Group #30760817 — subgroups

Subgroups — #30760817

Order 17152.

320 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 95 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	#22561150	C₂	1	1	yes	maximal, characteristic
2	#22560383	C₂	1	1	yes	maximal, characteristic
3	#22558985	C₂	1	1	yes	maximal, characteristic
4	#22558984	C₂	1	1	yes	maximal, characteristic
5	#22558638	C₂	1	1	yes	maximal, characteristic
6	#22558039	C₂	1	1	yes	maximal, characteristic
7	C₆₇×#1487	C₂	1	1	yes	maximal, characteristic
8	#16863449	C₂²	1	1	yes	characteristic
9	C₂×#14523978	—	2	2	no	—
10	#16863420	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×#14523954	C₂²	1	1	yes	characteristic
13	#16863151	—	2	2	no	—
14	#16863149	—	2	2	no	—
15	#16863148	—	2	2	no	—
16	Q₈⋊(C₆₇⋊C₈)	—	2	2	no	—
17	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
18	#431×C₆₇	C₂²	1	1	yes	characteristic
19	#423×C₆₇	C₂²	1	1	yes	characteristic
20	Q₈⋊C₈×C₆₇	—	2	2	no	—
21	C₂×#11761612	—	2	1	no	—
22	C₂²×C₆₇⋊C₈	—	2	1	no	—
23	C₂²×C₆₇⋊C₈	D₄	1	2	yes	—
24	#14523978	—	4	4	no	—
25	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
26	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
27	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
28	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
29	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
30	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
31	#14523954	—	2	1	no	—
32	#14523954	—	2	1	no	—
33	C₄×C₆₇⋊C₈	D₄	1	2	yes	—
34	C₂²×Q₈×C₆₇	Q₈	1	1	yes	characteristic
35	C₂×M₁₆×C₆₇	—	2	1	no	—
36	C₄×Q₈×C₆₇	—	2	1	no	—
37	C₄×Q₈×C₆₇	—	2	1	no	—
38	C₄×Q₈×C₆₇	—	2	1	no	—
39	C₄×Q₈×C₆₇	—	2	1	no	—
40	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
41	C₂×C₄⋊C₄×C₆₇	Q₈	1	1	yes	characteristic
42	C₂×C₄²×C₆₇	—	2	1	no	—
43	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
44	C₄⋊C₈×C₆₇	—	2	1	no	—
45	C₄⋊C₈×C₆₇	—	2	1	no	—
46	C₄⋊C₈×C₆₇	—	2	1	no	—
47	C₂²⋊C₈×C₆₇	—	2	1	no	—
48	C₄×C₈×C₆₇	D₄	1	2	yes	—
49	#11761612	—	4	2	no	—
50	C₂×C₆₇⋊C₈	—	2	2	no	—
51	C₂×C₆₇⋊C₈	—	2	2	no	—
52	C₂×C₆₇⋊C₈	—	2	2	no	—
53	C₂×C₆₇⋊C₈	—	4	1	no	—
54	C₂×C₆₇⋊C₈	—	4	1	no	—
55	C₂×C₆₇⋊C₈	—	4	2	no	—
56	C₂×C₆₇⋊C₈	Q₁₆	1	4	yes	—
57	C₂×Q₈×C₆₇	—	2	1	no	—
58	C₂×Q₈×C₆₇	—	2	1	no	—
59	C₂×Q₈×C₆₇	—	4	2	no	—
60	C₂²×C₄×C₆₇	—	2	1	no	—
61	C₂²×C₄×C₆₇	—	2	1	no	—
62	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
64	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
65	M₁₆×C₆₇	—	4	2	no	—
66	C₂×C₈×C₆₇	—	2	2	no	—
67	C₂×C₈×C₆₇	—	4	1	no	—
