Group #30774583 — subgroups

Subgroups — #30774583

Order 17152.

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

normal subgroups only

This group has 556 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	C₂²×D₁₀₇₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16863666	C₂	1	2	yes	maximal, complemented
3	C₂×#16863210	C₂	1	2	yes	maximal, complemented
4	#22558303	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2113	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14524068	—	2	2	no	—
7	C₂²×D₅₃₆	C₂²	1	2	yes	—
8	C₂×D₁₀₇₂	—	2	4	no	—
9	C₂×D₁₀₇₂	—	2	2	no	—
10	#16863666	—	2	4	no	—
11	#16863666	—	2	4	no	—
12	C₂×#14523979	C₂²	1	2	yes	—
13	C₂×#14523959	—	2	2	no	—
14	#16863210	—	2	4	no	—
15	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×M₃₂×C₆₇	C₂²	1	1	yes	characteristic
17	C₂²×C₁₆×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²⋊C₁₆×C₆₇	—	2	2	no	—
19	C₂²×D₂₆₈	—	2	2	no	—
20	#14524068	—	2	8	no	—
21	#14524068	—	4	4	no	—
22	C₂×#11761615	—	4	2	no	—
23	C₂×D₅₃₆	—	2	2	no	—
24	C₂×D₅₃₆	—	2	2	no	—
25	C₂×D₅₃₆	—	2	2	no	—
26	C₂×D₅₃₆	—	2	2	no	—
27	C₂×D₅₃₆	—	2	2	no	—
28	C₂×D₅₃₆	D₄	1	4	yes	—
29	C₂×#11761613	—	4	2	no	—
30	C₂×#11761612	—	2	2	no	—
31	D₁₀₇₂	—	2	8	no	—
32	#14523979	—	2	2	no	—
33	#14523979	D₄	1	4	yes	—
34	#14523959	—	2	8	no	—
35	C₂×#41×C₆₇	D₄	1	1	yes	characteristic
36	#131×C₆₇	—	2	2	no	—
37	#131×C₆₇	—	2	2	no	—
38	C₂×M₁₆×C₆₇	—	2	1	no	—
39	C₂×M₁₆×C₆₇	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₆₇	—	2	1	no	—
41	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
42	M₃₂×C₆₇	—	2	2	no	—
43	C₂×C₁₆×C₆₇	—	2	2	no	—
44	C₂×C₁₆×C₆₇	—	2	1	no	—
45	C₂×C₁₆×C₆₇	D₄	1	2	yes	—
46	C₂³×D₆₇	—	4	2	no	—
47	C₂×D₂₆₈	—	2	4	no	—
48	C₂×D₂₆₈	—	4	2	no	—
49	C₂×D₂₆₈	—	4	2	no	—
50	C₂×D₂₆₈	—	4	2	no	—
51	C₂×D₂₆₈	—	4	2	no	—
52	C₂×D₂₆₈	—	4	2	no	—
53	#11761615	—	4	8	no	—
54	D₅₃₆	—	2	4	no	—
55	D₅₃₆	—	2	4	no	—
56	D₅₃₆	—	4	2	no	—
57	D₅₃₆	—	4	2	no	—
58	#11761613	—	4	8	no	—
59	#11761612	—	2	4	no	—
60	#11761612	—	4	2	no	—
61	C₂×C₆₇⋊C₈	—	4	2	no	—
62	#41×C₆₇	—	2	2	no	—
63	#41×C₆₇	—	2	2	no	—
64	C₂×Q₈×C₆₇	D₈	1	1	yes	characteristic
65	C₂×D₄×C₆₇	—	2	1	no	—
66	C₂×D₄×C₆₇	D₈	1	1	yes	characteristic
67	C₂²×C₄×C₆₇	—	2	1	no	—
68	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
69	M₁₆×C₆₇	—	2	2	no	—
70	M₁₆×C₆₇	—	4	2	no	—
71	C₂×C₈×C₆₇	—	2	1	no	—
72	C₂×C₈×C₆₇	—	4	1	no	—
73	C₂×C₈×C₆₇	—	4	1	no	—
74	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
