Group #30773280 — subgroups

Subgroups — #30773280

Order 17152.

490 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 127 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	#22569857	C₂	1	1	yes	maximal, characteristic
2	#22561926	C₂	1	2	yes	maximal, complemented
3	#22560255	C₂	1	1	yes	maximal, characteristic, complemented
4	#22558311	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3407	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₅₃₆	C₂²	1	1	yes	characteristic
7	#16863960	—	2	1	no	—
8	#16863649	C₄	1	4	yes	complemented
9	#16863632	—	2	2	no	—
10	#16863434	C₂²	1	2	yes	—
11	#16863434	C₂²	1	1	yes	characteristic
12	#16863402	—	2	1	no	—
13	#16863370	—	2	1	no	—
14	#16863198	—	2	4	no	—
15	#16863153	—	2	1	no	—
16	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
17	#504×C₆₇	—	2	4	no	—
18	C₂×M₃₂×C₆₇	—	2	2	no	—
19	C₂×M₃₂×C₆₇	C₂²	1	2	yes	—
20	C₂²×D₂₆₈	—	2	1	no	—
21	C₂×D₅₃₆	—	2	2	no	—
22	C₂×D₅₃₆	—	2	1	no	—
23	C₂×D₅₃₆	—	2	2	no	—
24	C₂×D₅₃₆	C₂×C₄	1	2	yes	—
25	#14524039	—	4	1	no	—
26	#14524032	—	4	1	no	—
27	#14524017	—	2	4	no	—
28	#14524011	—	4	2	no	—
29	#14524002	—	2	1	no	—
30	#14524002	—	2	2	no	—
31	#14523977	—	2	1	no	—
32	#14523977	—	2	2	no	—
33	#14523975	—	2	2	no	—
34	#14523975	C₂×C₄	1	2	yes	—
35	#14523965	—	2	4	no	—
36	#14523958	—	4	2	no	—
37	C₂×#41×C₆₇	D₄	1	1	yes	characteristic
38	#131×C₆₇	—	2	2	no	—
39	#131×C₆₇	—	2	2	no	—
40	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
41	C₂×M₁₆×C₆₇	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₆₇	D₄	1	2	yes	—
43	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
44	M₃₂×C₆₇	—	2	4	no	—
45	M₃₂×C₆₇	—	2	2	no	—
46	M₃₂×C₆₇	—	2	2	no	—
47	C₂×C₁₆×C₆₇	—	2	4	no	—
48	C₂×C₁₆×C₆₇	D₄	1	4	yes	complemented
49	C₂³×D₆₇	—	4	1	no	—
50	C₂×D₂₆₈	—	2	2	no	—
51	C₂×D₂₆₈	—	4	2	no	—
52	C₂×D₂₆₈	—	4	2	no	—
53	C₂×D₂₆₈	—	4	1	no	—
54	C₂×C₂²⋊D₆₇	—	4	4	no	—
55	D₅₃₆	—	2	4	no	—
56	D₅₃₆	—	4	1	no	—
57	D₅₃₆	—	4	1	no	—
58	C₄⋊Dic₆₇	—	2	2	no	—
59	C₄⋊Dic₆₇	—	4	2	no	—
60	C₂²⋊Dic₆₇	—	4	1	no	—
61	C₂²⋊Dic₆₇	—	4	2	no	—
62	(C₂×D₆₇)⋊C₄	—	4	4	no	—
63	C₄×Dic₆₇	—	4	1	no	—
64	C₄×Dic₆₇	—	4	2	no	—
65	#41×C₆₇	—	2	2	no	—
66	#41×C₆₇	—	2	2	no	—
67	C₂×Q₈×C₆₇	SD₁₆	1	1	yes	characteristic
68	C₂×D₄×C₆₇	D₈	1	2	yes	—
69	C₂×D₄×C₆₇	SD₁₆	1	1	yes	characteristic
70	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
71	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
72	M₁₆×C₆₇	—	2	2	no	—
73	M₁₆×C₆₇	—	2	4	no	—
74	C₂×C₈×C₆₇	—	2	2	no	—
75	C₂×C₈×C₆₇	—	2	2	no	—