68	C₄⋊C₄×C₆₇	—	2	1	no	—
69	C₄⋊C₄×C₆₇	—	2	1	no	—
70	C₄⋊C₄×C₆₇	—	4	1	no	—
71	C₄⋊C₄×C₆₇	—	4	1	no	—
72	C₄²×C₆₇	—	4	1	no	—
73	C₄²×C₆₇	—	4	1	no	—
74	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₆₇	#41	1	1	yes	characteristic
77	C₄²×C₆₇	#41	1	1	yes	characteristic
78	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
79	Q₈×C₆₇	—	2	2	no	—
80	Q₈×C₆₇	—	2	2	no	—
81	Q₈×C₆₇	—	4	1	no	—
82	Q₈×C₆₇	—	4	1	no	—
83	C₂×C₄×C₆₇	—	2	2	no	—
84	C₂×C₄×C₆₇	—	4	1	no	—
85	C₂×C₄×C₆₇	—	4	1	no	—
86	C₂×C₄×C₆₇	—	4	1	no	—
87	C₂×C₄×C₆₇	—	4	1	no	—
88	C₂×C₄×C₆₇	—	4	2	no	—
89	C₂×C₄×C₆₇	—	4	1	no	—
90	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
91	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
92	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
93	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
94	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
95	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
96	C₂×C₄×C₆₇	C₂×Q₁₆	1	2	yes	—
97	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
98	C₈×C₆₇	—	4	2	no	—
99	C₈×C₆₇	—	8	1	no	—
100	C₆₇⋊C₈	—	2	4	no	—
101	C₆₇⋊C₈	—	4	2	no	—
102	C₆₇⋊C₈	—	8	1	no	—
103	C₆₇⋊C₈	—	8	1	no	—
104	C₂²×C₆₇	—	2	1	no	—
105	C₂²×C₆₇	—	2	1	no	—
106	C₂²×C₆₇	#399	1	1	yes	characteristic
107	C₂²×C₆₇	#477	1	2	yes	—
108	C₄×C₆₇	—	2	1	no	—
109	C₄×C₆₇	—	2	1	no	—
110	C₄×C₆₇	—	2	1	no	—
111	C₄×C₆₇	—	2	1	no	—
112	C₄×C₆₇	—	4	2	no	—
113	C₄×C₆₇	—	8	1	no	—
114	C₄×C₆₇	#484	1	2	yes	—
115	C₄×C₆₇	#494	1	1	yes	characteristic
116	C₄×C₆₇	#496	1	1	yes	characteristic
117	#10662	—	67	1	no	maximal, Sylow
118	C₂×C₆₇	—	2	2	no	—
119	C₂×C₆₇	#2091	1	1	yes	characteristic
120	C₂×C₆₇	#2095	1	1	yes	characteristic
121	C₂×C₆₇	#2098	1	1	yes	characteristic
122	#1985	—	67	1	no	—
123	#1849	—	67	1	no	—
124	#1571	—	67	1	no	—
125	#1571	—	67	1	no	—
126	#1487	—	67	1	no	—
127	#1487	D₆₇	1	1	yes	characteristic
128	#1275	—	67	1	no	—
129	C₆₇	#10662	1	1	yes	characteristic, complemented, Sylow
130	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic
131	#431	—	67	1	no	—
132	#431	C₂×D₆₇	1	1	yes	characteristic
133	C₂×#108	—	134	2	no	—
134	#423	—	67	1	no	—
135	#423	C₂×D₆₇	1	1	yes	characteristic
136	C₂×C₄⋊C₈	—	67	1	no	—
137	C₂×#97	—	67	1	no	—
138	#336	—	134	2	no	—
139	#335	—	134	2	no	—
140	#335	—	134	2	no	—
141	Q₈⋊C₈	—	2	2	no	—
142	Q₈⋊C₈	—	134	2	no	—
143	C₂²×Q₈	Dic₁₃₄	1	1	yes	characteristic
144	C₂×M₁₆	—	2	1	no	—
145	C₂×M₁₆	—	134	1	no	—
146	C₂²×C₈	—	67	2	no	—
147	C₂²×C₈	—	134	1	no	—
148	C₄×Q₈	—	2	1	no	—
149	C₄×Q₈	—	2	1	no	—
