Group #22572856 — subgroups

Subgroups — #22572856

Order 8576.

350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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	#16864116	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864103	C₂	1	1	yes	maximal, characteristic, complemented
3	#16863749	C₂	1	2	yes	maximal, complemented
4	#16863747	C₂	1	1	yes	maximal, characteristic, complemented
5	#16863702	C₂	1	2	yes	maximal, complemented
6	#16863686	C₂	1	1	yes	maximal, characteristic, complemented
7	#16863609	C₂	1	2	yes	maximal
8	#16863601	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×Dic₁₃₄	C₂	1	1	yes	maximal, characteristic, complemented
10	#16863487	C₂	1	2	yes	maximal, complemented
11	C₄×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic
12	C₂×#11761616	C₂²	1	2	yes	—
13	#14524043	C₂²	1	1	yes	characteristic
14	#14524043	C₂²	1	1	yes	characteristic
15	#14524036	—	2	2	no	—
16	#14524034	C₂²	1	2	yes	—
17	#14524030	C₂²	1	2	yes	—
18	#14524022	—	2	1	no	—
19	#14524022	—	2	1	no	—
20	#14524020	—	2	2	no	—
21	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic
22	#14524008	C₂²	1	2	yes	—
23	D₄×Dic₆₇	C₂²	1	2	yes	—
24	#14524002	—	2	1	no	—
25	C₂×C₄⋊Dic₆₇	—	2	1	no	—
26	#14523974	C₂²	1	2	yes	—
27	C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
28	Dic₆₇⋊C₈	C₂²	1	2	yes	—
29	#14523968	C₂²	1	2	yes	—
30	#14523968	C₂²	1	2	yes	—
31	#14523966	C₂²	1	2	yes	—
32	#14523964	C₂²	1	2	yes	—
33	C₈×Dic₆₇	C₂²	1	2	yes	—
34	C₂×D₈×C₆₇	C₂²	1	1	yes	characteristic
35	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
37	#107×C₆₇	C₂²	1	1	yes	characteristic
38	#102×C₆₇	C₂²	1	1	yes	characteristic
39	#102×C₆₇	C₂²	1	1	yes	characteristic
40	C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×Dic₁₃₄	—	2	1	no	—
42	C₂×Dic₁₃₄	D₄	1	1	yes	characteristic
43	C₂×Dic₁₃₄	C₂³	1	2	yes	—
44	C₂²×Dic₆₇	—	2	2	no	—
45	#11761616	—	2	4	no	—
46	C₂×C₆₇⋊C₈	C₂³	1	2	yes	—
47	C₄⋊Dic₆₇	—	2	1	no	—
48	C₄⋊Dic₆₇	—	2	1	no	—
49	C₄⋊Dic₆₇	—	2	1	no	—
50	C₄⋊Dic₆₇	—	2	2	no	—
51	C₄⋊Dic₆₇	D₄	1	1	yes	characteristic
52	C₄⋊Dic₆₇	C₂³	1	2	yes	—
53	Dic₆₇⋊C₄	—	2	2	no	—
54	Dic₆₇⋊C₄	—	2	2	no	—
55	Dic₆₇⋊C₄	D₄	1	2	yes	—
56	C₂²⋊Dic₆₇	—	2	2	no	—
57	C₂²⋊Dic₆₇	—	2	2	no	—
58	C₂²⋊Dic₆₇	—	2	2	no	—
59	C₄×Dic₆₇	—	2	2	no	—
60	C₄×Dic₆₇	C₂³	1	2	yes	—
61	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₆₇	—	2	1	no	—
64	C₂²×C₄×C₆₇	—	2	1	no	—
65	D₈×C₆₇	—	2	2	no	—
66	C₂×C₈×C₆₇	C₂³	1	1	yes	characteristic
