Group #31890732 — subgroups

Subgroups — #31890732

Order 18176.

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

normal subgroups only

This group has 346 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	#22597274	C₂	1	1	yes	maximal, characteristic
2	#22588478	C₂	1	1	yes	maximal, characteristic
3	#22587028	C₂	1	2	yes	maximal
4	#22586215	C₂	1	2	yes	maximal
5	C₂×#335×C₇₁	C₂	1	1	yes	maximal, characteristic
6	#17986556	C₂²	1	1	yes	characteristic
7	#17986129	—	2	1	no	—
8	#17986129	C₄	1	2	yes	—
9	C₈×Dic₁₄₂	—	2	1	no	—
10	C₈×Dic₁₄₂	C₄	1	2	yes	—
11	#17986025	—	2	1	no	—
12	#17986023	C₂²	1	2	yes	—
13	#17986023	C₂²	1	1	yes	characteristic
14	#17985954	—	2	1	no	—
15	#17985764	—	2	1	no	—
16	#17985764	—	2	1	no	—
17	#17985747	—	2	2	no	—
18	#17985746	—	2	2	no	—
19	C₂×C₄⋊C₈×C₇₁	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
21	#335×C₇₁	—	2	1	no	—
22	#335×C₇₁	—	2	1	no	—
23	C₂×#11765849	—	2	1	no	—
24	C₂×#11765849	—	2	2	no	—
25	#14556128	D₄	1	1	yes	characteristic
26	#14556128	D₄	1	1	yes	characteristic
27	#14556120	—	2	1	no	—
28	#14556107	—	2	1	no	—
29	#14556107	Q₈	1	2	yes	—
30	C₄×Dic₁₄₂	—	2	1	no	—
31	C₄×Dic₁₄₂	C₂×C₄	1	2	yes	—
32	#14556087	—	2	1	no	—
33	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
34	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
35	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
36	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
37	Dic₇₁⋊C₈	—	2	2	no	—
38	Dic₇₁⋊C₈	—	2	2	no	—
39	#14556038	—	2	2	no	—
40	C₈×Dic₇₁	—	2	2	no	—
41	C₂²×C₈×C₇₁	—	2	2	no	—
42	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
45	C₄⋊C₈×C₇₁	—	2	2	no	—
46	C₄⋊C₈×C₇₁	—	2	2	no	—
47	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
48	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
49	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
50	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
51	C₂×Dic₁₄₂	—	2	1	no	—
52	C₂×Dic₁₄₂	C₄⋊C₄	1	2	yes	—
53	#11765849	—	4	2	no	—
54	#11765849	—	4	2	no	—
55	#11765849	—	4	2	no	—
56	C₂×C₇₁⋊C₈	—	2	2	no	—
57	C₂×C₇₁⋊C₈	—	4	2	no	—
58	C₄⋊Dic₇₁	—	2	1	no	—
59	C₄⋊Dic₇₁	—	2	1	no	—
60	C₄⋊Dic₇₁	—	2	1	no	—
61	C₄⋊Dic₇₁	C₄⋊C₄	1	2	yes	—
62	Dic₇₁⋊C₄	—	2	2	no	—
63	Dic₇₁⋊C₄	—	2	2	no	—
64	C₂²⋊Dic₇₁	—	2	2	no	—
65	C₄×Dic₇₁	—	2	2	no	—
66	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
68	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
69	C₂×C₈×C₇₁	—	2	2	no	—
70	C₂×C₈×C₇₁	—	2	2	no	—
71	C₂×C₈×C₇₁	—	4	2	no	—
