Group #31890688 — subgroups

Subgroups — #31890688

Order 18176.

350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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	#22597274	C₂	1	1	yes	maximal, characteristic
2	#22587088	C₂	1	1	yes	maximal, characteristic
3	#22586903	C₂	1	2	yes	maximal
4	#22586198	C₂	1	2	yes	maximal
5	C₇₁×#1835	C₂	1	1	yes	maximal, characteristic
6	#17986556	C₂²	1	1	yes	characteristic
7	#17986129	—	2	1	no	—
8	#17986129	C₄	1	2	yes	complemented
9	C₈×Dic₁₄₂	—	2	1	no	—
10	C₈×Dic₁₄₂	C₄	1	2	yes	complemented
11	#17986052	C₂²	1	2	yes	—
12	#17986025	—	2	1	no	—
13	#17986023	C₂²	1	1	yes	characteristic
14	#17985954	—	2	1	no	—
15	#17985752	—	2	1	no	—
16	#17985750	—	2	1	no	—
17	#17985735	—	2	4	no	—
18	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
19	#382×C₇₁	C₂²	1	2	yes	—
20	#340×C₇₁	—	2	1	no	—
21	#340×C₇₁	—	2	1	no	—
22	C₂×#11765849	—	2	1	no	—
23	#14556128	Q₈	1	1	yes	characteristic
24	#14556128	Q₈	1	1	yes	characteristic
25	#14556120	—	2	1	no	—
26	#14556107	—	2	1	no	—
27	#14556107	D₄	1	2	yes	—
28	C₄×Dic₁₄₂	—	2	1	no	—
29	C₄×Dic₁₄₂	C₂×C₄	1	2	yes	—
30	#14556087	—	2	1	no	—
31	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
32	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
33	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
34	Dic₇₁⋊C₈	—	2	2	no	—
35	Dic₇₁⋊C₈	—	2	2	no	—
36	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
37	#14556038	—	2	2	no	—
38	C₄×C₇₁⋊C₈	—	2	2	no	—
39	C₈×Dic₇₁	—	2	2	no	—
40	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
43	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
44	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
47	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
48	#95×C₇₁	—	2	2	no	—
49	#95×C₇₁	—	2	2	no	—
50	C₂×Dic₁₄₂	—	2	1	no	—
51	C₂×Dic₁₄₂	C₄⋊C₄	1	2	yes	—
52	#11765849	—	4	2	no	—
53	C₂×C₇₁⋊C₈	—	2	2	no	—
54	C₂×C₇₁⋊C₈	—	4	2	no	—
55	C₄⋊Dic₇₁	—	2	1	no	—
56	C₄⋊Dic₇₁	—	2	1	no	—
57	C₄⋊Dic₇₁	—	2	1	no	—
58	C₄⋊Dic₇₁	C₄⋊C₄	1	2	yes	—
59	Dic₇₁⋊C₄	—	2	2	no	—
60	Dic₇₁⋊C₄	—	2	2	no	—
61	C₂²⋊Dic₇₁	—	2	2	no	—
62	C₄×Dic₇₁	—	2	2	no	—
63	C₂²×C₄×C₇₁	—	4	2	no	—
64	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
67	C₂×C₈×C₇₁	—	2	2	no	—
68	C₂×C₈×C₇₁	—	2	2	no	—
69	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₄⋊C₄×C₇₁	—	4	2	no	—
74	C₄⋊C₄×C₇₁	—	4	2	no	—
75	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
76	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₇₁	C₂×Q₈	1	1	yes	characteristic
