Group #30767451 — subgroups

Subgroups — #30767451

Order 17152.

232 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 99 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	#22562011	C₂	1	1	yes	maximal, characteristic
2	#22561963	C₂	1	1	yes	maximal, characteristic
3	C₈×#11761611	C₂	1	1	yes	maximal, characteristic
4	#22558279	C₂	1	1	yes	maximal, characteristic, complemented
5	#22558278	C₂	1	1	yes	maximal, characteristic, complemented
6	#22558272	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1367	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14523982	—	2	1	no	—
9	#16863447	C₄	1	1	yes	characteristic
10	C₄×#11761611	C₄	1	1	yes	characteristic
11	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
12	C₄⋊(C₆₇⋊C₁₆)	C₂²	1	1	yes	characteristic
13	C₄⋊(C₆₇⋊C₁₆)	C₂²	1	1	yes	characteristic
14	Dic₆₇⋊C₁₆	—	2	1	no	—
15	(C₂×D₆₇)⋊C₁₆	—	2	1	no	—
16	#16863171	—	2	1	no	—
17	#16863118	C₄	1	1	yes	characteristic
18	#16863117	C₄	1	1	yes	characteristic
19	C₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₄⋊C₁₆×C₆₇	C₂²	1	1	yes	characteristic
21	C₄⋊C₁₆×C₆₇	C₂²	1	1	yes	characteristic
22	C₈²×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#11761611	C₈	1	1	yes	characteristic
24	C₂×#11761611	C₈	1	1	yes	characteristic
25	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
26	C₂×C₈×D₆₇	Q₈	1	1	yes	characteristic
27	C₄²×D₆₇	C₂×C₄	1	1	yes	characteristic
28	#14523982	—	4	2	no	—
29	C₂×C₆₇⋊C₁₆	—	2	1	no	—
30	C₂×C₆₇⋊C₁₆	—	2	1	no	—
31	Dic₆₇⋊C₈	—	2	1	no	—
32	(C₂×D₆₇)⋊C₈	—	2	1	no	—
33	#14523953	C₈	1	1	yes	characteristic
34	#14523953	C₈	1	1	yes	characteristic
35	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
37	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
38	C₈×Dic₆₇	D₄	1	1	yes	characteristic
39	C₈×Dic₆₇	Q₈	1	1	yes	characteristic
40	C₂×C₁₆×C₆₇	—	2	1	no	—
41	C₂×C₁₆×C₆₇	—	2	1	no	—
42	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
45	C₂×C₄×D₆₇	C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₄×D₆₇	C₂×C₈	1	1	yes	characteristic
47	C₂×C₄×D₆₇	M₁₆	1	1	yes	characteristic
48	#11761611	—	2	2	no	—
49	#11761611	—	2	2	no	—
50	C₂×C₆₇⋊C₈	—	2	1	no	—
51	C₂×C₆₇⋊C₈	C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₆₇⋊C₈	C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₆₇⋊C₈	C₂×C₈	1	1	yes	characteristic
54	C₂×C₆₇⋊C₈	C₂×C₈	1	1	yes	characteristic
55	C₈×D₆₇	—	2	1	no	—
56	C₈×D₆₇	—	2	1	no	—
57	C₈×D₆₇	—	4	1	no	—
58	C₄×Dic₆₇	C₄⋊C₄	1	1	yes	characteristic
