Group #31907424 — subgroups

Subgroups — #31907424

Order 18176.

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

normal subgroups only

This group has 306 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	C₂×#17986129	C₂	1	1	yes	maximal, characteristic
2	#22590143	C₂	1	1	yes	maximal, characteristic
3	#22586323	C₂	1	4	yes	maximal, complemented
4	C₇₁×#2163	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×Dic₁₄₂	C₄	1	1	yes	characteristic
6	#17986129	—	2	1	no	—
7	#17986129	—	2	1	no	—
8	#17986129	C₄	1	2	yes	—
9	#17986129	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₇₁⋊C₈)	C₄	1	1	yes	characteristic
11	C₂×Dic₇₁⋊C₈	—	2	1	no	—
12	C₂×#14556038	—	2	1	no	—
13	C₄⋊(C₇₁⋊C₁₆)	C₂²	1	2	yes	—
14	C₂²⋊(C₇₁⋊C₁₆)	—	2	1	no	—
15	#17985775	—	2	1	no	—
16	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
17	C₄⋊C₁₆×C₇₁	—	2	1	no	—
18	C₂²⋊C₁₆×C₇₁	—	2	1	no	—
19	#346×C₇₁	C₂²	1	2	yes	—
20	C₂²×Dic₁₄₂	C₈	1	1	yes	characteristic
21	C₂²×C₇₁⋊C₈	—	2	1	no	—
22	C₄×Dic₁₄₂	—	2	1	no	—
23	C₄×Dic₁₄₂	—	2	1	no	—
24	C₄×Dic₁₄₂	C₈	1	2	yes	—
25	C₄×Dic₁₄₂	C₂×C₄	1	2	yes	—
26	C₂×C₄⋊Dic₇₁	C₈	1	1	yes	characteristic
27	C₂×Dic₇₁⋊C₄	—	2	1	no	—
28	C₂×C₄×Dic₇₁	—	2	1	no	—
29	C₂×C₇₁⋊C₁₆	—	2	2	no	—
30	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
31	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
32	Dic₇₁⋊C₈	—	2	2	no	—
33	Dic₇₁⋊C₈	—	2	2	no	—
34	#14556038	—	2	2	no	—
35	#14556038	—	2	2	no	—
36	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₆×C₇₁	—	2	2	no	—
40	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
41	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
42	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
43	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
44	C₂×Dic₁₄₂	—	2	1	no	—
45	C₂×Dic₁₄₂	—	4	2	no	—
46	C₂×Dic₁₄₂	C₂×C₈	1	2	yes	—
47	C₂²×Dic₇₁	—	2	1	no	—
48	C₂²×Dic₇₁	—	2	1	no	—
49	C₂×C₇₁⋊C₈	—	2	2	no	—
50	C₂×C₇₁⋊C₈	—	4	2	no	—
51	C₄⋊Dic₇₁	—	2	1	no	—
52	C₄⋊Dic₇₁	C₂×C₈	1	2	yes	—
53	Dic₇₁⋊C₄	—	2	2	no	—
54	Dic₇₁⋊C₄	—	2	2	no	—
55	C₄×Dic₇₁	—	2	2	no	—
56	C₄×Dic₇₁	—	2	2	no	—
57	C₇₁⋊C₁₆	—	4	2	no	—
58	C₂²×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
60	C₂²×C₄×C₇₁	M₁₆	1	1	yes	characteristic
61	C₂×C₈×C₇₁	—	2	2	no	—
62	C₂×C₈×C₇₁	—	4	1	no	—
63	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
66	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
68	C₄²×C₇₁	C₂×C₈	1	1	yes	characteristic
69	C₄²×C₇₁	M₁₆	1	1	yes	characteristic
