Group #30689568 — subgroups

Subgroups — C₆₇×#10317 #30689568

Order 17152.

554 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 170 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×#498×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#487×C₆₇	C₂	1	2	yes	maximal
3	C₆₇×#1990	C₂	1	2	yes	maximal
4	C₆₇×#1956	C₂	1	1	yes	maximal, characteristic
5	C₆₇×#1273	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
7	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
8	#498×C₆₇	—	2	4	no	—
9	#487×C₆₇	—	2	4	no	—
10	#487×C₆₇	—	2	4	no	—
11	C₂×#106×C₆₇	—	2	2	no	—
12	C₂×#103×C₆₇	—	2	4	no	—
13	C₂×#103×C₆₇	—	2	2	no	—
14	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
16	#384×C₆₇	C₂²	1	1	yes	characteristic
17	#340×C₆₇	—	2	4	no	—
18	C₂²×Q₈×C₆₇	—	2	1	no	—
19	C₂²×Q₈×C₆₇	—	2	2	no	—
20	C₂²×C₈×C₆₇	D₄	1	4	yes	—
21	C₂²×C₈×C₆₇	D₄	1	2	yes	—
22	C₄⋊Q₈×C₆₇	—	2	2	no	—
23	C₄⋊Q₈×C₆₇	—	2	2	no	—
24	C₄⋊Q₈×C₆₇	—	2	2	no	—
25	C₄⋊Q₈×C₆₇	—	2	2	no	—
26	C₄⋊Q₈×C₆₇	—	2	1	no	—
27	C₄⋊Q₈×C₆₇	D₄	1	2	yes	—
28	C₄⋊Q₈×C₆₇	D₄	1	4	yes	—
29	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
30	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
31	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
32	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
33	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
34	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
35	#106×C₆₇	—	2	8	no	—
36	#103×C₆₇	—	2	16	no	—
37	#103×C₆₇	—	4	4	no	—
38	C₄×C₈×C₆₇	—	2	2	no	—
39	C₄×C₈×C₆₇	—	2	2	no	—
40	C₄×C₈×C₆₇	—	2	2	no	—
41	C₂×Q₈×C₆₇	—	2	4	no	—
42	C₂×Q₈×C₆₇	—	2	2	no	—
43	C₂×Q₈×C₆₇	—	4	1	no	—
44	C₂×Q₈×C₆₇	—	4	2	no	—
45	C₂×Q₈×C₆₇	—	4	2	no	—
46	C₂×Q₈×C₆₇	—	4	4	no	—
47	C₂×Q₈×C₆₇	—	4	2	no	—
48	C₂×Q₈×C₆₇	—	4	4	no	—
49	C₂²×C₄×C₆₇	—	4	1	no	—
50	C₂²×C₄×C₆₇	—	4	2	no	—
51	C₂²×C₄×C₆₇	—	4	1	no	—
52	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
54	C₂×C₈×C₆₇	—	2	2	no	—
55	C₂×C₈×C₆₇	—	2	2	no	—
56	C₂×C₈×C₆₇	—	2	4	no	—
57	C₂×C₈×C₆₇	—	2	4	no	—
58	C₂×C₈×C₆₇	—	2	4	no	—
59	C₂×C₈×C₆₇	SD₁₆	1	4	yes	—
60	C₄⋊C₄×C₆₇	—	2	4	no	—
61	C₄⋊C₄×C₆₇	—	2	4	no	—
62	C₄⋊C₄×C₆₇	—	2	4	no	—
63	C₄⋊C₄×C₆₇	—	4	2	no	—
64	C₄⋊C₄×C₆₇	—	4	2	no	—
65	C₄⋊C₄×C₆₇	—	4	2	no	—
66	C₄⋊C₄×C₆₇	—	4	2	no	—
67	C₄⋊C₄×C₆₇	—	4	4	no	—
68	C₄²×C₆₇	C₂×D₄	1	2	yes	—
69	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₆₇	#41	1	1	yes	characteristic
71	C₂³×C₆₇	#127	1	1	yes	characteristic
72	Q₈×C₆₇	—	4	8	no	—
73	Q₈×C₆₇	—	4	4	no	—
74	Q₈×C₆₇	—	8	2	no	—
75	Q₈×C₆₇	—	8	4	no	—
76	C₂×C₄×C₆₇	—	4	2	no	—
77	C₂×C₄×C₆₇	—	4	4	no	—
78	C₂×C₄×C₆₇	—	8	1	no	—
79	C₂×C₄×C₆₇	—	8	2	no	—
80	C₂×C₄×C₆₇	—	8	1	no	—
81	C₂×C₄×C₆₇	—	8	2	no	—
82	C₂×C₄×C₆₇	—	8	1	no	—
83	C₂×C₄×C₆₇	—	8	2	no	—
84	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
85	C₂×C₄×C₆₇	#120	1	2	yes	—
86	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
87	C₂×C₄×C₆₇	#121	1	2	yes	—
88	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