59	C₄×Dic₆₇	C₂×C₈	1	1	yes	characteristic
60	C₄×Dic₆₇	M₁₆	1	1	yes	characteristic
61	C₆₇⋊C₁₆	—	4	1	no	—
62	C₆₇⋊C₁₆	—	4	1	no	—
63	C₂×C₈×C₆₇	—	2	1	no	—
64	C₂×C₈×C₆₇	C₂×C₈	1	1	yes	characteristic
65	C₂×C₈×C₆₇	C₂×C₈	1	1	yes	characteristic
66	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
67	C₂×C₈×C₆₇	C₂×Q₈	1	1	yes	characteristic
68	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
69	C₁₆×C₆₇	—	4	1	no	—
70	C₁₆×C₆₇	—	4	1	no	—
71	C₂²×D₆₇	C₄⋊C₈	1	1	yes	characteristic
72	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
73	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
74	C₂×C₄×C₆₇	C₂×M₁₆	1	1	yes	characteristic
75	C₂×Dic₆₇	C₄⋊C₈	1	1	yes	characteristic
76	C₂×Dic₆₇	C₄⋊C₈	1	1	yes	characteristic
77	C₂×Dic₆₇	C₄⋊C₈	1	1	yes	characteristic
78	C₄×D₆₇	—	2	1	no	—
79	C₄×D₆₇	—	2	1	no	—
80	C₄×D₆₇	—	2	1	no	—
81	C₄×D₆₇	—	2	1	no	—
82	C₄×D₆₇	—	4	1	no	—
83	C₈×C₆₇	—	2	1	no	—
84	C₈×C₆₇	—	2	1	no	—
85	C₈×C₆₇	—	4	1	no	—
86	C₈×C₆₇	M₃₂	1	2	yes	complemented
87	C₈×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
88	C₈×C₆₇	#137	1	1	yes	characteristic
89	C₆₇⋊C₈	—	2	1	no	—
90	C₆₇⋊C₈	—	2	1	no	—
91	C₆₇⋊C₈	—	2	1	no	—
92	C₆₇⋊C₈	—	4	1	no	—
93	C₆₇⋊C₈	M₃₂	1	2	yes	complemented
94	C₂²×C₆₇	C₂×C₄⋊C₈	1	1	yes	characteristic
95	C₂×D₆₇	—	2	1	no	—
96	C₂×D₆₇	—	2	1	no	—
97	C₂×D₆₇	—	2	1	no	—
98	C₄×C₆₇	—	2	1	no	—
99	C₄×C₆₇	#428	1	1	yes	characteristic
100	C₄×C₆₇	#430	1	1	yes	characteristic
101	C₄×C₆₇	C₂×M₃₂	1	1	yes	characteristic
102	C₄×C₆₇	C₂×M₃₂	1	1	yes	characteristic
103	Dic₆₇	—	2	1	no	—
104	Dic₆₇	—	2	1	no	—
105	Dic₆₇	—	2	1	no	—
106	#12017	—	67	1	no	maximal, Sylow
107	C₂×C₆₇	#1565	1	1	yes	characteristic
108	C₂×C₆₇	#2150	1	1	yes	characteristic
109	C₂×C₆₇	#2153	1	1	yes	characteristic
110	D₆₇	—	4	1	no	—
111	#2163	—	67	1	no	—
112	#2150	—	67	1	no	—
113	C₈×M₁₆	—	67	1	no	—
114	#1370	—	67	1	no	—
115	#1370	—	67	1	no	—
116	#1367	—	67	1	no	—
117	#1367	D₆₇	1	1	yes	characteristic, complemented
118	C₆₇	#12017	1	1	yes	characteristic, complemented, Sylow
119	C₂×M₃₂	—	134	1	no	—
120	#431	—	67	1	no	—
121	C₄×M₁₆	—	67	1	no	—
122	C₂×C₄×C₈	—	67	1	no	—
123	C₄⋊C₁₆	—	67	1	no	—
124	C₄⋊C₁₆	—	67	1	no	—
125	C₄⋊C₁₆	—	134	1	no	—
126	C₄⋊C₁₆	C₂×D₆₇	1	1	yes	characteristic
127	C₄⋊C₁₆	C₂×D₆₇	1	1	yes	characteristic
128	C₂²⋊C₁₆	—	134	1	no	—
129	#346	—	134	1	no	—
130	#322	—	67	1	no	—
131	#322	—	67	1	no	—
132	C₈²	—	67	1	no	—
133	C₈²	C₂×D₆₇	1	1	yes	characteristic
134	C₂×M₁₆	—	67	1	no	—
135	C₂×M₁₆	—	67	1	no	—
