Group #31891493 — subgroups

Subgroups — #31891493

Order 18176.

348 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 103 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	#22597425	C₂	1	1	yes	maximal, characteristic
2	#22587123	C₂	1	2	yes	maximal
3	#22586664	C₂	1	1	yes	maximal, characteristic
4	#22586239	C₂	1	2	yes	maximal
5	C₇₁×#1985	C₂	1	1	yes	maximal, characteristic
6	#17986130	—	2	2	no	—
7	#17986130	—	2	2	no	—
8	#17986056	—	2	1	no	—
9	#17986056	C₂²	1	2	yes	—
10	#17986052	—	2	1	no	—
11	#17986052	C₂²	1	2	yes	—
12	#17985751	—	2	2	no	—
13	#17985749	—	2	2	no	—
14	#17985725	C₄	1	2	yes	—
15	#17985725	C₄	1	2	yes	—
16	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
18	C₂×#97×C₇₁	C₂²	1	1	yes	characteristic
19	#336×C₇₁	—	2	1	no	—
20	#336×C₇₁	—	2	1	no	—
21	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
22	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
23	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
24	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
25	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
26	C₄⋊(C₇₁⋊C₈)	D₄	1	2	yes	—
27	C₄⋊(C₇₁⋊C₈)	D₄	1	2	yes	—
28	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
29	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	4	yes	—
30	#14556039	—	2	2	no	—
31	#14556039	—	2	2	no	—
32	C₄×C₇₁⋊C₈	—	2	2	no	—
33	C₄×C₇₁⋊C₈	—	2	2	no	—
34	C₂²×Q₈×C₇₁	Q₈	1	1	yes	characteristic
35	C₂²×C₈×C₇₁	—	2	1	no	—
36	C₂²×C₈×C₇₁	—	2	1	no	—
37	C₄×Q₈×C₇₁	—	2	2	no	—
38	C₄×Q₈×C₇₁	—	2	2	no	—
39	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₇₁	Q₈	1	1	yes	characteristic
42	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
45	C₄⋊C₈×C₇₁	—	2	2	no	—
46	#97×C₇₁	—	2	2	no	—
47	C₂×C₇₁⋊C₈	—	2	4	no	—
48	C₂×C₇₁⋊C₈	—	2	2	no	—
49	C₂×C₇₁⋊C₈	—	2	2	no	—
50	C₂×Q₈×C₇₁	—	2	2	no	—
51	C₂×Q₈×C₇₁	—	2	2	no	—
52	C₂×Q₈×C₇₁	—	4	1	no	—
53	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
55	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
60	C₂×C₈×C₇₁	—	2	2	no	—
61	C₂×C₈×C₇₁	—	4	1	no	—
62	C₂×C₈×C₇₁	—	4	1	no	—
63	C₂×C₈×C₇₁	—	4	2	no	—
64	C₂×C₈×C₇₁	—	4	1	no	—
65	C₄⋊C₄×C₇₁	—	2	2	no	—
66	C₄⋊C₄×C₇₁	—	2	2	no	—
67	C₄⋊C₄×C₇₁	—	2	2	no	—
68	C₄²×C₇₁	—	2	1	no	—
69	C₄²×C₇₁	—	2	1	no	—
70	C₄²×C₇₁	—	2	1	no	—
71	C₄²×C₇₁	—	2	1	no	—
72	C₄²×C₇₁	C₂×D₄	1	2	yes	—
73	C₄²×C₇₁	#41	1	2	yes	—
74	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
75	Q₈×C₇₁	—	4	4	no	—
76	C₂×C₄×C₇₁	—	2	1	no	—
77	C₂×C₄×C₇₁	—	2	1	no	—
78	C₂×C₄×C₇₁	—	2	1	no	—
79	C₂×C₄×C₇₁	—	2	1	no	—
80	C₂×C₄×C₇₁	—	2	1	no	—
81	C₂×C₄×C₇₁	—	2	1	no	—
82	C₂×C₄×C₇₁	—	2	1	no	—
83	C₂×C₄×C₇₁	—	2	1	no	—
84	C₂×C₄×C₇₁	—	2	1	no	—
85	C₂×C₄×C₇₁	—	2	1	no	—
86	C₂×C₄×C₇₁	—	2	1	no	—
87	C₂×C₄×C₇₁	—	4	1	no	—
88	C₂×C₄×C₇₁	—	4	1	no	—
89	C₂×C₄×C₇₁	—	4	1	no	—
90	C₂×C₄×C₇₁	#108	1	2	yes	—
91	C₂×C₄×C₇₁	C₄×D₄	1	2	yes	—
92	C₂×C₄×C₇₁	#120	1	1	yes	characteristic
93	C₂×C₄×C₇₁	C₂²⋊Q₈	1	2	yes	—
94	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
95	C₈×C₇₁	—	4	2	no	—
96	C₈×C₇₁	—	8	1	no	—
97	C₇₁⋊C₈	—	4	4	no	—
98	C₇₁⋊C₈	—	4	2	no	—
99	C₇₁⋊C₈	—	4	2	no	—
100	C₂²×C₇₁	—	2	1	no	—
101	C₂²×C₇₁	—	2	1	no	—
102	C₂²×C₇₁	#385	1	1	yes	characteristic
103	C₂²×C₇₁	C₂×#108	1	1	yes	characteristic
104	C₂²×C₇₁	#430	1	1	yes	characteristic
105	C₄×C₇₁	—	2	2	no	—
106	C₄×C₇₁	—	2	2	no	—
107	C₄×C₇₁	—	2	1	no	—
108	C₄×C₇₁	—	2	2	no	—
109	C₄×C₇₁	—	4	1	no	—
110	C₄×C₇₁	—	4	1	no	—
111	C₄×C₇₁	—	4	1	no	—
112	C₄×C₇₁	#454	1	1	yes	characteristic
113	C₄×C₇₁	#456	1	1	yes	characteristic
114	#8865	—	71	1	no	maximal, Sylow
115	C₂×C₇₁	—	2	1	no	—
116	C₂×C₇₁	—	2	1	no	—