70	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
71	C₁₆×C₇₁	—	4	2	no	—
72	C₂³×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
73	C₂×C₄×C₇₁	—	2	2	no	—
74	C₂×C₄×C₇₁	—	2	1	no	—
75	C₂×C₄×C₇₁	—	2	1	no	—
76	C₂×C₄×C₇₁	—	4	1	no	—
77	C₂×C₄×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
78	C₂×C₄×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
79	C₂×C₄×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
80	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
82	C₂×C₄×C₇₁	C₂×M₁₆	1	1	yes	characteristic
83	C₂×Dic₇₁	—	2	2	no	—
84	C₂×Dic₇₁	—	2	2	no	—
85	C₂×Dic₇₁	—	4	2	no	—
86	C₂×Dic₇₁	—	4	2	no	—
87	Dic₁₄₂	—	4	2	no	—
88	Dic₁₄₂	—	4	2	no	—
89	C₈×C₇₁	—	2	1	no	—
90	C₈×C₇₁	—	2	1	no	—
91	C₈×C₇₁	—	2	1	no	—
92	C₈×C₇₁	#137	1	2	yes	—
93	C₇₁⋊C₈	—	4	2	no	—
94	C₂²×C₇₁	—	2	1	no	—
95	C₂²×C₇₁	—	2	1	no	—
96	C₂²×C₇₁	#349	1	2	yes	—
97	C₂²×C₇₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
98	C₄×C₇₁	—	2	1	no	—
99	C₄×C₇₁	—	2	1	no	—
100	C₄×C₇₁	—	2	1	no	—
101	C₄×C₇₁	—	2	1	no	—
102	C₄×C₇₁	—	2	1	no	—
103	C₄×C₇₁	#419	1	1	yes	characteristic
104	C₄×C₇₁	#421	1	1	yes	characteristic
105	Dic₇₁	—	4	2	no	—
106	Dic₇₁	—	4	2	no	—
107	#11644	—	71	1	no	maximal, Sylow
108	C₂×C₇₁	—	2	2	no	—
109	C₂×C₇₁	#1479	1	1	yes	characteristic
110	C₂×C₇₁	C₂×#349	1	1	yes	characteristic
111	C₂×C₇₁	#2117	1	1	yes	characteristic
112	C₂×#446	—	71	1	no	—
113	#2163	—	71	1	no	—
114	#2163	D₇₁	1	1	yes	characteristic
115	#1338	—	71	4	no	—
116	C₇₁	#11644	1	1	yes	characteristic, complemented, Sylow
117	C₂×C₄×Q₈	—	71	1	no	—
118	#446	—	71	2	no	—
119	#446	—	71	2	no	—
120	#446	—	142	1	no	—
121	#446	—	142	1	no	—
122	C₂×C₄⋊C₈	—	71	1	no	—
123	C₂×C₄⋊C₈	—	142	1	no	—
124	C₂×#97	—	142	1	no	—
125	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
126	C₄⋊C₁₆	—	2	1	no	—
127	C₄⋊C₁₆	—	71	2	no	—
128	C₂²⋊C₁₆	—	2	1	no	—
129	C₂²⋊C₁₆	—	142	1	no	—
130	#346	—	142	1	no	—
131	#346	C₂×D₇₁	1	2	yes	—
132	C₂²×Q₈	—	71	1	no	—
133	C₂²×C₈	—	142	1	no	—
134	C₂²×C₈	D₂₈₄	1	1	yes	characteristic
135	C₂²×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
136	C₄×Q₈	—	71	2	no	—
137	C₄×Q₈	—	71	2	no	—
138	C₄×Q₈	—	142	1	no	—
139	C₄×Q₈	—	142	1	no	—
140	C₂×C₄⋊C₄	—	71	1	no	—
141	C₂×C₄⋊C₄	—	142	1	no	—
142	C₂×C₄²	—	142	1	no	—
143	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
144	C₂×C₁₆	—	2	2	no	—
145	C₂×C₁₆	—	142	2	no	—
146	C₄⋊C₈	—	71	2	no	—
147	C₄⋊C₈	—	142	2	no	—
148	C₄⋊C₈	—	142	2	no	—
149	C₄⋊C₈	—	142	1	no	—
150	#97	—	142	2	no	—
151	#97	—	142	2	no	—