78	C₄²×C₇₁	#41	1	1	yes	characteristic
79	C₂³×C₇₁	#121	1	1	yes	characteristic
80	C₂×C₄×C₇₁	—	4	1	no	—
81	C₂×C₄×C₇₁	—	4	1	no	—
82	C₂×C₄×C₇₁	—	8	2	no	—
83	C₂×C₄×C₇₁	—	8	2	no	—
84	C₂×C₄×C₇₁	—	8	2	no	—
85	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₇₁	#117	1	1	yes	characteristic
88	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
89	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
90	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
91	C₂×C₄×C₇₁	#135	1	2	yes	—
92	C₂×C₄×C₇₁	#137	1	2	yes	—
93	C₂×Dic₇₁	—	2	2	no	—
94	C₂×Dic₇₁	—	2	2	no	—
95	Dic₁₄₂	—	4	2	no	—
96	Dic₁₄₂	—	4	2	no	—
97	C₈×C₇₁	—	2	1	no	—
98	C₈×C₇₁	—	2	1	no	—
99	C₈×C₇₁	—	2	1	no	—
100	C₈×C₇₁	—	2	1	no	—
101	C₇₁⋊C₈	—	4	2	no	—
102	C₇₁⋊C₈	—	8	2	no	—
103	C₂²×C₇₁	—	2	1	no	—
104	C₂²×C₇₁	—	2	1	no	—
105	C₂²×C₇₁	#380	1	1	yes	characteristic
106	C₂²×C₇₁	#464	1	2	yes	—
107	C₄×C₇₁	—	2	1	no	—
108	C₄×C₇₁	—	2	1	no	—
109	C₄×C₇₁	—	2	1	no	—
110	C₄×C₇₁	—	2	1	no	—
111	C₄×C₇₁	—	16	2	no	—
112	C₄×C₇₁	#416	1	1	yes	characteristic
113	C₄×C₇₁	#419	1	1	yes	characteristic
114	C₄×C₇₁	#479	1	2	yes	—
115	Dic₇₁	—	4	2	no	—
116	Dic₇₁	—	4	2	no	—
117	#8681	—	71	1	no	maximal, Sylow
118	C₂×C₇₁	—	2	2	no	—
119	C₂×C₇₁	#1805	1	1	yes	characteristic
120	C₂×C₇₁	#1812	1	1	yes	characteristic
121	C₂×C₇₁	#1814	1	1	yes	characteristic
122	#2960	—	71	1	no	—
123	#1835	D₇₁	1	1	yes	characteristic
124	#1564	—	71	1	no	—
125	#1518	—	71	2	no	—
126	#1286	—	71	2	no	—
127	C₇₁	#8681	1	1	yes	characteristic, complemented, Sylow
128	#533	—	71	1	no	—
129	#446	—	71	2	no	—
130	#446	—	142	1	no	—
131	C₈×Q₈	—	71	2	no	—
132	C₈×Q₈	—	142	1	no	—
133	#431	—	71	2	no	—
134	#424	—	142	1	no	—
135	#423	—	71	1	no	—
136	#405	—	142	1	no	—
137	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
138	#382	C₂×D₇₁	1	2	yes	—
139	#340	—	2	1	no	—
140	#340	—	2	1	no	—
141	#335	—	142	1	no	—
142	#334	—	142	1	no	—
143	#328	—	142	4	no	—
144	C₂×M₁₆	—	142	1	no	—
145	C₂²×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
146	C₂²×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
147	C₄⋊Q₈	—	71	1	no	—
148	C₄⋊Q₈	—	71	1	no	—
149	#125	—	142	1	no	—
150	C₂²⋊Q₈	—	71	2	no	—
151	C₂²⋊Q₈	—	142	1	no	—
152	C₄×Q₈	—	71	2	no	—
153	C₄×Q₈	—	142	1	no	—
154	#117	—	142	1	no	—
155	C₂×C₄⋊C₄	—	2	2	no	—
156	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
157	C₄⋊C₈	—	71	2	no	—
158	C₄⋊C₈	—	142	2	no	—
159	C₄⋊C₈	—	142	2	no	—
160	C₄⋊C₈	—	142	2	no	—
161	C₄⋊C₈	—	142	1	no	—
162	C₂²⋊C₈	—	142	2	no	—
