Group #22558713 — subgroups

Subgroups — #22558713

Order 8576.

334 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 85 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	#16863360	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₇⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
3	#16863133	C₂	1	2	yes	maximal, complemented
4	#16863130	C₂	1	2	yes	maximal, complemented
5	#525×C₆₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×Dic₆₇	—	2	1	no	—
7	C₂×#11761612	—	2	1	no	—
8	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
9	C₂²⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
10	C₆₇⋊#95	—	2	1	no	—
11	C₆₇⋊#95	C₂²	1	2	yes	—
12	C₂×#41×C₆₇	C₄	1	1	yes	characteristic, complemented
13	C₂³×C₄×C₆₇	C₂²	1	1	yes	characteristic
14	#123×C₆₇	—	2	1	no	—
15	C₂²⋊Q₈×C₆₇	C₄	1	1	yes	characteristic, complemented
16	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
17	#121×C₆₇	C₄	1	1	yes	characteristic, complemented
18	#121×C₆₇	C₂²	1	1	yes	characteristic
19	#120×C₆₇	—	2	1	no	—
20	C₄×D₄×C₆₇	—	2	1	no	—
21	C₄×D₄×C₆₇	—	2	1	no	—
22	#117×C₆₇	C₄	1	1	yes	characteristic, complemented
23	C₂²×Dic₆₇	—	2	4	no	—
24	C₂²×Dic₆₇	—	2	2	no	—
25	C₂²×Dic₆₇	—	4	2	no	—
26	C₂²×Dic₆₇	—	4	2	no	—
27	#11761612	—	4	2	no	—
28	C₂×C₆₇⋊C₈	—	2	2	no	—
29	C₂⁴×C₆₇	D₄	1	1	yes	characteristic
30	#41×C₆₇	—	4	2	no	—
31	C₂×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
32	C₂×D₄×C₆₇	—	2	1	no	—
33	C₂×D₄×C₆₇	—	2	1	no	—
34	C₂×D₄×C₆₇	—	2	1	no	—
35	C₂×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
36	C₂²×C₄×C₆₇	—	2	1	no	—
37	C₂²×C₄×C₆₇	—	4	2	no	—
38	C₂²×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₆₇	D₄	1	1	yes	characteristic
41	C₂²×C₄×C₆₇	D₄	1	1	yes	characteristic
42	C₂²×C₄×C₆₇	D₄	1	1	yes	characteristic
43	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
44	C₄⋊C₄×C₆₇	—	2	1	no	—
45	C₄⋊C₄×C₆₇	—	2	1	no	—
46	C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
47	C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
48	C₂²⋊C₄×C₆₇	—	2	1	no	—
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	C₄²×C₆₇	—	2	1	no	—
54	C₂³×C₆₇	—	2	2	no	—
55	C₂³×C₆₇	—	2	2	no	—
56	C₂³×C₆₇	—	2	1	no	—
57	C₂³×C₆₇	—	2	1	no	—
58	C₂³×C₆₇	—	2	1	no	—
59	C₂³×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
60	C₂³×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
61	C₂³×C₆₇	C₂×D₄	1	1	yes	characteristic
62	Q₈×C₆₇	—	4	1	no	—
63	D₄×C₆₇	—	4	1	no	—
64	D₄×C₆₇	—	4	2	no	—
65	D₄×C₆₇	—	4	2	no	—
66	D₄×C₆₇	—	4	1	no	—
67	D₄×C₆₇	—	4	1	no	—
68	C₂×C₄×C₆₇	—	2	2	no	—
69	C₂×C₄×C₆₇	—	2	2	no	—
70	C₂×C₄×C₆₇	—	2	1	no	—
71	C₂×C₄×C₆₇	—	2	1	no	—
72	C₂×C₄×C₆₇	—	2	1	no	—
73	C₂×C₄×C₆₇	—	4	1	no	—
74	C₂×C₄×C₆₇	—	4	1	no	—
75	C₂×C₄×C₆₇	—	4	1	no	—
76	C₂×C₄×C₆₇	—	4	1	no	—
77	C₂×C₄×C₆₇	—	4	2	no	—
78	C₂×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
82	C₂×Dic₆₇	—	2	4	no	—
83	C₂×Dic₆₇	—	4	8	no	—
84	C₂×Dic₆₇	—	4	2	no	—
85	C₂×Dic₆₇	—	4	2	no	—
86	C₆₇⋊C₈	—	4	2	no	—
87	C₂²×C₆₇	—	2	4	no	—
88	C₂²×C₆₇	—	2	4	no	—
89	C₂²×C₆₇	—	2	1	no	—
90	C₂²×C₆₇	—	2	1	no	—
91	C₂²×C₆₇	—	2	1	no	—
92	C₂²×C₆₇	—	2	1	no	—
93	C₂²×C₆₇	—	2	1	no	—
94	C₂²×C₆₇	—	2	1	no	—
95	C₂²×C₆₇	—	4	1	no	—
96	C₂²×C₆₇	—	4	1	no	—
97	C₂²×C₆₇	—	4	1	no	—
98	C₂²×C₆₇	#99	1	2	yes	—
99	C₂²×C₆₇	#104	1	2	yes	—
100	C₂²×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
102	C₂²×C₆₇	#137	1	1	yes	characteristic
103	C₄×C₆₇	—	2	1	no	—
104	C₄×C₆₇	—	2	1	no	—
105	C₄×C₆₇	—	2	1	no	—
106	C₄×C₆₇	—	2	1	no	—
107	C₄×C₆₇	—	4	1	no	—
108	C₄×C₆₇	—	4	1	no	—
109	C₄×C₆₇	—	4	1	no	—
110	Dic₆₇	—	4	4	no	—
111	C₂×C₆₇	—	2	1	no	—
112	C₂×C₆₇	—	2	2	no	—
113	C₂×C₆₇	—	2	2	no	—
114	C₂×C₆₇	—	2	1	no	—
115	C₂×C₆₇	—	8	1	no	—
116	C₂×C₆₇	C₂×#99	1	1	yes	characteristic
117	C₂×C₆₇	#417	1	1	yes	characteristic
