Group #30754648 — subgroups

Subgroups — #30754648

Order 17152.

558 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 167 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	#22560326	C₂	1	1	yes	maximal, characteristic
2	C₄×#14523954	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈⋊(C₆₇⋊C₈)	C₂	1	4	yes	maximal
4	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
6	C₂×#14523954	—	2	2	no	—
7	C₂×C₄×C₆₇⋊C₈	C₂²	1	2	yes	—
8	#16863151	—	2	2	no	—
9	Q₈⋊(C₆₇⋊C₈)	—	2	8	no	—
10	C₂×C₄⋊Q₈×C₆₇	C₄	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
12	#391×C₆₇	C₄	1	2	yes	—
13	#389×C₆₇	—	2	2	no	—
14	#384×C₆₇	C₄	1	1	yes	characteristic
15	C₄×C₄⋊C₄×C₆₇	—	2	2	no	—
16	C₄³×C₆₇	C₂²	1	1	yes	characteristic
17	C₂²×C₆₇⋊C₈	—	2	2	no	—
18	C₂²×C₆₇⋊C₈	—	2	2	no	—
19	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
20	#14523954	—	2	8	no	—
21	C₄×C₆₇⋊C₈	—	2	2	no	—
22	C₄×C₆₇⋊C₈	D₄	1	4	yes	—
23	C₂²×Q₈×C₆₇	C₂×C₄	1	2	yes	—
24	C₄⋊Q₈×C₆₇	—	2	4	no	—
25	C₄×Q₈×C₆₇	—	2	4	no	—
26	C₄×Q₈×C₆₇	—	2	4	no	—
27	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
28	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
29	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
30	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₆₇	—	2	2	no	—
32	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₆₇	D₄	1	2	yes	—
35	C₂×C₄²×C₆₇	D₄	1	2	yes	—
36	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
37	#95×C₆₇	—	2	4	no	—
38	C₂×C₆₇⋊C₈	—	2	8	no	—
39	C₂×C₆₇⋊C₈	—	2	4	no	—
40	C₂×C₆₇⋊C₈	—	4	2	no	—
41	C₂×C₆₇⋊C₈	—	4	4	no	—
42	C₂×Q₈×C₆₇	—	2	2	no	—
43	C₂×Q₈×C₆₇	—	2	4	no	—
44	C₂×Q₈×C₆₇	—	2	4	no	—
45	C₂×Q₈×C₆₇	M₁₆	1	4	yes	—
46	C₂²×C₄×C₆₇	—	2	2	no	—
47	C₂²×C₄×C₆₇	—	2	2	no	—
48	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
49	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
50	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
53	C₄⋊C₄×C₆₇	—	2	8	no	—
54	C₄⋊C₄×C₆₇	—	2	4	no	—
55	C₄⋊C₄×C₆₇	—	4	4	no	—
56	C₄⋊C₄×C₆₇	—	4	4	no	—
57	C₄²×C₆₇	—	2	4	no	—
58	C₄²×C₆₇	—	2	2	no	—
59	C₄²×C₆₇	—	2	2	no	—
60	C₄²×C₆₇	—	2	4	no	—
61	C₄²×C₆₇	—	4	2	no	—
62	C₄²×C₆₇	—	4	2	no	—
63	C₄²×C₆₇	C₂×D₄	1	2	yes	—
64	C₄²×C₆₇	#41	1	2	yes	—
65	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
66	Q₈×C₆₇	—	2	8	no	—
67	Q₈×C₆₇	—	4	4	no	—
68	C₂×C₄×C₆₇	—	2	2	no	—
69	C₂×C₄×C₆₇	—	2	2	no	—
70	C₂×C₄×C₆₇	—	2	2	no	—
71	C₂×C₄×C₆₇	—	2	4	no	—
72	C₂×C₄×C₆₇	—	2	2	no	—
73	C₂×C₄×C₆₇	—	2	2	no	—
74	C₂×C₄×C₆₇	—	2	2	no	—
75	C₂×C₄×C₆₇	—	4	2	no	—
76	C₂×C₄×C₆₇	—	4	2	no	—
77	C₂×C₄×C₆₇	—	4	2	no	—
78	C₂×C₄×C₆₇	—	4	4	no	—
79	C₂×C₄×C₆₇	#104	1	4	yes	—
80	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
81	C₂×C₄×C₆₇	#121	1	2	yes	—
82	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
83	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
84	C₂×C₄×C₆₇	C₂×M₁₆	1	2	yes	—
85	C₂×C₄×C₆₇	#131	1	2	yes	—
86	C₂×C₄×C₆₇	#137	1	4	yes	—
87	C₆₇⋊C₈	—	2	8	no	—
88	C₆₇⋊C₈	—	8	2	no	—
89	C₂²×C₆₇	#390	1	1	yes	characteristic
90	C₂²×C₆₇	#407	1	1	yes	characteristic
91	C₂²×C₆₇	#408	1	1	yes	characteristic
92	C₂²×C₆₇	#419	1	2	yes	—
93	C₂²×C₆₇	C₂×#104	1	2	yes	—
94	C₄×C₆₇	—	2	2	no	—
95	C₄×C₆₇	—	2	4	no	—
96	C₄×C₆₇	—	4	4	no	—
97	C₄×C₆₇	—	4	2	no	—
98	C₄×C₆₇	—	8	2	no	—
99	C₄×C₆₇	#435	1	4	yes	—
100	C₄×C₆₇	#491	1	2	yes	—
101	C₄×C₆₇	#497	1	2	yes	—
102	#9647	—	67	1	no	maximal, Sylow
