Group #31010331 — subgroups

Subgroups — #31010331

Order 17152.

650 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 650 conjugacy classes of subgroups — too many to draw. Only its 171 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×#16863812	C₂	1	1	yes	maximal, characteristic
2	#22569860	C₂	1	2	yes	maximal
3	#22562314	C₂	1	4	yes	maximal, complemented
4	#22562297	C₂	1	4	yes	maximal, complemented
5	#22561993	C₂	1	1	yes	maximal, characteristic, complemented
6	#22561929	C₂	1	2	yes	maximal, complemented
7	C₂²×Q₃₂×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14524049	C₂²	1	1	yes	characteristic
9	#16863970	—	2	2	no	—
10	#16863812	—	2	4	no	—
11	C₂×#14523983	C₂²	1	1	yes	characteristic
12	C₂×#14523982	C₂²	1	2	yes	—
13	C₂×C₁₆×D₆₇	C₂²	1	2	yes	—
14	#16863651	—	2	4	no	—
15	#16863634	C₂²	1	8	yes	—
16	#16863434	C₂²	1	2	yes	—
17	#16863405	—	2	2	no	—
18	#16863224	C₂²	1	2	yes	—
19	#16863222	C₂²	1	2	yes	—
20	#16863200	C₂²	1	8	yes	—
21	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	—
22	C₂×Q₃₂×C₆₇	—	2	4	no	—
23	C₂×Q₃₂×C₆₇	C₂²	1	2	yes	—
24	C₂×Q₃₂×C₆₇	C₂²	1	2	yes	—
25	C₂²×C₁₆×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#11761628	D₄	1	1	yes	characteristic
27	#14524049	—	2	2	no	—
28	#14524049	—	2	2	no	—
29	C₂×#11761612	D₄	1	1	yes	characteristic
30	C₂×#11761611	D₄	1	2	yes	—
31	C₂×C₈×D₆₇	C₂³	1	2	yes	—
32	#14524041	—	4	2	no	—
33	#14524032	—	4	2	no	—
34	#14524026	—	4	4	no	—
35	#14524019	—	2	8	no	—
36	#14524002	—	2	2	no	—
37	#14523983	—	2	2	no	—
38	#14523982	—	2	4	no	—
39	C₂×C₆₇⋊C₁₆	C₂³	1	2	yes	—
40	C₁₆×D₆₇	—	2	4	no	—
41	#14523977	C₂³	1	4	yes	—
42	#14523975	—	2	2	no	—
43	#14523967	—	2	8	no	—
44	C₂²×Q₈×C₆₇	—	2	2	no	—
45	C₂×Q₁₆×C₆₇	—	2	4	no	—
46	C₂×Q₁₆×C₆₇	—	2	2	no	—
47	C₂×Q₁₆×C₆₇	—	2	4	no	—
48	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
49	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
50	Q₃₂×C₆₇	—	2	4	no	—
51	Q₃₂×C₆₇	—	2	4	no	—
52	C₂×C₁₆×C₆₇	D₄	1	4	yes	—
53	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
54	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
55	#11761628	—	2	2	no	—
56	#11761628	—	2	2	no	—
57	C₂×Dic₁₃₄	D₈	1	1	yes	characteristic
58	C₂×D₂₆₈	D₈	1	1	yes	characteristic
59	C₂×C₂²⋊D₆₇	D₈	1	2	yes	—
60	C₂×C₄×D₆₇	C₂×D₄	1	2	yes	—
61	#11761612	—	2	2	no	—
62	#11761611	—	2	4	no	—
63	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
64	C₈×D₆₇	—	2	2	no	—
65	C₈×D₆₇	—	2	2	no	—
66	C₄⋊Dic₆₇	—	2	4	no	—
67	Dic₆₇⋊C₄	—	4	8	no	—
68	C₂²⋊Dic₆₇	—	4	2	no	—
69	(C₂×D₆₇)⋊C₄	—	4	8	no	—
70	C₄×Dic₆₇	—	4	2	no	—
71	C₆₇⋊C₁₆	—	2	2	no	—