136	C₂²×C₈	—	67	1	no	—
137	C₂²×C₈	—	67	1	no	—
138	C₂×C₄²	—	67	1	no	—
139	M₃₂	—	268	2	no	—
140	C₂×C₁₆	—	2	1	no	—
141	C₂×C₁₆	—	2	1	no	—
142	C₂×C₁₆	—	134	1	no	—
143	C₂×C₁₆	—	134	1	no	—
144	C₄⋊C₈	—	134	1	no	—
145	C₂²⋊C₈	—	134	1	no	—
146	#97	—	67	1	no	—
147	#97	—	67	1	no	—
148	C₄×C₈	—	67	1	no	—
149	C₄×C₈	—	67	1	no	—
150	C₄×C₈	—	67	1	no	—
151	C₄×C₈	—	67	1	no	—
152	C₄×C₈	—	67	1	no	—
153	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
154	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
155	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
156	C₂²×C₄	—	67	1	no	—
157	C₂²×C₄	—	67	1	no	—
158	C₂²×C₄	—	67	1	no	—
159	M₁₆	—	134	2	no	—
160	M₁₆	—	134	2	no	—
161	C₂×C₈	—	2	1	no	—
162	C₂×C₈	—	268	1	no	—
163	C₂×C₈	—	67	1	no	—
164	C₂×C₈	—	67	1	no	—
165	C₂×C₈	—	67	1	no	—
166	C₂×C₈	—	67	1	no	—
167	C₂×C₈	—	134	1	no	—
168	C₂×C₈	—	134	1	no	—
169	C₂×C₈	—	134	1	no	—
170	C₂×C₈	C₈×D₆₇	1	1	yes	characteristic
171	C₂×C₈	C₈×D₆₇	1	1	yes	characteristic
172	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
173	C₂×C₈	Q₈×D₆₇	1	1	yes	characteristic
174	C₄²	—	67	1	no	—
175	C₄²	—	67	1	no	—
176	C₄²	—	67	1	no	—
177	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
178	C₁₆	—	4	1	no	—
179	C₁₆	—	4	1	no	—
180	C₁₆	—	268	1	no	—
181	C₁₆	—	268	1	no	—
182	C₂³	—	67	1	no	—
183	C₂×C₄	—	268	1	no	—
184	C₂×C₄	—	67	1	no	—
185	C₂×C₄	—	67	1	no	—
186	C₂×C₄	—	67	1	no	—
187	C₂×C₄	—	134	1	no	—
188	C₂×C₄	—	134	1	no	—
189	C₂×C₄	—	134	1	no	—
190	C₂×C₄	—	134	1	no	—
191	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
192	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
193	C₂×C₄	M₁₆×D₆₇	1	1	yes	characteristic
194	C₈	—	2	1	no	—
195	C₈	—	2	1	no	—
196	C₈	—	4	1	no	—
197	C₈	—	268	1	no	—
198	C₈	—	67	2	no	—
199	C₈	—	134	1	no	—
200	C₈	—	134	1	no	—
201	C₈	—	134	1	no	—
202	C₈	#14523982	1	2	yes	complemented
203	C₈	#14524070	1	1	yes	characteristic
204	C₈	#14524072	1	1	yes	characteristic
205	C₂²	—	134	1	no	—
206	C₂²	—	134	1	no	—
207	C₂²	—	134	1	no	—
208	C₂²	C₄⋊C₈×D₆₇	1	1	yes	characteristic
209	C₄	—	2	1	no	—
210	C₄	—	134	1	no	—
211	C₄	—	134	1	no	—
212	C₄	—	134	1	no	—
213	C₄	#16863435	1	1	yes	characteristic
214	C₄	#16863443	1	1	yes	characteristic
215	C₄	M₃₂×D₆₇	1	1	yes	characteristic
216	C₄	C₂×#14523982	1	1	yes	characteristic
217	C₂	—	268	1	no	—
218	C₂	#22558958	1	1	yes	characteristic
219	C₂	#22561963	1	1	yes	characteristic
220	C₂	#22561973	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22562011