150	C₄×Q₈	—	2	1	no	—
151	C₄×Q₈	—	2	1	no	—
152	C₂×C₄⋊C₄	—	2	1	no	—
153	C₂×C₄⋊C₄	Dic₁₃₄	1	1	yes	characteristic
154	C₂×C₄²	—	2	1	no	—
155	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
156	#108	—	268	4	no	—
157	C₄⋊C₈	—	2	1	no	—
158	C₄⋊C₈	—	2	1	no	—
159	C₄⋊C₈	—	2	1	no	—
160	C₄⋊C₈	—	134	1	no	—
161	C₄⋊C₈	—	134	1	no	—
162	C₄⋊C₈	—	134	1	no	—
163	C₄⋊C₈	—	134	1	no	—
164	C₄⋊C₈	—	134	1	no	—
165	C₂²⋊C₈	—	2	1	no	—
166	C₂²⋊C₈	—	134	1	no	—
167	#97	—	134	1	no	—
168	#97	—	134	1	no	—
169	C₄×C₈	—	67	2	no	—
170	C₄×C₈	C₂²⋊D₆₇	1	2	yes	—
171	C₂×Q₈	—	2	1	no	—
172	C₂×Q₈	—	2	1	no	—
173	C₂×Q₈	—	4	2	no	—
174	C₂²×C₄	—	2	1	no	—
175	C₂²×C₄	—	2	1	no	—
176	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
177	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
178	C₂²×C₄	#11761627	1	1	yes	characteristic
179	M₁₆	—	4	2	no	—
180	M₁₆	—	268	2	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	4	1	no	—
183	C₂×C₈	—	268	1	no	—
184	C₂×C₈	—	268	1	no	—
185	C₂×C₈	—	268	2	no	—
186	C₂×C₈	—	67	4	no	—
187	C₂×C₈	—	134	2	no	—
188	C₂×C₈	—	134	2	no	—
189	C₂×C₈	—	134	2	no	—
190	C₄⋊C₄	—	2	1	no	—
191	C₄⋊C₄	—	2	1	no	—
192	C₄⋊C₄	—	4	1	no	—
193	C₄⋊C₄	—	4	1	no	—
194	C₄²	—	4	1	no	—
195	C₄²	—	4	1	no	—
196	C₄²	D₄×D₆₇	1	1	yes	characteristic
197	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
198	C₄²	#11761627	1	1	yes	characteristic
199	C₄²	#11761628	1	1	yes	characteristic
200	C₂³	#14524020	1	1	yes	characteristic
201	Q₈	—	2	2	no	—
202	Q₈	—	2	2	no	—
203	Q₈	—	4	1	no	—
204	Q₈	—	4	1	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	#14524020	1	1	yes	characteristic
213	C₂×C₄	#14524022	1	1	yes	characteristic
214	C₂×C₄	#14524024	1	1	yes	characteristic
215	C₂×C₄	#14524025	1	1	yes	characteristic
216	C₂×C₄	#14524025	1	1	yes	characteristic
217	C₂×C₄	#14524039	1	1	yes	characteristic
218	C₂×C₄	Q₁₆×D₆₇	1	2	yes	—
219	C₂×C₄	#14524070	1	2	yes	—
220	C₈	—	4	2	no	—
221	C₈	—	8	1	no	—
222	C₈	—	268	2	no	—
223	C₈	—	536	1	no	—
224	C₈	—	536	1	no	—
225	C₈	—	134	4	no	—
226	C₂²	—	2	1	no	—
227	C₂²	—	2	1	no	—
228	C₂²	#16863332	1	1	yes	characteristic
229	C₂²	#16863689	1	2	yes	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	4	2	no	—
235	C₄	—	8	1	no	—
236	C₄	#16863730	1	2	yes	—
237	C₄	#16863774	1	1	yes	characteristic
238	C₄	#16863782	1	1	yes	characteristic
239	C₂	—	2	2	no	—
240	C₂	#22561725	1	1	yes	characteristic
241	C₂	#22561745	1	1	yes	characteristic
242	C₂	#22561764	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22561150

