Group #30772393 — subgroups

Subgroups — #30772393

Order 17152.

414 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 131 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×#16863218	C₂	1	2	yes	maximal, complemented
2	#22561820	C₂	1	1	yes	maximal, characteristic
3	#22560247	C₂	1	1	yes	maximal, characteristic
4	#22558307	C₂	1	2	yes	maximal, complemented
5	C₂×#427×C₆₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#14523983	C₂²	1	2	yes	—
7	C₂×#14523979	C₂²	1	1	yes	characteristic
8	C₂×#14523979	C₂²	1	1	yes	characteristic
9	#16863360	—	2	1	no	—
10	#16863218	—	2	4	no	—
11	C₂²⋊(C₆₇⋊C₁₆)	C₄	1	4	yes	complemented
12	#16863161	—	2	1	no	—
13	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
14	C₂×#117×C₆₇	—	2	1	no	—
15	#427×C₆₇	—	2	4	no	—
16	C₂×#107×C₆₇	—	2	1	no	—
17	C₂×#106×C₆₇	C₂²	1	2	yes	—
18	C₂×#11761612	—	2	1	no	—
19	C₂×#11761612	—	2	1	no	—
20	#14523983	—	2	2	no	—
21	#14523983	—	2	2	no	—
22	C₂×C₆₇⋊C₁₆	C₂×C₄	1	4	yes	—
23	#14523979	—	2	2	no	—
24	#14523979	—	2	2	no	—
25	C₂²⋊(C₆₇⋊C₈)	—	4	2	no	—
26	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
27	C₂²×C₈×C₆₇	—	2	2	no	—
28	C₂²×C₈×C₆₇	—	2	2	no	—
29	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
30	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
31	C₂²×C₈×C₆₇	Q₈	1	2	yes	—
32	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
33	#117×C₆₇	—	2	4	no	—
34	#117×C₆₇	—	4	2	no	—
35	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
36	C₂×C₂²⋊C₄×C₆₇	—	4	1	no	—
37	C₂×C₄²×C₆₇	—	4	1	no	—
38	#107×C₆₇	—	2	4	no	—
39	#106×C₆₇	—	2	2	no	—
40	#106×C₆₇	D₄	1	4	yes	—
41	#11761612	—	4	1	no	—
42	#11761612	—	4	1	no	—
43	#11761612	—	4	1	no	—
44	#11761612	—	4	1	no	—
45	C₂×C₆₇⋊C₈	—	4	1	no	—
46	C₂×C₆₇⋊C₈	—	4	1	no	—
47	C₆₇⋊C₁₆	—	2	4	no	—
48	C₂⁴×C₆₇	SD₁₆	1	1	yes	characteristic
49	C₂²×C₄×C₆₇	—	2	1	no	—
50	C₂²×C₄×C₆₇	—	2	1	no	—
51	C₂²×C₄×C₆₇	—	2	1	no	—
52	C₂²×C₄×C₆₇	—	2	1	no	—
53	C₂²×C₄×C₆₇	—	4	2	no	—
54	C₂²×C₄×C₆₇	C₄⋊C₄	1	2	yes	—
55	C₂²×C₄×C₆₇	SD₁₆	1	2	yes	—
56	C₂²×C₄×C₆₇	SD₁₆	1	1	yes	characteristic
57	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
58	C₂×C₈×C₆₇	—	2	1	no	—
59	C₂×C₈×C₆₇	—	2	1	no	—
60	C₂×C₈×C₆₇	—	2	4	no	—
61	C₂×C₈×C₆₇	—	2	4	no	—
62	C₂×C₈×C₆₇	C₄⋊C₄	1	2	yes	—
63	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
65	C₂×C₈×C₆₇	C₂×Q₈	1	1	yes	characteristic
66	C₂×C₈×C₆₇	#41	1	2	yes	—
67	C₄⋊C₄×C₆₇	—	2	4	no	—