C₂

yes

maximal, characteristic

#22561963

C₂

yes

maximal, characteristic

C₈×#11761611

C₂

yes

maximal, characteristic

#22558279

C₂

yes

maximal, characteristic, complemented

#22558278

C₂

yes

maximal, characteristic, complemented

#22558272

C₂

yes

maximal, characteristic, complemented

C₆₇×#1367

C₂

yes

maximal, characteristic, complemented

C₂×#14523982

—

#16863447

C₄

yes

characteristic

C₄×#11761611

C₄

yes

characteristic

C₄×C₈×D₆₇

C₂²

yes

characteristic

C₄⋊(C₆₇⋊C₁₆)

C₂²

yes

characteristic

C₄⋊(C₆₇⋊C₁₆)

C₂²

yes

characteristic

Dic₆₇⋊C₁₆

—

(C₂×D₆₇)⋊C₁₆

—

#16863171

—

#16863118

C₄

yes

characteristic

#16863117

C₄

yes

characteristic

C₈×C₆₇⋊C₈

C₂²

yes

characteristic

C₄⋊C₁₆×C₆₇

C₂²

yes

characteristic

C₄⋊C₁₆×C₆₇

C₂²

yes

characteristic

C₈²×C₆₇

C₂²

yes

characteristic

C₂×#11761611

C₈

yes

characteristic

C₂×#11761611

C₈

yes

characteristic

C₂×C₈×D₆₇

D₄

yes

characteristic

C₂×C₈×D₆₇

Q₈

yes

characteristic

C₄²×D₆₇

C₂×C₄

yes

characteristic

#14523982

—

C₂×C₆₇⋊C₁₆

—

C₂×C₆₇⋊C₁₆

—

Dic₆₇⋊C₈

—

(C₂×D₆₇)⋊C₈

—

#14523953

C₈

yes

characteristic

#14523953

C₈

yes

characteristic

C₄×C₆₇⋊C₈

C₂×C₄

yes

characteristic

C₄×C₆₇⋊C₈

C₂×C₄

yes

characteristic

C₄×C₆₇⋊C₈

C₂×C₄

yes

characteristic

C₈×Dic₆₇

D₄

yes

characteristic

C₈×Dic₆₇

Q₈

yes

characteristic

C₂×C₁₆×C₆₇

—

C₂×C₁₆×C₆₇

—

C₄×C₈×C₆₇

C₂×C₄

yes

characteristic

C₄×C₈×C₆₇

C₂×C₄

yes

characteristic

C₄×C₈×C₆₇

C₂³

yes

characteristic

C₂×C₄×D₆₇

C₄⋊C₄

yes

characteristic

C₂×C₄×D₆₇

C₂×C₈

yes

characteristic

C₂×C₄×D₆₇

M₁₆

yes

characteristic

#11761611

—

#11761611

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₆₇⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₆₇⋊C₈