67	C₂×C₈×C₆₇	C₂³	1	1	yes	characteristic
68	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
69	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
70	C₂²⋊C₄×C₆₇	—	2	1	no	—
71	C₂²⋊C₄×C₆₇	—	2	1	no	—
72	C₄²×C₆₇	C₂³	1	1	yes	characteristic
73	C₂³×C₆₇	—	2	1	no	—
74	C₂³×C₆₇	—	2	1	no	—
75	D₄×C₆₇	—	2	1	no	—
76	D₄×C₆₇	—	2	1	no	—
77	D₄×C₆₇	—	2	1	no	—
78	D₄×C₆₇	#41	1	2	yes	—
79	C₂×C₄×C₆₇	—	2	1	no	—
80	C₂×C₄×C₆₇	—	2	1	no	—
81	C₂×C₄×C₆₇	—	4	2	no	—
82	C₂×C₄×C₆₇	—	4	2	no	—
83	C₂×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
84	C₂×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
86	C₂×Dic₆₇	—	2	2	no	—
87	C₂×Dic₆₇	—	2	2	no	—
88	C₂×Dic₆₇	—	8	2	no	—
89	C₂×Dic₆₇	C₂×D₄	1	2	yes	—
90	C₂×Dic₆₇	C₂×D₄	1	2	yes	—
91	Dic₁₃₄	—	2	2	no	—
92	Dic₁₃₄	—	2	2	no	—
93	Dic₁₃₄	—	2	2	no	—
94	Dic₁₃₄	—	8	1	no	—
95	C₈×C₆₇	—	2	1	no	—
96	C₈×C₆₇	—	2	1	no	—
97	C₆₇⋊C₈	—	2	2	no	—
98	C₂²×C₆₇	—	2	2	no	—
99	C₂²×C₆₇	—	4	1	no	—
100	C₂²×C₆₇	—	4	1	no	—
101	C₂²×C₆₇	—	4	1	no	—
102	C₂²×C₆₇	—	4	1	no	—
103	C₂²×C₆₇	—	4	1	no	—
104	C₂²×C₆₇	C₂²×D₄	1	1	yes	characteristic
105	C₄×C₆₇	—	2	1	no	—
106	C₄×C₆₇	—	4	1	no	—
107	C₄×C₆₇	—	4	1	no	—
108	C₄×C₆₇	#135	1	2	yes	—
109	C₄×C₆₇	C₂×#41	1	1	yes	characteristic
110	C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
111	Dic₆₇	—	2	2	no	—
112	Dic₆₇	—	2	2	no	—
113	Dic₆₇	—	4	2	no	—
114	Dic₆₇	—	4	2	no	—
115	C₂×C₆₇	—	4	2	no	—
116	C₂×C₆₇	—	8	1	no	—
117	C₂×C₆₇	#548	1	1	yes	characteristic
118	C₂×C₆₇	C₂×#135	1	1	yes	characteristic
119	C₂×C₆₇	#577	1	1	yes	characteristic
120	#3360	—	67	1	no	maximal, Sylow
121	C₆₇	#3360	1	1	yes	characteristic, complemented, Sylow
122	#556	—	67	1	no	—
123	#554	—	67	1	no	—
124	#488	—	67	2	no	—
125	#487	—	67	1	no	—
126	#479	—	67	2	no	—
127	#476	—	67	1	no	—
128	#463	—	67	2	no	—
129	#461	—	67	1	no	—
130	C₈×Q₈	—	67	1	no	—
131	C₄×SD₁₆	—	67	2	no	—
132	C₄×D₈	D₆₇	1	1	yes	characteristic
133	C₂×SD₁₆	—	67	2	no	—
134	C₂×D₈	C₂×D₆₇	1	1	yes	characteristic
135	C₄⋊Q₈	—	67	1	no	—
136	C₄⋊Q₈	—	67	1	no	—
137	#126	—	134	2	no	—
138	#125	—	67	2	no	—
139	#124	—	67	2	no	—
140	C₂²⋊Q₈	—	134	2	no	—
141	C₂²⋊Q₈	—	134	1	no	—
142	C₂²⋊Q₈	—	134	1	no	—
143	C₄×Q₈	—	67	1	no	—
144	C₄×Q₈	—	67	2	no	—
145	C₄×D₄	—	67	2	no	—
146	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
147	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
148	#117	—	134	1	no	—
149	C₂×C₄⋊C₄	—	134	1	no	—
150	#107	C₂×D₆₇	1	1	yes	characteristic
