Group #31890612 — subgroups

Subgroups — #31890612

Order 18176.

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

normal subgroups only

This group has 358 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	C₂×#17986129	C₂	1	1	yes	maximal, characteristic
2	#22588478	C₂	1	1	yes	maximal, characteristic
3	#22586770	C₂	1	2	yes	maximal
4	#22586236	C₂	1	2	yes	maximal
5	C₇₁×#1564	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₁₄₂	C₂²	1	1	yes	characteristic
7	#17986129	—	2	1	no	—
8	#17986129	—	2	1	no	—
9	#17986129	C₄	1	2	yes	—
10	#17986129	C₄	1	2	yes	—
11	#17986023	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×Dic₇₁⋊C₈	—	2	1	no	—
14	C₂×#14556038	—	2	1	no	—
15	#17985764	—	2	1	no	—
16	#17985764	—	2	1	no	—
17	#17985731	—	2	4	no	—
18	#431×C₇₁	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
20	#335×C₇₁	—	2	1	no	—
21	#334×C₇₁	—	2	1	no	—
22	C₂²×Dic₁₄₂	Q₈	1	1	yes	characteristic
23	C₂×#11765849	—	2	2	no	—
24	C₂²×C₇₁⋊C₈	—	2	1	no	—
25	C₄×Dic₁₄₂	—	2	1	no	—
26	C₄×Dic₁₄₂	—	2	1	no	—
27	C₄×Dic₁₄₂	C₂×C₄	1	2	yes	—
28	C₄×Dic₁₄₂	D₄	1	2	yes	—
29	C₂×C₄⋊Dic₇₁	Q₈	1	1	yes	characteristic
30	C₂×Dic₇₁⋊C₄	—	2	1	no	—
31	C₂×C₄×Dic₇₁	—	2	1	no	—
32	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
33	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
34	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
35	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
36	Dic₇₁⋊C₈	—	2	2	no	—
37	Dic₇₁⋊C₈	—	2	2	no	—
38	#14556038	—	2	2	no	—
39	#14556038	—	2	2	no	—
40	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₇₁	—	2	2	no	—
44	C₂²⋊C₈×C₇₁	—	2	2	no	—
45	C₄×C₈×C₇₁	—	2	2	no	—
46	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
47	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
48	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
49	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
50	C₂×Dic₁₄₂	—	2	1	no	—
51	C₂×Dic₁₄₂	—	4	2	no	—
52	C₂×Dic₁₄₂	C₄⋊C₄	1	2	yes	—
53	C₂²×Dic₇₁	—	2	1	no	—
54	C₂²×Dic₇₁	—	2	1	no	—
55	#11765849	—	4	2	no	—
56	#11765849	—	4	2	no	—
57	C₂×C₇₁⋊C₈	—	2	2	no	—
58	C₂×C₇₁⋊C₈	—	4	2	no	—
59	C₂×C₇₁⋊C₈	—	4	2	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	C₄×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	C₂²⋊C₄	1	1	yes	characteristic
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	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
77	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₇₁	#41	1	1	yes	characteristic
80	C₂³×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
81	C₂×C₄×C₇₁	—	2	2	no	—
82	C₂×C₄×C₇₁	—	4	1	no	—
83	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₇₁	#117	1	1	yes	characteristic
86	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
87	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
88	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
89	C₂×C₄×C₇₁	#135	1	2	yes	—
90	C₂×C₄×C₇₁	#137	1	2	yes	—
91	C₂×Dic₇₁	—	2	2	no	—
92	C₂×Dic₇₁	—	2	2	no	—
93	C₂×Dic₇₁	—	4	2	no	—
94	C₂×Dic₇₁	—	4	2	no	—
95	Dic₁₄₂	—	2	4	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	C₈×C₇₁	—	8	2	no	—
102	C₇₁⋊C₈	—	4	2	no	—
103	C₇₁⋊C₈	—	8	2	no	—
104	C₂²×C₇₁	—	2	1	no	—
105	C₂²×C₇₁	—	2	1	no	—
106	C₂²×C₇₁	#380	1	1	yes	characteristic
107	C₂²×C₇₁	#479	1	2	yes	—
108	C₄×C₇₁	—	2	1	no	—
109	C₄×C₇₁	—	2	1	no	—
110	C₄×C₇₁	—	2	1	no	—
111	C₄×C₇₁	#416	1	1	yes	characteristic
112	C₄×C₇₁	#419	1	1	yes	characteristic
113	C₄×C₇₁	#430	1	2	yes	—
114	C₄×C₇₁	#464	1	2	yes	—