76	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
77	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
79	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
80	C₂×C₈×C₆₇	#41	1	2	yes	—
81	C₁₆×C₆₇	—	2	4	no	—
82	C₂³×C₆₇	#102	1	2	yes	—
83	C₂³×C₆₇	C₂×D₈	1	1	yes	characteristic
84	C₂²×D₆₇	—	4	2	no	—
85	C₂²×D₆₇	—	8	2	no	—
86	C₂²×D₆₇	—	16	2	no	—
87	Q₈×C₆₇	—	2	2	no	—
88	D₄×C₆₇	—	2	4	no	—
89	D₄×C₆₇	—	2	2	no	—
90	C₂×C₄×C₆₇	—	2	2	no	—
91	C₂×C₄×C₆₇	—	2	2	no	—
92	C₂×C₄×C₆₇	#102	1	2	yes	—
93	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₆₇	#121	1	2	yes	—
95	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
96	C₂×C₄×C₆₇	#135	1	2	yes	—
97	C₂²⋊D₆₇	—	16	4	no	—
98	C₂×Dic₆₇	—	4	2	no	—
99	C₂×Dic₆₇	—	8	2	no	—
100	D₂₆₈	—	4	2	no	—
101	D₂₆₈	—	4	2	no	—
102	D₂₆₈	—	8	2	no	—
103	C₈×C₆₇	—	2	2	no	—
104	C₈×C₆₇	C₄×D₄	1	2	yes	—
105	C₈×C₆₇	#120	1	1	yes	characteristic
106	C₈×C₆₇	#123	1	1	yes	characteristic
107	C₂²×C₆₇	—	2	2	no	—
108	C₂²×C₆₇	—	4	1	no	—
109	C₂²×C₆₇	—	4	2	no	—
110	C₂²×C₆₇	C₂×#102	1	1	yes	characteristic
111	C₂²×C₆₇	#466	1	2	yes	—
112	C₂×D₆₇	—	8	4	no	—
113	C₂×D₆₇	—	8	2	no	—
114	C₂×D₆₇	—	16	4	no	—
115	C₄×C₆₇	—	2	2	no	—
116	C₄×C₆₇	#386	1	1	yes	characteristic
117	C₄×C₆₇	#416	1	1	yes	characteristic
118	C₄×C₆₇	#465	1	2	yes	—
119	Dic₆₇	—	8	2	no	—
120	Dic₆₇	—	16	2	no	—
121	#13074	—	67	1	no	maximal, Sylow
122	C₂×C₆₇	—	2	1	no	—
123	C₂×C₆₇	—	2	2	no	—
124	C₂×C₆₇	—	4	2	no	—
125	C₂×C₆₇	#1893	1	1	yes	characteristic
126	D₆₇	—	16	2	no	—
127	#3407	D₆₇	1	1	yes	characteristic, complemented
128	#3058	—	67	1	no	—
129	#2140	—	67	2	no	—
130	#1812	—	67	1	no	—
131	#1384	—	67	2	no	—
132	C₆₇	#13074	1	1	yes	characteristic, complemented, Sylow
133	C₂²×D₈	—	67	1	no	—
134	C₂×#131	C₂×D₆₇	1	1	yes	characteristic
135	#535	—	134	1	no	—
136	#504	—	2	4	no	—
137	C₂×M₃₂	—	2	2	no	—
138	C₂×M₃₂	C₂×D₆₇	1	2	yes	—
139	#469	—	67	4	no	—
140	#466	—	134	2	no	—
141	#427	—	67	1	no	—
142	#427	—	67	2	no	—
143	#418	—	134	1	no	—
144	#410	—	134	1	no	—
145	#357	—	134	4	no	—
146	H(3,ℤ/4)	—	134	1	no	—
147	C₂×#41	D₂₆₈	1	1	yes	characteristic
148	C₂²×D₄	—	134	1	no	—
149	C₂×D₈	—	67	2	no	—
150	C₂×D₈	—	134	1	no	—
151	C₂×D₈	—	134	2	no	—
152	C₂×D₈	—	134	2	no	—
153	#131	—	2	2	no	—
154	#131	—	2	2	no	—
155	C₂×M₁₆	C₄×D₆₇	1	2	yes	—
156	C₂×M₁₆	D₂₆₈	1	1	yes	characteristic
157	C₂²×C₈	C₂²⋊D₆₇	1	2	yes	—
158	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
159	#127	—	268	1	no	—
160	#124	—	268	1	no	—
161	#121	—	134	4	no	—
162	#120	—	268	2	no	—
163	#117	—	134	2	no	—
164	#117	—	134	1	no	—