103	C₂×C₆₇	#1485	1	2	yes	—
104	C₂×C₆₇	#1491	1	2	yes	—
105	C₂×C₆₇	#1955	1	1	yes	characteristic
106	C₂×C₆₇	#1960	1	1	yes	characteristic
107	C₂×C₆₇	#1962	1	1	yes	characteristic
108	C₄×C₄⋊Q₈	D₆₇	1	1	yes	characteristic
109	#1831	—	67	1	no	—
110	C₄×#97	—	67	1	no	—
111	C₂×Q₈⋊C₈	—	67	4	no	—
112	C₆₇	#9647	1	1	yes	characteristic, complemented, Sylow
113	C₂×C₄⋊Q₈	Dic₆₇	1	1	yes	characteristic
114	C₂×C₄×Q₈	C₂×D₆₇	1	2	yes	—
115	C₂×C₄⋊C₈	—	67	2	no	—
116	C₂×#97	—	134	2	no	—
117	C₂×C₄×C₈	—	67	2	no	—
118	#391	Dic₆₇	1	2	yes	—
119	#389	—	2	2	no	—
120	#384	Dic₆₇	1	1	yes	characteristic
121	C₄×C₄⋊C₄	—	2	2	no	—
122	C₄³	C₂×D₆₇	1	1	yes	characteristic
123	#336	—	134	2	no	—
124	Q₈⋊C₈	—	134	8	no	—
125	C₂²×Q₈	C₂×Dic₆₇	1	2	yes	—
126	C₂²×C₈	—	134	2	no	—
127	C₂²×C₈	—	134	2	no	—
128	C₄⋊Q₈	—	2	4	no	—
129	C₄×Q₈	—	2	4	no	—
130	C₄×Q₈	—	2	4	no	—
131	C₂×C₄⋊C₄	—	2	2	no	—
132	C₂×C₄⋊C₄	—	2	2	no	—
133	C₂×C₄⋊C₄	—	2	2	no	—
134	C₂×C₄⋊C₄	C₂×Dic₆₇	1	2	yes	—
135	C₂×C₄²	—	2	2	no	—
136	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
137	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
138	C₂×C₄²	C₂²⋊D₆₇	1	2	yes	—
139	C₂×C₄²	C₂²⋊D₆₇	1	2	yes	—
140	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
141	C₄⋊C₈	—	134	4	no	—
142	#97	—	134	8	no	—
143	C₄×C₈	—	67	4	no	—
144	C₄×C₈	—	134	2	no	—
145	#95	—	2	4	no	—
146	C₂×Q₈	—	2	2	no	—
147	C₂×Q₈	—	2	4	no	—
148	C₂×Q₈	—	2	4	no	—
149	C₂×Q₈	#11761612	1	4	yes	—
150	C₂²×C₄	—	2	2	no	—
151	C₂²×C₄	—	2	2	no	—
152	C₂²×C₄	C₂²⋊Dic₆₇	1	2	yes	—
153	C₂²×C₄	C₂²⋊Dic₆₇	1	2	yes	—
154	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
155	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
156	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
157	C₂×C₈	—	268	2	no	—
158	C₂×C₈	—	268	4	no	—
159	C₂×C₈	—	134	8	no	—
160	C₂×C₈	—	134	4	no	—
161	C₄⋊C₄	—	2	8	no	—
162	C₄⋊C₄	—	2	4	no	—
163	C₄⋊C₄	—	4	4	no	—
164	C₄⋊C₄	—	4	4	no	—
165	C₄²	—	2	4	no	—
166	C₄²	—	2	2	no	—
167	C₄²	—	2	2	no	—
168	C₄²	—	2	4	no	—
169	C₄²	—	4	2	no	—
170	C₄²	—	4	2	no	—
171	C₄²	D₄×D₆₇	1	2	yes	—
172	C₄²	#11761627	1	2	yes	—
173	C₂³	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
174	Q₈	—	2	8	no	—
175	Q₈	—	4	4	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	4	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	4	2	no	—
184	C₂×C₄	—	4	2	no	—
185	C₂×C₄	—	4	2	no	—
186	C₂×C₄	—	4	4	no	—
187	C₂×C₄	#14523970	1	4	yes	—
188	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
189	C₂×C₄	#14524014	1	2	yes	—
190	C₂×C₄	#14524030	1	1	yes	characteristic
191	C₂×C₄	#14524039	1	1	yes	characteristic
192	C₂×C₄	C₂×#11761612	1	2	yes	—
193	C₂×C₄	#14524050	1	2	yes	—
194	C₂×C₄	#14524074	1	4	yes	—
195	C₈	—	536	2	no	—
196	C₈	—	134	8	no	—
197	C₂²	#16863299	1	1	yes	characteristic
198	C₂²	#16863360	1	1	yes	characteristic
199	C₂²	#16863363	1	1	yes	characteristic
200	C₂²	#16863405	1	2	yes	—
201	C₂²	C₂×#14523970	1	2	yes	—
202	C₄	—	2	2	no	—
203	C₄	—	2	4	no	—
204	C₄	—	4	2	no	—
205	C₄	—	4	4	no	—
206	C₄	—	8	2	no	—
207	C₄	#16863468	1	4	yes	—
208	C₄	#16863764	1	2	yes	—
209	C₄	#16863788	1	2	yes	—
210	C₂	#22558630	1	2	yes	—
211	C₂	#22558656	1	2	yes	—
212	C₂	#22561008	1	1	yes	characteristic
213	C₂	#22561030	1	1	yes	characteristic
214	C₂	#22561038	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22560326