115	Dic₇₁	—	4	2	no	—
116	Dic₇₁	—	4	2	no	—
117	#8665	—	71	1	no	maximal, Sylow
118	C₂×C₇₁	—	2	2	no	—
119	C₂×C₇₁	#1805	1	1	yes	characteristic
120	C₂×C₇₁	#1811	1	1	yes	characteristic
121	C₂×C₇₁	#1814	1	1	yes	characteristic
122	C₂×#446	—	71	1	no	—
123	#1837	—	71	1	no	—
124	#1564	D₇₁	1	1	yes	characteristic
125	#1487	—	71	2	no	—
126	#1301	—	71	2	no	—
127	C₇₁	#8665	1	1	yes	characteristic, complemented, Sylow
128	C₂×C₄×Q₈	—	71	1	no	—
129	#446	—	71	2	no	—
130	#446	—	71	2	no	—
131	#446	—	142	1	no	—
132	#446	—	142	1	no	—
133	#431	C₂×D₇₁	1	2	yes	—
134	#423	—	71	2	no	—
135	C₂×C₄⋊C₈	—	71	1	no	—
136	C₂×C₄⋊C₈	—	142	1	no	—
137	C₂×#97	—	142	1	no	—
138	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
139	#341	—	142	1	no	—
140	#341	—	142	1	no	—
141	#335	—	2	1	no	—
142	#334	—	2	1	no	—
143	Q₈⋊C₈	—	142	4	no	—
144	C₂²×Q₈	—	71	1	no	—
145	C₂×M₁₆	—	142	2	no	—
146	C₂²×C₈	—	142	1	no	—
147	C₂²×C₈	D₂₈₄	1	1	yes	characteristic
148	C₂²×C₈	D₂₈₄	1	1	yes	characteristic
149	C₄×Q₈	—	71	2	no	—
150	C₄×Q₈	—	71	2	no	—
151	C₄×Q₈	—	142	1	no	—
152	C₄×Q₈	—	142	1	no	—
153	C₂×C₄⋊C₄	—	71	1	no	—
154	C₂×C₄⋊C₄	—	142	1	no	—
155	C₂×C₄²	—	142	1	no	—
156	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	71	2	no	—
159	C₄⋊C₈	—	142	2	no	—
160	C₄⋊C₈	—	142	2	no	—
161	C₄⋊C₈	—	142	2	no	—
162	C₄⋊C₈	—	142	1	no	—
163	C₄⋊C₈	—	142	2	no	—
164	C₂²⋊C₈	—	2	2	no	—
165	#97	—	142	2	no	—
166	#97	—	142	2	no	—
167	C₄×C₈	—	2	2	no	—
168	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
169	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
170	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
171	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
172	C₂×Q₈	—	284	2	no	—
173	C₂×Q₈	—	71	2	no	—
174	C₂×Q₈	—	142	1	no	—
175	C₂²×C₄	—	142	1	no	—
176	C₂²×C₄	—	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	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	4	2	no	—
185	C₂×C₈	—	284	2	no	—
186	C₂×C₈	—	284	2	no	—
187	C₂×C₈	—	142	2	no	—
188	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
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	C₄⋊C₄	—	71	2	no	—
193	C₄⋊C₄	—	142	2	no	—
194	C₄⋊C₄	—	142	2	no	—
195	C₄⋊C₄	—	142	1	no	—
196	C₄²	—	142	2	no	—
197	C₄²	—	142	2	no	—
198	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
199	C₄²	D₄×D₇₁	1	1	yes	characteristic
200	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
201	C₄²	#11765866	1	1	yes	characteristic
202	C₂³	#14556108	1	1	yes	characteristic
203	Q₈	—	284	2	no	—
204	Q₈	—	142	4	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	284	2	no	—
208	C₂×C₄	—	284	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	#14556099	1	1	yes	characteristic
215	C₂×C₄	#14556103	1	1	yes	characteristic
216	C₂×C₄	#14556104	1	1	yes	characteristic
217	C₂×C₄	#14556150	1	2	yes	—
218	C₂×C₄	#14556161	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	—	8	2	no	—
224	C₈	—	284	2	no	—
225	C₈	—	568	2	no	—
226	C₂²	—	2	1	no	—
227	C₂²	—	2	1	no	—
228	C₂²	#17985856	1	1	yes	characteristic
229	C₂²	#17986307	1	2	yes	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	284	2	no	—
234	C₄	—	284	2	no	—
235	C₄	#17985996	1	1	yes	characteristic
236	C₄	#17986009	1	1	yes	characteristic
237	C₄	#17986046	1	2	yes	—
238	C₄	#17986222	1	2	yes	—
239	C₂	—	2	2	no	—
240	C₂	#22588356	1	1	yes	characteristic
241	C₂	#22588379	1	1	yes	characteristic
242	C₂	#22588391	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17986129