68	C₄⋊C₄×C₆₇	—	4	2	no	—
69	C₂²⋊C₄×C₆₇	—	4	4	no	—
70	C₄²×C₆₇	—	4	4	no	—
71	C₂³×C₆₇	—	2	1	no	—
72	C₂³×C₆₇	—	2	1	no	—
73	C₂³×C₆₇	—	4	2	no	—
74	C₂³×C₆₇	#106	1	2	yes	—
75	C₂³×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
76	C₂×C₄×C₆₇	—	2	1	no	—
77	C₂×C₄×C₆₇	—	2	1	no	—
78	C₂×C₄×C₆₇	—	2	2	no	—
79	C₂×C₄×C₆₇	—	2	2	no	—
80	C₂×C₄×C₆₇	—	2	2	no	—
81	C₂×C₄×C₆₇	—	2	2	no	—
82	C₂×C₄×C₆₇	—	4	4	no	—
83	C₂×C₄×C₆₇	—	8	4	no	—
84	C₂×C₄×C₆₇	#106	1	2	yes	—
85	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
87	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
88	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
89	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
90	C₂×C₄×C₆₇	#137	1	1	yes	characteristic
91	C₈×C₆₇	—	2	2	no	—
92	C₈×C₆₇	C₄×D₄	1	2	yes	—
93	C₈×C₆₇	C₂²⋊Q₈	1	2	yes	—
94	C₆₇⋊C₈	—	8	1	no	—
95	C₆₇⋊C₈	—	8	1	no	—
96	C₂²×C₆₇	—	2	2	no	—
97	C₂²×C₆₇	—	2	2	no	—
98	C₂²×C₆₇	—	2	4	no	—
99	C₂²×C₆₇	—	4	2	no	—
100	C₂²×C₆₇	—	4	2	no	—
101	C₂²×C₆₇	C₂×#106	1	1	yes	characteristic
102	C₂²×C₆₇	#450	1	1	yes	characteristic
103	C₂²×C₆₇	#483	1	1	yes	characteristic
104	C₄×C₆₇	—	2	2	no	—
105	C₄×C₆₇	—	8	4	no	—
106	C₄×C₆₇	#385	1	1	yes	characteristic
107	C₄×C₆₇	#428	1	1	yes	characteristic
108	C₄×C₆₇	#448	1	1	yes	characteristic
109	C₄×C₆₇	#481	1	1	yes	characteristic
110	#12930	—	67	1	no	maximal, Sylow
111	C₂×C₆₇	—	2	1	no	—
112	C₂×C₆₇	—	2	1	no	—
113	C₂×C₆₇	—	4	2	no	—
114	C₂×C₆₇	#1853	1	1	yes	characteristic
115	C₂×C₆₇	#2155	1	2	yes	—
116	C₂×#427	D₆₇	1	1	yes	characteristic
117	C₂×#365	—	67	2	no	—
118	#2112	—	67	1	no	—
119	#1810	—	67	1	no	—
120	#1383	—	67	2	no	—
121	C₆₇	#12930	1	1	yes	characteristic, complemented, Sylow
122	C₂³×C₈	C₂×D₆₇	1	1	yes	characteristic
123	C₂×#117	—	2	1	no	—
124	C₂×M₃₂	—	67	2	no	—
125	C₂×#108	—	67	1	no	—
126	C₂×#108	—	67	1	no	—
127	#427	—	2	4	no	—
128	C₂×#107	—	2	1	no	—
129	C₂×#106	C₂×D₆₇	1	2	yes	—
130	#407	—	134	1	no	—
131	#365	—	134	4	no	—
132	C₂²⋊C₁₆	—	67	4	no	—
133	#341	—	134	1	no	—
134	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
135	C₂×M₁₆	—	134	1	no	—
136	C₂×M₁₆	—	134	1	no	—
137	C₂²×C₈	—	2	2	no	—
138	C₂²×C₈	—	2	2	no	—
139	C₂²×C₈	Dic₁₃₄	1	2	yes	—
140	C₂²×C₈	C₄×D₆₇	1	2	yes	—
141	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
142	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
143	#117	—	2	4	no	—
144	#117	—	4	2	no	—
145	C₂×C₄⋊C₄	—	2	2	no	—
146	C₂×C₂²⋊C₄	—	4	1	no	—