C₂

yes

maximal, characteristic

#22560383

C₂

yes

maximal, characteristic

#22558985

C₂

yes

maximal, characteristic

#22558984

C₂

yes

maximal, characteristic

#22558638

C₂

yes

maximal, characteristic

#22558039

C₂

yes

maximal, characteristic

C₆₇×#1487

C₂

yes

maximal, characteristic

#16863449

C₂²

yes

characteristic

C₂×#14523978

—

#16863420

C₂²

yes

characteristic

C₂×C₄⋊(C₆₇⋊C₈)

C₂²

yes

characteristic

C₂×#14523954

C₂²

yes

—

—

—

Q₈⋊(C₆₇⋊C₈)

—

C₂×C₄×Q₈×C₆₇

C₂²

yes

characteristic

#431×C₆₇

C₂²

yes

characteristic

#423×C₆₇

C₂²

yes

characteristic

Q₈⋊C₈×C₆₇

—

C₂×#11761612

—

C₂²×C₆₇⋊C₈

—

C₂²×C₆₇⋊C₈

D₄

yes

—

#14523978

—

C₄⋊(C₆₇⋊C₈)

—

C₄⋊(C₆₇⋊C₈)

—

C₄⋊(C₆₇⋊C₈)

—

C₄⋊(C₆₇⋊C₈)

—

C₄⋊(C₆₇⋊C₈)

—

C₂²⋊(C₆₇⋊C₈)

—

#14523954

—

#14523954

—

C₄×C₆₇⋊C₈

D₄

yes

—

C₂²×Q₈×C₆₇

Q₈

yes

characteristic

C₂×M₁₆×C₆₇

—

C₄×Q₈×C₆₇

—

C₄×Q₈×C₆₇

—

C₄×Q₈×C₆₇

—

C₄×Q₈×C₆₇

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₄⋊C₄×C₆₇

Q₈

yes

characteristic

C₂×C₄²×C₆₇

—

C₂×C₄²×C₆₇

C₂³

yes

characteristic

C₄⋊C₈×C₆₇

—

C₄⋊C₈×C₆₇

—

C₄⋊C₈×C₆₇

—

C₂²⋊C₈×C₆₇

—

C₄×C₈×C₆₇

D₄

yes

—

#11761612

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

Q₁₆

yes

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₇

C₂×Q₈

yes

characteristic

C₂²×C₄×C₆₇

#41

yes

characteristic

M₁₆×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄²×C₆₇

—

C₄²×C₆₇

—

C₄²×C₆₇

C₂×D₄

yes

characteristic

C₄²×C₆₇

C₂×D₄

yes

C₄²×C₆₇

yes

C₄²×C₆₇

yes

C₂³×C₆₇

C₂²⋊Q₈

yes

characteristic

Q₈×C₆₇

—

Q₈×C₆₇

—

Q₈×C₆₇

—

Q₈×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⋊Q₈

yes

characteristic

C₂×C₄×C₆₇

C₂²⋊Q₈

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

C₂×Q₁₆

yes

—

C₂×C₄×C₆₇

AGL(1,ℤ/8)