151	#106	—	67	2	no	—
152	C₄⋊C₈	—	67	2	no	—
153	C₄⋊C₈	—	67	1	no	—
154	#103	—	67	2	no	—
155	#103	—	67	2	no	—
156	#103	—	67	2	no	—
157	#102	—	67	2	no	—
158	#102	C₂×D₆₇	1	1	yes	characteristic
159	#102	C₂×D₆₇	1	1	yes	characteristic
160	C₄×C₈	—	67	2	no	—
161	C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
162	C₂×Q₈	—	67	1	no	—
163	C₂×Q₈	—	67	2	no	—
164	C₂×Q₈	—	134	1	no	—
165	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
166	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
167	C₂²×C₄	—	2	1	no	—
168	C₂²×C₄	—	2	1	no	—
169	C₂²×C₄	—	134	2	no	—
170	SD₁₆	—	134	4	no	—
171	D₈	—	2	2	no	—
172	C₂×C₈	—	67	2	no	—
173	C₂×C₈	C₂²×D₆₇	1	1	yes	characteristic
174	C₂×C₈	C₂²×D₆₇	1	1	yes	characteristic
175	C₄⋊C₄	—	67	1	no	—
176	C₄⋊C₄	—	67	2	no	—
177	C₄⋊C₄	—	67	2	no	—
178	C₄⋊C₄	—	134	2	no	—
179	C₄⋊C₄	—	134	2	no	—
180	C₄⋊C₄	—	134	2	no	—
181	C₄⋊C₄	—	134	1	no	—
182	C₄⋊C₄	—	134	1	no	—
183	C₄⋊C₄	—	134	1	no	—
184	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
185	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
186	C₂²⋊C₄	—	2	1	no	—
187	C₂²⋊C₄	—	2	1	no	—
188	C₂²⋊C₄	—	134	2	no	—
189	C₂²⋊C₄	—	134	2	no	—
190	C₂²⋊C₄	—	134	2	no	—
191	C₄²	—	67	2	no	—
192	C₄²	—	134	2	no	—
193	C₄²	C₂²×D₆₇	1	1	yes	characteristic
194	C₂³	—	2	1	no	—
195	C₂³	—	2	1	no	—
196	Q₈	—	536	1	no	—
197	Q₈	—	134	2	no	—
198	Q₈	—	134	2	no	—
199	Q₈	—	134	2	no	—
200	D₄	—	2	1	no	—
201	D₄	—	2	1	no	—
202	D₄	—	2	1	no	—
203	D₄	#11761628	1	2	yes	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	536	2	no	—
209	C₂×C₄	—	67	2	no	—
210	C₂×C₄	—	67	2	no	—
211	C₂×C₄	—	134	2	no	—
212	C₂×C₄	—	134	2	no	—
213	C₂×C₄	D₄×D₆₇	1	1	yes	characteristic
214	C₂×C₄	D₄×D₆₇	1	1	yes	characteristic
215	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
216	C₈	—	2	1	no	—
217	C₈	—	2	1	no	—
218	C₈	—	134	2	no	—
219	C₂²	—	2	2	no	—
220	C₂²	—	4	1	no	—
221	C₂²	—	4	1	no	—
222	C₂²	—	4	1	no	—
223	C₂²	—	4	1	no	—
224	C₂²	—	4	1	no	—
225	C₂²	C₂×D₄×D₆₇	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	4	1	no	—
228	C₄	—	4	1	no	—
229	C₄	—	268	2	no	—
230	C₄	—	268	2	no	—
231	C₄	—	134	2	no	—
232	C₄	—	134	2	no	—
233	C₄	#14524062	1	2	yes	—
234	C₄	C₂×#11761628	1	1	yes	characteristic
235	C₄	#14524090	1	1	yes	characteristic
236	C₂	—	4	2	no	—
237	C₂	—	8	1	no	—
238	C₂	#16864055	1	1	yes	characteristic
239	C₂	C₂×#14524062	1	1	yes	characteristic
240	C₂	#16864203	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16864116