118	C₂×C₆₇	C₂×#104	1	1	yes	characteristic
119	#1504	—	67	1	no	maximal, Sylow
120	C₆₇	#1504	1	1	yes	characteristic, complemented, Sylow
121	#525	D₆₇	1	1	yes	characteristic
122	#407	—	67	1	no	—
123	C₂×#95	—	67	1	no	—
124	#328	—	67	2	no	—
125	#327	—	67	2	no	—
126	C₂×#41	Dic₆₇	1	1	yes	characteristic, complemented
127	C₂³×C₄	—	134	1	no	—
128	C₂³×C₄	C₂×D₆₇	1	1	yes	characteristic
129	C₂×M₁₆	—	134	1	no	—
130	#123	—	2	1	no	—
131	C₂²⋊Q₈	Dic₆₇	1	1	yes	characteristic, complemented
132	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
133	#121	Dic₆₇	1	1	yes	characteristic, complemented
134	#121	C₂×D₆₇	1	1	yes	characteristic
135	#120	—	2	1	no	—
136	C₄×D₄	—	2	1	no	—
137	C₄×D₄	—	2	1	no	—
138	#117	Dic₆₇	1	1	yes	characteristic, complemented
139	C₂²⋊C₈	—	67	2	no	—
140	C₂²⋊C₈	—	134	1	no	—
141	#95	—	67	2	no	—
142	#95	—	134	1	no	—
143	C₂⁴	C₂²⋊D₆₇	1	1	yes	characteristic
144	#41	—	4	2	no	—
145	C₂×Q₈	C₂×Dic₆₇	1	1	yes	characteristic, complemented
146	C₂×D₄	—	2	1	no	—
147	C₂×D₄	—	2	1	no	—
148	C₂×D₄	—	2	1	no	—
149	C₂×D₄	C₂×Dic₆₇	1	1	yes	characteristic, complemented
150	C₂²×C₄	—	2	1	no	—
151	C₂²×C₄	—	4	2	no	—
152	C₂²×C₄	—	268	2	no	—
153	C₂²×C₄	—	268	2	no	—
154	C₂²×C₄	—	134	4	no	—
155	C₂²×C₄	—	134	2	no	—
156	C₂²×C₄	C₂×Dic₆₇	1	1	yes	characteristic
157	C₂²×C₄	C₂×Dic₆₇	1	1	yes	characteristic
158	C₂²×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
159	C₂²×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
160	C₂²×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
161	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
162	M₁₆	—	268	2	no	—
163	C₂×C₈	—	134	2	no	—
164	C₄⋊C₄	—	2	1	no	—
165	C₄⋊C₄	—	2	1	no	—
166	C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic, complemented
167	C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic, complemented
168	C₂²⋊C₄	—	2	1	no	—
169	C₂²⋊C₄	—	2	1	no	—
170	C₂²⋊C₄	—	2	1	no	—
171	C₂²⋊C₄	—	2	1	no	—
172	C₂²⋊C₄	—	2	1	no	—
173	C₄²	—	2	1	no	—
174	C₂³	—	2	2	no	—
175	C₂³	—	2	2	no	—
176	C₂³	—	2	1	no	—
177	C₂³	—	2	1	no	—
178	C₂³	—	2	1	no	—
179	C₂³	C₂²⋊Dic₆₇	1	1	yes	characteristic
180	C₂³	C₂²⋊Dic₆₇	1	1	yes	characteristic
181	C₂³	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
182	Q₈	—	4	1	no	—
183	D₄	—	4	1	no	—
184	D₄	—	4	2	no	—
185	D₄	—	4	2	no	—
186	D₄	—	4	1	no	—
187	D₄	—	4	1	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	2	1	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	4	1	no	—
195	C₂×C₄	—	4	1	no	—
196	C₂×C₄	—	4	1	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	268	8	no	—
199	C₂×C₄	—	268	2	no	—
200	C₂×C₄	—	268	2	no	—
201	C₂×C₄	—	134	4	no	—
202	C₂×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
203	C₂×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
204	C₂×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
205	C₂×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
206	C₈	—	268	2	no	—
207	C₂²	—	2	4	no	—
208	C₂²	—	2	4	no	—
209	C₂²	—	2	1	no	—
210	C₂²	—	2	1	no	—
211	C₂²	—	2	1	no	—
212	C₂²	—	2	1	no	—
213	C₂²	—	2	1	no	—
214	C₂²	—	2	1	no	—
215	C₂²	—	4	1	no	—
216	C₂²	—	4	1	no	—
217	C₂²	—	4	1	no	—
218	C₂²	#14523958	1	2	yes	—
219	C₂²	#14523970	1	2	yes	—
220	C₂²	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
221	C₂²	#14524068	1	1	yes	characteristic
222	C₂²	#14524073	1	1	yes	characteristic
223	C₄	—	2	1	no	—
224	C₄	—	2	1	no	—
225	C₄	—	2	1	no	—
226	C₄	—	2	1	no	—
227	C₄	—	4	1	no	—
228	C₄	—	4	1	no	—
229	C₄	—	4	1	no	—
230	C₄	—	268	4	no	—
231	C₂	—	2	1	no	—
232	C₂	—	2	2	no	—
233	C₂	—	2	2	no	—
234	C₂	—	2	1	no	—
235	C₂	—	8	1	no	—
236	C₂	C₂×#14523958	1	1	yes	characteristic
237	C₂	#16863397	1	1	yes	characteristic
238	C₂	C₂×#14523970	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16863360