72	C₂×Q₈×C₆₇	—	2	4	no	—
73	C₂×Q₈×C₆₇	—	4	2	no	—
74	C₂×Q₈×C₆₇	—	4	4	no	—
75	C₂×Q₈×C₆₇	—	4	4	no	—
76	C₂²×C₄×C₆₇	—	4	2	no	—
77	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
78	Q₁₆×C₆₇	—	2	4	no	—
79	Q₁₆×C₆₇	—	2	4	no	—
80	Q₁₆×C₆₇	—	4	4	no	—
81	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
82	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
83	C₂×C₈×C₆₇	#41	1	2	yes	—
84	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
85	C₁₆×C₆₇	C₂×D₄	1	2	yes	—
86	C₁₆×C₆₇	C₂×D₄	1	2	yes	—
87	C₂³×C₆₇	C₂×D₈	1	1	yes	characteristic
88	C₂²×D₆₇	C₂×D₈	1	2	yes	—
89	Q₈×C₆₇	—	4	4	no	—
90	Q₈×C₆₇	—	4	4	no	—
91	Q₈×C₆₇	—	8	4	no	—
92	C₂×C₄×C₆₇	—	4	4	no	—
93	C₂×C₄×C₆₇	—	8	4	no	—
94	C₂×C₄×C₆₇	#121	1	2	yes	—
95	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
96	C₂×C₄×C₆₇	#135	1	2	yes	—
97	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
98	C₂²⋊D₆₇	—	2	4	no	—
99	C₂×Dic₆₇	—	4	4	no	—
100	C₂×Dic₆₇	C₂×D₈	1	2	yes	—
101	D₂₆₈	—	2	2	no	—
102	C₄×D₆₇	—	2	2	no	—
103	C₄×D₆₇	—	2	2	no	—
104	Dic₁₃₄	—	2	2	no	—
105	C₈×C₆₇	#121	1	2	yes	—
106	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
107	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
108	C₆₇⋊C₈	—	2	2	no	—
109	C₂²×C₆₇	—	2	2	no	—
110	C₂²×C₆₇	#466	1	2	yes	—
111	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
112	C₂×D₆₇	—	2	4	no	—
113	C₂×D₆₇	—	2	2	no	—
114	C₄×C₆₇	—	8	4	no	—
115	C₄×C₆₇	#466	1	2	yes	—
116	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
117	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
118	Dic₆₇	—	2	2	no	—
119	Dic₆₇	—	8	4	no	—
120	#33608	—	67	1	no	maximal, Sylow
121	C₂×C₆₇	—	2	2	no	—
122	C₂×C₆₇	C₂×#466	1	1	yes	characteristic
123	C₂×C₆₇	#3417	1	2	yes	—
124	D₆₇	—	4	2	no	—
125	C₂²×Q₃₂	D₆₇	1	1	yes	characteristic, complemented
126	C₂×#504	—	67	1	no	—
127	#3059	—	67	2	no	—
128	#2219	—	67	4	no	—
129	#2216	—	67	4	no	—
130	#2158	—	67	1	no	—
131	#2141	—	67	2	no	—
132	C₆₇	#33608	1	1	yes	characteristic, complemented, Sylow
133	C₂²×Q₁₆	C₂×D₆₇	1	2	yes	—
134	C₂×#131	—	67	1	no	—
135	#536	—	134	2	no	—
136	C₂×Q₃₂	—	2	4	no	—
137	C₂×Q₃₂	C₂×D₆₇	1	2	yes	—
138	C₂×Q₃₂	C₂×D₆₇	1	2	yes	—
139	#504	—	134	4	no	—
140	C₂×M₃₂	—	67	1	no	—
141	C₂×M₃₂	—	67	2	no	—
142	C₂²×C₁₆	—	67	2	no	—
143	C₂²×C₁₆	C₂×D₆₇	1	1	yes	characteristic
144	#470	—	134	4	no	—
145	#467	—	67	8	no	—
146	#427	—	67	2	no	—
147	#419	—	134	2	no	—
148	#367	—	67	2	no	—
149	#366	—	67	2	no	—
150	#358	—	67	8	no	—
151	C₂×#41	—	67	1	no	—
152	C₂²×Q₈	—	2	2	no	—
153	C₂×Q₁₆	—	2	2	no	—
154	C₂×Q₁₆	—	2	4	no	—
155	C₂×Q₁₆	—	2	4	no	—
156	C₂×Q₁₆	C₂²×D₆₇	1	4	yes	—
157	#131	—	134	2	no	—