C₂×C₈

yes

characteristic

C₂×C₆₇⋊C₈

C₂×C₈

yes

characteristic

C₈×D₆₇

—

C₈×D₆₇

—

C₈×D₆₇

—

C₄×Dic₆₇

C₄⋊C₄

yes

characteristic

C₄×Dic₆₇

C₂×C₈

yes

characteristic

C₄×Dic₆₇

M₁₆

yes

characteristic

C₆₇⋊C₁₆

—

C₆₇⋊C₁₆

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

C₂×C₈

yes

characteristic

C₂×C₈×C₆₇

C₂×C₈

yes

characteristic

C₂×C₈×C₆₇

C₂×D₄

yes

characteristic

C₂×C₈×C₆₇

C₂×Q₈

yes

characteristic

C₄²×C₆₇

C₂²×C₄

yes

characteristic

C₁₆×C₆₇

—

C₁₆×C₆₇

—

C₂²×D₆₇

C₄⋊C₈

yes

characteristic

C₂×C₄×C₆₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₇

C₂²×C₈

yes

characteristic

C₂×C₄×C₆₇

C₂×M₁₆

yes

characteristic

C₂×Dic₆₇

C₄⋊C₈

yes

characteristic

C₂×Dic₆₇

C₄⋊C₈

yes

characteristic

C₂×Dic₆₇

C₄⋊C₈

yes

characteristic

C₄×D₆₇

—

C₄×D₆₇

—

C₄×D₆₇

—

C₄×D₆₇

—

C₄×D₆₇

—

C₈×C₆₇

—

C₈×C₆₇

—

C₈×C₆₇

—

C₈×C₆₇

M₃₂

yes

C₈×C₆₇

yes

C₈×C₆₇

yes

C₆₇⋊C₈

—

C₆₇⋊C₈

—

C₆₇⋊C₈

—

C₆₇⋊C₈

—

C₆₇⋊C₈

M₃₂

yes

complemented

C₂²×C₆₇

C₂×C₄⋊C₈

yes

characteristic

C₂×D₆₇

—

C₂×D₆₇

—

C₂×D₆₇

—

C₄×C₆₇

—

C₄×C₆₇

#428

yes

characteristic

100

C₄×C₆₇

#430

yes

characteristic

101

C₄×C₆₇

C₂×M₃₂

yes

characteristic

102

C₄×C₆₇

C₂×M₃₂

yes

characteristic

103

Dic₆₇

—

104

Dic₆₇

—

105

Dic₆₇

—

106

#12017

—

maximal, Sylow

107

C₂×C₆₇

#1565

yes

characteristic

108

C₂×C₆₇

#2150

yes

characteristic

109

C₂×C₆₇

#2153

yes

characteristic

110

D₆₇

—

111

#2163

—

112

#2150

—

113

C₈×M₁₆

—

114

#1370

—

115

#1370

—

116

#1367

—

117

#1367

D₆₇

yes

characteristic, complemented

118

C₆₇

#12017

yes

characteristic, complemented, Sylow

119

C₂×M₃₂

—

134

—

120

#431

—

121

C₄×M₁₆

—

122

C₂×C₄×C₈

—

123

C₄⋊C₁₆

—

124

C₄⋊C₁₆

—

125

C₄⋊C₁₆

—

134

—

126

C₄⋊C₁₆

C₂×D₆₇

yes

characteristic

127

C₄⋊C₁₆

C₂×D₆₇

yes

characteristic

128

C₂²⋊C₁₆

—

134

—

129

#346

—

134

—

130

#322

—

131

#322

—

132

C₈²

—

133

C₈²

C₂×D₆₇

yes

characteristic

134

C₂×M₁₆

—

135

C₂×M₁₆

—

136

C₂²×C₈

—

137

C₂²×C₈

—

138

C₂×C₄²

—

139

M₃₂

—

268

—

140

C₂×C₁₆

—

141

C₂×C₁₆

—

142

C₂×C₁₆

—

134

—

143

C₂×C₁₆

—

134

—

144

C₄⋊C₈

—

134

—

145

C₂²⋊C₈

—

134

—

146

#97

—

147

#97

—

148

C₄×C₈

—

149

C₄×C₈

—

150

C₄×C₈

—

151

C₄×C₈

—

152

C₄×C₈

—

153

C₄×C₈

C₄×D₆₇

yes

characteristic

154

C₄×C₈

C₄×D₆₇

yes

characteristic

155

C₄×C₈

C₂²×D₆₇

yes

characteristic

156

C₂²×C₄

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

M₁₆

—

134

—

160

M₁₆

—

134

—

161

C₂×C₈

—

162

C₂×C₈

—

268

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

134

—

168

C₂×C₈

—

134

—

169

C₂×C₈