165	M₃₂	—	2	4	no	—
166	M₃₂	—	2	2	no	—
167	M₃₂	—	2	2	no	—
168	C₂×C₁₆	—	2	4	no	—
169	C₂×C₁₆	C₂²⋊D₆₇	1	4	yes	complemented
170	#107	—	134	2	no	—
171	#107	—	134	1	no	—
172	#106	—	67	2	no	—
173	#106	—	134	2	no	—
174	#102	—	134	4	no	—
175	#99	—	268	2	no	—
176	C₂⁴	—	268	1	no	—
177	#41	—	2	2	no	—
178	#41	—	2	2	no	—
179	C₂×Q₈	#11761617	1	1	yes	characteristic
180	C₂×D₄	—	268	4	no	—
181	C₂×D₄	—	268	2	no	—
182	C₂×D₄	—	268	1	no	—
183	C₂×D₄	—	268	2	no	—
184	C₂×D₄	—	134	2	no	—
185	C₂×D₄	D₅₃₆	1	2	yes	—
186	C₂×D₄	#11761617	1	1	yes	characteristic
187	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	2	yes	—
188	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
189	D₈	—	268	1	no	—
190	D₈	—	268	1	no	—
191	D₈	—	134	4	no	—
192	M₁₆	—	2	2	no	—
193	M₁₆	—	2	4	no	—
194	C₂×C₈	—	2	2	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	(C₂×D₆₇)⋊C₄	1	2	yes	—
197	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
198	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
199	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
200	C₂×C₈	#11761628	1	2	yes	—
201	C₄⋊C₄	—	268	2	no	—
202	C₄⋊C₄	—	134	2	no	—
203	C₂²⋊C₄	—	268	1	no	—
204	C₂²⋊C₄	—	268	4	no	—
205	C₂²⋊C₄	—	268	2	no	—
206	C₄²	—	268	1	no	—
207	C₄²	—	268	2	no	—
208	C₁₆	—	2	4	no	—
209	C₂³	—	268	2	no	—
210	C₂³	—	536	2	no	—
211	C₂³	—	1072	2	no	—
212	C₂³	#14523965	1	2	yes	—
213	C₂³	C₂×D₅₃₆	1	1	yes	characteristic
214	Q₈	—	2	2	no	—
215	D₄	—	2	4	no	—
216	D₄	—	2	2	no	—
217	D₄	—	268	2	no	—
218	D₄	—	268	2	no	—
219	D₄	—	536	2	no	—
220	D₄	—	1072	4	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	268	2	no	—
224	C₂×C₄	—	536	2	no	—
225	C₂×C₄	#14523965	1	2	yes	—
226	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
227	C₂×C₄	#14524017	1	2	yes	—
228	C₂×C₄	C₂×#11761617	1	1	yes	characteristic
229	C₂×C₄	#14524065	1	2	yes	—
230	C₈	—	2	2	no	—
231	C₈	C₄×C₂²⋊D₆₇	1	2	yes	—
232	C₈	#14524012	1	1	yes	characteristic
233	C₈	#14524026	1	1	yes	characteristic
234	C₂²	—	2	2	no	—
235	C₂²	—	4	1	no	—
236	C₂²	—	4	2	no	—
237	C₂²	—	536	4	no	—
238	C₂²	—	536	2	no	—
239	C₂²	—	1072	4	no	—
240	C₂²	C₂×#14523965	1	1	yes	characteristic
241	C₂²	#16863632	1	2	yes	—
242	C₄	—	2	2	no	—
243	C₄	—	536	2	no	—
244	C₄	—	1072	2	no	—
245	C₄	#16863275	1	1	yes	characteristic
246	C₄	#16863393	1	1	yes	characteristic
247	C₄	#16863625	1	2	yes	—
248	C₂	—	2	1	no	—
249	C₂	—	2	2	no	—
250	C₂	—	4	2	no	—
251	C₂	—	1072	2	no	—
252	C₂	#22560637	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22569857