C₂

yes

maximal, characteristic

#22588478

C₂

yes

maximal, characteristic

#22586770

C₂

yes

maximal

#22586236

C₂

yes

maximal

C₇₁×#1564

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₄₂

C₂²

yes

—

—

C₄

yes

—

#17986129

C₄

yes

—

#17986023

C₂²

yes

—

C₂×C₄⋊(C₇₁⋊C₈)

C₂²

yes

characteristic

C₂×Dic₇₁⋊C₈

—

—

—

—

—

#431×C₇₁

C₂²

yes

—

C₂×C₄×C₈×C₇₁

C₂²

yes

characteristic

#335×C₇₁

—

#334×C₇₁

—

C₂²×Dic₁₄₂

Q₈

yes

characteristic

C₂×#11765849

—

C₂²×C₇₁⋊C₈

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

C₂×C₄

yes

—

C₄×Dic₁₄₂

D₄

yes

—

C₂×C₄⋊Dic₇₁

Q₈

yes

characteristic

C₂×Dic₇₁⋊C₄

—

C₂×C₄×Dic₇₁

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

C₂×C₄

yes

—

Dic₇₁⋊C₈

—

Dic₇₁⋊C₈

—

#14556038

—

#14556038

—

C₂²×C₈×C₇₁

D₄

yes

characteristic

C₂²×C₈×C₇₁

D₄

yes

characteristic

C₂×C₄²×C₇₁

C₂³

yes

characteristic

C₄⋊C₈×C₇₁

—

C₂²⋊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

—

C₂×Dic₁₄₂

C₄⋊C₄

yes

—

C₂²×Dic₇₁

—

C₂²×Dic₇₁

—

#11765849

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

C₄⋊C₄

yes

—

Dic₇₁⋊C₄

—

Dic₇₁⋊C₄

—

C₄×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

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×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