152	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
153	C₄×C₈	D₂₈₄	1	1	yes	characteristic
154	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
155	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
156	C₂×Q₈	—	284	2	no	—
157	C₂×Q₈	—	71	2	no	—
158	C₂×Q₈	—	142	1	no	—
159	C₂²×C₄	—	142	1	no	—
160	C₂²×C₄	—	142	1	no	—
161	C₂²×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
162	C₂²×C₄	C₈×D₇₁	1	1	yes	characteristic
163	C₂²×C₄	#11765848	1	1	yes	characteristic
164	C₂×C₈	—	2	2	no	—
165	C₂×C₈	—	4	1	no	—
166	C₂×C₈	—	284	2	no	—
167	C₂×C₈	—	142	2	no	—
168	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
169	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
170	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
171	C₂×C₈	C₂×D₂₈₄	1	1	yes	characteristic
172	C₄⋊C₄	—	71	2	no	—
173	C₄⋊C₄	—	142	2	no	—
174	C₄⋊C₄	—	142	1	no	—
175	C₄⋊C₄	—	142	2	no	—
176	C₄²	—	142	2	no	—
177	C₄²	—	142	2	no	—
178	C₄²	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
179	C₄²	C₈×D₇₁	1	1	yes	characteristic
180	C₄²	#11765848	1	1	yes	characteristic
181	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
182	C₁₆	—	4	2	no	—
183	C₁₆	—	284	2	no	—
184	C₂³	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
185	Q₈	—	284	2	no	—
186	Q₈	—	284	2	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	4	1	no	—
191	C₂×C₄	—	284	2	no	—
192	C₂×C₄	—	284	2	no	—
193	C₂×C₄	—	142	2	no	—
194	C₂×C₄	—	142	2	no	—
195	C₂×C₄	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
196	C₂×C₄	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
197	C₂×C₄	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
198	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
199	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
200	C₂×C₄	C₂×#11765848	1	1	yes	characteristic
201	C₈	—	2	1	no	—
202	C₈	—	2	1	no	—
203	C₈	—	2	1	no	—
204	C₈	—	284	2	no	—
205	C₈	#14556161	1	2	yes	—
206	C₂²	—	2	1	no	—
207	C₂²	—	2	1	no	—
208	C₂²	#17985780	1	2	yes	—
209	C₂²	C₂×(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
210	C₄	—	2	1	no	—
211	C₄	—	2	1	no	—
212	C₄	—	2	1	no	—
213	C₄	—	2	1	no	—
214	C₄	—	2	1	no	—
215	C₄	—	284	2	no	—
216	C₄	—	284	2	no	—
217	C₄	#17986009	1	1	yes	characteristic
218	C₄	#17986017	1	1	yes	characteristic
219	C₂	—	2	2	no	—
220	C₂	#22586736	1	1	yes	characteristic
221	C₂	C₂×#17985780	1	1	yes	characteristic
222	C₂	#22589969	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17986129

