Group #31896655 — subgroups

Subgroups — #31896655

Order 18176.

392 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 107 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	#22598926	C₂	1	1	yes	maximal, characteristic
2	#22586934	C₂	1	2	yes	maximal
3	#22586762	C₂	1	2	yes	maximal
4	#22586629	C₂	1	1	yes	maximal, characteristic
5	C₄×#108×C₇₁	C₂	1	1	yes	maximal, characteristic
6	#17986556	C₂²	1	2	yes	—
7	#17986404	C₄	1	1	yes	characteristic
8	#17986379	C₄	1	1	yes	characteristic
9	#17986350	C₄	1	2	yes	—
10	#17986240	—	2	1	no	—
11	#17986240	—	2	1	no	—
12	C₄×Dic₂₈₄	—	2	1	no	—
13	C₄×Dic₂₈₄	—	2	1	no	—
14	#17986052	C₂²	1	1	yes	characteristic
15	C₄×#11765849	C₂²	1	1	yes	characteristic
16	#17985740	—	2	4	no	—
17	#17985731	—	2	4	no	—
18	#17985721	—	2	1	no	—
19	#17985720	—	2	1	no	—
20	C₂×#108×C₇₁	—	2	1	no	—
21	C₄×M₁₆×C₇₁	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
23	#341×C₇₁	—	2	1	no	—
24	C₂×Dic₂₈₄	—	2	1	no	—
25	C₂×Dic₂₈₄	—	2	1	no	—
26	C₂×#11765849	—	2	1	no	—
27	#14556128	C₂×C₄	1	2	yes	—
28	#14556128	C₂×C₄	1	2	yes	—
29	#14556120	—	2	2	no	—
30	#14556107	—	2	2	no	—
31	#14556107	—	2	2	no	—
32	C₄×Dic₁₄₂	—	2	2	no	—
33	C₄×Dic₁₄₂	—	2	2	no	—
34	#14556087	—	2	2	no	—
35	#14556062	—	2	1	no	—
36	#14556062	—	2	1	no	—
37	C₄⋊(C₇₁⋊C₈)	D₄	1	2	yes	—
38	#14556053	—	2	2	no	—
39	#14556053	—	2	2	no	—
40	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
41	#14556039	D₄	1	2	yes	—
42	C₄×C₇₁⋊C₈	—	2	1	no	—
43	C₄×C₇₁⋊C₈	—	2	1	no	—
44	C₂×M₁₆×C₇₁	—	2	2	no	—
45	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
48	#108×C₇₁	—	2	4	no	—
49	#97×C₇₁	—	2	2	no	—
50	C₄×C₈×C₇₁	—	2	2	no	—
51	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
52	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
53	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
54	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
55	C₂×Dic₁₄₂	—	2	2	no	—
56	C₂×Dic₁₄₂	—	2	2	no	—
57	Dic₂₈₄	—	4	2	no	—
58	Dic₂₈₄	—	4	2	no	—
59	#11765849	—	4	2	no	—
60	C₂×C₇₁⋊C₈	—	2	2	no	—
61	C₂×C₇₁⋊C₈	—	2	2	no	—
62	C₄⋊Dic₇₁	—	2	2	no	—
63	C₄⋊Dic₇₁	—	2	2	no	—
64	C₄⋊Dic₇₁	—	2	2	no	—
65	C₄⋊Dic₇₁	—	2	2	no	—
66	Dic₇₁⋊C₄	—	4	2	no	—
67	Dic₇₁⋊C₄	—	4	2	no	—
68	C₂²⋊Dic₇₁	—	4	2	no	—
69	C₄×Dic₇₁	—	4	2	no	—
70	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
72	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
73	M₁₆×C₇₁	—	2	4	no	—
74	M₁₆×C₇₁	—	4	2	no	—
75	C₂×C₈×C₇₁	—	2	2	no	—
76	C₂×C₈×C₇₁	—	4	1	no	—
77	C₂×C₈×C₇₁	—	4	2	no	—
78	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
82	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