72	C₂×C₈×C₇₁	—	8	2	no	—
73	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
78	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₇₁	#41	1	1	yes	characteristic
81	C₂³×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
82	C₂×C₄×C₇₁	—	2	1	no	—
83	C₂×C₄×C₇₁	—	2	1	no	—
84	C₂×C₄×C₇₁	—	4	1	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	#121	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	1	no	—
96	Dic₁₄₂	—	4	1	no	—
97	Dic₁₄₂	—	4	2	no	—
98	C₈×C₇₁	—	2	1	no	—
99	C₈×C₇₁	—	2	1	no	—
100	C₈×C₇₁	—	2	1	no	—
101	C₈×C₇₁	—	2	1	no	—
102	C₈×C₇₁	—	8	2	no	—
103	C₇₁⋊C₈	—	4	2	no	—
104	C₇₁⋊C₈	—	8	2	no	—
105	C₂²×C₇₁	—	2	1	no	—
106	C₂²×C₇₁	—	2	1	no	—
107	C₂²×C₇₁	#380	1	1	yes	characteristic
108	C₂²×C₇₁	#479	1	2	yes	—
109	C₄×C₇₁	—	2	1	no	—
110	C₄×C₇₁	—	2	1	no	—
111	C₄×C₇₁	—	2	1	no	—
112	C₄×C₇₁	#416	1	1	yes	characteristic
113	C₄×C₇₁	#419	1	1	yes	characteristic
114	C₄×C₇₁	#464	1	2	yes	—
115	C₄×C₇₁	#472	1	1	yes	characteristic
116	C₄×C₇₁	#473	1	1	yes	characteristic
117	Dic₇₁	—	4	2	no	—
118	Dic₇₁	—	4	2	no	—
119	#8689	—	71	1	no	maximal, Sylow
120	C₂×C₇₁	—	2	2	no	—
121	C₂×C₇₁	#1805	1	1	yes	characteristic
122	C₂×C₇₁	#1813	1	1	yes	characteristic
123	C₂×C₇₁	#1816	1	1	yes	characteristic
124	#2960	—	71	1	no	—
125	#1837	—	71	1	no	—
126	C₂×#335	D₇₁	1	1	yes	characteristic
127	#1550	—	71	2	no	—
128	#1292	—	71	2	no	—
129	C₇₁	#8689	1	1	yes	characteristic, complemented, Sylow
130	#533	—	71	1	no	—
131	#446	—	71	2	no	—
132	#446	—	142	1	no	—
133	C₈×Q₈	—	71	2	no	—
134	C₈×Q₈	—	142	1	no	—
135	#424	—	142	1	no	—
136	#423	—	71	1	no	—
137	#423	—	71	2	no	—
138	C₂×C₄⋊C₈	C₂×D₇₁	1	2	yes	—
139	#405	—	142	1	no	—
140	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
141	#341	—	142	1	no	—
142	#341	—	142	1	no	—
143	#335	—	2	1	no	—
144	#335	—	2	1	no	—
145	#333	—	142	2	no	—
146	#332	—	142	2	no	—
147	C₂×M₁₆	—	142	2	no	—
148	C₂×M₁₆	—	142	1	no	—
149	C₂²×C₈	—	2	2	no	—
150	C₂²×C₈	D₂₈₄	1	1	yes	characteristic
151	C₂²×C₈	D₂₈₄	1	1	yes	characteristic
152	C₄⋊Q₈	—	71	1	no	—
153	C₄⋊Q₈	—	71	1	no	—
154	#125	—	142	1	no	—
155	C₂²⋊Q₈	—	71	2	no	—
156	C₂²⋊Q₈	—	142	1	no	—
157	C₄×Q₈	—	71	2	no	—
158	C₄×Q₈	—	142	1	no	—
159	#117	—	142	1	no	—
160	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
161	C₄⋊C₈	—	2	2	no	—
162	C₄⋊C₈	—	2	2	no	—
163	C₄⋊C₈	—	71	2	no	—
164	C₄⋊C₈	—	142	2	no	—
165	C₄⋊C₈	—	142	2	no	—
166	C₄⋊C₈	—	142	2	no	—
167	C₄⋊C₈	—	142	1	no	—
168	C₄⋊C₈	—	142	2	no	—
169	#97	—	142	2	no	—
170	C₄×C₈	—	142	2	no	—