117	C₂×C₇₁	#1855	1	1	yes	characteristic
118	C₂×C₇₁	#1857	1	1	yes	characteristic
119	C₂×C₇₁	#1868	1	1	yes	characteristic
120	#2983	—	71	1	no	—
121	#1985	D₇₁	1	1	yes	characteristic
122	#1573	—	71	2	no	—
123	#1461	—	71	1	no	—
124	#1302	—	71	2	no	—
125	C₇₁	#8865	1	1	yes	characteristic, complemented, Sylow
126	C₂×C₄×Q₈	C₂×D₇₁	1	1	yes	characteristic
127	#446	—	142	2	no	—
128	#446	—	142	2	no	—
129	#432	—	71	2	no	—
130	#432	—	142	1	no	—
131	#431	—	71	2	no	—
132	#431	—	142	1	no	—
133	C₂×C₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
134	C₂×#97	C₂×D₇₁	1	1	yes	characteristic
135	#336	—	2	1	no	—
136	#336	—	2	1	no	—
137	#335	—	142	2	no	—
138	#334	—	142	2	no	—
139	#324	—	71	2	no	—
140	#324	—	71	2	no	—
141	C₂²×Q₈	Dic₁₄₂	1	1	yes	characteristic
142	C₂²×C₈	—	2	1	no	—
143	C₂²×C₈	—	2	1	no	—
144	C₄×Q₈	—	2	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₂×C₄⋊C₄	Dic₁₄₂	1	1	yes	characteristic
147	C₂×C₄⋊C₄	C₄×D₇₁	1	1	yes	characteristic
148	C₂×C₄⋊C₄	C₄×D₇₁	1	1	yes	characteristic
149	C₂×C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
150	C₂×C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
151	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
152	C₄⋊C₈	—	2	2	no	—
153	C₄⋊C₈	—	71	2	no	—
154	C₄⋊C₈	—	71	2	no	—
155	C₄⋊C₈	—	142	1	no	—
156	C₄⋊C₈	—	142	1	no	—
157	C₄⋊C₈	—	142	1	no	—
158	C₄⋊C₈	—	142	1	no	—
159	C₄⋊C₈	—	142	2	no	—
160	C₂²⋊C₈	—	71	4	no	—
161	C₂²⋊C₈	—	142	2	no	—
162	#97	—	2	2	no	—
163	#97	—	142	2	no	—
164	#97	—	142	2	no	—
165	C₄×C₈	—	142	2	no	—
166	C₄×C₈	—	142	2	no	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	2	no	—
169	C₂×Q₈	—	4	1	no	—
170	C₂²×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
171	C₂²×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
172	C₂²×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
173	C₂²×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
174	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
175	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
176	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
177	C₂×C₈	—	2	2	no	—
178	C₂×C₈	—	4	1	no	—
179	C₂×C₈	—	4	1	no	—
180	C₂×C₈	—	4	2	no	—
181	C₂×C₈	—	4	1	no	—
182	C₂×C₈	—	142	4	no	—
183	C₂×C₈	—	142	2	no	—
184	C₂×C₈	—	142	2	no	—
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	—	2	2	no	—
187	C₄⋊C₄	—	2	2	no	—
188	C₄²	—	2	1	no	—
189	C₄²	—	2	1	no	—
190	C₄²	—	2	1	no	—
191	C₄²	—	2	1	no	—
192	C₄²	D₄×D₇₁	1	2	yes	—
193	C₄²	#11765864	1	2	yes	—
194	C₂³	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
195	Q₈	—	4	4	no	—
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	1	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	#14556063	1	2	yes	—
211	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	2	yes	—
212	C₂×C₄	#14556096	1	1	yes	characteristic
213	C₂×C₄	#14556105	1	2	yes	—
214	C₂×C₄	#14556109	1	1	yes	characteristic
215	C₈	—	4	2	no	—
216	C₈	—	8	1	no	—
217	C₈	—	284	4	no	—
218	C₈	—	284	2	no	—
219	C₈	—	284	2	no	—
220	C₂²	—	2	1	no	—
221	C₂²	—	2	1	no	—
222	C₂²	#17985871	1	1	yes	characteristic
223	C₂²	C₂×#14556063	1	1	yes	characteristic
224	C₂²	#17986047	1	1	yes	characteristic
225	C₄	—	2	2	no	—
226	C₄	—	2	2	no	—
227	C₄	—	2	1	no	—
228	C₄	—	2	2	no	—
229	C₄	—	4	1	no	—
230	C₄	—	4	1	no	—
231	C₄	—	4	1	no	—
232	C₄	#17986171	1	1	yes	characteristic
233	C₄	#17986181	1	1	yes	characteristic
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	#22588544	1	1	yes	characteristic
237	C₂	#22588554	1	1	yes	characteristic
238	C₂	#22588625	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22597425