83	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
84	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
85	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
86	C₂³×C₇₁	#124	1	1	yes	characteristic
87	C₂×C₄×C₇₁	—	2	1	no	—
88	C₂×C₄×C₇₁	—	2	1	no	—
89	C₂×C₄×C₇₁	—	2	2	no	—
90	C₂×C₄×C₇₁	—	2	2	no	—
91	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
93	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
94	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
95	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
96	C₂×C₄×C₇₁	#127	1	1	yes	characteristic
97	C₂×Dic₇₁	—	4	2	no	—
98	C₂×Dic₇₁	—	4	2	no	—
99	Dic₁₄₂	—	4	2	no	—
100	Dic₁₄₂	—	4	2	no	—
101	Dic₁₄₂	—	4	4	no	—
102	C₈×C₇₁	—	2	1	no	—
103	C₈×C₇₁	—	2	1	no	—
104	C₈×C₇₁	—	2	1	no	—
105	C₈×C₇₁	—	4	4	no	—
106	C₈×C₇₁	#104	1	2	yes	—
107	C₇₁⋊C₈	—	4	2	no	—
108	C₇₁⋊C₈	—	4	2	no	—
109	C₂²×C₇₁	—	2	1	no	—
110	C₂²×C₇₁	—	2	1	no	—
111	C₂²×C₇₁	—	2	1	no	—
112	C₂²×C₇₁	#390	1	1	yes	characteristic
113	C₄×C₇₁	—	2	1	no	—
114	C₄×C₇₁	—	2	1	no	—
115	C₄×C₇₁	—	2	1	no	—
116	C₄×C₇₁	C₂×#104	1	1	yes	characteristic
117	C₄×C₇₁	#421	1	1	yes	characteristic
118	C₄×C₇₁	#444	1	2	yes	—
119	C₄×C₇₁	#473	1	2	yes	—
120	Dic₇₁	—	8	2	no	—
121	Dic₇₁	—	8	2	no	—
122	#9727	—	71	1	no	maximal, Sylow
123	C₂×C₇₁	—	4	1	no	—
124	C₂×C₇₁	#1975	1	1	yes	characteristic
125	C₂×C₇₁	#1979	1	1	yes	characteristic
126	C₂×C₇₁	#1980	1	1	yes	characteristic
127	#3170	—	71	1	no	—
128	C₄×#108	D₇₁	1	1	yes	characteristic
129	#1526	—	71	2	no	—
130	#1485	—	71	2	no	—
131	#1451	—	71	1	no	—
132	C₇₁	#9727	1	1	yes	characteristic, complemented, Sylow
133	#533	—	71	2	no	—
134	#500	—	71	1	no	—
135	#494	—	71	1	no	—
136	#487	—	71	2	no	—
137	#467	—	142	1	no	—
138	#467	—	142	1	no	—
139	C₄×Q₁₆	—	142	1	no	—
140	C₄×Q₁₆	—	142	1	no	—
141	#431	—	71	1	no	—
142	C₂×#108	—	2	1	no	—
143	C₄×M₁₆	—	71	1	no	—
144	C₄×M₁₆	C₂×D₇₁	1	2	yes	—
145	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
146	#341	—	2	1	no	—
147	#330	—	142	4	no	—
148	Q₈⋊C₈	—	142	4	no	—
149	#322	—	142	1	no	—
150	#322	—	142	1	no	—
151	C₂×Q₁₆	—	142	1	no	—
152	C₂×Q₁₆	—	142	1	no	—
153	C₂×M₁₆	—	2	2	no	—
154	C₂×M₁₆	—	142	1	no	—
155	C₂²×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
156	C₂²×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
157	C₄⋊Q₈	—	71	2	no	—
158	C₄⋊Q₈	—	71	2	no	—
159	#125	—	142	2	no	—
160	C₂²⋊Q₈	—	142	2	no	—
161	C₂²⋊Q₈	—	142	2	no	—
162	C₄×Q₈	—	142	2	no	—
163	C₄×Q₈	—	142	2	no	—
164	#117	—	142	2	no	—
165	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
166	#108	—	2	4	no	—
167	#107	—	142	1	no	—
168	#107	—	142	1	no	—