171	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
172	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
173	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
174	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
175	C₂×Q₈	—	71	2	no	—
176	C₂×Q₈	—	142	1	no	—
177	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
178	C₂²×C₄	Q₈×D₇₁	1	1	yes	characteristic
179	C₂²×C₄	#11765864	1	1	yes	characteristic
180	M₁₆	—	284	2	no	—
181	M₁₆	—	284	2	no	—
182	M₁₆	—	284	2	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	4	2	no	—
186	C₂×C₈	—	8	2	no	—
187	C₂×C₈	—	284	2	no	—
188	C₂×C₈	—	142	2	no	—
189	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
190	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
191	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
192	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
193	C₄⋊C₄	—	71	2	no	—
194	C₄⋊C₄	—	142	2	no	—
195	C₄⋊C₄	—	142	1	no	—
196	C₄⋊C₄	—	142	1	no	—
197	C₄⋊C₄	—	142	1	no	—
198	C₄⋊C₄	—	142	2	no	—
199	C₂²⋊C₄	—	142	2	no	—
200	C₄²	—	142	2	no	—
201	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
202	C₄²	D₄×D₇₁	1	1	yes	characteristic
203	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
204	C₄²	#11765866	1	1	yes	characteristic
205	C₂³	#14556108	1	1	yes	characteristic
206	Q₈	—	284	2	no	—
207	Q₈	—	284	1	no	—
208	Q₈	—	284	1	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	142	2	no	—
213	C₂×C₄	—	142	2	no	—
214	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
215	C₂×C₄	C₄⋊C₄×D₇₁	1	1	yes	characteristic
216	C₂×C₄	#14556086	1	1	yes	characteristic
217	C₂×C₄	#14556099	1	1	yes	characteristic
218	C₂×C₄	#14556103	1	1	yes	characteristic
219	C₂×C₄	#14556104	1	1	yes	characteristic
220	C₂×C₄	#14556150	1	2	yes	—
221	C₂×C₄	#14556161	1	2	yes	—
222	C₈	—	2	1	no	—
223	C₈	—	2	1	no	—
224	C₈	—	2	1	no	—
225	C₈	—	2	1	no	—
226	C₈	—	8	2	no	—
227	C₈	—	284	2	no	—
228	C₈	—	568	2	no	—
229	C₂²	—	2	1	no	—
230	C₂²	—	2	1	no	—
231	C₂²	#17985856	1	1	yes	characteristic
232	C₂²	#17986307	1	2	yes	—
233	C₄	—	2	1	no	—
234	C₄	—	2	1	no	—
235	C₄	—	2	1	no	—
236	C₄	—	284	2	no	—
237	C₄	—	284	2	no	—
238	C₄	#17985996	1	1	yes	characteristic
239	C₄	#17986009	1	1	yes	characteristic
240	C₄	#17986222	1	2	yes	—
241	C₄	#17986266	1	1	yes	characteristic
242	C₄	#17986271	1	1	yes	characteristic
243	C₂	—	2	2	no	—
244	C₂	#22588356	1	1	yes	characteristic
245	C₂	#22588387	1	1	yes	characteristic
246	C₂	#22588405	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22597274