C₂

yes

maximal, characteristic

C₄×#14523954

C₂

yes

maximal, characteristic

C₂×Q₈⋊(C₆₇⋊C₈)

C₂

yes

maximal

C₄×C₄⋊Q₈×C₆₇

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₆₇⋊C₈)

C₂²

yes

—

C₂×#14523954

—

C₂×C₄×C₆₇⋊C₈

C₂²

yes

—

#16863151

—

Q₈⋊(C₆₇⋊C₈)

—

C₂×C₄⋊Q₈×C₆₇

C₄

yes

characteristic

C₂×C₄×Q₈×C₆₇

C₂²

yes

—

#391×C₆₇

C₄

yes

—

#389×C₆₇

—

#384×C₆₇

C₄

yes

characteristic

C₄×C₄⋊C₄×C₆₇

—

C₄³×C₆₇

C₂²

yes

characteristic

C₂²×C₆₇⋊C₈

—

C₂²×C₆₇⋊C₈

—

C₄⋊(C₆₇⋊C₈)

—

#14523954

—

C₄×C₆₇⋊C₈

—

C₄×C₆₇⋊C₈

D₄

yes

—

C₂²×Q₈×C₆₇

C₂×C₄

yes

—

C₄⋊Q₈×C₆₇

—

C₄×Q₈×C₆₇

—

C₄×Q₈×C₆₇

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₄⋊C₄×C₆₇

C₂×C₄

yes

—

C₂×C₄²×C₆₇

—

C₂×C₄²×C₆₇

C₂×C₄

yes

characteristic

C₂×C₄²×C₆₇

C₂×C₄

yes

characteristic

C₂×C₄²×C₆₇

D₄

yes

—

C₂×C₄²×C₆₇

D₄

yes

—

C₂×C₄²×C₆₇

C₂³

yes

characteristic

#95×C₆₇

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

M₁₆

yes

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₆₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₆₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄²×C₆₇