147	C₂×C₄²	—	4	1	no	—
148	M₃₂	—	134	2	no	—
149	M₃₂	—	134	2	no	—
150	C₂×C₁₆	—	67	4	no	—
151	#108	—	134	2	no	—
152	#108	—	134	2	no	—
153	#107	—	2	4	no	—
154	#106	—	2	2	no	—
155	#106	C₂²⋊D₆₇	1	4	yes	—
156	C₂²⋊C₈	—	268	2	no	—
157	C₂⁴	#11761616	1	1	yes	characteristic
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	2	1	no	—
160	C₂²×C₄	—	2	1	no	—
161	C₂²×C₄	—	2	1	no	—
162	C₂²×C₄	—	4	2	no	—
163	C₂²×C₄	Dic₆₇⋊C₄	1	2	yes	—
164	C₂²×C₄	#11761615	1	2	yes	—
165	C₂²×C₄	#11761616	1	1	yes	characteristic
166	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
167	M₁₆	—	268	1	no	—
168	M₁₆	—	268	1	no	—
169	M₁₆	—	268	1	no	—
170	M₁₆	—	268	1	no	—
171	C₂×C₈	—	2	1	no	—
172	C₂×C₈	—	2	1	no	—
173	C₂×C₈	—	2	4	no	—
174	C₂×C₈	—	2	4	no	—
175	C₂×C₈	—	268	1	no	—
176	C₂×C₈	—	268	1	no	—
177	C₂×C₈	Dic₆₇⋊C₄	1	2	yes	—
178	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
179	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
180	C₂×C₈	C₂×Dic₁₃₄	1	1	yes	characteristic
181	C₂×C₈	#11761628	1	2	yes	—
182	C₄⋊C₄	—	2	4	no	—
183	C₄⋊C₄	—	4	2	no	—
184	C₂²⋊C₄	—	4	4	no	—
185	C₄²	—	4	4	no	—
186	C₁₆	—	134	4	no	—
187	C₂³	—	2	1	no	—
188	C₂³	—	2	1	no	—
189	C₂³	—	4	2	no	—
190	C₂³	#14523974	1	2	yes	—
191	C₂³	C₂×#11761616	1	1	yes	characteristic
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	4	4	no	—
199	C₂×C₄	—	8	4	no	—
200	C₂×C₄	#14523974	1	2	yes	—
201	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
202	C₂×C₄	#14524012	1	1	yes	characteristic
203	C₂×C₄	#14524026	1	1	yes	characteristic
204	C₂×C₄	C₂×#11761615	1	1	yes	characteristic
205	C₂×C₄	#14524069	1	1	yes	characteristic
206	C₂×C₄	#14524074	1	1	yes	characteristic
207	C₈	—	2	2	no	—
208	C₈	—	536	1	no	—
209	C₈	—	536	1	no	—
210	C₈	C₄×C₂²⋊D₆₇	1	2	yes	—
211	C₈	#14524022	1	2	yes	—
212	C₂²	—	2	2	no	—
213	C₂²	—	2	2	no	—
214	C₂²	—	2	4	no	—
215	C₂²	—	4	2	no	—
216	C₂²	—	4	2	no	—
217	C₂²	C₂×#14523974	1	1	yes	characteristic
218	C₂²	#16863547	1	1	yes	characteristic
219	C₂²	#16863726	1	1	yes	characteristic
220	C₄	—	2	2	no	—
221	C₄	—	8	4	no	—
222	C₄	#16863269	1	1	yes	characteristic
223	C₄	#16863436	1	1	yes	characteristic
224	C₄	#16863535	1	1	yes	characteristic
225	C₄	#16863714	1	1	yes	characteristic
226	C₂	—	2	1	no	—
227	C₂	—	2	1	no	—
228	C₂	—	4	2	no	—
229	C₂	#22560402	1	1	yes	characteristic
230	C₂	#22561981	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16863218