C₂

yes

maximal, characteristic, complemented

C₂×C₆₇⋊#95

C₂

yes

maximal, characteristic, complemented

#16863133

C₂

yes

maximal, complemented

#16863130

C₂

yes

maximal, complemented

#525×C₆₇

C₂

yes

maximal, characteristic

C₂³×Dic₆₇

—

C₂×#11761612

—

C₂²⋊(C₆₇⋊C₈)

—

C₂²⋊(C₆₇⋊C₈)

C₂²

yes

—

C₆₇⋊#95

—

C₆₇⋊#95

C₂²

yes

—

C₂×#41×C₆₇

C₄

yes

characteristic, complemented

C₂³×C₄×C₆₇

C₂²

yes

characteristic

#123×C₆₇

—

C₂²⋊Q₈×C₆₇

C₄

yes

characteristic, complemented

C₂²⋊Q₈×C₆₇

C₂²

yes

characteristic

#121×C₆₇

C₄

yes

characteristic, complemented

#121×C₆₇

C₂²

yes

characteristic

#120×C₆₇

—

C₄×D₄×C₆₇

—

C₄×D₄×C₆₇

—

#117×C₆₇

C₄

yes

characteristic, complemented

C₂²×Dic₆₇

—

C₂²×Dic₆₇

—

C₂²×Dic₆₇

—

C₂²×Dic₆₇

—

#11761612

—

C₂×C₆₇⋊C₈

—

C₂⁴×C₆₇

D₄

yes

characteristic

#41×C₆₇

—

C₂×Q₈×C₆₇

C₂×C₄

yes

characteristic, complemented

C₂×D₄×C₆₇

—

C₂×D₄×C₆₇

—

C₂×D₄×C₆₇

—

C₂×D₄×C₆₇

C₂×C₄

yes

characteristic, complemented

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₆₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₆₇