C₂

yes

maximal, characteristic

#22587123

C₂

yes

maximal

#22586664

C₂

yes

maximal, characteristic

#22586239

C₂

yes

maximal

C₇₁×#1985

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

—

#17986052

—

#17986052

C₂²

yes

—

#17985751

—

#17985749

—

#17985725

C₄

yes

—

#17985725

C₄

yes

—

C₂×C₄×Q₈×C₇₁

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₇₁

C₂²

yes

characteristic

C₂×#97×C₇₁

C₂²

yes

characteristic

#336×C₇₁

—

#336×C₇₁

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

D₄

yes

—

C₄⋊(C₇₁⋊C₈)

D₄

yes

—

C₂²⋊(C₇₁⋊C₈)

—

C₂²⋊(C₇₁⋊C₈)

C₂×C₄

yes

—

#14556039

—

#14556039

—

C₄×C₇₁⋊C₈

—

C₄×C₇₁⋊C₈

—

C₂²×Q₈×C₇₁

Q₈

yes

characteristic

C₂²×C₈×C₇₁

—

C₂²×C₈×C₇₁

—

C₄×Q₈×C₇₁

—

C₄×Q₈×C₇₁

—

C₂×C₄⋊C₄×C₇₁

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₇₁

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₇₁

Q₈

yes

characteristic

C₂×C₄²×C₇₁

D₄

yes

characteristic

C₂×C₄²×C₇₁

D₄

yes

characteristic

C₂×C₄²×C₇₁

C₂³

yes

characteristic

C₄⋊C₈×C₇₁

—

#97×C₇₁

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂²×C₄×C₇₁

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₇₁

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₇₁

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₇₁

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₇₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₁