—

C₄²×C₆₇

—

C₄²×C₆₇

—

C₄²×C₆₇

—

C₄²×C₆₇

—

C₄²×C₆₇

—

C₄²×C₆₇

C₂×D₄

yes

—

C₄²×C₆₇

#41

yes

—

C₂³×C₆₇

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₆₇

—

Q₈×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

#104

yes

—

C₂×C₄×C₆₇

C₄×D₄

yes

—

C₂×C₄×C₆₇

#121

yes

—

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

C₂×M₁₆

yes

—

C₂×C₄×C₆₇

#131

yes

—

C₂×C₄×C₆₇

#137

yes

—

C₆₇⋊C₈

—

C₆₇⋊C₈

—

C₂²×C₆₇

yes

C₂²×C₆₇

yes

C₂²×C₆₇

yes

C₂²×C₆₇

yes

—

C₂²×C₆₇

C₂×#104

yes

—

C₄×C₆₇

—

C₄×C₆₇

—

C₄×C₆₇

—

C₄×C₆₇

—

C₄×C₆₇

—

C₄×C₆₇

#435

yes

—

100

C₄×C₆₇

#491

yes

—

101

C₄×C₆₇

#497

yes

—

102

#9647

—

maximal, Sylow

103

C₂×C₆₇

#1485

yes

—

104

C₂×C₆₇

#1491

yes

—

105

C₂×C₆₇

#1955

yes

characteristic

106

C₂×C₆₇

#1960

yes

characteristic

107

C₂×C₆₇

#1962

yes

characteristic

108

C₄×C₄⋊Q₈

D₆₇

yes

characteristic

109

#1831

—

110

C₄×#97

—

111

C₂×Q₈⋊C₈

—

112

C₆₇

#9647

yes

characteristic, complemented, Sylow

113

C₂×C₄⋊Q₈

Dic₆₇

yes

characteristic

114

C₂×C₄×Q₈

C₂×D₆₇

yes

—

115

C₂×C₄⋊C₈

—

116

C₂×#97

—

134

—

117

C₂×C₄×C₈

—

118

#391

Dic₆₇

yes

—

119

#389

—

120

#384

Dic₆₇

yes

characteristic

121

C₄×C₄⋊C₄

—

122

C₄³

C₂×D₆₇

yes

characteristic

123

#336

—

134

—

124

Q₈⋊C₈

—

134

—

125

C₂²×Q₈

C₂×Dic₆₇

yes

—

126

C₂²×C₈

—

134

—

127

C₂²×C₈

—

134

—

128

C₄⋊Q₈

—

129

C₄×Q₈

—

130

C₄×Q₈

—

131

C₂×C₄⋊C₄

—

132

C₂×C₄⋊C₄

—

133

C₂×C₄⋊C₄

—

134

C₂×C₄⋊C₄

C₂×Dic₆₇

yes

—

135

C₂×C₄²

—

136

C₂×C₄²

C₂×Dic₆₇

yes

characteristic

137

C₂×C₄²

C₂×Dic₆₇

yes

characteristic

138

C₂×C₄²

C₂²⋊D₆₇

yes

—

139

C₂×C₄²

C₂²⋊D₆₇

yes

—

140

C₂×C₄²

C₂²×D₆₇

yes

characteristic

141

C₄⋊C₈

—

134

—

142

#97

—

134

—

143

C₄×C₈

—

144

C₄×C₈

—

134

—

145

#95

—

146

C₂×Q₈

—

147

C₂×Q₈

—

148

C₂×Q₈

—

149

C₂×Q₈

#11761612

yes

—

150

C₂²×C₄

—

151

C₂²×C₄

—

152

C₂²×C₄

C₂²⋊Dic₆₇

yes

—

153

C₂²×C₄

C₂²⋊Dic₆₇

yes

—

154

C₂²×C₄

C₂²×Dic₆₇

yes

characteristic

155

C₂²×C₄

C₂×C₂²⋊D₆₇

yes

characteristic

156

C₂²×C₄

C₂×C₂²⋊D₆₇

yes

characteristic

157

C₂×C₈

—

268

—

158

C₂×C₈

—

268

—

159

C₂×C₈