D₄

yes

characteristic

C₂²×C₄×C₆₇

D₄

yes

characteristic

C₂²×C₄×C₆₇

D₄

yes

characteristic

C₂²×C₄×C₆₇

C₂³

yes

characteristic

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

C₂×C₄

yes

characteristic, complemented

C₄⋊C₄×C₆₇

C₂×C₄

yes

characteristic, complemented

C₂²⋊C₄×C₆₇

—

C₂²⋊C₄×C₆₇

—

C₂²⋊C₄×C₆₇

—

C₂²⋊C₄×C₆₇

—

C₂²⋊C₄×C₆₇

—

C₄²×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

C₂²⋊C₄

yes

characteristic

C₂³×C₆₇

C₂²⋊C₄

yes

characteristic

C₂³×C₆₇

C₂×D₄

yes

characteristic

Q₈×C₆₇

—

D₄×C₆₇

—

D₄×C₆₇

—

D₄×C₆₇

—

D₄×C₆₇

—

D₄×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

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₆₇⋊C₈

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

#99

yes

—

C₂²×C₆₇

#104

yes

—

100

C₂²×C₆₇

C₂×C₂²⋊C₄

yes

characteristic

101

C₂²×C₆₇

AGL(1,ℤ/8)

yes

characteristic

102

C₂²×C₆₇

#137

yes

characteristic

103

C₄×C₆₇

—

104

C₄×C₆₇

—

105

C₄×C₆₇

—

106

C₄×C₆₇

—

107

C₄×C₆₇

—

108

C₄×C₆₇

—

109

C₄×C₆₇

—

110

Dic₆₇

—

111

C₂×C₆₇

—

112

C₂×C₆₇

—

113

C₂×C₆₇

—

114

C₂×C₆₇

—

115

C₂×C₆₇

—

116

C₂×C₆₇

C₂×#99

yes

characteristic

117

C₂×C₆₇

#417

yes

characteristic

118

C₂×C₆₇

yes

119

—

120

C₆₇

#1504

yes

characteristic, complemented, Sylow

121

#525

D₆₇

yes

characteristic

122

#407

—

123

C₂×#95

—

124

#328

—

125

#327

—

126

C₂×#41

Dic₆₇

yes

characteristic, complemented

127

C₂³×C₄

—

134

—

128

C₂³×C₄

C₂×D₆₇

yes

characteristic

129

C₂×M₁₆

—

134

—

130

#123

—

131

C₂²⋊Q₈

Dic₆₇

yes

characteristic, complemented

132

C₂²⋊Q₈

C₂×D₆₇

yes

characteristic

133

#121

Dic₆₇

yes

characteristic, complemented

134

#121

C₂×D₆₇

yes

characteristic

135

#120

—

136

C₄×D₄

—

137

C₄×D₄

—

138

#117

Dic₆₇

yes

characteristic, complemented

139

C₂²⋊C₈

—

140

C₂²⋊C₈

—

134

—

141

#95

—

142

#95

—

134

—

143

C₂⁴

C₂²⋊D₆₇

yes

characteristic

144

#41

—

145

C₂×Q₈

C₂×Dic₆₇

yes

characteristic, complemented

146

C₂×D₄

—

147

C₂×D₄

—

148

C₂×D₄

—

149

C₂×D₄

C₂×Dic₆₇

yes

characteristic, complemented

150

C₂²×C₄

—

151

C₂²×C₄

—

152

C₂²×C₄

—

268

—

153

C₂²×C₄

—

268

—

154

C₂²×C₄

—

134

—

155

C₂²×C₄

—

134

—

156

C₂²×C₄

C₂×Dic₆₇

yes

characteristic

157

C₂²×C₄

C₂×Dic₆₇

yes

characteristic

158

C₂²×C₄

C₂²⋊D₆₇

yes

characteristic

159

C₂²×C₄

C₂²⋊D₆₇

yes

characteristic

160

C₂²×C₄

C₂²⋊D₆₇

yes

characteristic

161

C₂²×C₄

C₂²×D₆₇

yes

characteristic

162

M₁₆

—

268

—

163

C₂×C₈

—

134

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

C₂×Dic₆₇

yes

characteristic, complemented

167

C₄⋊C₄

C₂×Dic₆₇

yes

characteristic, complemented

168

C₂²⋊C₄

—

169

C₂²⋊C₄

—

170

C₂²⋊C₄

—

171

C₂²⋊C₄

—

172

C₂²⋊C₄

—

173

C₄²

—

174

C₂³

—

175

C₂³

—

176

C₂³

—

177

C₂³

—

178

C₂³

—

179

C₂³