C₂

yes

maximal, characteristic

#22561926

C₂

yes

maximal, complemented

#22560255

C₂

yes

maximal, characteristic, complemented

#22558311

C₂

yes

maximal, complemented

C₆₇×#3407

C₂

yes

maximal, characteristic, complemented

C₂²×D₅₃₆

C₂²

yes

characteristic

#16863960

—

#16863649

C₄

yes

complemented

#16863632

—

#16863434

C₂²

yes

—

#16863434

C₂²

yes

—

—

—

—

C₂×#131×C₆₇

C₂²

yes

characteristic

#504×C₆₇

—

C₂×M₃₂×C₆₇

—

C₂×M₃₂×C₆₇

C₂²

yes

—

C₂²×D₂₆₈

—

C₂×D₅₃₆

—

C₂×D₅₃₆

—

C₂×D₅₃₆

—

C₂×D₅₃₆

C₂×C₄

yes

—

—

—

—

—

—

—

—

—

—

C₂×C₄

yes

—

#14523965

—

#14523958

—

C₂×#41×C₆₇

D₄

yes

characteristic

#131×C₆₇

—

#131×C₆₇

—

C₂×M₁₆×C₆₇

C₂×C₄

yes

—

C₂×M₁₆×C₆₇

D₄

yes

characteristic

C₂²×C₈×C₆₇

D₄

yes

—

C₂²×C₈×C₆₇

C₂³

yes

characteristic

M₃₂×C₆₇

—

M₃₂×C₆₇

—

M₃₂×C₆₇

—

C₂×C₁₆×C₆₇

—

C₂×C₁₆×C₆₇

D₄

yes

complemented

C₂³×D₆₇

—

C₂×D₂₆₈

—

C₂×D₂₆₈

—

C₂×D₂₆₈

—

C₂×D₂₆₈

—

C₂×C₂²⋊D₆₇

—

D₅₃₆

—

D₅₃₆

—

D₅₃₆

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₂²⋊Dic₆₇

—

C₂²⋊Dic₆₇

—

(C₂×D₆₇)⋊C₄

—

C₄×Dic₆₇

—

C₄×Dic₆₇

—

#41×C₆₇

—

#41×C₆₇

—

C₂×Q₈×C₆₇

SD₁₆

yes

characteristic

C₂×D₄×C₆₇

D₈

yes

—

C₂×D₄×C₆₇

SD₁₆

yes

characteristic

C₂²×C₄×C₆₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

M₁₆×C₆₇

—

M₁₆×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

C₂²⋊C₄

yes

—

C₂×C₈×C₆₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₆₇

C₂×D₄

yes

—

C₂×C₈×C₆₇

C₂×D₄

yes

characteristic

C₂×C₈×C₆₇

#41

yes

—

C₁₆×C₆₇

—

C₂³×C₆₇

#102

yes

—

C₂³×C₆₇

C₂×D₈

yes

characteristic

C₂²×D₆₇

—

C₂²×D₆₇

—

C₂²×D₆₇

—

Q₈×C₆₇

—

D₄×C₆₇

—

D₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

#102

yes

—

C₂×C₄×C₆₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₇

#121

yes

—

C₂×C₄×C₆₇

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₆₇

#135

yes

—

C₂²⋊D₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

100

D₂₆₈

—

101

D₂₆₈

—

102

D₂₆₈

—

103

C₈×C₆₇

—

104

C₈×C₆₇

C₄×D₄

yes

—

105

C₈×C₆₇

#120

yes

characteristic

106

C₈×C₆₇

#123

yes

characteristic

107

C₂²×C₆₇

—

108

C₂²×C₆₇

—

109

C₂²×C₆₇

—

110

C₂²×C₆₇

C₂×#102

yes

characteristic

111

C₂²×C₆₇

#466

yes

—

112

C₂×D₆₇

—

113

C₂×D₆₇

—

114

C₂×D₆₇

—

115

C₄×C₆₇

—

116

C₄×C₆₇

#386

yes

characteristic

117

C₄×C₆₇

#416

yes

characteristic

118

C₄×C₆₇

#465

yes

—

119

Dic₆₇

—

120

Dic₆₇

—

121

#13074

—

maximal, Sylow

122

C₂×C₆₇

—

123

C₂×C₆₇

—

124

C₂×C₆₇

—

125

C₂×C₆₇

#1893

yes

characteristic

126

D₆₇

—

127

#3407

D₆₇

yes

characteristic, complemented

128

#3058

—

129

#2140

—

130

#1812

—

131

#1384

—

132

C₆₇

#13074

yes

characteristic, complemented, Sylow

133

C₂²×D₈

—

134

C₂×#131

C₂×D₆₇

yes

characteristic

135

#535

—

134

—

136

#504

—

137

C₂×M₃₂

—

138

C₂×M₃₂

C₂×D₆₇

yes

—

139

#469

—

140

#466

—

134

—

141

#427

—

142

#427

—

143

#418

—

134

—

144

#410

—

134

—

145

#357

—

134

—

146

H(3,ℤ/4)

