Group #30760565 — subgroups

Subgroups — #30760565

Order 17152.

402 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 123 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	#22560337	C₂	1	1	yes	maximal, characteristic, complemented
2	#22560209	C₂	1	2	yes	maximal
3	#22558093	C₂	1	2	yes	maximal, complemented
4	#22558044	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1954	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
7	C₂×#14523964	—	2	2	no	—
8	#16863266	C₂²	1	2	yes	—
9	#16863159	—	2	2	no	—
10	#16863158	—	2	2	no	—
11	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊C₈×C₆₇	—	2	2	no	—
14	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
15	C₂²×C₆₇⋊C₈	—	2	2	no	—
16	C₂×C₄⋊Dic₆₇	—	2	2	no	—
17	C₂×C₄⋊Dic₆₇	—	2	2	no	—
18	C₂×C₄⋊Dic₆₇	—	2	2	no	—
19	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
20	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
21	#14523964	—	4	4	no	—
22	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₆₇	—	2	1	no	—
24	C₂²×C₈×C₆₇	—	2	1	no	—
25	C₂²×C₈×C₆₇	D₄	1	2	yes	—
26	C₄×D₄×C₆₇	—	2	2	no	—
27	C₄×D₄×C₆₇	—	2	2	no	—
28	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
30	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
31	C₄⋊C₈×C₆₇	—	2	2	no	—
32	C₂²⋊C₈×C₆₇	—	4	4	no	—
33	C₄×C₈×C₆₇	—	2	2	no	—
34	C₂²×Dic₆₇	—	4	2	no	—
35	C₂×C₆₇⋊C₈	—	4	2	no	—
36	C₂×C₆₇⋊C₈	—	4	2	no	—
37	C₂×C₆₇⋊C₈	—	4	2	no	—
38	C₄⋊Dic₆₇	—	4	2	no	—
39	C₄⋊Dic₆₇	—	4	2	no	—
40	C₄⋊Dic₆₇	—	4	2	no	—
41	C₄⋊Dic₆₇	—	4	2	no	—
42	C₄⋊Dic₆₇	—	8	2	no	—
43	C₂⁴×C₆₇	—	2	1	no	—
44	C₂×D₄×C₆₇	—	2	2	no	—
45	C₂×D₄×C₆₇	—	2	1	no	—
46	C₂×D₄×C₆₇	—	2	2	no	—
47	C₂×D₄×C₆₇	D₈	1	2	yes	—
48	C₂²×C₄×C₆₇	—	2	1	no	—
49	C₂²×C₄×C₆₇	—	4	1	no	—
50	C₂²×C₄×C₆₇	—	4	1	no	—
51	C₂²×C₄×C₆₇	—	4	2	no	—
52	C₂²×C₄×C₆₇	—	4	2	no	—
53	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
56	C₂×C₈×C₆₇	—	2	2	no	—
57	C₂×C₈×C₆₇	—	2	2	no	—
58	C₂×C₈×C₆₇	—	2	2	no	—
59	C₂×C₈×C₆₇	—	4	1	no	—
60	C₂×C₈×C₆₇	—	4	2	no	—
61	C₄⋊C₄×C₆₇	—	2	2	no	—
62	C₂²⋊C₄×C₆₇	—	4	2	no	—
63	C₄²×C₆₇	#41	1	2	yes	—
64	C₄²×C₆₇	#41	1	2	yes	—
65	C₂³×C₆₇	—	2	2	no	—
66	C₂³×C₆₇	—	4	1	no	—
67	C₂³×C₆₇	—	4	2	no	—
68	C₂³×C₆₇	—	4	1	no	—
69	C₂³×C₆₇	—	4	2	no	—
70	C₂³×C₆₇	#121	1	1	yes	characteristic
71	D₄×C₆₇	—	2	4	no	—
72	D₄×C₆₇	—	4	2	no	—
73	C₂×C₄×C₆₇	—	2	2	no	—
74	C₂×C₄×C₆₇	—	4	1	no	—
75	C₂×C₄×C₆₇	—	4	2	no	—
76	C₂×C₄×C₆₇	—	8	2	no	—