163	#97	—	142	2	no	—
164	C₄×C₈	—	142	2	no	—
165	C₄×C₈	—	142	2	no	—
166	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
167	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
168	C₄×C₈	D₂₈₄	1	1	yes	characteristic
169	C₄×C₈	D₂₈₄	1	1	yes	characteristic
170	#95	—	2	2	no	—
171	#95	—	2	2	no	—
172	C₂×Q₈	—	71	2	no	—
173	C₂×Q₈	—	142	1	no	—
174	C₂²×C₄	—	4	2	no	—
175	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
176	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
177	C₂²×C₄	#11765864	1	1	yes	characteristic
178	M₁₆	—	284	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	284	2	no	—
182	C₂×C₈	—	142	2	no	—
183	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
184	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
185	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
186	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄⋊C₄	—	71	2	no	—
190	C₄⋊C₄	—	142	2	no	—
191	C₄⋊C₄	—	142	2	no	—
192	C₄⋊C₄	—	142	1	no	—
193	C₄⋊C₄	—	142	1	no	—
194	C₄⋊C₄	—	142	1	no	—
195	C₂²⋊C₄	—	142	2	no	—
196	C₄²	—	142	2	no	—
197	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
198	C₄²	C₂×D₂₈₄	1	1	yes	characteristic
199	C₄²	Q₈×D₇₁	1	1	yes	characteristic
200	C₄²	#11765866	1	1	yes	characteristic
201	C₂³	#14556099	1	1	yes	characteristic
202	Q₈	—	284	2	no	—
203	Q₈	—	284	2	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	8	2	no	—
207	C₂×C₄	—	8	2	no	—
208	C₂×C₄	—	8	2	no	—
209	C₂×C₄	—	142	2	no	—
210	C₂×C₄	—	142	2	no	—
211	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
212	C₂×C₄	C₄⋊C₄×D₇₁	1	1	yes	characteristic
213	C₂×C₄	#14556086	1	1	yes	characteristic
214	C₂×C₄	#14556103	1	1	yes	characteristic
215	C₂×C₄	#14556104	1	1	yes	characteristic
216	C₂×C₄	#14556108	1	1	yes	characteristic
217	C₂×C₄	#14556148	1	2	yes	—
218	C₂×C₄	#14556158	1	2	yes	—
219	C₈	—	2	1	no	—
220	C₈	—	2	1	no	—
221	C₈	—	2	1	no	—
222	C₈	—	2	1	no	—
223	C₈	—	284	2	no	—
224	C₈	—	568	2	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	2	1	no	—
227	C₂²	#17985856	1	1	yes	characteristic
228	C₂²	#17986218	1	2	yes	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	16	2	no	—
234	C₄	—	284	2	no	—
235	C₄	—	284	2	no	—
236	C₄	#17985993	1	1	yes	characteristic
237	C₄	#17986007	1	1	yes	characteristic
238	C₄	#17986303	1	2	yes	—
239	C₂	—	2	2	no	—
240	C₂	#22588352	1	1	yes	characteristic
241	C₂	#22588383	1	1	yes	characteristic
242	C₂	#22588391	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22597274