169	C₄⋊C₈	—	71	2	no	—
170	#103	—	142	2	no	—
171	#103	—	142	2	no	—
172	C₂²⋊C₈	—	142	1	no	—
173	#97	—	2	2	no	—
174	#97	—	71	2	no	—
175	C₄×C₈	—	2	2	no	—
176	C₄×C₈	—	142	1	no	—
177	C₄×C₈	—	142	1	no	—
178	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
179	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
180	C₄×C₈	D₂₈₄	1	1	yes	characteristic
181	C₄×C₈	D₂₈₄	1	1	yes	characteristic
182	C₂×Q₈	—	142	2	no	—
183	C₂×Q₈	—	142	2	no	—
184	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
185	C₂²×C₄	#11765866	1	1	yes	characteristic
186	C₂²×C₄	#11765866	1	1	yes	characteristic
187	Q₁₆	—	284	2	no	—
188	Q₁₆	—	284	2	no	—
189	M₁₆	—	2	4	no	—
190	M₁₆	—	4	2	no	—
191	M₁₆	—	284	2	no	—
192	C₂×C₈	—	2	2	no	—
193	C₂×C₈	—	4	1	no	—
194	C₂×C₈	—	4	2	no	—
195	C₂×C₈	—	142	2	no	—
196	C₂×C₈	—	142	2	no	—
197	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
198	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
199	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
200	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
201	C₄⋊C₄	—	284	2	no	—
202	C₄⋊C₄	—	284	2	no	—
203	C₄⋊C₄	—	142	2	no	—
204	C₄⋊C₄	—	142	2	no	—
205	C₄⋊C₄	—	142	2	no	—
206	C₄⋊C₄	—	142	2	no	—
207	C₂²⋊C₄	—	284	2	no	—
208	C₄²	—	284	2	no	—
209	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
210	C₄²	D₄×D₇₁	1	1	yes	characteristic
211	C₄²	D₄×D₇₁	1	1	yes	characteristic
212	C₄²	C₂×D₂₈₄	1	1	yes	characteristic
213	C₂³	#14556117	1	1	yes	characteristic
214	Q₈	—	284	4	no	—
215	Q₈	—	284	2	no	—
216	Q₈	—	284	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	284	2	no	—
222	C₂×C₄	—	284	2	no	—
223	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
224	C₂×C₄	#14556090	1	1	yes	characteristic
225	C₂×C₄	#14556090	1	1	yes	characteristic
226	C₂×C₄	#14556103	1	1	yes	characteristic
227	C₂×C₄	#14556103	1	1	yes	characteristic
228	C₂×C₄	#14556124	1	1	yes	characteristic
229	C₈	—	2	1	no	—
230	C₈	—	2	1	no	—
231	C₈	—	2	1	no	—
232	C₈	—	4	4	no	—
233	C₈	—	284	2	no	—
234	C₈	—	284	2	no	—
235	C₈	#14556056	1	2	yes	—
236	C₂²	—	2	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	1	no	—
239	C₂²	#17985900	1	1	yes	characteristic
240	C₄	—	2	1	no	—
241	C₄	—	2	1	no	—
242	C₄	—	2	1	no	—
243	C₄	—	568	2	no	—
244	C₄	—	568	2	no	—
245	C₄	C₂×#14556056	1	1	yes	characteristic
246	C₄	#17986017	1	1	yes	characteristic
247	C₄	#17986120	1	2	yes	—
248	C₄	#17986275	1	2	yes	—
249	C₂	—	4	1	no	—
250	C₂	#22589231	1	1	yes	characteristic
251	C₂	#22589253	1	1	yes	characteristic
252	C₂	#22589258	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22598926