—

134

—

147

C₂×#41

D₂₆₈

yes

characteristic

148

C₂²×D₄

—

134

—

149

C₂×D₈

—

150

C₂×D₈

—

134

—

151

C₂×D₈

—

134

—

152

C₂×D₈

—

134

—

153

#131

—

154

#131

—

155

C₂×M₁₆

C₄×D₆₇

yes

—

156

C₂×M₁₆

D₂₆₈

yes

characteristic

157

C₂²×C₈

C₂²⋊D₆₇

yes

—

158

C₂²×C₈

C₂²×D₆₇

yes

characteristic

159

#127

—

268

—

160

#124

—

268

—

161

#121

—

134

—

162

#120

—

268

—

163

#117

—

134

—

164

#117

—

134

—

165

M₃₂

—

166

M₃₂

—

167

M₃₂

—

168

C₂×C₁₆

—

169

C₂×C₁₆

C₂²⋊D₆₇

yes

complemented

170

#107

—

134

—

171

#107

—

134

—

172

#106

—

173

#106

—

134

—

174

#102

—

134

—

175

#99

—

268

—

176

C₂⁴

—

268

—

177

#41

—

178

#41

—

179

C₂×Q₈

#11761617

yes

characteristic

180

C₂×D₄

—

268

—

181

C₂×D₄

—

268

—

182

C₂×D₄

—

268

—

183

C₂×D₄

—

268

—

184

C₂×D₄

—

134

—

185

C₂×D₄

D₅₃₆

yes

—

186

C₂×D₄

#11761617

yes

characteristic

187

C₂²×C₄

(C₂×D₆₇)⋊C₄

yes

—

188

C₂²×C₄

C₂×D₂₆₈

yes

characteristic

189

D₈

—

268

—

190

D₈

—

268

—

191

D₈

—

134

—

192

M₁₆

—

193

M₁₆

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

(C₂×D₆₇)⋊C₄

yes

—

197

C₂×C₈

C₂×C₄×D₆₇

yes

characteristic

198

C₂×C₈

C₂×C₂²⋊D₆₇

yes

—

199

C₂×C₈

C₂×C₂²⋊D₆₇

yes

characteristic

200

C₂×C₈

#11761628

yes

—

201

C₄⋊C₄

—

268

—

202

C₄⋊C₄

—

134

—

203

C₂²⋊C₄

—

268

—

204

C₂²⋊C₄

—

268

—

205

C₂²⋊C₄

—

268

—

206

C₄²

—

268

—

207

C₄²

—

268

—

208

C₁₆

—

209

C₂³

—

268

—

210

C₂³

—

536

—

211

C₂³

—

1072

—

212

C₂³

#14523965

yes

—

213

C₂³

C₂×D₅₃₆

yes

characteristic

214

Q₈

—

215

D₄

—

216

D₄

—

217

D₄

—

268

—

218

D₄

—

268

—

219

D₄

—

536

—

220

D₄

—

1072

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

268

—

224

C₂×C₄

—

536

—

225

C₂×C₄

#14523965

yes

—

226

C₂×C₄

C₂×(C₂×D₆₇)⋊C₄

yes

characteristic

227

C₂×C₄

#14524017

yes

—

228

C₂×C₄