—

134

—

160

C₂×C₈

—

134

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄²

—

166

C₄²

—

167

C₄²

—

168

C₄²

—

169

C₄²

—

170

C₄²

—

171

C₄²

D₄×D₆₇

yes

—

172

C₄²

#11761627

yes

—

173

C₂³

C₂×C₂²⋊Dic₆₇

yes

characteristic

174

Q₈

—

175

Q₈

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

#14523970

yes

—

188

C₂×C₄

D₄×Dic₆₇

yes

—

189

C₂×C₄

#14524014

yes

—

190

C₂×C₄

#14524030

yes

characteristic

191

C₂×C₄

#14524039

yes

characteristic

192

C₂×C₄

C₂×#11761612

yes

—

193

C₂×C₄

#14524050

yes

—

194

C₂×C₄

#14524074

yes

—

195

C₈

—

536

—

196

C₈

—

134

—

197

C₂²

#16863299

yes

characteristic

198

C₂²

#16863360

yes

characteristic

199

C₂²

#16863363

yes

characteristic

200

C₂²

#16863405

yes

—

201

C₂²

C₂×#14523970

yes

—

202

C₄

—

203

C₄

—

204

C₄

—

205

C₄

—

206

C₄

—

207

C₄

#16863468

yes

—

208

C₄

#16863764

yes

—

209

C₄

#16863788

yes

—

210

C₂

#22558630

yes

—

211

C₂

#22558656

yes

—

212

C₂

#22561008

yes

characteristic

213

C₂

#22561030

yes

characteristic

214

C₂

#22561038

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₆₇
commutator	C₂²×C₄×C₆₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₄×C₄⋊Q₈×C₆₇	C₂
socle, prime radical	C₂³×C₆₇	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	C₄×C₄⋊Q₈	D₆₇
hypocenter	C₆₇	#9647
LCS	G ▷ C₂²×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×C₄⋊Q₈

subgroup

G/H

center

C₂²×C₄

C₂×C₂²⋊D₆₇

commutator

C₂²×C₄×C₆₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₆₇

Fitting

C₄×C₄⋊Q₈×C₆₇

C₂

socle, prime radical

C₂³×C₆₇

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₆₇

C₂³

hypercenter

C₄×C₄⋊Q₈

D₆₇

hypocenter

C₆₇

#9647

LCS

G ▷ C₂²×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×C₄⋊Q₈

N	H ≅ G/N	type
112. C₆₇	#9647	semidirect

H ≅ G/N

type

112. C₆₇

#9647

semidirect

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

subgroup	index
#22560326	2
C₄×#14523954	2
C₂×Q₈⋊(C₆₇⋊C₈)	2
C₄×C₄⋊Q₈×C₆₇	2
#9647	67

subgroup

index

#22560326

C₄×#14523954

C₂×Q₈⋊(C₆₇⋊C₈)

C₄×C₄⋊Q₈×C₆₇

#9647

Subgroups — #30754648

Conjugacy classes of subgroups

Complements

Maximal subgroups