77	C₂×C₄×C₆₇	—	8	1	no	—
78	C₂×C₄×C₆₇	—	8	1	no	—
79	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
80	C₂×C₄×C₆₇	#123	1	2	yes	—
81	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
82	C₂×C₄×C₆₇	#126	1	2	yes	—
83	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
84	C₂×C₄×C₆₇	#135	1	2	yes	—
85	C₂×C₄×C₆₇	#135	1	1	yes	characteristic
86	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
87	C₂×C₄×C₆₇	#137	1	2	yes	—
88	C₂×Dic₆₇	—	8	2	no	—
89	C₂×Dic₆₇	—	8	2	no	—
90	C₂×Dic₆₇	—	8	2	no	—
91	C₈×C₆₇	—	4	2	no	—
92	C₈×C₆₇	—	8	1	no	—
93	C₆₇⋊C₈	—	8	2	no	—
94	C₂²×C₆₇	—	4	2	no	—
95	C₂²×C₆₇	—	4	4	no	—
96	C₂²×C₆₇	—	8	1	no	—
97	C₂²×C₆₇	—	8	1	no	—
98	C₂²×C₆₇	—	8	2	no	—
99	C₂²×C₆₇	#397	1	1	yes	characteristic
100	C₂²×C₆₇	#463	1	2	yes	—
101	C₂²×C₆₇	#466	1	1	yes	characteristic
102	C₂²×C₆₇	#470	1	1	yes	characteristic
103	C₂²×C₆₇	#471	1	2	yes	—
104	C₄×C₆₇	—	2	2	no	—
105	C₄×C₆₇	—	8	1	no	—
106	C₄×C₆₇	#480	1	2	yes	—
107	C₄×C₆₇	#482	1	2	yes	—
108	C₄×C₆₇	#485	1	2	yes	—
109	C₄×C₆₇	#488	1	1	yes	characteristic
110	C₄×C₆₇	#490	1	1	yes	characteristic
111	Dic₆₇	—	16	2	no	—
112	#10621	—	67	1	no	maximal, Sylow
113	C₂×C₆₇	—	8	2	no	—
114	C₂×C₆₇	#1681	1	2	yes	—
115	C₂×C₆₇	#1703	1	2	yes	—
116	C₂×C₆₇	#2073	1	1	yes	characteristic
117	C₂×C₆₇	#2075	1	1	yes	characteristic
118	C₂×C₆₇	#2079	1	1	yes	characteristic
119	#1954	D₆₇	1	1	yes	characteristic
120	#1834	—	67	1	no	—
121	#1802	—	67	2	no	—
122	#1296	—	67	2	no	—
123	#1277	—	67	1	no	—
124	C₆₇	#10621	1	1	yes	characteristic, complemented, Sylow
125	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
126	C₂×C₄⋊C₈	—	67	2	no	—
127	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
128	C₂×#102	—	134	2	no	—
129	C₂×C₂²⋊C₈	—	2	2	no	—
130	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
131	#384	—	67	2	no	—
132	#340	—	134	2	no	—
133	#340	—	134	2	no	—
134	C₂²×D₄	D₂₆₈	1	1	yes	characteristic
135	C₂³×C₄	—	2	1	no	—
136	C₂²×C₈	—	2	1	no	—
137	C₂²×C₈	—	134	2	no	—
138	C₂²×C₈	C₂²⋊D₆₇	1	2	yes	—
139	C₄×D₄	—	2	2	no	—
140	C₄×D₄	—	2	2	no	—
141	C₂×C₄⋊C₄	—	134	2	no	—
142	C₂×C₄⋊C₄	—	134	2	no	—
143	C₂×C₄⋊C₄	—	134	2	no	—
144	C₂×C₄⋊C₄	D₂₆₈	1	1	yes	characteristic
145	C₂×C₂²⋊C₄	—	2	1	no	—
146	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
147	C₄⋊C₈	—	2	2	no	—
148	C₄⋊C₈	—	134	2	no	—
149	C₄⋊C₈	—	134	2	no	—
150	#102	—	268	4	no	—
151	C₂²⋊C₈	—	4	4	no	—