C₂

yes

maximal, complemented

#22561820

C₂

yes

maximal, characteristic

#22560247

C₂

yes

maximal, characteristic

#22558307

C₂

yes

maximal, complemented

C₂×#427×C₆₇

C₂

yes

maximal, characteristic

C₂×#14523983

C₂²

yes

—

C₂×#14523979

C₂²

yes

characteristic

C₂×#14523979

C₂²

yes

characteristic

#16863360

—

#16863218

—

C₂²⋊(C₆₇⋊C₁₆)

C₄

yes

complemented

#16863161

—

C₂³×C₈×C₆₇

C₂²

yes

characteristic

C₂×#117×C₆₇

—

#427×C₆₇

—

C₂×#107×C₆₇

—

C₂×#106×C₆₇

C₂²

yes

—

—

—

—

—

C₂×C₆₇⋊C₁₆

C₂×C₄

yes

—

#14523979

—

#14523979

—

C₂²⋊(C₆₇⋊C₈)

—

C₂³×C₄×C₆₇

D₄

yes

characteristic

C₂²×C₈×C₆₇

—

C₂²×C₈×C₆₇

—

C₂²×C₈×C₆₇

C₂×C₄

yes

—

C₂²×C₈×C₆₇

D₄

yes

characteristic

C₂²×C₈×C₆₇

Q₈

yes

—

C₂²×C₈×C₆₇

C₂³

yes

characteristic

#117×C₆₇

—

#117×C₆₇

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₂²⋊C₄×C₆₇

—

C₂×C₄²×C₆₇

—

#107×C₆₇

—

#106×C₆₇

—

#106×C₆₇

D₄

yes

—

—

—

—

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₆₇⋊C₁₆

—

C₂⁴×C₆₇

SD₁₆

yes

characteristic

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

C₄⋊C₄

yes

—

C₂²×C₄×C₆₇

SD₁₆

yes

—

C₂²×C₄×C₆₇

SD₁₆

yes

characteristic

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

C₄⋊C₄

yes

—

C₂×C₈×C₆₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₆₇

C₂×D₄

yes

—

C₂×C₈×C₆₇

C₂×Q₈

yes

characteristic

C₂×C₈×C₆₇

#41

yes

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₂²⋊C₄×C₆₇

—

C₄²×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

#106

yes

—

C₂³×C₆₇

C₂×SD₁₆

yes

characteristic

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

#106

yes

—

C₂×C₄×C₆₇

C₂×C₄⋊C₄

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

C₂×SD₁₆

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

yes

C₈×C₆₇

—

C₈×C₆₇

C₄×D₄

yes

—

C₈×C₆₇

C₂²⋊Q₈

yes

—

C₆₇⋊C₈

—

C₆₇⋊C₈

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

100

C₂²×C₆₇

—

101

C₂²×C₆₇

C₂×#106

yes

characteristic

102

C₂²×C₆₇

#450

yes

characteristic

103

C₂²×C₆₇

#483

yes

characteristic

104

C₄×C₆₇

—

105

C₄×C₆₇

—

106

C₄×C₆₇

#385

yes

characteristic

107

C₄×C₆₇

#428

yes

characteristic

108

C₄×C₆₇

#448

yes

characteristic

109

C₄×C₆₇

yes

110

—

111

C₂×C₆₇

—

112

C₂×C₆₇

—

113

C₂×C₆₇

—

114

C₂×C₆₇

#1853

yes

characteristic

115

C₂×C₆₇

#2155

yes

—

116

C₂×#427

D₆₇

yes

characteristic

117

C₂×#365

—

118

#2112

—

119

#1810

—

120

#1383

—

121

C₆₇

#12930

yes

characteristic, complemented, Sylow

122

C₂³×C₈

C₂×D₆₇

yes

characteristic

123

C₂×#117

—

124

C₂×M₃₂

—

125

C₂×#108

—

126

C₂×#108

—

127

#427

—

128

C₂×#107

—

129

C₂×#106

C₂×D₆₇

yes

—

130

#407

—

134

—

131

#365

—

134

—

132

C₂²⋊C₁₆

—

133

#341

—

134

—

134

C₂³×C₄

C₂²⋊D₆₇

yes

characteristic

135

C₂×M₁₆

—

134

—

136

C₂×M₁₆

—

134

—

137

C₂²×C₈

—

138

C₂²×C₈

—

139

C₂²×C₈

Dic₁₃₄

yes

—

140

C₂²×C₈

C₄×D₆₇

yes

—

141

C₂²×C₈

C₂²⋊D₆₇

yes

characteristic

142

C₂²×C₈

C₂²×D₆₇

yes

characteristic

143

#117

—

144

#117

—

145

C₂×C₄⋊C₄