75	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
76	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
77	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
78	C₁₆×C₆₇	—	2	2	no	—
79	C₁₆×C₆₇	—	4	1	no	—
80	C₂³×C₆₇	—	2	1	no	—
81	C₂³×C₆₇	#135	1	1	yes	characteristic
82	C₂²×D₆₇	—	4	4	no	—
83	C₂²×D₆₇	—	8	2	no	—
84	C₂²×D₆₇	—	8	2	no	—
85	C₂²×D₆₇	—	16	4	no	—
86	Q₈×C₆₇	—	2	2	no	—
87	D₄×C₆₇	—	2	2	no	—
88	D₄×C₆₇	—	4	2	no	—
89	C₂×C₄×C₆₇	—	2	1	no	—
90	C₂×C₄×C₆₇	—	4	1	no	—
91	C₂×C₄×C₆₇	—	4	1	no	—
92	C₂×C₄×C₆₇	#120	1	2	yes	—
93	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
94	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
95	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
96	D₂₆₈	—	4	4	no	—
97	D₂₆₈	—	4	4	no	—
98	D₂₆₈	—	8	2	no	—
99	D₂₆₈	—	8	2	no	—
100	C₈×C₆₇	—	4	1	no	—
101	C₈×C₆₇	#120	1	1	yes	characteristic
102	C₈×C₆₇	#121	1	2	yes	—
103	C₈×C₆₇	#127	1	1	yes	characteristic
104	C₆₇⋊C₈	—	4	4	no	—
105	C₂²×C₆₇	—	2	2	no	—
106	C₂²×C₆₇	—	4	2	no	—
107	C₂²×C₆₇	—	4	1	no	—
108	C₂²×C₆₇	#449	1	2	yes	—
109	C₂²×C₆₇	#466	1	1	yes	characteristic
110	C₂×D₆₇	—	8	4	no	—
111	C₂×D₆₇	—	16	4	no	—
112	C₂×D₆₇	—	16	4	no	—
113	C₂×D₆₇	—	16	4	no	—
114	C₄×C₆₇	—	4	1	no	—
115	C₄×C₆₇	#392	1	1	yes	characteristic
116	C₄×C₆₇	#447	1	2	yes	—
117	C₄×C₆₇	#469	1	1	yes	characteristic
118	#13313	—	67	1	no	maximal, Sylow
119	C₂×C₆₇	—	2	2	no	—
120	C₂×C₆₇	—	8	1	no	—
121	C₂×C₆₇	#1999	1	1	yes	characteristic
122	C₂×C₆₇	#2221	1	2	yes	—
123	D₆₇	—	16	4	no	—
124	C₂²×D₁₆	—	67	1	no	—
125	C₂×#472	—	67	2	no	—
126	C₂×#361	—	67	2	no	—
127	#2113	D₆₇	1	1	yes	characteristic, complemented
128	#1381	—	67	1	no	—
129	C₆₇	#13313	1	1	yes	characteristic, complemented, Sylow
130	C₂×AGL(1,ℤ/8)	—	134	2	no	—
131	C₂²×D₈	—	67	2	no	—
132	C₂×#131	C₂×D₆₇	1	1	yes	characteristic
133	C₂×D₁₆	—	134	4	no	—
134	C₂×D₁₆	—	134	2	no	—
135	C₂×M₃₂	C₂×D₆₇	1	1	yes	characteristic
136	C₂²×C₁₆	C₂×D₆₇	1	1	yes	characteristic
137	#472	—	134	4	no	—
138	#472	—	134	4	no	—
139	C₂×#108	—	67	2	no	—
140	C₂×#100	—	134	2	no	—
141	#361	—	134	4	no	—
142	C₂²⋊C₁₆	—	2	2	no	—
143	C₂×#41	D₂₆₈	1	1	yes	characteristic
144	C₂²×D₄	—	134	2	no	—
145	AGL(1,ℤ/8)	—	268	4	no	—
146	AGL(1,ℤ/8)	—	134	8	no	—
147	C₂×SD₁₆	—	268	2	no	—
148	C₂×D₈	—	268	2	no	—
149	C₂×D₈	—	67	4	no	—
150	C₂×D₈	—	134	2	no	—
151	C₂×D₈	—	134	2	no	—
152	C₂×D₈	—	134	2	no	—
153	C₂×D₈	—	134	2	no	—
154	C₂×D₈	—	134	2	no	—
155	#131	—	2	2	no	—
156	#131	—	2	2	no	—