C₂×#11761617

yes

characteristic

229

C₂×C₄

#14524065

yes

—

230

C₈

—

231

C₈

C₄×C₂²⋊D₆₇

yes

—

232

C₈

#14524012

yes

characteristic

233

C₈

#14524026

yes

characteristic

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

536

—

238

C₂²

—

536

—

239

C₂²

—

1072

—

240

C₂²

C₂×#14523965

yes

characteristic

241

C₂²

#16863632

yes

—

242

C₄

—

243

C₄

—

536

—

244

C₄

—

1072

—

245

C₄

#16863275

yes

characteristic

246

C₄

#16863393

yes

characteristic

247

C₄

#16863625

yes

—

248

C₂

—

249

C₂

—

250

C₂

—

251

C₂

—

1072

—

252

C₂

#22560637

yes

characteristic

	subgroup	G/H
center	C₂	#22560637
commutator	C₂×C₈×C₆₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₆₇
Fitting	C₆₇×#3407	C₂
socle	C₂×C₆₇	#1893
prime radical	#22569857	C₂
cosocle	C₂²×C₈×C₆₇	C₂³
hypercenter	#3407	D₆₇
hypocenter	C₆₇	#13074
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3407

subgroup

G/H

center

C₂

#22560637

commutator

C₂×C₈×C₆₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₆₇

Fitting

C₆₇×#3407

C₂

C₂×C₆₇

C₂

C₂²×C₈×C₆₇

C₂³

D₆₇

C₆₇

G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3407

N	H ≅ G/N	type
2. #22561926	C₂	semidirect
3. #22560255	C₂	semidirect
4. #22558311	C₂	semidirect
5. C₆₇×#3407	C₂	semidirect
8. #16863649	C₄	semidirect
48. C₂×C₁₆×C₆₇	D₄	semidirect
127. #3407	D₆₇	semidirect
132. C₆₇	#13074	semidirect
169. C₂×C₁₆	C₂²⋊D₆₇	semidirect

H ≅ G/N

type

2. #22561926

C₂

semidirect

3. #22560255

C₂

semidirect

4. #22558311

C₂

semidirect

5. C₆₇×#3407

C₂

semidirect

8. #16863649

C₄

semidirect

48. C₂×C₁₆×C₆₇

D₄

semidirect

127. #3407

D₆₇

semidirect

132. C₆₇

#13074

semidirect

169. C₂×C₁₆

C₂²⋊D₆₇

semidirect

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

subgroup	index
#22569857	2
#22561926	2
#22560255	2
#22558311	2
C₆₇×#3407	2
#13074	67

subgroup

index

C₆₇×#3407

Subgroups — #30773280

Conjugacy classes of subgroups

Complements

Maximal subgroups