C₂

yes

maximal, characteristic

#22587088

C₂

yes

maximal, characteristic

#22586903

C₂

yes

maximal

#22586198

C₂

yes

maximal

C₇₁×#1835

C₂

yes

maximal, characteristic

#17986556

C₂²

yes

characteristic

#17986129

—

#17986129

C₄

yes

complemented

C₈×Dic₁₄₂

—

C₈×Dic₁₄₂

C₄

yes

complemented

#17986052

C₂²

yes

—

#17986025

—

#17986023

C₂²

yes

—

—

—

—

C₂×C₄×C₈×C₇₁

C₂²

yes

characteristic

#382×C₇₁

C₂²

yes

—

#340×C₇₁

—

#340×C₇₁

—

C₂×#11765849

—

#14556128

Q₈

yes

characteristic

#14556128

Q₈

yes

—

—

D₄

yes

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

C₂×C₄

yes

—

#14556087

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

C₂×C₄

yes

—

Dic₇₁⋊C₈

—

Dic₇₁⋊C₈

—

C₂²⋊(C₇₁⋊C₈)

—

#14556038

—

C₄×C₇₁⋊C₈

—

C₈×Dic₇₁

—

C₂²×C₈×C₇₁

D₄

yes

characteristic

C₂²×C₈×C₇₁

D₄

yes

characteristic

C₂×C₄⋊C₄×C₇₁

—

C₂×C₄²×C₇₁

C₂³

yes

characteristic

C₄×C₈×C₇₁

C₂×C₄

yes

characteristic

C₄×C₈×C₇₁

C₂×C₄

yes

characteristic

C₄×C₈×C₇₁

D₄

yes

characteristic

C₄×C₈×C₇₁

D₄

yes

characteristic

#95×C₇₁

—

#95×C₇₁

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

C₄⋊C₄

yes

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

C₄⋊C₄

yes

—

Dic₇₁⋊C₄

—

Dic₇₁⋊C₄

—

C₂²⋊Dic₇₁

—

C₄×Dic₇₁

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₁

#41

yes

characteristic

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₁

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄²×C₇₁

C₂²×C₄

yes

characteristic

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂×Q₈

yes

C₄²×C₇₁

yes

C₂³×C₇₁

yes

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₁

C₂×C₄⋊C₄

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₁

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₁

#135

yes

—

C₂×C₄×C₇₁

#137

yes

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

Dic₁₄₂

—

Dic₁₄₂

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

100

C₈×C₇₁

—

101

C₇₁⋊C₈

—

102

C₇₁⋊C₈

—

103

C₂²×C₇₁

—

104

C₂²×C₇₁

—

105

C₂²×C₇₁

#380

yes

characteristic

106

C₂²×C₇₁

#464

yes

—

107

C₄×C₇₁

—

108

C₄×C₇₁

—

109

C₄×C₇₁

—

110

C₄×C₇₁

—

111

C₄×C₇₁

—

112

C₄×C₇₁

#416

yes

characteristic

113

C₄×C₇₁

#419

yes

characteristic

114

C₄×C₇₁

#479

yes

—

115

Dic₇₁

—

116

Dic₇₁

—

117

#8681

—

maximal, Sylow

118

C₂×C₇₁

—

119

C₂×C₇₁

#1805

yes

characteristic

120

C₂×C₇₁

#1812

yes

characteristic

121

C₂×C₇₁

#1814

yes

characteristic

122

#2960

—

123

#1835

D₇₁

yes

characteristic

124

#1564

—

125

#1518

—

126

#1286

—

127

C₇₁

#8681

yes

characteristic, complemented, Sylow

128

#533

—

129

#446

—

130

#446

—

142

—

131

C₈×Q₈

—

132

C₈×Q₈

—

142

—

133

#431

—

134

#424

—

142

—

135

#423

—

136

#405

—

142

—

137

C₂×C₄×C₈

C₂×D₇₁

yes

characteristic

138

#382

C₂×D₇₁

yes

—

139

#340

—

140

#340

—

141

#335

—

142

—

142

#334

—

142

—

143

#328

—

142

—

144

C₂×M₁₆

—

142

—

145

C₂²×C₈

C₂²⋊D₇₁

yes

characteristic

146

C₂²×C₈

C₂²⋊D₇₁

yes

characteristic

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

149

#125

—

142

—

150

C₂²⋊Q₈

—

151

C₂²⋊Q₈

—

142

—

152

C₄×Q₈

—

153

C₄×Q₈

—

142

—

154

#117

—

142