152	C₄×C₈	—	2	2	no	—
153	C₂⁴	—	2	1	no	—
154	C₂×D₄	—	2	2	no	—
155	C₂×D₄	—	2	1	no	—
156	C₂×D₄	—	2	2	no	—
157	C₂×D₄	D₅₃₆	1	2	yes	—
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	4	1	no	—
160	C₂²×C₄	—	4	1	no	—
161	C₂²×C₄	—	4	2	no	—
162	C₂²×C₄	—	4	2	no	—
163	C₂²×C₄	—	268	2	no	—
164	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
165	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
166	C₂²×C₄	#11761628	1	1	yes	characteristic
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	4	1	no	—
171	C₂×C₈	—	4	2	no	—
172	C₂×C₈	—	268	2	no	—
173	C₂×C₈	—	268	2	no	—
174	C₂×C₈	—	268	2	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	268	2	no	—
177	C₄⋊C₄	—	268	2	no	—
178	C₄⋊C₄	—	268	2	no	—
179	C₄⋊C₄	—	268	2	no	—
180	C₄⋊C₄	—	536	2	no	—
181	C₂²⋊C₄	—	4	2	no	—
182	C₄²	#11761627	1	2	yes	—
183	C₄²	#11761627	1	2	yes	—
184	C₂³	—	2	2	no	—
185	C₂³	—	4	1	no	—
186	C₂³	—	4	2	no	—
187	C₂³	—	4	1	no	—
188	C₂³	—	4	2	no	—
189	C₂³	#14524017	1	1	yes	characteristic
190	D₄	—	2	4	no	—
191	D₄	—	4	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	8	1	no	—
196	C₂×C₄	—	8	1	no	—
197	C₂×C₄	—	8	2	no	—
198	C₂×C₄	—	536	2	no	—
199	C₂×C₄	—	536	2	no	—
200	C₂×C₄	—	536	2	no	—
201	C₂×C₄	#14524024	1	1	yes	characteristic
202	C₂×C₄	#14524027	1	2	yes	—
203	C₂×C₄	#14524030	1	1	yes	characteristic
204	C₂×C₄	#14524036	1	2	yes	—
205	C₂×C₄	C₂×D₅₃₆	1	1	yes	characteristic
206	C₂×C₄	#14524063	1	2	yes	—
207	C₂×C₄	#14524065	1	1	yes	characteristic
208	C₂×C₄	#14524069	1	2	yes	—
209	C₂×C₄	#14524076	1	2	yes	—
210	C₈	—	4	2	no	—
211	C₈	—	8	1	no	—
212	C₈	—	536	2	no	—
213	C₂²	—	4	2	no	—
214	C₂²	—	4	4	no	—
215	C₂²	—	8	2	no	—
216	C₂²	—	8	1	no	—
217	C₂²	—	8	1	no	—
218	C₂²	#16863321	1	1	yes	characteristic
219	C₂²	#16863611	1	2	yes	—
220	C₂²	#16863632	1	1	yes	characteristic
221	C₂²	#16863654	1	1	yes	characteristic
222	C₂²	#16863659	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	8	1	no	—
225	C₄	—	1072	2	no	—
226	C₄	#16863710	1	2	yes	—
227	C₄	#16863717	1	2	yes	—
228	C₄	#16863738	1	2	yes	—
229	C₄	#16863750	1	1	yes	characteristic
230	C₄	#16863760	1	1	yes	characteristic
231	C₂	—	8	2	no	—
232	C₂	#22559646	1	2	yes	—
233	C₂	#22559784	1	2	yes	—
234	C₂	#22561622	1	1	yes	characteristic
235	C₂	#22561632	1	1	yes	characteristic
236	C₂	#22561654	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22560337