158	#131	—	134	2	no	—
159	C₂×M₁₆	—	67	1	no	—
160	C₂×M₁₆	—	67	2	no	—
161	C₂²×C₈	—	67	2	no	—
162	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
163	C₄⋊Q₈	—	268	2	no	—
164	#124	—	268	2	no	—
165	#123	—	268	4	no	—
166	C₂²⋊Q₈	—	134	8	no	—
167	#117	—	134	2	no	—
168	Q₃₂	—	2	4	no	—
169	Q₃₂	—	2	4	no	—
170	M₃₂	—	134	2	no	—
171	M₃₂	—	134	4	no	—
172	C₂×C₁₆	—	67	2	no	—
173	C₂×C₁₆	—	134	4	no	—
174	C₂×C₁₆	C₂²⋊D₆₇	1	4	yes	—
175	C₂×C₁₆	C₂²×D₆₇	1	1	yes	characteristic
176	C₂×C₁₆	C₂²×D₆₇	1	1	yes	characteristic
177	#107	—	67	4	no	—
178	#106	—	134	2	no	—
179	#103	—	134	8	no	—
180	#41	—	134	2	no	—
181	#41	—	134	2	no	—
182	C₂×Q₈	—	2	4	no	—
183	C₂×Q₈	—	4	2	no	—
184	C₂×Q₈	—	4	4	no	—
185	C₂×Q₈	—	4	4	no	—
186	C₂×Q₈	—	67	1	no	—
187	C₂×D₄	—	67	2	no	—
188	C₂×D₄	—	67	1	no	—
189	C₂²×C₄	—	4	2	no	—
190	C₂²×C₄	—	67	2	no	—
191	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
192	Q₁₆	—	2	4	no	—
193	Q₁₆	—	2	4	no	—
194	Q₁₆	—	4	4	no	—
195	M₁₆	—	134	2	no	—
196	M₁₆	—	134	4	no	—
197	C₂×C₈	—	67	2	no	—
198	C₂×C₈	—	134	2	no	—
199	C₂×C₈	—	134	2	no	—
200	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
201	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
202	C₂×C₈	#11761627	1	2	yes	—
203	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
204	C₄⋊C₄	—	268	8	no	—
205	C₄⋊C₄	—	134	4	no	—
206	C₂²⋊C₄	—	268	8	no	—
207	C₂²⋊C₄	—	268	2	no	—
208	C₄²	—	268	2	no	—
209	C₁₆	—	134	2	no	—
210	C₁₆	C₂×C₂²⋊D₆₇	1	2	yes	—
211	C₁₆	C₂×C₂²⋊D₆₇	1	2	yes	—
212	C₂³	—	67	2	no	—
213	C₂³	D₈×D₆₇	1	1	yes	characteristic
214	Q₈	—	4	4	no	—
215	Q₈	—	4	4	no	—
216	Q₈	—	8	4	no	—
217	Q₈	—	134	2	no	—
218	D₄	—	134	4	no	—
219	D₄	—	134	2	no	—
220	C₂×C₄	—	4	4	no	—
221	C₂×C₄	—	8	4	no	—
222	C₂×C₄	—	268	4	no	—
223	C₂×C₄	—	67	2	no	—
224	C₂×C₄	—	134	2	no	—
225	C₂×C₄	—	134	2	no	—
226	C₂×C₄	#14524014	1	2	yes	—
227	C₂×C₄	D₈×D₆₇	1	1	yes	characteristic
228	C₂×C₄	#14524062	1	2	yes	—
229	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
230	C₈	—	134	2	no	—
231	C₈	#14524014	1	2	yes	—
232	C₈	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
233	C₈	C₂×#11761627	1	1	yes	characteristic
234	C₂²	—	2	2	no	—
235	C₂²	—	134	2	no	—
236	C₂²	—	134	4	no	—
237	C₂²	#16863629	1	2	yes	—
238	C₂²	C₂×D₈×D₆₇	1	1	yes	characteristic
239	C₄	—	8	4	no	—
240	C₄	—	536	4	no	—
241	C₄	—	134	2	no	—
242	C₄	#16863629	1	2	yes	—
243	C₄	C₂×#14524014	1	1	yes	characteristic
244	C₄	C₂×#14524062	1	1	yes	characteristic
245	C₂	—	2	2	no	—
246	C₂	—	268	2	no	—
247	C₂	C₂×#16863629	1	1	yes	characteristic
248	C₂	#22573358	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16863812