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄²

C₂²×D₇₁

yes

characteristic

157

C₄⋊C₈

—

158

C₄⋊C₈

—

142

—

159

C₄⋊C₈

—

142

—

160

C₄⋊C₈

—

142

—

161

C₄⋊C₈

—

142

—

162

C₂²⋊C₈

—

142

—

163

#97

—

142

—

164

C₄×C₈

—

142

—

165

C₄×C₈

—

142

—

166

C₄×C₈

C₄×D₇₁

yes

characteristic

167

C₄×C₈

C₄×D₇₁

yes

characteristic

168

C₄×C₈

D₂₈₄

yes

characteristic

169

C₄×C₈

D₂₈₄

yes

characteristic

170

#95

—

171

#95

—

172

C₂×Q₈

—

173

C₂×Q₈

—

142

—

174

C₂²×C₄

—

175

C₂²×C₄

D₄×D₇₁

yes

characteristic

176

C₂²×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

177

C₂²×C₄

#11765864

yes

characteristic

178

M₁₆

—

284

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

284

—

182

C₂×C₈

—

142

—

183

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

184

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

185

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

186

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

142

—

191

C₄⋊C₄

—

142

—

192

C₄⋊C₄

—

142

—

193

C₄⋊C₄

—

142

—

194

C₄⋊C₄

—

142

—

195

C₂²⋊C₄

—

142

—

196

C₄²

—

142

—

197

C₄²

C₂×C₄×D₇₁

yes

characteristic

198

C₄²

C₂×D₂₈₄

yes

characteristic

199

C₄²

Q₈×D₇₁

yes

characteristic

200

C₄²

#11765866

yes

characteristic

201

C₂³

#14556099

yes

characteristic

202

Q₈

—

284

—

203

Q₈

—

284

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

142

—

210

C₂×C₄

—

142

—

211

C₂×C₄

C₂×(C₂×D₇₁)⋊C₄

yes

characteristic

212

C₂×C₄

C₄⋊C₄×D₇₁

yes

characteristic

213

C₂×C₄

#14556086

yes

characteristic

214

C₂×C₄

#14556103

yes

characteristic

215

C₂×C₄

#14556104

yes

characteristic

216

C₂×C₄

#14556108

yes

characteristic

217

C₂×C₄

#14556148

yes

—

218

C₂×C₄

#14556158

yes

—

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

284

—

224

C₈

—

568

—

225

C₂²

—

226

C₂²

—

227

C₂²

#17985856

yes

characteristic

228

C₂²

#17986218

yes

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

284

—

235

C₄

—

284

—

236

C₄

#17985993

yes

characteristic

237

C₄

#17986007

yes

characteristic

238

C₄

#17986303

yes

—

239

C₂

—

240

C₂

#22588352

yes

characteristic

241

C₂

#22588383

yes

characteristic

242

C₂

#22588391

yes

characteristic

	subgroup	G/H
center	C₂²	#17985856
commutator	C₄²×C₇₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₇₁×#1835	C₂
socle	C₂²×C₇₁	#380
prime radical	C₂³×C₇₁	#121
cosocle	C₂×C₄²×C₇₁	C₂³
hypercenter	#1835	D₇₁
hypocenter	C₇₁	#8681
LCS	G ▷ C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1835

subgroup

G/H

center

C₂²

#17985856

commutator

C₄²×C₇₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₇₁×#1835

C₂

C₂²×C₇₁

C₂³×C₇₁

C₂×C₄²×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1835

N	H ≅ G/N	type
8. #17986129	C₄	semidirect
10. C₈×Dic₁₄₂	C₄	semidirect
127. C₇₁	#8681	semidirect

H ≅ G/N

type

8. #17986129

C₄

semidirect

10. C₈×Dic₁₄₂

C₄

semidirect

127. C₇₁

#8681

semidirect

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

subgroup	index
#22597274	2
#22587088	2
#22586903	2
#22586198	2
C₇₁×#1835	2
#8681	71

subgroup

index

C₇₁×#1835

Subgroups — #31890688

Conjugacy classes of subgroups

Complements

Maximal subgroups