157	C₂×M₁₆	—	2	1	no	—
158	C₂×M₁₆	—	134	2	no	—
159	C₂×M₁₆	D₂₆₈	1	1	yes	characteristic
160	C₂²×C₈	—	2	1	no	—
161	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
162	D₁₆	—	134	8	no	—
163	M₃₂	—	2	2	no	—
164	C₂×C₁₆	—	2	2	no	—
165	C₂×C₁₆	—	2	1	no	—
166	C₂×C₁₆	C₂²⋊D₆₇	1	2	yes	—
167	#108	—	67	4	no	—
168	#108	—	134	2	no	—
169	#100	—	134	8	no	—
170	C₂⁴	—	268	2	no	—
171	#41	—	2	2	no	—
172	#41	—	2	2	no	—
173	C₂×Q₈	D₅₃₆	1	1	yes	characteristic
174	C₂×D₄	—	2	1	no	—
175	C₂×D₄	—	268	2	no	—
176	C₂×D₄	—	268	2	no	—
177	C₂×D₄	—	268	2	no	—
178	C₂×D₄	—	268	2	no	—
179	C₂×D₄	—	268	2	no	—
180	C₂×D₄	—	134	4	no	—
181	C₂×D₄	D₅₃₆	1	1	yes	characteristic
182	C₂²×C₄	—	2	1	no	—
183	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
184	SD₁₆	—	268	8	no	—
185	D₈	—	268	8	no	—
186	D₈	—	268	2	no	—
187	D₈	—	268	2	no	—
188	D₈	—	134	4	no	—
189	D₈	—	134	4	no	—
190	M₁₆	—	2	2	no	—
191	M₁₆	—	4	2	no	—
192	M₁₆	—	268	2	no	—
193	M₁₆	—	134	4	no	—
194	C₂×C₈	—	2	1	no	—
195	C₂×C₈	—	4	1	no	—
196	C₂×C₈	—	4	1	no	—
197	C₂×C₈	—	268	2	no	—
198	C₂×C₈	D₄×D₆₇	1	2	yes	—
199	C₂×C₈	D₄×D₆₇	1	2	yes	—
200	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
201	C₂×C₈	#11761628	1	1	yes	characteristic
202	C₁₆	—	2	2	no	—
203	C₁₆	—	4	1	no	—
204	C₂³	—	2	1	no	—
205	C₂³	—	268	4	no	—
206	C₂³	—	536	2	no	—
207	C₂³	—	536	2	no	—
208	C₂³	—	1072	4	no	—
209	C₂³	#14524065	1	1	yes	characteristic
210	Q₈	—	2	2	no	—
211	D₄	—	2	2	no	—
212	D₄	—	4	2	no	—
213	D₄	—	268	4	no	—
214	D₄	—	268	4	no	—
215	D₄	—	536	2	no	—
216	D₄	—	536	2	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	4	1	no	—
219	C₂×C₄	—	4	1	no	—
220	C₂×C₄	#14524013	1	2	yes	—
221	C₂×C₄	#14524017	1	1	yes	characteristic
222	C₂×C₄	C₂×D₅₃₆	1	1	yes	characteristic
223	C₂×C₄	#14524071	1	2	yes	—
224	C₈	—	4	1	no	—
225	C₈	—	268	4	no	—
226	C₈	#14524011	1	1	yes	characteristic
227	C₈	#14524016	1	2	yes	—
228	C₈	#14524039	1	1	yes	characteristic
229	C₂²	—	2	2	no	—
230	C₂²	—	4	2	no	—
231	C₂²	—	4	1	no	—
232	C₂²	—	536	4	no	—
233	C₂²	—	1072	4	no	—
234	C₂²	—	1072	4	no	—
235	C₂²	—	1072	4	no	—
236	C₂²	#16863543	1	2	yes	—
237	C₂²	#16863632	1	1	yes	characteristic
238	C₄	—	4	1	no	—
239	C₄	#16863305	1	1	yes	characteristic
240	C₄	#16863532	1	2	yes	—
241	C₄	#16863649	1	1	yes	characteristic
242	C₂	—	2	2	no	—
243	C₂	—	8	1	no	—
244	C₂	—	1072	4	no	—
245	C₂	#22561207	1	1	yes	characteristic
246	C₂	#22562329	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₁₀₇₂