—

146

C₂×C₂²⋊C₄

—

147

C₂×C₄²

—

148

M₃₂

—

134

—

149

M₃₂

—

134

—

150

C₂×C₁₆

—

151

#108

—

134

—

152

#108

—

134

—

153

#107

—

154

#106

—

155

#106

C₂²⋊D₆₇

yes

—

156

C₂²⋊C₈

—

268

—

157

C₂⁴

#11761616

yes

characteristic

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

Dic₆₇⋊C₄

yes

—

164

C₂²×C₄

#11761615

yes

—

165

C₂²×C₄

#11761616

yes

characteristic

166

C₂²×C₄

C₂×C₂²⋊D₆₇

yes

characteristic

167

M₁₆

—

268

—

168

M₁₆

—

268

—

169

M₁₆

—

268

—

170

M₁₆

—

268

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

268

—

176

C₂×C₈

—

268

—

177

C₂×C₈

Dic₆₇⋊C₄

yes

—

178

C₂×C₈

C₂×C₄×D₆₇

yes

characteristic

179

C₂×C₈

C₂×C₂²⋊D₆₇

yes

—

180

C₂×C₈

C₂×Dic₁₃₄

yes

characteristic

181

C₂×C₈

#11761628

yes

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₂²⋊C₄

—

185

C₄²

—

186

C₁₆

—

134

—

187

C₂³

—

188

C₂³

—

189

C₂³

—

190

C₂³

#14523974

yes

—

191

C₂³

C₂×#11761616

yes

characteristic

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

#14523974

yes

—

201

C₂×C₄

C₂×Dic₆₇⋊C₄

yes

characteristic

202

C₂×C₄

#14524012

yes

characteristic

203

C₂×C₄

#14524026

yes

characteristic

204

C₂×C₄

C₂×#11761615

yes

characteristic

205

C₂×C₄

#14524069

yes

characteristic

206

C₂×C₄

#14524074

yes

characteristic

207

C₈

—

208

C₈

—

536

—

209

C₈

—

536

—

210

C₈

C₄×C₂²⋊D₆₇

yes

—

211

C₈

#14524022

yes

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

C₂×#14523974

yes

characteristic

218

C₂²

#16863547

yes

characteristic

219

C₂²

#16863726

yes

characteristic

220

C₄

—

221

C₄

—

222

C₄

#16863269

yes

characteristic

223

C₄

#16863436

yes

characteristic

224

C₄

#16863535

yes

characteristic

225

C₄

#16863714

yes

characteristic

226

C₂

—

227

C₂

—

228

C₂

—

229

C₂

#22560402

yes

characteristic

230

C₂

#22561981

yes

—

	subgroup	G/H
center	C₂²	C₂×#14523974
commutator	C₂×C₈×C₆₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₆₇
Fitting	C₂×#427×C₆₇	C₂
socle	C₂²×C₆₇	C₂×#106
prime radical	C₂⁴×C₆₇	SD₁₆
cosocle	C₂²×C₈×C₆₇	C₂³
hypercenter	C₂×#427	D₆₇
hypocenter	C₆₇	#12930
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂×#427

subgroup

G/H

center

C₂²

C₂×#14523974

commutator

C₂×C₈×C₆₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₆₇

Fitting

C₂×#427×C₆₇

C₂

socle

C₂²×C₆₇

C₂×#106

prime radical

C₂⁴×C₆₇

SD₁₆

cosocle

C₂²×C₈×C₆₇

C₂³

D₆₇

C₆₇

G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂×#427

N	H ≅ G/N	type
1. C₂×#16863218	C₂	semidirect
4. #22558307	C₂	semidirect
11. C₂²⋊(C₆₇⋊C₁₆)	C₄	semidirect
121. C₆₇	#12930	semidirect

H ≅ G/N

type

1. C₂×#16863218

C₂

semidirect

4. #22558307

C₂

semidirect

11. C₂²⋊(C₆₇⋊C₁₆)

C₄

semidirect

121. C₆₇

#12930

semidirect

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

subgroup	index
C₂×#16863218	2
#22561820	2
#22560247	2
#22558307	2
C₂×#427×C₆₇	2
#12930	67

subgroup

index

C₂×#427×C₆₇

Subgroups — #30772393

Conjugacy classes of subgroups

Complements

Maximal subgroups