C₂

yes

maximal, characteristic

#22590143

C₂

yes

maximal, characteristic

#22586323

C₂

yes

maximal, complemented

C₇₁×#2163

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₄₂

C₄

yes

—

—

C₄

yes

—

#17986129

C₂²

yes

—

C₂×C₄⋊(C₇₁⋊C₈)

C₄

yes

characteristic

C₂×Dic₇₁⋊C₈

—

C₂×#14556038

—

C₄⋊(C₇₁⋊C₁₆)

C₂²

yes

—

C₂²⋊(C₇₁⋊C₁₆)

—

#17985775

—

C₂×C₄×C₈×C₇₁

C₂²

yes

characteristic

C₄⋊C₁₆×C₇₁

—

C₂²⋊C₁₆×C₇₁

—

#346×C₇₁

C₂²

yes

—

C₂²×Dic₁₄₂

C₈

yes

characteristic

C₂²×C₇₁⋊C₈

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

C₈

yes

—

C₄×Dic₁₄₂

C₂×C₄

yes

—

C₂×C₄⋊Dic₇₁

C₈

yes

characteristic

C₂×Dic₇₁⋊C₄

—

C₂×C₄×Dic₇₁

—

C₂×C₇₁⋊C₁₆

—

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

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₁

—

C₄×C₈×C₇₁

C₂×C₄

yes

characteristic

C₄×C₈×C₇₁

D₄

yes

characteristic

C₄×C₈×C₇₁

D₄

yes

characteristic

C₄×C₈×C₇₁

C₂³

yes

characteristic

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

C₂×C₈

yes

—

C₂²×Dic₇₁

—

C₂²×Dic₇₁

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

C₂×C₈

yes

—

Dic₇₁⋊C₄

—

Dic₇₁⋊C₄

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₇₁⋊C₁₆

—

C₂²×C₄×C₇₁

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₁

C₂×C₈

yes

characteristic

C₂²×C₄×C₇₁

M₁₆

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

C₂×D₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂²⋊C₄

yes

characteristic

C₄²×C₇₁

C₂×C₈

yes

characteristic

C₄²×C₇₁

M₁₆

yes

characteristic

C₄²×C₇₁

C₂²×C₄

yes

characteristic

C₁₆×C₇₁

—

C₂³×C₇₁

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₁

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₁

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₁

C₂²×C₈

yes

characteristic

C₂×C₄×C₇₁

C₂×M₁₆

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

Dic₁₄₂

—

Dic₁₄₂

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

#137

yes

—

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

#349

yes

—

C₂²×C₇₁

C₂×C₂²⋊C₈

yes

characteristic

C₄×C₇₁

—

C₄×C₇₁

—

100

C₄×C₇₁

—

101

C₄×C₇₁

—

102

C₄×C₇₁

—

103

C₄×C₇₁

#419

yes

characteristic

104

C₄×C₇₁

#421

yes

characteristic

105

Dic₇₁

—

106

Dic₇₁

—

107

#11644

—

maximal, Sylow

108

C₂×C₇₁

—

109

C₂×C₇₁

#1479

yes

characteristic

110

C₂×C₇₁

C₂×#349

yes

characteristic

111

C₂×C₇₁

#2117

yes

characteristic

112

C₂×#446

—

113

#2163

—

114

#2163

D₇₁

yes

characteristic

115

#1338

—

116

C₇₁

#11644

yes

characteristic, complemented, Sylow

117

C₂×C₄×Q₈

—

118

#446

—

119

#446

—

120

#446

—

142

—

121

#446

—

142

—

122

C₂×C₄⋊C₈

—

123

C₂×C₄⋊C₈

—

142

—

124

C₂×#97

—

142

—

125

C₂×C₄×C₈

C₂×D₇₁

yes

characteristic

126

C₄⋊C₁₆

—

127

C₄⋊C₁₆

—

128

C₂²⋊C₁₆

—

129

C₂²⋊C₁₆

—

142

—

130

#346

—

142

—

131

#346

C₂×D₇₁

yes

—

132

C₂²×Q₈

—

133

C₂²×C₈

—

142

—

134

C₂²×C₈

D₂₈₄

yes

characteristic

135

C₂²×C₈

C₂²⋊D₇₁

yes

characteristic

136

C₄×Q₈

—

137

C₄×Q₈

—

138

C₄×Q₈

—

142

—

139

C₄×Q₈

—

142

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄⋊C₄

—

142

—

142

C₂×C₄²

—

142

—

143

C₂×C₄²