C₂

yes

maximal, characteristic, complemented

C₂×#16863666

C₂

yes

maximal, complemented

C₂×#16863210

C₂

yes

maximal, complemented

#22558303

C₂

yes

maximal, characteristic, complemented

C₆₇×#2113

C₂

yes

maximal, characteristic, complemented

C₂×#14524068

—

C₂²×D₅₃₆

C₂²

yes

—

C₂×D₁₀₇₂

—

C₂×D₁₀₇₂

—

#16863666

—

#16863666

—

C₂×#14523979

C₂²

yes

—

C₂×#14523959

—

#16863210

—

C₂×#131×C₆₇

C₂²

yes

characteristic

C₂×M₃₂×C₆₇

C₂²

yes

characteristic

C₂²×C₁₆×C₆₇

C₂²

yes

characteristic

C₂²⋊C₁₆×C₆₇

—

C₂²×D₂₆₈

—

#14524068

—

#14524068

—

C₂×#11761615

—

C₂×D₅₃₆

—

C₂×D₅₃₆

—

C₂×D₅₃₆

—

C₂×D₅₃₆

—

C₂×D₅₃₆

—

C₂×D₅₃₆

D₄

yes

—

C₂×#11761613

—

C₂×#11761612

—

D₁₀₇₂

—

#14523979

—

#14523979

D₄

yes

—

#14523959

—

C₂×#41×C₆₇

D₄

yes

characteristic

#131×C₆₇

—

#131×C₆₇

—

C₂×M₁₆×C₆₇

—

C₂×M₁₆×C₆₇

D₄

yes

characteristic

C₂²×C₈×C₆₇

—

C₂²×C₈×C₆₇

C₂³

yes

characteristic

M₃₂×C₆₇

—

C₂×C₁₆×C₆₇

—

C₂×C₁₆×C₆₇

—

C₂×C₁₆×C₆₇

D₄

yes

—

C₂³×D₆₇

—

C₂×D₂₆₈

—

C₂×D₂₆₈

—

C₂×D₂₆₈

—

C₂×D₂₆₈

—

C₂×D₂₆₈

—

C₂×D₂₆₈

—

#11761615

—

D₅₃₆

—

D₅₃₆

—

D₅₃₆

—

D₅₃₆

—

#11761613

—

#11761612

—

#11761612

—

C₂×C₆₇⋊C₈

—

#41×C₆₇

—

#41×C₆₇

—

C₂×Q₈×C₆₇

D₈

yes

characteristic

C₂×D₄×C₆₇

—

C₂×D₄×C₆₇

D₈

yes

characteristic

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

M₁₆×C₆₇

—

M₁₆×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

C₂×D₄

yes

—

C₂×C₈×C₆₇

C₂×D₄

yes

—

C₂×C₈×C₆₇

C₂×D₄

yes

characteristic

C₂×C₈×C₆₇

#41

yes

characteristic

C₁₆×C₆₇

—

C₁₆×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

#135

yes

characteristic

C₂²×D₆₇

—

C₂²×D₆₇

—

C₂²×D₆₇

—

C₂²×D₆₇

—

Q₈×C₆₇

—

D₄×C₆₇

—

D₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

#120

yes

—

C₂×C₄×C₆₇

#121

yes

characteristic

C₂×C₄×C₆₇

C₂×D₈

yes

characteristic

C₂×C₄×C₆₇

AGL(1,ℤ/8)