C₂

yes

maximal, characteristic

#22588478

C₂

yes

maximal, characteristic

#22587028

C₂

yes

maximal

#22586215

C₂

yes

maximal

C₂×#335×C₇₁

C₂

yes

maximal, characteristic

#17986556

C₂²

yes

characteristic

#17986129

—

#17986129

C₄

yes

—

C₈×Dic₁₄₂

—

C₈×Dic₁₄₂

C₄

yes

—

#17986025

—

#17986023

C₂²

yes

—

#17986023

C₂²

yes

—

—

—

—

—

C₂×C₄⋊C₈×C₇₁

C₂²

yes

—

C₂×C₄×C₈×C₇₁

C₂²

yes

characteristic

#335×C₇₁

—

#335×C₇₁

—

C₂×#11765849

—

C₂×#11765849

—

#14556128

D₄

yes

characteristic

#14556128

D₄

yes

—

—

Q₈

yes

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

C₂×C₄

yes

—

#14556087

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

C₂×C₄

yes

—

Dic₇₁⋊C₈

—

Dic₇₁⋊C₈

—

#14556038

—

C₈×Dic₇₁

—

C₂²×C₈×C₇₁

—

C₂²×C₈×C₇₁

D₄

yes

characteristic

C₂²×C₈×C₇₁

D₄

yes

characteristic

C₂×C₄²×C₇₁

C₂³

yes

characteristic

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

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

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

C₄⋊C₄

yes

—

#11765849

—

#11765849

—

#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

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₁

C₂×Q₈

yes

characteristic

C₂²×C₄×C₇₁

#41

yes

characteristic

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

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

C₄²×C₇₁

C₂²×C₄

yes

characteristic

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

#41

yes

characteristic

C₂³×C₇₁

C₂²⋊Q₈

yes

characteristic

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

yes

C₂×C₄×C₇₁

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₁

#135

yes

—

C₂×C₄×C₇₁

#137

yes

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

Dic₁₄₂

—

Dic₁₄₂

—

Dic₁₄₂

—

C₈×C₇₁

—

C₈×C₇₁

—

100

C₈×C₇₁

—

101

C₈×C₇₁

—

102

C₈×C₇₁

—

103

C₇₁⋊C₈

—

104

C₇₁⋊C₈

—

105

C₂²×C₇₁

—

106

C₂²×C₇₁

—

107

C₂²×C₇₁

#380

yes

characteristic

108

C₂²×C₇₁

#479

yes

—

109

C₄×C₇₁

—

110

C₄×C₇₁

—

111

C₄×C₇₁

—

112

C₄×C₇₁

#416

yes

characteristic

113

C₄×C₇₁

#419

yes

characteristic

114

C₄×C₇₁

#464

yes

—

115

C₄×C₇₁

#472

yes

characteristic

116

C₄×C₇₁

#473

yes

characteristic

117

Dic₇₁

—

118

Dic₇₁

—

119

#8689

—

maximal, Sylow

120

C₂×C₇₁

—

121

C₂×C₇₁

#1805

yes

characteristic

122

C₂×C₇₁

#1813

yes

characteristic

123

C₂×C₇₁

#1816

yes

characteristic

124

#2960

—

125

#1837

—

126

C₂×#335

D₇₁

yes

characteristic

127

#1550

—

128

#1292

—

129

C₇₁

#8689

yes

characteristic, complemented, Sylow

130

#533

—

131

#446

—

132

#446

—

142

—

133

C₈×Q₈

—

134

C₈×Q₈

—

142

—

135

#424

—

142

—

136

#423

—

137

#423

—

138

C₂×C₄⋊C₈

C₂×D₇₁

yes

—

139

#405

—

142

—

140

C₂×C₄×C₈

C₂×D₇₁

yes

characteristic

141

#341

—

142

—

142

#341

—

142

—

143

#335

—

144

#335

—

145

#333

—

142

—

146

#332

—

142

—

147

C₂×M₁₆

—

142

—

148

C₂×M₁₆

—

142

—

149

C₂²×C₈

—

150

C₂²×C₈

D₂₈₄

yes

characteristic

151

C₂²×C₈

D₂₈₄

yes

characteristic

152

C₄⋊Q₈

—

153

C₄⋊Q₈

—

154

#125

—

142

—

155

C₂²⋊Q₈

—

156

C₂²⋊Q₈

—

142

—

157

C₄×Q₈

—

158

C₄×Q₈

—

142

—

159

#117

—

142

—

160

C₂×C₄²

C₂²×D₇₁

yes

characteristic