C₂×Q₈

yes

characteristic

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

C₂×D₄

yes

—

C₄²×C₇₁

#41

yes

—

C₂³×C₇₁

C₂×C₄⋊C₄

yes

characteristic

Q₈×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

#108

yes

—

C₂×C₄×C₇₁

C₄×D₄

yes

—

C₂×C₄×C₇₁

#120

yes

characteristic

C₂×C₄×C₇₁

C₂²⋊Q₈

yes

—

C₂×C₄×C₇₁

#123

yes

characteristic

C₈×C₇₁

—

C₈×C₇₁

—

C₇₁⋊C₈

—

C₇₁⋊C₈

—

C₇₁⋊C₈

—

100

C₂²×C₇₁

—

101

C₂²×C₇₁

—

102

C₂²×C₇₁

#385

yes

characteristic

103

C₂²×C₇₁

C₂×#108

yes

characteristic

104

C₂²×C₇₁

#430

yes

characteristic

105

C₄×C₇₁

—

106

C₄×C₇₁

—

107

C₄×C₇₁

—

108

C₄×C₇₁

—

109

C₄×C₇₁

—

110

C₄×C₇₁

—

111

C₄×C₇₁

—

112

C₄×C₇₁

#454

yes

characteristic

113

C₄×C₇₁

yes

114

—

115

C₂×C₇₁

—

116

C₂×C₇₁

—

117

C₂×C₇₁

#1855

yes

characteristic

118

C₂×C₇₁

#1857

yes

characteristic

119

C₂×C₇₁

#1868

yes

characteristic

120

#2983

—

121

#1985

D₇₁

yes

characteristic

122

#1573

—

123

#1461

—

124

#1302

—

125

C₇₁

#8865

yes

characteristic, complemented, Sylow

126

C₂×C₄×Q₈

C₂×D₇₁

yes

characteristic

127

#446

—

142

—

128

#446

—

142

—

129

#432

—

130

#432

—

142

—

131

#431

—

132

#431

—

142

—

133

C₂×C₄⋊C₈

C₂×D₇₁

yes

characteristic

134

C₂×#97

C₂×D₇₁

yes

characteristic

135

#336

—

136

#336

—

137

#335

—

142

—

138

#334

—

142

—

139

#324

—

140

#324

—

141

C₂²×Q₈

Dic₁₄₂

yes

characteristic

142

C₂²×C₈

—

143

C₂²×C₈

—

144

C₄×Q₈

—

145

C₄×Q₈

—

146

C₂×C₄⋊C₄

Dic₁₄₂

yes

characteristic

147

C₂×C₄⋊C₄

C₄×D₇₁

yes

characteristic

148

C₂×C₄⋊C₄

C₄×D₇₁

yes

characteristic

149

C₂×C₄²

C₂²⋊D₇₁

yes

characteristic

150

C₂×C₄²

C₂²⋊D₇₁

yes

characteristic

151

C₂×C₄²

C₂²×D₇₁

yes

characteristic

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

142

—

156

C₄⋊C₈

—

142

—

157

C₄⋊C₈

—

142

—

158

C₄⋊C₈

—

142

—

159

C₄⋊C₈

—

142

—

160

C₂²⋊C₈

—

161

C₂²⋊C₈

—

142

—

162

#97

—

163

#97

—

142

—

164

#97

—

142

—

165

C₄×C₈

—

142

—

166

C₄×C₈

—

142

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂²×C₄

Dic₇₁⋊C₄

yes

characteristic

171

C₂²×C₄

Dic₇₁⋊C₄

yes

characteristic

172

C₂²×C₄

Dic₇₁⋊C₄

yes

characteristic

173

C₂²×C₄

Dic₇₁⋊C₄

yes

characteristic

174

C₂²×C₄

C₂×C₄×D₇₁

yes

characteristic

175

C₂²×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

176

C₂²×C₄

C₂×Dic₁₄₂

yes

characteristic

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

142

—

183

C₂×C₈

—

142

—

184

C₂×C₈

—

142

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄²

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

D₄×D₇₁

yes

—

193

C₄²

#11765864

yes

—

194

C₂³

C₂×Dic₇₁⋊C₄

yes

characteristic

195

Q₈

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

#14556063

yes

—

211

C₂×C₄

(C₂²⋊D₇₁)⋊C₄

yes

—

212

C₂×C₄

#14556096

yes

characteristic

213

C₂×C₄

#14556105

yes

—

214

C₂×C₄

#14556109

yes

characteristic

215

C₈

—

216

C₈

—

217

C₈

—

284

—

218

C₈

—

284

—

219

C₈

—

284

—

220

C₂²

—

221

C₂²

—

222

C₂²

#17985871

yes

characteristic

223

C₂²

C₂×#14556063

yes

characteristic

224

C₂²

#17986047

yes

characteristic

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

#17986171

yes

characteristic

233

C₄

#17986181

yes

characteristic

234

C₂

—

235

C₂

—

236

C₂

#22588544

yes

characteristic

237

C₂

#22588554

yes

characteristic

238

C₂

#22588625

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14556096
commutator	C₂²×C₄×C₇₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₇₁×#1985	C₂
socle	C₂²×C₇₁	#385
prime radical	C₂³×C₇₁	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₇₁	C₂³
hypercenter	#1985	D₇₁
hypocenter	C₇₁	#8865
LCS	G ▷ C₂²×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1985

subgroup

G/H

center

C₂×C₄

#14556096

commutator

C₂²×C₄×C₇₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₇₁×#1985

C₂

socle

C₂²×C₇₁

#385

prime radical

C₂³×C₇₁

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂²×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1985

N	H ≅ G/N	type
125. C₇₁	#8865	semidirect

H ≅ G/N

type

125. C₇₁

#8865

semidirect

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

subgroup	index
#22597425	2
#22587123	2
#22586664	2
#22586239	2
C₇₁×#1985	2
#8865	71

subgroup

index

C₇₁×#1985

Subgroups — #31891493

Conjugacy classes of subgroups

Complements

Maximal subgroups