C₂²⋊Dic₆₇

yes

characteristic

180

C₂³

C₂²⋊Dic₆₇

yes

characteristic

181

C₂³

C₂×C₂²⋊D₆₇

yes

characteristic

182

Q₈

—

183

D₄

—

184

D₄

—

185

D₄

—

186

D₄

—

187

D₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

268

—

199

C₂×C₄

—

268

—

200

C₂×C₄

—

268

—

201

C₂×C₄

—

134

—

202

C₂×C₄

C₂²⋊Dic₆₇

yes

characteristic

203

C₂×C₄

C₂²⋊Dic₆₇

yes

characteristic

204

C₂×C₄

C₂²×Dic₆₇

yes

characteristic

205

C₂×C₄

C₂×C₂²⋊D₆₇

yes

characteristic

206

C₈

—

268

—

207

C₂²

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

#14523958

yes

—

219

C₂²

#14523970

yes

—

220

C₂²

C₂×C₂²⋊Dic₆₇

yes

characteristic

221

C₂²

#14524068

yes

characteristic

222

C₂²

#14524073

yes

characteristic

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

268

—

231

C₂

—

232

C₂

—

233

C₂

—

234

C₂

—

235

C₂

—

236

C₂

C₂×#14523958

yes

characteristic

237

C₂

#16863397

yes

characteristic

238

C₂

C₂×#14523970

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₆₇
commutator	C₂×C₄×C₆₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₇
Fitting	#525×C₆₇	C₂
socle	C₂²×C₆₇	C₂×C₂²⋊C₄
hypercenter	#525	D₆₇
hypocenter	C₆₇	#1504
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #525

subgroup

G/H

center

C₂²

C₂×C₂²⋊Dic₆₇

commutator

C₂×C₄×C₆₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₆₇

Fitting

#525×C₆₇

C₂

socle

C₂²×C₆₇

C₂×C₂²⋊C₄

D₆₇

C₆₇

G ▷ C₂×C₄×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #525

N	H ≅ G/N	type
1. #16863360	C₂	semidirect
2. C₂×C₆₇⋊#95	C₂	semidirect
3. #16863133	C₂	semidirect
4. #16863130	C₂	semidirect
12. C₂×#41×C₆₇	C₄	semidirect
15. C₂²⋊Q₈×C₆₇	C₄	semidirect
17. #121×C₆₇	C₄	semidirect
22. #117×C₆₇	C₄	semidirect
31. C₂×Q₈×C₆₇	C₂×C₄	semidirect
35. C₂×D₄×C₆₇	C₂×C₄	semidirect
46. C₄⋊C₄×C₆₇	C₂×C₄	semidirect
47. C₄⋊C₄×C₆₇	C₂×C₄	semidirect
120. C₆₇	#1504	semidirect
126. C₂×#41	Dic₆₇	semidirect
131. C₂²⋊Q₈	Dic₆₇	semidirect
133. #121	Dic₆₇	semidirect
138. #117	Dic₆₇	semidirect
145. C₂×Q₈	C₂×Dic₆₇	semidirect
149. C₂×D₄	C₂×Dic₆₇	semidirect
166. C₄⋊C₄	C₂×Dic₆₇	semidirect
167. C₄⋊C₄	C₂×Dic₆₇	semidirect

H ≅ G/N

type

1. #16863360

C₂

semidirect

2. C₂×C₆₇⋊#95

C₂

semidirect

3. #16863133

C₂

semidirect

4. #16863130

C₂

semidirect

12. C₂×#41×C₆₇

C₄

semidirect

15. C₂²⋊Q₈×C₆₇

C₄

semidirect

17. #121×C₆₇

C₄

semidirect

22. #117×C₆₇

C₄

semidirect

31. C₂×Q₈×C₆₇

C₂×C₄

semidirect

35. C₂×D₄×C₆₇

C₂×C₄

semidirect

46. C₄⋊C₄×C₆₇

C₂×C₄

semidirect

47. C₄⋊C₄×C₆₇

C₂×C₄

semidirect

120. C₆₇

#1504

semidirect

126. C₂×#41

Dic₆₇

semidirect

131. C₂²⋊Q₈

Dic₆₇

semidirect

133. #121

Dic₆₇

semidirect

138. #117

Dic₆₇

semidirect

145. C₂×Q₈

C₂×Dic₆₇

semidirect

149. C₂×D₄

C₂×Dic₆₇

semidirect

166. C₄⋊C₄

C₂×Dic₆₇

semidirect

167. C₄⋊C₄

C₂×Dic₆₇

semidirect

Subgroups — #22558713

Conjugacy classes of subgroups

Complements