C₂

yes

maximal, characteristic, complemented

#16864103

C₂

yes

maximal, characteristic, complemented

#16863749

C₂

yes

maximal, complemented

#16863747

C₂

yes

maximal, characteristic, complemented

#16863702

C₂

yes

maximal, complemented

#16863686

C₂

yes

maximal, characteristic, complemented

#16863609

C₂

yes

maximal

#16863601

C₂

yes

maximal, characteristic, complemented

C₈×Dic₁₃₄

C₂

yes

maximal, characteristic, complemented

#16863487

C₂

yes

maximal, complemented

C₄×D₈×C₆₇

C₂

yes

maximal, characteristic

C₂×#11761616

C₂²

yes

—

#14524043

C₂²

yes

characteristic

#14524043

C₂²

yes

characteristic

#14524036

—

#14524034

C₂²

yes

—

#14524030

C₂²

yes

—

#14524022

—

#14524022

—

#14524020

—

C₄×Dic₁₃₄

C₂²

yes

characteristic

#14524008

C₂²

yes

—

D₄×Dic₆₇

C₂²

yes

—

#14524002

—

C₂×C₄⋊Dic₆₇

—

#14523974

C₂²

yes

—

C₄⋊(C₆₇⋊C₈)

C₂²

yes

characteristic

Dic₆₇⋊C₈

C₂²

yes

—

#14523968

C₂²

yes

—

#14523968

C₂²

yes

—

#14523966

C₂²

yes

—

#14523964

C₂²

yes

—

C₈×Dic₆₇

C₂²

yes

—

C₂×D₈×C₆₇

C₂²

yes

characteristic

C₄×D₄×C₆₇

C₂²

yes

characteristic

C₄×D₄×C₆₇

C₂²

yes

characteristic

#107×C₆₇

C₂²

yes

characteristic

#102×C₆₇

C₂²

yes

characteristic

#102×C₆₇

C₂²

yes

characteristic

C₄×C₈×C₆₇

C₂²

yes

characteristic

C₂×Dic₁₃₄

—

C₂×Dic₁₃₄

D₄

yes

characteristic

C₂×Dic₁₃₄

C₂³

yes

—

C₂²×Dic₆₇

—

#11761616

—

C₂×C₆₇⋊C₈

C₂³

yes

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

D₄

yes

characteristic

C₄⋊Dic₆₇

C₂³

yes

—

Dic₆₇⋊C₄

—

Dic₆₇⋊C₄

—

Dic₆₇⋊C₄

D₄

yes

—

C₂²⋊Dic₆₇

—

C₂²⋊Dic₆₇

—

C₂²⋊Dic₆₇

—

C₄×Dic₆₇

—

C₄×Dic₆₇

C₂³

yes

—

C₂×D₄×C₆₇

C₂³

yes

characteristic

C₂×D₄×C₆₇

C₂³

yes

characteristic

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

D₈×C₆₇

—

C₂×C₈×C₆₇

C₂³

yes

characteristic

C₂×C₈×C₆₇

C₂³

yes

characteristic

C₄⋊C₄×C₆₇

C₂³

yes

characteristic

C₄⋊C₄×C₆₇

C₂³

yes

characteristic

C₂²⋊C₄×C₆₇

—

C₂²⋊C₄×C₆₇

—

C₄²×C₆₇

C₂³

yes

characteristic

C₂³×C₆₇

—

C₂³×C₆₇

—

D₄×C₆₇

—

D₄×C₆₇

—

D₄×C₆₇

—

D₄×C₆₇

#41

yes

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂×C₄×C₆₇

C₂⁴

yes

characteristic

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

C₂×D₄

yes

—

C₂×Dic₆₇

C₂×D₄

yes

—

Dic₁₃₄

—

Dic₁₃₄

—

Dic₁₃₄

—

Dic₁₃₄

—

C₈×C₆₇

—

C₈×C₆₇

—

C₆₇⋊C₈

—

C₂²×C₆₇

—

C₂²×C₆₇

—

100

C₂²×C₆₇

—

101

C₂²×C₆₇

—

102

C₂²×C₆₇

—

103

C₂²×C₆₇

—

104

C₂²×C₆₇

C₂²×D₄

yes

characteristic

105

C₄×C₆₇

—

106

C₄×C₆₇

—

107

C₄×C₆₇

—

108

C₄×C₆₇

#135

yes

—

109

C₄×C₆₇

C₂×#41

yes

characteristic

110

C₄×C₆₇

2₋¹⁺⁴

yes

characteristic

111

Dic₆₇

—

112

Dic₆₇

—

113

Dic₆₇

—

114

Dic₆₇

—

115

C₂×C₆₇

—

116

C₂×C₆₇

—

117

C₂×C₆₇

#548

yes

characteristic

118

C₂×C₆₇

C₂×#135

yes

characteristic

119

C₂×C₆₇

yes

120

—

121

C₆₇

#3360

yes

characteristic, complemented, Sylow

122

#556

—

123

#554

—

124

#488

—

125

#487

—

126

#479

—

127

#476

—

128

#463

—

129

#461

—

130

C₈×Q₈

—

131

C₄×SD₁₆

—

132

C₄×D₈

D₆₇

yes

characteristic

133

C₂×SD₁₆

—

134

C₂×D₈

C₂×D₆₇

yes

characteristic

135

C₄⋊Q₈

—

136

C₄⋊Q₈

—

137

#126

—

134

—

138

#125

—

139

#124

—

140

C₂²⋊Q₈

—

134

—

141

C₂²⋊Q₈

—

134

—

142

C₂²⋊Q₈

—

134

—

143

C₄×Q₈

—