yes

—

D₂₆₈

—

D₂₆₈

—

D₂₆₈

—

D₂₆₈

—

100

C₈×C₆₇

—

101

C₈×C₆₇

#120

yes

characteristic

102

C₈×C₆₇

#121

yes

—

103

C₈×C₆₇

#127

yes

characteristic

104

C₆₇⋊C₈

—

105

C₂²×C₆₇

—

106

C₂²×C₆₇

—

107

C₂²×C₆₇

—

108

C₂²×C₆₇

#449

yes

—

109

C₂²×C₆₇

#466

yes

characteristic

110

C₂×D₆₇

—

111

C₂×D₆₇

—

112

C₂×D₆₇

—

113

C₂×D₆₇

—

114

C₄×C₆₇

—

115

C₄×C₆₇

#392

yes

characteristic

116

C₄×C₆₇

#447

yes

—

117

C₄×C₆₇

yes

118

—

119

C₂×C₆₇

—

120

C₂×C₆₇

—

121

C₂×C₆₇

#1999

yes

characteristic

122

C₂×C₆₇

#2221

yes

—

123

D₆₇

—

124

C₂²×D₁₆

—

125

C₂×#472

—

126

C₂×#361

—

127

#2113

D₆₇

yes

characteristic, complemented

128

#1381

—

129

C₆₇

#13313

yes

characteristic, complemented, Sylow

130

C₂×AGL(1,ℤ/8)

—

134

—

131

C₂²×D₈

—

132

C₂×#131

C₂×D₆₇

yes

characteristic

133

C₂×D₁₆

—

134

—

134

C₂×D₁₆

—

134

—

135

C₂×M₃₂

C₂×D₆₇

yes

characteristic

136

C₂²×C₁₆

C₂×D₆₇

yes

characteristic

137

#472

—

134

—

138

#472

—

134

—

139

C₂×#108

—

140

C₂×#100

—

134

—

141

#361

—

134

—

142

C₂²⋊C₁₆

—

143

C₂×#41

D₂₆₈

yes

characteristic

144

C₂²×D₄

—

134

—

145

AGL(1,ℤ/8)

—

268

—

146

AGL(1,ℤ/8)