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

Dic₁₄₂

—

Dic₁₄₂

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

100

C₈×C₇₁

—

101

C₈×C₇₁

—

102

C₇₁⋊C₈

—

103

C₇₁⋊C₈

—

104

C₂²×C₇₁

—

105

C₂²×C₇₁

—

106

C₂²×C₇₁

#380

yes

characteristic

107

C₂²×C₇₁

#479

yes

—

108

C₄×C₇₁

—

109

C₄×C₇₁

—

110

C₄×C₇₁

—

111

C₄×C₇₁

#416

yes

characteristic

112

C₄×C₇₁

#419

yes

characteristic

113

C₄×C₇₁

#430

yes

—

114

C₄×C₇₁

#464

yes

—

115

Dic₇₁

—

116

Dic₇₁

—

117

#8665

—

maximal, Sylow

118

C₂×C₇₁

—

119

C₂×C₇₁

#1805

yes

characteristic

120

C₂×C₇₁

#1811

yes

characteristic

121

C₂×C₇₁

#1814

yes

characteristic

122

C₂×#446

—

123

#1837

—

124

#1564

D₇₁

yes

characteristic

125

#1487

—

126

#1301

—

127

C₇₁

#8665

yes

characteristic, complemented, Sylow

128

C₂×C₄×Q₈

—

129

#446

—

130

#446

—

131

#446

—

142

—

132

#446

—

142

—

133

#431

C₂×D₇₁

yes

—

134

#423

—

135

C₂×C₄⋊C₈

—

136

C₂×C₄⋊C₈

—

142

—

137

C₂×#97

—

142

—

138

C₂×C₄×C₈

C₂×D₇₁

yes

characteristic

139

#341

—

142

—

140

#341

—

142

—

141

#335

—

142

#334

—

143

Q₈⋊C₈

—

142

—

144

C₂²×Q₈

—

145

C₂×M₁₆

—

142

—

146

C₂²×C₈

—

142

—

147

C₂²×C₈

D₂₈₄

yes

characteristic

148

C₂²×C₈

D₂₈₄

yes

characteristic

149

C₄×Q₈

—

150

C₄×Q₈

—

151

C₄×Q₈

—

142

—

152

C₄×Q₈

—

142

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

142

—

155

C₂×C₄²

—

142

—

156

C₂×C₄²

C₂²×D₇₁

yes

characteristic

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

142

—

160

C₄⋊C₈

—

142

—

161

C₄⋊C₈

—

142

—

162

C₄⋊C₈

—

142

—

163

C₄⋊C₈

—

142

—

164

C₂²⋊C₈

—

165

#97

—

142

—

166

#97

—

142

—

167

C₄×C₈

—

168

C₄×C₈

C₄×D₇₁

yes

characteristic

169

C₄×C₈

C₄×D₇₁

yes

characteristic

170

C₄×C₈

C₂²⋊D₇₁

yes

characteristic

171

C₄×C₈

C₂²⋊D₇₁

yes

characteristic

172

C₂×Q₈

—

284

—

173

C₂×Q₈

—

174

C₂×Q₈

—

142

—

175

C₂²×C₄

—

142

—

176

C₂²×C₄

—

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

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

284

—

186

C₂×C₈

—

284

—

187

C₂×C₈

—

142

—

188

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

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

C₄⋊C₄

—

193

C₄⋊C₄

—

142

—

194

C₄⋊C₄

—

142

—

195

C₄⋊C₄

—

142

—

196

C₄²

—

142

—

197

C₄²

—

142

—

198

C₄²

C₂×C₄×D₇₁

yes

characteristic

199

C₄²

D₄×D₇₁

yes

characteristic

200

C₄²

C₂×C₂²⋊D₇₁

yes

characteristic

201

C₄²

#11765866

yes

characteristic

202

C₂³

#14556108

yes

characteristic

203

Q₈

—

284

—

204

Q₈

—

142

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

284

—

208

C₂×C₄

—

284

—

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

#14556099

yes

characteristic

215

C₂×C₄

#14556103

yes

characteristic

216

C₂×C₄

#14556104

yes

characteristic

217

C₂×C₄

#14556150

yes

—

218

C₂×C₄

#14556161

yes

—

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

224

C₈

—

284

—

225

C₈

—

568

—

226

C₂²

—

227

C₂²

—

228

C₂²

#17985856

yes

characteristic

229

C₂²

#17986307

yes

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

284

—

234

C₄

—

284

—

235

C₄

#17985996

yes

characteristic

236

C₄

#17986009

yes

characteristic

237

C₄

#17986046

yes

—

238

C₄

#17986222

yes

—

239

C₂

—

240

C₂

#22588356

yes

characteristic

241

C₂

#22588379

yes

characteristic

242

C₂

#22588391

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14556103
commutator	C₄²×C₇₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₇₁×#1564	C₂
socle	C₂²×C₇₁	#380
prime radical	C₂³×C₇₁	C₂²⋊Q₈
cosocle	C₂×C₄²×C₇₁	C₂³
hypercenter	#1564	D₇₁
hypocenter	C₇₁	#8665
LCS	G ▷ C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

subgroup

G/H

center

C₂×C₄

#14556103

commutator

C₄²×C₇₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₇₁×#1564

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 ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

N	H ≅ G/N	type
127. C₇₁	#8665	semidirect

H ≅ G/N

type

127. C₇₁

#8665

semidirect

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

subgroup	index
C₂×#17986129	2
#22588478	2
#22586770	2
#22586236	2
C₇₁×#1564	2
#8665	71

subgroup

index

C₇₁×#1564

Subgroups — #31890612

Conjugacy classes of subgroups

Complements

Maximal subgroups