C₂

yes

maximal, characteristic

#22586934

C₂

yes

maximal

#22586762

C₂

yes

maximal

#22586629

C₂

yes

maximal, characteristic

C₄×#108×C₇₁

C₂

yes

maximal, characteristic

#17986556

C₂²

yes

—

#17986404

C₄

yes

characteristic

#17986379

C₄

yes

characteristic

#17986350

C₄

yes

—

#17986240

—

#17986240

—

C₄×Dic₂₈₄

—

C₄×Dic₂₈₄

—

#17986052

C₂²

yes

characteristic

C₄×#11765849

C₂²

yes

—

—

—

—

C₂×#108×C₇₁

—

C₄×M₁₆×C₇₁

C₂²

yes

—

C₂×C₄×C₈×C₇₁

C₂²

yes

characteristic

#341×C₇₁

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

—

C₂×#11765849

—

#14556128

C₂×C₄

yes

—

#14556128

C₂×C₄

yes

—

#14556120

—

#14556107

—

#14556107

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

—

#14556087

—

#14556062

—

#14556062

—

C₄⋊(C₇₁⋊C₈)

D₄

yes

—

#14556053

—

#14556053

—

C₂²⋊(C₇₁⋊C₈)

—

#14556039

D₄

yes

—

C₄×C₇₁⋊C₈

—

C₄×C₇₁⋊C₈

—

C₂×M₁₆×C₇₁

—

C₂²×C₈×C₇₁

D₄

yes

characteristic

C₂²×C₈×C₇₁

D₄

yes

characteristic

C₂×C₄²×C₇₁

C₂³

yes

characteristic

#108×C₇₁

—

#97×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

—

Dic₂₈₄

—

Dic₂₈₄

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

Dic₇₁⋊C₄

—

Dic₇₁⋊C₄

—

C₂²⋊Dic₇₁

—

C₄×Dic₇₁

—

C₂²×C₄×C₇₁

C₂×D₄

yes

C₂²×C₄×C₇₁

yes

C₂²×C₄×C₇₁

yes

M₁₆×C₇₁

—

M₁₆×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

C₂×D₄

yes

characteristic

C₂³×C₇₁

#124

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₁

C₄×D₄

yes

characteristic

C₂×C₄×C₇₁

C₄×D₄

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×Dic₇₁

—

C₂×Dic₇₁

—

Dic₁₄₂

—

100

Dic₁₄₂

—

101

Dic₁₄₂

—

102

C₈×C₇₁

—

103

C₈×C₇₁

—

104

C₈×C₇₁

—

105

C₈×C₇₁

—

106

C₈×C₇₁

#104

yes

—

107

C₇₁⋊C₈

—

108

C₇₁⋊C₈

—

109

C₂²×C₇₁

—

110

C₂²×C₇₁

—

111

C₂²×C₇₁

—

112

C₂²×C₇₁

#390

yes

characteristic

113

C₄×C₇₁

—

114

C₄×C₇₁

—

115

C₄×C₇₁

—

116

C₄×C₇₁

C₂×#104

yes

characteristic

117

C₄×C₇₁

#421

yes

characteristic

118

C₄×C₇₁

#444

yes

—

119

C₄×C₇₁

#473

yes

—

120

Dic₇₁

—

121

Dic₇₁

—

122

#9727

—

maximal, Sylow

123

C₂×C₇₁

—

124

C₂×C₇₁

#1975

yes

characteristic

125

C₂×C₇₁

#1979

yes

characteristic

126

C₂×C₇₁

#1980

yes

characteristic

127

#3170

—

128

C₄×#108

D₇₁

yes

characteristic

129

#1526

—

130

#1485

—

131

#1451

—

132

C₇₁

#9727

yes

characteristic, complemented, Sylow

133

#533

—

134

#500

—

135

#494

—

136

#487

—

137

#467

—

142

—

138

#467

—

142

—

139

C₄×Q₁₆

—

142

—

140

C₄×Q₁₆

—

142

—

141

#431

—

142

C₂×#108

—

143

C₄×M₁₆

—

144

C₄×M₁₆

C₂×D₇₁

yes

—

145

C₂×C₄×C₈

C₂×D₇₁

yes

characteristic

146

#341

—

147

#330

—

142

—

148

Q₈⋊C₈

—

142

—

149

#322

—

142

—

150

#322

—

142

—

151

C₂×Q₁₆

—

142

—

152

C₂×Q₁₆

—

142

—

153

C₂×M₁₆

—

154

C₂×M₁₆

—

142

—

155

C₂²×C₈

C₂²⋊D₇₁

yes

characteristic

156

C₂²×C₈

C₂²⋊D₇₁

yes

characteristic

157

C₄⋊Q₈

—

158

C₄⋊Q₈

—

159

#125

—

142

—

160

C₂²⋊Q₈

—

142

—

161

C₂²⋊Q₈

—

142

—

162

C₄×Q₈

—

142

—

163

C₄×Q₈

—

142

—

164

#117

—

142

—

165

C₂×C₄²

C₂²×D₇₁

yes

characteristic

166

#108

—

167

#107

—

142

—