144

C₄×Q₈

—

145

C₄×D₄

—

146

C₄×D₄

C₂×D₆₇

yes

characteristic

147

C₄×D₄

C₂×D₆₇

yes

characteristic

148

#117

—

134

—

149

C₂×C₄⋊C₄

—

134

—

150

#107

C₂×D₆₇

yes

characteristic

151

#106

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

#103

—

155

#103

—

156

#103

—

157

#102

—

158

#102

C₂×D₆₇

yes

characteristic

159

#102

C₂×D₆₇

yes

characteristic

160

C₄×C₈

—

161

C₄×C₈

C₂×D₆₇

yes

characteristic

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

134

—

165

C₂×D₄

C₂²×D₆₇

yes

characteristic

166

C₂×D₄

C₂²×D₆₇

yes

characteristic

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

134

—

170

SD₁₆

—

134

—

171

D₈

—

172

C₂×C₈

—

173

C₂×C₈

C₂²×D₆₇

yes

characteristic

174

C₂×C₈

C₂²×D₆₇

yes

characteristic

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

134

—

179

C₄⋊C₄

—

134

—

180

C₄⋊C₄

—

134

—

181

C₄⋊C₄

—

134

—

182

C₄⋊C₄

—

134

—

183

C₄⋊C₄

—

134

—

184

C₄⋊C₄

C₂²×D₆₇

yes

characteristic

185

C₄⋊C₄

C₂²×D₆₇

yes

characteristic

186

C₂²⋊C₄

—

187

C₂²⋊C₄

—

188

C₂²⋊C₄

—

134

—

189

C₂²⋊C₄

—

134

—

190

C₂²⋊C₄

—

134

—

191

C₄²

—

192

C₄²

—

134

—

193

C₄²

C₂²×D₆₇

yes

characteristic

194

C₂³

—

195

C₂³

—

196

Q₈

—

536

—

197

Q₈

—

134

—

198

Q₈

—

134

—

199

Q₈

—

134

—

200

D₄

—

201

D₄

—

202

D₄

—

203

D₄

#11761628

yes

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

536

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

134

—

212

C₂×C₄

—

134

—

213

C₂×C₄

D₄×D₆₇

yes

characteristic

214

C₂×C₄

D₄×D₆₇

yes

characteristic

215

C₂×C₄

C₂³×D₆₇

yes

characteristic

216

C₈

—

217

C₈

—

218

C₈

—

134

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

223

C₂²

—

224

C₂²

—

225

C₂²

C₂×D₄×D₆₇

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

268

—

230

C₄

—

268

—

231

C₄

—

134

—

232

C₄

—

134

—

233

C₄

#14524062

yes

—

234

C₄

C₂×#11761628

yes

characteristic

235

C₄

#14524090

yes

characteristic

236

C₂

—

237

C₂

—

238

C₂

#16864055

yes

characteristic

239

C₂

C₂×#14524062

yes

characteristic

240

C₂

#16864203

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₆₇
Fitting	C₄×D₈×C₆₇	C₂
socle	C₂²×C₆₇	C₂²×D₄
hypercenter	C₄×D₈	D₆₇
hypocenter	C₆₇	#3360
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×D₈

subgroup

G/H

center

C₂²

C₂×D₄×D₆₇

commutator

C₂×C₄×C₆₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₆₇

Fitting

C₄×D₈×C₆₇

C₂

socle

C₂²×C₆₇

C₂²×D₄

hypercenter

C₄×D₈

D₆₇

hypocenter

C₆₇

#3360

LCS

G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×D₈

N	H ≅ G/N	type
1. #16864116	C₂	semidirect
2. #16864103	C₂	semidirect
3. #16863749	C₂	semidirect
4. #16863747	C₂	semidirect
5. #16863702	C₂	semidirect
6. #16863686	C₂	semidirect
8. #16863601	C₂	semidirect
9. C₈×Dic₁₃₄	C₂	semidirect
10. #16863487	C₂	semidirect
121. C₆₇	#3360	semidirect

H ≅ G/N

type

1. #16864116

C₂

semidirect

2. #16864103

C₂

semidirect

3. #16863749

C₂

semidirect

4. #16863747

C₂

semidirect

5. #16863702

C₂

semidirect

6. #16863686

C₂

semidirect

8. #16863601

C₂

semidirect

9. C₈×Dic₁₃₄

C₂

semidirect

10. #16863487

C₂

semidirect

121. C₆₇

#3360

semidirect

Subgroups — #22572856

Conjugacy classes of subgroups

Complements