C₄×D₇₁

yes

characteristic

144

C₂×C₁₆

—

145

C₂×C₁₆

—

142

—

146

C₄⋊C₈

—

147

C₄⋊C₈

—

142

—

148

C₄⋊C₈

—

142

—

149

C₄⋊C₈

—

142

—

150

#97

—

142

—

151

#97

—

142

—

152

C₄×C₈

C₄×D₇₁

yes

characteristic

153

C₄×C₈

D₂₈₄

yes

characteristic

154

C₄×C₈

C₂²⋊D₇₁

yes

characteristic

155

C₄×C₈

C₂²×D₇₁

yes

characteristic

156

C₂×Q₈

—

284

—

157

C₂×Q₈

—

158

C₂×Q₈

—

142

—

159

C₂²×C₄

—

142

—

160

C₂²×C₄

—

142

—

161

C₂²×C₄

(C₂×D₇₁)⋊C₄

yes

characteristic

162

C₂²×C₄

C₈×D₇₁

yes

characteristic

163

C₂²×C₄

#11765848

yes

characteristic

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

284

—

167

C₂×C₈

—

142

—

168

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

169

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

170

C₂×C₈

C₂×C₂²⋊D₇₁

yes

characteristic

171

C₂×C₈

C₂×D₂₈₄

yes

characteristic

172

C₄⋊C₄

—

173

C₄⋊C₄

—

142

—

174

C₄⋊C₄

—

142

—

175

C₄⋊C₄

—

142

—

176

C₄²

—

142

—

177

C₄²

—

142

—

178

C₄²

(C₂×D₇₁)⋊C₄

yes

characteristic

179

C₄²

C₈×D₇₁

yes

characteristic

180

C₄²

#11765848

yes

characteristic

181

C₄²

C₂×C₄×D₇₁

yes

characteristic

182

C₁₆

—

183

C₁₆

—

284

—

184

C₂³

(C₂×D₇₁)⋊C₈

yes

characteristic

185

Q₈

—

284

—

186

Q₈

—

284

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

284

—

192

C₂×C₄

—

284

—

193

C₂×C₄

—

142

—

194

C₂×C₄

—

142

—

195

C₂×C₄

(C₂×D₇₁)⋊C₈

yes

characteristic

196

C₂×C₄

(C₂×D₇₁)⋊C₈

yes

characteristic

197

C₂×C₄

(C₂×D₇₁)⋊C₈

yes

characteristic

198

C₂×C₄

C₂×(C₂×D₇₁)⋊C₄

yes

characteristic

199

C₂×C₄

C₂×C₈×D₇₁

yes

characteristic

200

C₂×C₄

C₂×#11765848

yes

characteristic

201

C₈

—

202

C₈

—

203

C₈

—

204

C₈

—

284

—

205

C₈

#14556161

yes

—

206

C₂²

—

207

C₂²

—

208

C₂²

#17985780

yes

—

209

C₂²

C₂×(C₂×D₇₁)⋊C₈

yes

characteristic

210

C₄

—

211

C₄

—

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

284

—

216

C₄

—

284

—

217

C₄

#17986009

yes

characteristic

218

C₄

#17986017

yes

characteristic

219

C₂

—

220

C₂

#22586736

yes

characteristic

221

C₂

C₂×#17985780

yes

characteristic

222

C₂

#22589969

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄
commutator	C₂×C₄×C₇₁	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₇₁
Fitting	C₇₁×#2163	C₂
socle	C₂²×C₇₁	C₂×C₂²⋊C₈
prime radical	C₂³×C₇₁	C₂²⋊C₈
cosocle	C₄×C₈×C₇₁	C₂³
hypercenter	#2163	D₇₁
hypocenter	C₇₁	#11644
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2163

subgroup

G/H

center

C₂×C₄

C₂×(C₂×D₇₁)⋊C₄

commutator

C₂×C₄×C₇₁

C₂²×C₈

Frattini

C₄×C₈

C₂²×D₇₁

Fitting

C₇₁×#2163

C₂

socle

C₂²×C₇₁

C₂×C₂²⋊C₈

prime radical

C₂³×C₇₁

C₂²⋊C₈

cosocle

C₄×C₈×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2163

N	H ≅ G/N	type
3. #22586323	C₂	semidirect
116. C₇₁	#11644	semidirect

H ≅ G/N

type

3. #22586323

C₂

semidirect

116. C₇₁

#11644

semidirect

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

subgroup	index
C₂×#17986129	2
#22590143	2
#22586323	2
C₇₁×#2163	2
#11644	71

subgroup

index

C₇₁×#2163

Subgroups — #31907424

Conjugacy classes of subgroups

Complements

Maximal subgroups