C₂×#117

—

142

—

124

C₂×M₃₂

—

125

C₂×#108

C₂×D₇₁

yes

characteristic

126

C₂×#108

C₂×D₇₁

yes

characteristic

127

#427

—

142

—

128

C₂×#107

—

142

—

129

C₂×#106

—

130

#407

—

131

#365

—

142

—

132

C₂²⋊C₁₆

—

133

#341

—

134

C₂³×C₄

C₂²⋊D₇₁

yes

characteristic

135

C₂×M₁₆

—

136

C₂×M₁₆

—

137

C₂²×C₈

—

138

C₂²×C₈

—

139

C₂²×C₈

Dic₁₄₂

yes

—

140

C₂²×C₈

C₄×D₇₁

yes

—

141

C₂²×C₈

C₂²⋊D₇₁

yes

characteristic

142

C₂²×C₈

C₂²×D₇₁

yes

characteristic

143

#117

—

284

—

144

#117

—

142

—

145

C₂×C₄⋊C₄

—

142

—

146

C₂×C₂²⋊C₄

—

284

—

147

C₂×C₄²

—

284

—

148

M₃₂

—

142

—

149

M₃₂

—

142

—

150

C₂×C₁₆

—

151

#108

—

152

#108

—

153

#107

—

142

—

154

#106

—

155

#106

—

142

—

156

C₂²⋊C₈

—

157

C₂⁴

#11765852

yes

characteristic

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

284

—

163

C₂²×C₄

Dic₇₁⋊C₄

yes

—

164

C₂²×C₄

#11765852

yes

characteristic

165

C₂²×C₄

#11765853

yes

—

166

C₂²×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

167

M₁₆

—

168

M₁₆

—

169

M₁₆

—

170

M₁₆

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

Dic₇₁⋊C₄

yes

—

178

C₂×C₈

C₂×C₄×D₇₁

yes

characteristic

179

C₂×C₈

D₄×D₇₁

yes

—

180

C₂×C₈

C₂×Dic₁₄₂

yes

characteristic

181

C₂×C₈

#11765864

yes

—

182

C₄⋊C₄

—

284

—

183

C₄⋊C₄

—

142

—

184

C₂²⋊C₄

—

284

—

185

C₄²

—

284

—

186

C₁₆

—

142

—

187

C₂³

—

188

C₂³

—

189

C₂³

—

190

C₂³

#14556059

yes

—

191

C₂³

C₂×#11765852

yes

characteristic

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

284

—

199

C₂×C₄

—

568

—

200

C₂×C₄

#14556059

yes

—

201

C₂×C₄

C₂×Dic₇₁⋊C₄

yes

characteristic

202

C₂×C₄

#14556096

yes

characteristic

203

C₂×C₄

#14556109

yes

characteristic

204

C₂×C₄

C₂×#11765853

yes

characteristic

205

C₂×C₄

#14556153

yes

characteristic

206

C₂×C₄

#14556158

yes

characteristic

207

C₈

—

208

C₈

—

209

C₈

—

210

C₈

(C₂²⋊D₇₁)⋊C₄

yes

—

211

C₈

#14556105

yes

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

C₂×#14556059

yes

characteristic

218

C₂²

#17986149

yes

characteristic

219

C₂²

#17986327

yes

characteristic

220

C₄

—

221

C₄

—

568

—

222

C₄

#17985871

yes

characteristic

223

C₄

#17986042

yes

characteristic

224

C₄

#17986137

yes

characteristic

225

C₄

#17986315

yes

characteristic

226

C₂

—

227

C₂

—

228

C₂

—

229

C₂

#22588532

yes

characteristic

230

C₂

#22590114

yes

—

	subgroup	G/H
center	C₂²	C₂×#14556059
commutator	C₂×C₈×C₇₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₁
Fitting	C₇₁×#1810	C₂
socle	C₂²×C₇₁	C₂×#106
prime radical	C₂⁴×C₇₁	SD₁₆
cosocle	C₂²×C₈×C₇₁	C₂³
hypercenter	#1810	D₇₁
hypocenter	C₇₁	#12930
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1810

subgroup

G/H

center

C₂²

C₂×#14556059

commutator

C₂×C₈×C₇₁

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₁

Fitting

C₇₁×#1810

C₂

socle

C₂²×C₇₁

C₂×#106

prime radical

C₂⁴×C₇₁

SD₁₆

cosocle

C₂²×C₈×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1810

N	H ≅ G/N	type
2. C₂×#17985823	C₂	semidirect
4. #22586440	C₂	semidirect
12. C₂²⋊(C₇₁⋊C₁₆)	C₄	semidirect
121. C₇₁	#12930	semidirect

H ≅ G/N

type

2. C₂×#17985823

C₂

semidirect

4. #22586440

C₂

semidirect

12. C₂²⋊(C₇₁⋊C₁₆)

C₄

semidirect

121. C₇₁

#12930

semidirect

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

subgroup	index
C₂×#17986037	2
C₂×#17985823	2
#22589951	2
#22586440	2
C₇₁×#1810	2
#12930	71

subgroup

index

C₇₁×#1810

Subgroups — #31914013

Conjugacy classes of subgroups

Complements

Maximal subgroups