168

#107

—

142

—

169

C₄⋊C₈

—

170

#103

—

142

—

171

#103

—

142

—

172

C₂²⋊C₈

—

142

—

173

#97

—

174

#97

—

175

C₄×C₈

—

176

C₄×C₈

—

142

—

177

C₄×C₈

—

142

—

178

C₄×C₈

C₄×D₇₁

yes

characteristic

179

C₄×C₈

C₄×D₇₁

yes

characteristic

180

C₄×C₈

D₂₈₄

yes

characteristic

181

C₄×C₈

D₂₈₄

yes

characteristic

182

C₂×Q₈

—

142

—

183

C₂×Q₈

—

142

—

184

C₂²×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

185

C₂²×C₄

#11765866

yes

characteristic

186

C₂²×C₄

#11765866

yes

characteristic

187

Q₁₆

—

284

—

188

Q₁₆

—

284

—

189

M₁₆

—

190

M₁₆

—

191

M₁₆

—

284

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

142

—

196

C₂×C₈

—

142

—

197

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

198

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

199

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

200

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

201

C₄⋊C₄

—

284

—

202

C₄⋊C₄

—

284

—

203

C₄⋊C₄

—

142

—

204

C₄⋊C₄

—

142

—

205

C₄⋊C₄

—

142

—

206

C₄⋊C₄

—

142

—

207

C₂²⋊C₄

—

284

—

208

C₄²

—

284

—

209

C₄²

C₂×C₄×D₇₁

yes

characteristic

210

C₄²

D₄×D₇₁

yes

characteristic

211

C₄²

D₄×D₇₁

yes

characteristic

212

C₄²

C₂×D₂₈₄

yes

characteristic

213

C₂³

#14556117

yes

characteristic

214

Q₈

—

284

—

215

Q₈

—

284

—

216

Q₈

—

284

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

284

—

222

C₂×C₄

—

284

—

223

C₂×C₄

C₂×(C₂×D₇₁)⋊C₄

yes

characteristic

224

C₂×C₄

#14556090

yes

characteristic

225

C₂×C₄

#14556090

yes

characteristic

226

C₂×C₄

#14556103

yes

characteristic

227

C₂×C₄

#14556103

yes

characteristic

228

C₂×C₄

#14556124

yes

characteristic

229

C₈

—

230

C₈

—

231

C₈

—

232

C₈

—

233

C₈

—

284

—

234

C₈

—

284

—

235

C₈

#14556056

yes

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

#17985900

yes

characteristic

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

568

—

244

C₄

—

568

—

245

C₄

C₂×#14556056

yes

characteristic

246

C₄

#17986017

yes

characteristic

247

C₄

#17986120

yes

—

248

C₄

#17986275

yes

—

249

C₂

—

250

C₂

#22589231

yes

characteristic

251

C₂

#22589253

yes

characteristic

252

C₂

#22589258

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14556103
commutator	C₄²×C₇₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₄×#108×C₇₁	C₂
socle	C₂²×C₇₁	#390
prime radical	C₂³×C₇₁	#124
cosocle	C₂×C₄²×C₇₁	C₂³
hypercenter	C₄×#108	D₇₁
hypocenter	C₇₁	#9727
LCS	G ▷ C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#108

subgroup

G/H

center

C₂×C₄

#14556103

commutator

C₄²×C₇₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₄×#108×C₇₁

C₂

C₂²×C₇₁

C₂³×C₇₁

C₂×C₄²×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#108

N	H ≅ G/N	type
132. C₇₁	#9727	semidirect

H ≅ G/N

type

132. C₇₁

#9727

semidirect

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

subgroup	index
#22598926	2
#22586934	2
#22586762	2
#22586629	2
C₄×#108×C₇₁	2
#9727	71

subgroup

index

C₄×#108×C₇₁

Subgroups — #31896655

Conjugacy classes of subgroups

Complements

Maximal subgroups