yes

—

C₈×C₆₇

—

C₈×C₆₇

—

100

C₆₇⋊C₈

—

101

C₆₇⋊C₈

—

102

C₆₇⋊C₈

—

103

C₆₇⋊C₈

—

104

C₂²×C₆₇

—

105

C₂²×C₆₇

—

106

C₂²×C₆₇

#399

yes

characteristic

107

C₂²×C₆₇

#477

yes

—

108

C₄×C₆₇

—

109

C₄×C₆₇

—

110

C₄×C₆₇

—

111

C₄×C₆₇

—

112

C₄×C₆₇

—

113

C₄×C₆₇

—

114

C₄×C₆₇

#484

yes

—

115

C₄×C₆₇

#494

yes

characteristic

116

C₄×C₆₇

yes

117

—

118

C₂×C₆₇

—

119

C₂×C₆₇

#2091

yes

characteristic

120

C₂×C₆₇

#2095

yes

characteristic

121

C₂×C₆₇

#2098

yes

characteristic

122

#1985

—

123

#1849

—

124

#1571

—

125

#1571

—

126

#1487

—

127

#1487

D₆₇

yes

characteristic

128

#1275

—

129

C₆₇

#10662

yes

characteristic, complemented, Sylow

130

C₂×C₄×Q₈

C₂×D₆₇

yes

characteristic

131

#431

—

132

#431

C₂×D₆₇

yes

characteristic

133

C₂×#108

—

134

—

134

#423

—

135

#423

C₂×D₆₇

yes

characteristic

136

C₂×C₄⋊C₈

—

137

C₂×#97

—

138

#336

—

134

—

139

#335

—

134

—

140

#335

—

134

—

141

Q₈⋊C₈

—

142

Q₈⋊C₈

—

134

—

143

C₂²×Q₈

Dic₁₃₄

yes

characteristic

144

C₂×M₁₆

—

145

C₂×M₁₆

—

134

—

146

C₂²×C₈

—

147

C₂²×C₈

—

134

—

148

C₄×Q₈

—

149

C₄×Q₈

—

150

C₄×Q₈

—

151

C₄×Q₈

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄⋊C₄

Dic₁₃₄

yes

characteristic

154

C₂×C₄²

—

155

C₂×C₄²

C₂²×D₆₇

yes

characteristic

156

#108

—

268

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

134

—

161

C₄⋊C₈

—

134

—

162

C₄⋊C₈

—

134

—

163

C₄⋊C₈

—

134

—

164

C₄⋊C₈

—

134

—

165

C₂²⋊C₈

—

166

C₂²⋊C₈

—

134

—

167

#97

—

134

—

168

#97

—

134

—

169

C₄×C₈

—

170

C₄×C₈

C₂²⋊D₆₇

yes

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

D₄×D₆₇

yes

characteristic

177

C₂²×C₄

C₂×Dic₁₃₄

yes

characteristic

178

C₂²×C₄

#11761627

yes

characteristic

179

M₁₆

—

180

M₁₆

—

268

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

268

—

184

C₂×C₈

—

268

—

185

C₂×C₈

—

268

—

186

C₂×C₈

—

187

C₂×C₈

—

134

—

188

C₂×C₈

—

134

—

189

C₂×C₈

—

134

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄²

—

195

C₄²

—

196

C₄²

D₄×D₆₇

yes

characteristic

197

C₄²

C₂×C₂²⋊D₆₇

yes

characteristic

198

C₄²

#11761627

yes

characteristic

199

C₄²

#11761628

yes

characteristic

200

C₂³

#14524020

yes

characteristic

201

Q₈

—

202

Q₈

—

203

Q₈

—

204

Q₈

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

#14524020

yes

characteristic

213

C₂×C₄

#14524022

yes

characteristic

214

C₂×C₄

#14524024

yes

characteristic

215

C₂×C₄

#14524025

yes

characteristic

216

C₂×C₄

#14524025

yes

characteristic

217

C₂×C₄

#14524039

yes

characteristic

218

C₂×C₄

Q₁₆×D₆₇

yes

—

219

C₂×C₄

#14524070

yes

—

220

C₈

—

221

C₈

—

222

C₈

—

268

—

223

C₈

—

536

—

224

C₈

—

536

—

225

C₈

—

134

—

226

C₂²

—

227

C₂²

—

228

C₂²

#16863332

yes

characteristic

229

C₂²

#16863689

yes

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

#16863730

yes

—

237

C₄

#16863774

yes

characteristic

238

C₄

#16863782

yes

characteristic

239

C₂

—

240

C₂

#22561725

yes

characteristic

241

C₂

#22561745

yes

characteristic

242

C₂

#22561764

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14524039
commutator, cosocle	C₂×C₄²×C₆₇	C₂³
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₆₇×#1487	C₂
socle	C₂²×C₆₇	#399
prime radical	C₂³×C₆₇	C₂²⋊Q₈
hypercenter	#1487	D₆₇
hypocenter	C₆₇	#10662
LCS	G ▷ C₂×C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1487

subgroup

G/H

center

C₂×C₄

#14524039

commutator, cosocle

C₂×C₄²×C₆₇

C₂³

Frattini

C₂×C₄²

C₂²×D₆₇

Fitting

C₆₇×#1487

C₂

socle

C₂²×C₆₇

#399

prime radical

C₂³×C₆₇

C₂²⋊Q₈

D₆₇

C₆₇

G ▷ C₂×C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1487

N	H ≅ G/N	type
129. C₆₇	#10662	semidirect

H ≅ G/N

type

129. C₆₇

#10662

semidirect

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

subgroup	index
#22561150	2
#22560383	2
#22558985	2
#22558984	2
#22558638	2
#22558039	2
C₆₇×#1487	2
#10662	67

subgroup

index

C₆₇×#1487

Subgroups — #30760817

Conjugacy classes of subgroups

Complements

Maximal subgroups