C₂

yes

maximal, characteristic

#22569860

C₂

yes

maximal

#22562314

C₂

yes

maximal, complemented

#22562297

C₂

yes

maximal, complemented

#22561993

C₂

yes

maximal, characteristic, complemented

#22561929

C₂

yes

maximal, complemented

C₂²×Q₃₂×C₆₇

C₂

yes

maximal, characteristic, complemented

C₂×#14524049

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×#14523982

C₂²

yes

—

C₂×C₁₆×D₆₇

C₂²

yes

—

#16863651

—

#16863634

C₂²

yes

—

#16863434

C₂²

yes

—

#16863405

—

#16863224

C₂²

yes

—

#16863222

C₂²

yes

—

#16863200

C₂²

yes

—

C₂²×Q₁₆×C₆₇

C₂²

yes

—

C₂×Q₃₂×C₆₇

—

C₂×Q₃₂×C₆₇

C₂²

yes

—

C₂×Q₃₂×C₆₇

C₂²

yes

—

C₂²×C₁₆×C₆₇

C₂²

yes

characteristic

C₂×#11761628

D₄

yes

—

—

D₄

yes

characteristic

C₂×#11761611

D₄

yes

—

C₂×C₈×D₆₇

C₂³

yes

—

—

—

—

—

—

—

—

C₂×C₆₇⋊C₁₆

C₂³

yes

—

C₁₆×D₆₇

—

#14523977

C₂³

yes

—

#14523975

—

#14523967

—

C₂²×Q₈×C₆₇

—

C₂×Q₁₆×C₆₇

—

C₂×Q₁₆×C₆₇

—

C₂×Q₁₆×C₆₇

—

C₂×Q₁₆×C₆₇

C₂³

yes

—

C₂²×C₈×C₆₇

C₂³

yes

characteristic

Q₃₂×C₆₇

—

Q₃₂×C₆₇

—

C₂×C₁₆×C₆₇

D₄

yes

—

C₂×C₁₆×C₆₇

C₂³

yes

characteristic

C₂×C₁₆×C₆₇

C₂³

yes

characteristic

#11761628

—

#11761628

—

C₂×Dic₁₃₄

D₈

yes

characteristic

C₂×D₂₆₈

D₈

yes

characteristic

C₂×C₂²⋊D₆₇

D₈

yes

—

C₂×C₄×D₆₇

C₂×D₄

yes

—

#11761612

—

#11761611

—

C₂×C₆₇⋊C₈

C₂×D₄

yes

—

C₈×D₆₇

—

C₈×D₆₇

—

C₄⋊Dic₆₇

—

Dic₆₇⋊C₄

—

C₂²⋊Dic₆₇

—

(C₂×D₆₇)⋊C₄

—

C₄×Dic₆₇

—

C₆₇⋊C₁₆

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

Q₁₆×C₆₇

—

Q₁₆×C₆₇

—

Q₁₆×C₆₇

—

C₂×C₈×C₆₇

C₂×D₄

yes

characteristic

C₂×C₈×C₆₇

C₂×D₄

yes

—

C₂×C₈×C₆₇

#41

yes

—

C₂×C₈×C₆₇

C₂⁴

yes

characteristic

C₁₆×C₆₇

C₂×D₄

yes

—

C₁₆×C₆₇

C₂×D₄

yes

—

C₂³×C₆₇

C₂×D₈

yes

characteristic

C₂²×D₆₇

C₂×D₈

yes

—

Q₈×C₆₇

—

Q₈×C₆₇

—

Q₈×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

#121

yes

—

C₂×C₄×C₆₇

C₂×D₈

yes

characteristic

C₂×C₄×C₆₇

#135

yes

—

C₂×C₄×C₆₇

C₂²×D₄

yes

characteristic

C₂²⋊D₆₇

—

C₂×Dic₆₇

—

100

C₂×Dic₆₇

C₂×D₈

yes

—

101

D₂₆₈

—

102

C₄×D₆₇

—

103

C₄×D₆₇

—

104

Dic₁₃₄

—

105

C₈×C₆₇

#121

yes

—

106

C₈×C₆₇

C₂²×D₄

yes

characteristic

107

C₈×C₆₇

C₂×#41

yes

characteristic

108

C₆₇⋊C₈

—

109