C₂

yes

maximal, characteristic, complemented

#22560209

C₂

yes

maximal

#22558093

C₂

yes

maximal, complemented

#22558044

C₂

yes

maximal, characteristic, complemented

C₆₇×#1954

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₆₇⋊C₈)

C₂²

yes

—

C₂×#14523964

—

#16863266

C₂²

yes

—

#16863159

—

#16863158

—

C₂×C₄×D₄×C₆₇

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₆₇

C₂²

yes

characteristic

C₂×C₂²⋊C₈×C₆₇

—

C₂×C₄×C₈×C₆₇

C₂²

yes

characteristic

C₂²×C₆₇⋊C₈

—

C₂×C₄⋊Dic₆₇

—

C₂×C₄⋊Dic₆₇

—

C₂×C₄⋊Dic₆₇

—

C₄⋊(C₆₇⋊C₈)

—

C₄⋊(C₆₇⋊C₈)

—

#14523964

—

C₂²×D₄×C₆₇

D₄

yes

characteristic

C₂³×C₄×C₆₇

—

C₂²×C₈×C₆₇

—

C₂²×C₈×C₆₇

D₄

yes

—

C₄×D₄×C₆₇

—

C₄×D₄×C₆₇

—

C₂×C₄⋊C₄×C₆₇

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₆₇

—

C₂×C₄²×C₆₇

C₂³

yes

characteristic

C₄⋊C₈×C₆₇

—

C₂²⋊C₈×C₆₇

—

C₄×C₈×C₆₇

—

C₂²×Dic₆₇

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₂⁴×C₆₇

—

C₂×D₄×C₆₇

—

C₂×D₄×C₆₇

—

C₂×D₄×C₆₇

—

C₂×D₄×C₆₇

D₈

yes

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₇

#41

yes

characteristic

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₄⋊C₄×C₆₇

—

C₂²⋊C₄×C₆₇

—

C₄²×C₆₇

#41

yes

—

C₄²×C₆₇

#41

yes

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

#121

yes

characteristic

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

#123

yes

characteristic

C₂×C₄×C₆₇

#123

yes

—

C₂×C₄×C₆₇

#124

yes

characteristic

C₂×C₄×C₆₇

#126

yes

—

C₂×C₄×C₆₇

C₂×D₈

yes

characteristic

C₂×C₄×C₆₇

#135

yes

—

C₂×C₄×C₆₇

#135

yes

characteristic

C₂×C₄×C₆₇

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₆₇

#137

yes

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₈×C₆₇

—

C₈×C₆₇

—

C₆₇⋊C₈

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

#397

yes

characteristic

100

C₂²×C₆₇

#463

yes

—

101

C₂²×C₆₇

#466

yes

characteristic

102

C₂²×C₆₇

#470

yes

characteristic

103

C₂²×C₆₇

#471

yes

—

104

C₄×C₆₇

—

105

C₄×C₆₇

—

106

C₄×C₆₇

#480

yes

—

107

C₄×C₆₇

#482

yes

—

108

C₄×C₆₇

#485

yes

—

109

C₄×C₆₇

#488

yes

characteristic

110

C₄×C₆₇

#490

yes

characteristic

111

Dic₆₇

—

112

#10621

—

maximal, Sylow

113

C₂×C₆₇

—

114

C₂×C₆₇

#1681

yes

—

115

C₂×C₆₇

#1703

yes

—

116

C₂×C₆₇

#2073

yes

characteristic

117

C₂×C₆₇

#2075

yes

characteristic

118

C₂×C₆₇

#2079

yes

characteristic

119

#1954

D₆₇

yes

characteristic

120

#1834

—

121

#1802

—

122

#1296

—

123

#1277

—

124

C₆₇

#10621

yes

characteristic, complemented, Sylow

125

C₂×C₄×D₄

C₂×D₆₇

yes

characteristic

126

C₂×C₄⋊C₈

—

127

C₂×C₄⋊C₈

C₂×D₆₇

yes

characteristic

128

C₂×#102

—

134

—

129

C₂×C₂²⋊C₈

—

130

C₂×C₄×C₈

C₂×D₆₇

yes

characteristic

131

#384

—

132

#340

—

134

—

133

#340

—

134

—

134

C₂²×D₄

D₂₆₈

yes

characteristic

135

C₂³×C₄

—

136

C₂²×C₈

—

137

C₂²×C₈

—

134

—

138

C₂²×C₈

C₂²⋊D₆₇

yes

—

139

C₄×D₄

—

140

C₄×D₄

—

141

C₂×C₄⋊C₄

—

134

—

142

C₂×C₄⋊C₄

—

134

—

143

C₂×C₄⋊C₄

—

134

—

144

C₂×C₄⋊C₄

D₂₆₈

yes

characteristic

145

C₂×C₂²⋊C₄