—

134

—

147

C₂×SD₁₆

—

268

—

148

C₂×D₈

—

268

—

149

C₂×D₈

—

150

C₂×D₈

—

134

—

151

C₂×D₈

—

134

—

152

C₂×D₈

—

134

—

153

C₂×D₈

—

134

—

154

C₂×D₈

—

134

—

155

#131

—

156

#131

—

157

C₂×M₁₆

—

158

C₂×M₁₆

—

134

—

159

C₂×M₁₆

D₂₆₈

yes

characteristic

160

C₂²×C₈

—

161

C₂²×C₈

C₂²×D₆₇

yes

characteristic

162

D₁₆

—

134

—

163

M₃₂

—

164

C₂×C₁₆

—

165

C₂×C₁₆

—

166

C₂×C₁₆

C₂²⋊D₆₇

yes

—

167

#108

—

168

#108

—

134

—

169

#100

—

134

—

170

C₂⁴

—

268

—

171

#41

—

172

#41

—

173

C₂×Q₈

D₅₃₆

yes

characteristic

174

C₂×D₄

—

175

C₂×D₄

—

268

—

176

C₂×D₄

—

268

—

177

C₂×D₄

—

268

—

178

C₂×D₄

—

268

—

179

C₂×D₄

—

268

—

180

C₂×D₄

—

134

—

181

C₂×D₄

D₅₃₆

yes

characteristic

182

C₂²×C₄

—

183

C₂²×C₄

C₂×D₂₆₈

yes

characteristic

184

SD₁₆

—

268

—

185

D₈

—

268

—

186

D₈

—

268

—

187

D₈

—

268

—

188

D₈

—

134

—

189

D₈

—

134

—

190

M₁₆

—

191

M₁₆

—

192

M₁₆

—

268

—

193

M₁₆

—

134

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

268

—

198

C₂×C₈

D₄×D₆₇

yes

—

199

C₂×C₈

D₄×D₆₇

yes

—

200

C₂×C₈

C₂×C₂²⋊D₆₇

yes

characteristic

201

C₂×C₈

#11761628

yes

characteristic

202

C₁₆

—

203

C₁₆

—

204

C₂³

—

205

C₂³

—

268

—

206

C₂³

—

536

—

207

C₂³

—

536

—

208

C₂³

—

1072

—

209

C₂³

#14524065

yes

characteristic

210

Q₈

—

211

D₄

—

212

D₄

—

213

D₄

—

268

—

214

D₄

—

268

—

215

D₄

—

536

—

216

D₄

—

536

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

#14524013

yes

—

221

C₂×C₄

#14524017

yes

characteristic

222

C₂×C₄

C₂×D₅₃₆

yes

characteristic

223

C₂×C₄

#14524071

yes

—

224

C₈

—

225

C₈

—

268

—

226

C₈

#14524011

yes

characteristic

227

C₈

#14524016

yes

—

228

C₈

#14524039

yes

characteristic

229

C₂²

—

230

C₂²

—

231

C₂²

—

232

C₂²

—

536

—

233

C₂²

—

1072

—

234

C₂²

—

1072

—

235

C₂²

—

1072

—

236

C₂²

#16863543

yes

—

237

C₂²

#16863632

yes

characteristic

238

C₄

—

239

C₄

#16863305

yes

characteristic

240

C₄

#16863532

yes

—

241

C₄

#16863649

yes

characteristic

242

C₂

—

243

C₂

—

244

C₂

—

1072

—

245

C₂

#22561207

yes

characteristic

246

C₂

#22562329

yes

—

	subgroup	G/H
center	C₂²	#16863632
commutator, cosocle	C₂²×C₈×C₆₇	C₂³
Frattini	C₂²×C₈	C₂²×D₆₇
Fitting	C₆₇×#2113	C₂
socle	C₂²×C₆₇	#466
hypercenter	#2113	D₆₇
hypocenter	C₆₇	#13313
LCS	G ▷ C₂²×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#131 ◁ #2113

subgroup

G/H

center

C₂²

#16863632

commutator, cosocle

C₂²×C₈×C₆₇

C₂³

Frattini

C₂²×C₈

C₂²×D₆₇

Fitting

C₆₇×#2113

C₂

C₂²×C₆₇

D₆₇

C₆₇

G ▷ C₂²×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#131 ◁ #2113

N	H ≅ G/N	type
1. C₂²×D₁₀₇₂	C₂	semidirect
2. C₂×#16863666	C₂	semidirect
3. C₂×#16863210	C₂	semidirect
4. #22558303	C₂	semidirect
5. C₆₇×#2113	C₂	semidirect
127. #2113	D₆₇	semidirect
129. C₆₇	#13313	semidirect

H ≅ G/N

type

1. C₂²×D₁₀₇₂

C₂

semidirect

2. C₂×#16863666

C₂

semidirect

3. C₂×#16863210

C₂

semidirect

4. #22558303

C₂

semidirect

5. C₆₇×#2113

C₂

semidirect

127. #2113

D₆₇

semidirect

129. C₆₇

#13313

semidirect

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

subgroup	index
C₂²×D₁₀₇₂	2
C₂×#16863666	2
C₂×#16863210	2
#22558303	2
C₆₇×#2113	2
#13313	67

subgroup

index

C₂²×D₁₀₇₂

C₆₇×#2113

Subgroups — #30774583

Conjugacy classes of subgroups

Complements

Maximal subgroups