C₂²×C₆₇

—

110

C₂²×C₆₇

#466

yes

—

111

C₂²×C₆₇

C₂²×D₈

yes

characteristic

112

C₂×D₆₇

—

113

C₂×D₆₇

—

114

C₄×C₆₇

—

115

C₄×C₆₇

#466

yes

—

116

C₄×C₆₇

C₂×#121

yes

characteristic

117

C₄×C₆₇

C₂×#135

yes

characteristic

118

Dic₆₇

—

119

Dic₆₇

—

120

#33608

—

maximal, Sylow

121

C₂×C₆₇

—

122

C₂×C₆₇

C₂×#466

yes

characteristic

123

C₂×C₆₇

#3417

yes

—

124

D₆₇

—

125

C₂²×Q₃₂

D₆₇

yes

characteristic, complemented

126

C₂×#504

—

127

#3059

—

128

#2219

—

129

#2216

—

130

#2158

—

131

#2141

—

132

C₆₇

#33608

yes

characteristic, complemented, Sylow

133

C₂²×Q₁₆

C₂×D₆₇

yes

—

134

C₂×#131

—

135

#536

—

134

—

136

C₂×Q₃₂

—

137

C₂×Q₃₂

C₂×D₆₇

yes

—

138

C₂×Q₃₂

C₂×D₆₇

yes

—

139

#504

—

134

—

140

C₂×M₃₂

—

141

C₂×M₃₂

—

142

C₂²×C₁₆

—

143

C₂²×C₁₆

C₂×D₆₇

yes

characteristic

144

#470

—

134

—

145

#467

—

146

#427

—

147

#419

—

134

—

148

#367

—

149

#366

—

150

#358

—

151

C₂×#41

—

152

C₂²×Q₈

—

153

C₂×Q₁₆

—

154

C₂×Q₁₆

—

155

C₂×Q₁₆

—

156

C₂×Q₁₆

C₂²×D₆₇

yes

—

157

#131

—

134

—

158

#131

—

134

—

159

C₂×M₁₆

—

160

C₂×M₁₆

—

161

C₂²×C₈

—

162

C₂²×C₈

C₂²×D₆₇

yes

characteristic

163

C₄⋊Q₈

—

268

—

164

#124

—

268

—

165

#123

—

268

—

166

C₂²⋊Q₈

—

134

—

167

#117

—

134

—

168

Q₃₂

—

169

Q₃₂

—

170

M₃₂

—

134

—

171

M₃₂

—

134

—

172

C₂×C₁₆

—

173

C₂×C₁₆

—

134

—

174

C₂×C₁₆

C₂²⋊D₆₇

yes

—

175

C₂×C₁₆

C₂²×D₆₇

yes

characteristic

176

C₂×C₁₆

C₂²×D₆₇

yes

characteristic

177

#107

—

178

#106

—

134

—

179

#103

—

134

—

180

#41

—

134

—

181

#41

—

134

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

D₄×D₆₇

yes

characteristic

192

Q₁₆

—

193

Q₁₆

—

194

Q₁₆

—

195

M₁₆

—

134

—

196

M₁₆

—

134

—

197

C₂×C₈

—

198

C₂×C₈

—

134

—

199

C₂×C₈

—

134

—

200

C₂×C₈

D₄×D₆₇

yes

characteristic

201

C₂×C₈

C₂×C₂²⋊D₆₇

yes

—

202

C₂×C₈

#11761627

yes

—

203

C₂×C₈

C₂³×D₆₇

yes

characteristic

204

C₄⋊C₄

—

268

—

205

C₄⋊C₄

—

134

—

206

C₂²⋊C₄

—

268

—

207

C₂²⋊C₄

—

268

—

208

C₄²

—

268

—

209

C₁₆

—

134

—

210

C₁₆

C₂×C₂²⋊D₆₇

yes

—

211

C₁₆

C₂×C₂²⋊D₆₇

yes

—

212

C₂³

—

213