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

142

—

165

C₄⋊C₈

—

142

—

166

C₄⋊C₈

—

142

—

167

C₄⋊C₈

—

142

—

168

C₄⋊C₈

—

142

—

169

#97

—

142

—

170

C₄×C₈

—

142

—

171

C₄×C₈

C₄×D₇₁

yes

characteristic

172

C₄×C₈

C₄×D₇₁

yes

characteristic

173

C₄×C₈

C₂²⋊D₇₁

yes

characteristic

174

C₄×C₈

C₂²⋊D₇₁

yes

characteristic

175

C₂×Q₈

—

176

C₂×Q₈

—

142

—

177

C₂²×C₄

C₂×D₂₈₄

yes

characteristic

178

C₂²×C₄

Q₈×D₇₁

yes

characteristic

179

C₂²×C₄

#11765864

yes

characteristic

180

M₁₆

—

284

—

181

M₁₆

—

284

—

182

M₁₆

—

284

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

284

—

188

C₂×C₈

—

142

—

189

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

190

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

191

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

192

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

193

C₄⋊C₄

—

194

C₄⋊C₄

—

142

—

195

C₄⋊C₄

—

142

—

196

C₄⋊C₄

—

142

—

197

C₄⋊C₄

—

142

—

198

C₄⋊C₄

—

142

—

199

C₂²⋊C₄

—

142

—

200

C₄²

—

142

—

201

C₄²

C₂×C₄×D₇₁

yes

characteristic

202

C₄²

D₄×D₇₁

yes

characteristic

203

C₄²

C₂×C₂²⋊D₇₁

yes

characteristic

204

C₄²

#11765866

yes

characteristic

205

C₂³

#14556108

yes

characteristic

206

Q₈

—

284

—

207

Q₈

—

284

—

208

Q₈

—

284

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

142

—

213

C₂×C₄

—

142

—

214

C₂×C₄

C₂×(C₂×D₇₁)⋊C₄

yes

characteristic

215

C₂×C₄

C₄⋊C₄×D₇₁

yes

characteristic

216

C₂×C₄

#14556086

yes

characteristic

217

C₂×C₄

#14556099

yes

characteristic

218

C₂×C₄

#14556103

yes

characteristic

219

C₂×C₄

#14556104

yes

characteristic

220

C₂×C₄

#14556150

yes

—

221

C₂×C₄

#14556161

yes

—

222

C₈

—

223

C₈

—

224

C₈

—

225

C₈

—

226

C₈

—

227

C₈

—

284

—

228

C₈

—

568

—

229

C₂²

—

230

C₂²

—

231

C₂²

#17985856

yes

characteristic

232

C₂²

#17986307

yes

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

284

—

237

C₄

—

284

—

238

C₄

#17985996

yes

characteristic

239

C₄

#17986009

yes

characteristic

240

C₄

#17986222

yes

—

241

C₄

#17986266

yes

characteristic

242

C₄

#17986271

yes

characteristic

243

C₂

—

244

C₂

#22588356

yes

characteristic

245

C₂

#22588387

yes

characteristic

246

C₂

#22588405

yes

characteristic

	subgroup	G/H
center	C₂²	#17985856
commutator	C₄²×C₇₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₂×#335×C₇₁	C₂
socle	C₂²×C₇₁	#380
prime radical	C₂³×C₇₁	C₂²⋊Q₈
cosocle	C₂×C₄²×C₇₁	C₂³
hypercenter	C₂×#335	D₇₁
hypocenter	C₇₁	#8689
LCS	G ▷ C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#335

subgroup

G/H

center

C₂²

#17985856

commutator

C₄²×C₇₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₂×#335×C₇₁

C₂

socle

C₂²×C₇₁

#380

prime radical

C₂³×C₇₁

C₂²⋊Q₈

cosocle

C₂×C₄²×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#335

N	H ≅ G/N	type
129. C₇₁	#8689	semidirect

H ≅ G/N

type

129. C₇₁

#8689

semidirect

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

subgroup	index
#22597274	2
#22588478	2
#22587028	2
#22586215	2
C₂×#335×C₇₁	2
#8689	71

subgroup

index

C₂×#335×C₇₁

Subgroups — #31890732

Conjugacy classes of subgroups

Complements

Maximal subgroups