—

134

—

170

C₂×C₈

C₈×D₆₇

yes

characteristic

171

C₂×C₈

C₈×D₆₇

yes

characteristic

172

C₂×C₈

D₄×D₆₇

yes

characteristic

173

C₂×C₈

Q₈×D₆₇

yes

characteristic

174

C₄²

—

175

C₄²

—

176

C₄²

—

177

C₄²

C₂×C₄×D₆₇

yes

characteristic

178

C₁₆

—

179

C₁₆

—

180

C₁₆

—

268

—

181

C₁₆

—

268

—

182

C₂³

—

183

C₂×C₄

—

268

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

134

—

188

C₂×C₄

—

134

—

189

C₂×C₄

—

134

—

190

C₂×C₄

—

134

—

191

C₂×C₄

C₄⋊C₄×D₆₇

yes

characteristic

192

C₂×C₄

C₂×C₈×D₆₇

yes

characteristic

193

C₂×C₄

M₁₆×D₆₇

yes

characteristic

194

C₈

—

195

C₈

—

196

C₈

—

197

C₈

—

268

—

198

C₈

—

199

C₈

—

134

—

200

C₈

—

134

—

201

C₈

—

134

—

202

C₈

#14523982

yes

complemented

203

C₈

#14524070

yes

characteristic

204

C₈

#14524072

yes

characteristic

205

C₂²

—

134

—

206

C₂²

—

134

—

207

C₂²

—

134

—

208

C₂²

C₄⋊C₈×D₆₇

yes

characteristic

209

C₄

—

210

C₄

—

134

—

211

C₄

—

134

—

212

C₄

—

134

—

213

C₄

#16863435

yes

characteristic

214

C₄

#16863443

yes

characteristic

215

C₄

M₃₂×D₆₇

yes

characteristic

216

C₄

C₂×#14523982

yes

characteristic

217

C₂

—

268

—

218

C₂

#22558958

yes

characteristic

219

C₂

#22561963

yes

characteristic

220

C₂

#22561973

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₆₇
Fitting	C₆₇×#1367	C₂
socle	C₂²×C₆₇	C₂×C₄⋊C₈
prime radical	C₂²×D₆₇	C₄⋊C₈
cosocle	C₄×C₈×C₆₇	C₂³
hypercenter	#1367	D₆₇
hypocenter	C₆₇	#12017
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1367

subgroup

G/H

center

C₂×C₈

D₄×D₆₇

commutator

C₂×C₄×C₆₇

C₂²×C₈

Frattini

C₄×C₈

C₂²×D₆₇

Fitting

C₆₇×#1367

C₂

socle

C₂²×C₆₇

C₂×C₄⋊C₈

prime radical

C₂²×D₆₇

C₄⋊C₈

cosocle

C₄×C₈×C₆₇

C₂³

D₆₇

C₆₇

G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1367

N	H ≅ G/N	type
4. #22558279	C₂	semidirect
5. #22558278	C₂	semidirect
6. #22558272	C₂	semidirect
7. C₆₇×#1367	C₂	semidirect
86. C₈×C₆₇	M₃₂	semidirect
93. C₆₇⋊C₈	M₃₂	semidirect
117. #1367	D₆₇	semidirect
118. C₆₇	#12017	semidirect
202. C₈	#14523982	semidirect

H ≅ G/N

type

4. #22558279

C₂

semidirect

5. #22558278

C₂

semidirect

6. #22558272

C₂

semidirect

7. C₆₇×#1367

C₂

semidirect

86. C₈×C₆₇

M₃₂

semidirect

93. C₆₇⋊C₈

M₃₂

semidirect

117. #1367

D₆₇

semidirect

118. C₆₇

#12017

semidirect

202. C₈

#14523982

semidirect

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

subgroup	index
#22562011	2
#22561963	2
C₈×#11761611	2
#22558279	2
#22558278	2
#22558272	2
C₆₇×#1367	2
#12017	67

subgroup

index

C₆₇×#1367

Subgroups — #30767451

Conjugacy classes of subgroups

Complements

Maximal subgroups