—

146

C₂×C₄²

C₂²×D₆₇

yes

characteristic

147

C₄⋊C₈

—

148

C₄⋊C₈

—

134

—

149

C₄⋊C₈

—

134

—

150

#102

—

268

—

151

C₂²⋊C₈

—

152

C₄×C₈

—

153

C₂⁴

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂×D₄

D₅₃₆

yes

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

268

—

164

C₂²×C₄

C₂×C₂²⋊D₆₇

yes

characteristic

165

C₂²×C₄

C₂×D₂₆₈

yes

characteristic

166

C₂²×C₄

#11761628

yes

characteristic

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

268

—

173

C₂×C₈

—

268

—

174

C₂×C₈

—

268

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

268

—

177

C₄⋊C₄

—

268

—

178

C₄⋊C₄

—

268

—

179

C₄⋊C₄

—

268

—

180

C₄⋊C₄

—

536

—

181

C₂²⋊C₄

—

182

C₄²

#11761627

yes

—

183

C₄²

#11761627

yes

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

—

188

C₂³

—

189

C₂³

#14524017

yes

characteristic

190

D₄

—

191

D₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

536

—

199

C₂×C₄

—

536

—

200

C₂×C₄

—

536

—

201

C₂×C₄

#14524024

yes

characteristic

202

C₂×C₄

#14524027

yes

—

203

C₂×C₄

#14524030

yes

characteristic

204

C₂×C₄

#14524036

yes

—

205

C₂×C₄

C₂×D₅₃₆

yes

characteristic

206

C₂×C₄

#14524063

yes

—

207

C₂×C₄

#14524065

yes

characteristic

208

C₂×C₄

#14524069

yes

—

209

C₂×C₄

#14524076

yes

—

210

C₈

—

211

C₈

—

212

C₈

—

536

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

#16863321

yes

characteristic

219

C₂²

#16863611

yes

—

220

C₂²

#16863632

yes

characteristic

221

C₂²

#16863654

yes

characteristic

222

C₂²

#16863659

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

1072

—

226

C₄

#16863710

yes

—

227

C₄

#16863717

yes

—

228

C₄

#16863738

yes

—

229

C₄

#16863750

yes

characteristic

230

C₄

#16863760

yes

characteristic

231

C₂

—

232

C₂

#22559646

yes

—

233

C₂

#22559784

yes

—

234

C₂

#22561622

yes

characteristic

235

C₂

#22561632

yes

characteristic

236

C₂

#22561654

yes

characteristic

	subgroup	G/H
center	C₂³	#14524017
commutator, cosocle	C₂×C₄²×C₆₇	C₂³
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₆₇×#1954	C₂
socle	C₂³×C₆₇	#121
prime radical	C₂²×D₄×C₆₇	D₄
hypercenter	#1954	D₆₇
hypocenter	C₆₇	#10621
LCS	G ▷ C₂×C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

subgroup

G/H

center

C₂³

#14524017

commutator, cosocle

C₂×C₄²×C₆₇

C₂³

Frattini

C₂×C₄²

C₂²×D₆₇

Fitting

C₆₇×#1954

C₂

socle

C₂³×C₆₇

#121

prime radical

C₂²×D₄×C₆₇

D₄

D₆₇

C₆₇

G ▷ C₂×C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

N	H ≅ G/N	type
1. #22560337	C₂	semidirect
3. #22558093	C₂	semidirect
4. #22558044	C₂	semidirect
124. C₆₇	#10621	semidirect

H ≅ G/N

type

1. #22560337

C₂

semidirect

3. #22558093

C₂

semidirect

4. #22558044

C₂

semidirect

124. C₆₇

#10621

semidirect

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

subgroup	index
#22560337	2
#22560209	2
#22558093	2
#22558044	2
C₆₇×#1954	2
#10621	67

subgroup

index

C₆₇×#1954

Subgroups — #30760565

Conjugacy classes of subgroups

Complements

Maximal subgroups