C₂³

D₈×D₆₇

yes

characteristic

214

Q₈

—

215

Q₈

—

216

Q₈

—

217

Q₈

—

134

—

218

D₄

—

134

—

219

D₄

—

134

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

268

—

223

C₂×C₄

—

224

C₂×C₄

—

134

—

225

C₂×C₄

—

134

—

226

C₂×C₄

#14524014

yes

—

227

C₂×C₄

D₈×D₆₇

yes

characteristic

228

C₂×C₄

#14524062

yes

—

229

C₂×C₄

C₂×D₄×D₆₇

yes

characteristic

230

C₈

—

134

—

231

C₈

#14524014

yes

—

232

C₈

C₂²×C₂²⋊D₆₇

yes

characteristic

233

C₈

C₂×#11761627

yes

characteristic

234

C₂²

—

235

C₂²

—

134

—

236

C₂²

—

134

—

237

C₂²

#16863629

yes

—

238

C₂²

C₂×D₈×D₆₇

yes

characteristic

239

C₄

—

240

C₄

—

536

—

241

C₄

—

134

—

242

C₄

#16863629

yes

—

243

C₄

C₂×#14524014

yes

characteristic

244

C₄

C₂×#14524062

yes

characteristic

245

C₂

—

246

C₂

—

268

—

247

C₂

C₂×#16863629

yes

characteristic

248

C₂

#22573358

yes

—

	subgroup	G/H
center	C₂²	C₂×D₈×D₆₇
commutator, cosocle	C₂×C₈×C₆₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₆₇
Fitting	C₂²×Q₃₂×C₆₇	C₂
socle	C₂²×C₆₇	C₂²×D₈
prime radical	C₂×#11761628	D₄
hypercenter	C₂²×Q₃₂	D₆₇
hypocenter	C₆₇	#33608
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

subgroup

G/H

center

C₂²

C₂×D₈×D₆₇

commutator, cosocle

C₂×C₈×C₆₇

C₂⁴

Frattini

C₂×C₈

C₂³×D₆₇

Fitting

C₂²×Q₃₂×C₆₇

C₂

socle

C₂²×C₆₇

C₂²×D₈

prime radical

C₂×#11761628

D₄

hypercenter

C₂²×Q₃₂

D₆₇

hypocenter

C₆₇

#33608

LCS

G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

N	H ≅ G/N	type
3. #22562314	C₂	semidirect
4. #22562297	C₂	semidirect
5. #22561993	C₂	semidirect
6. #22561929	C₂	semidirect
7. C₂²×Q₃₂×C₆₇	C₂	semidirect
125. C₂²×Q₃₂	D₆₇	semidirect
132. C₆₇	#33608	semidirect

H ≅ G/N

type

3. #22562314

C₂

semidirect

4. #22562297

C₂

semidirect

5. #22561993

C₂

semidirect

6. #22561929

C₂

semidirect

7. C₂²×Q₃₂×C₆₇

C₂

semidirect

125. C₂²×Q₃₂

D₆₇

semidirect

132. C₆₇

#33608

semidirect

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

subgroup	index
C₂×#16863812	2
#22569860	2
#22562314	2
#22562297	2
#22561993	2
#22561929	2
C₂²×Q₃₂×C₆₇	2
#33608	67

subgroup

index

C₂²×Q₃₂×C₆₇

Subgroups — #31010331

Conjugacy classes of subgroups

Complements

Maximal subgroups