89	C₂×C₄×C₆₇	#135	1	4	yes	—
90	C₂×C₄×C₆₇	#137	1	2	yes	—
91	C₂×C₄×C₆₇	#137	1	4	yes	—
92	C₈×C₆₇	—	2	4	no	—
93	C₈×C₆₇	—	4	4	no	—
94	C₂²×C₆₇	#392	1	1	yes	characteristic
95	C₂²×C₆₇	#492	1	1	yes	characteristic
96	C₂²×C₆₇	#495	1	2	yes	—
97	C₂²×C₆₇	#497	1	2	yes	—
98	C₂²×C₆₇	#497	1	1	yes	characteristic
99	C₄×C₆₇	—	8	2	no	—
100	C₄×C₆₇	—	8	4	no	—
101	C₄×C₆₇	—	16	1	no	—
102	C₄×C₆₇	#448	1	2	yes	—
103	C₄×C₆₇	#452	1	4	yes	—
104	C₄×C₆₇	#461	1	2	yes	—
105	C₄×C₆₇	#464	1	4	yes	—
106	#10317	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂×C₆₇	#1708	1	1	yes	characteristic
108	C₂×C₆₇	#1716	1	1	yes	characteristic
109	C₂×C₆₇	#1718	1	2	yes	—
110	C₂×C₆₇	#2013	1	1	yes	characteristic
111	C₂×C₆₇	#2015	1	2	yes	—
112	C₂×#498	C₂×C₆₇	1	1	yes	characteristic
113	C₂×#487	C₂×C₆₇	1	2	yes	—
114	#1990	C₂×C₆₇	1	2	yes	—
115	#1956	C₂×C₆₇	1	1	yes	characteristic
116	#1273	C₂×C₆₇	1	1	yes	characteristic
117	C₆₇	#10317	1	1	yes	characteristic, direct product factor, Sylow
118	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
119	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
120	#498	—	2	4	no	—
121	#487	—	2	4	no	—
122	#487	—	2	4	no	—
123	C₂×#106	—	2	2	no	—
124	C₂×#103	—	2	4	no	—
125	C₂×#103	—	2	2	no	—
126	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
127	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
128	#384	C₂²×C₆₇	1	1	yes	characteristic
129	#340	—	2	4	no	—
130	C₂²×Q₈	—	2	1	no	—
131	C₂²×Q₈	—	2	2	no	—
132	C₂²×C₈	D₄×C₆₇	1	4	yes	—
133	C₂²×C₈	D₄×C₆₇	1	2	yes	—
134	C₄⋊Q₈	—	2	2	no	—
135	C₄⋊Q₈	—	2	2	no	—
136	C₄⋊Q₈	—	2	2	no	—
137	C₄⋊Q₈	—	2	2	no	—
138	C₄⋊Q₈	—	2	1	no	—
139	C₄⋊Q₈	D₄×C₆₇	1	2	yes	—
140	C₄⋊Q₈	D₄×C₆₇	1	4	yes	—
141	C₂×C₄⋊C₄	—	2	2	no	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	—	2	2	no	—
145	C₂×C₄⋊C₄	—	2	1	no	—
146	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
147	#106	—	2	8	no	—
148	#103	—	2	16	no	—
149	#103	—	4	4	no	—
150	C₄×C₈	—	2	2	no	—
151	C₄×C₈	—	2	2	no	—
152	C₄×C₈	—	2	2	no	—
153	C₂×Q₈	—	2	4	no	—
154	C₂×Q₈	—	2	2	no	—
155	C₂×Q₈	—	4	1	no	—
156	C₂×Q₈	—	4	2	no	—
157	C₂×Q₈	—	4	2	no	—
158	C₂×Q₈	—	4	4	no	—
159	C₂×Q₈	—	4	2	no	—
160	C₂×Q₈	—	4	4	no	—
161	C₂²×C₄	—	4	1	no	—
162	C₂²×C₄	—	4	2	no	—
163	C₂²×C₄	—	4	1	no	—
164	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
165	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
166	C₂×C₈	—	2	2	no	—
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	4	no	—
169	C₂×C₈	—	2	4	no	—
170	C₂×C₈	—	2	4	no	—
171	C₂×C₈	SD₁₆×C₆₇	1	4	yes	—
172	C₄⋊C₄	—	2	4	no	—
173	C₄⋊C₄	—	2	4	no	—
174	C₄⋊C₄	—	2	4	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄⋊C₄	—	4	4	no	—
180	C₄²	C₂×D₄×C₆₇	1	2	yes	—
181	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
182	C₄²	#41×C₆₇	1	1	yes	characteristic
183	C₂³	#127×C₆₇	1	1	yes	characteristic
184	Q₈	—	4	8	no	—
185	Q₈	—	4	4	no	—
186	Q₈	—	8	2	no	—
187	Q₈	—	8	4	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	—	4	4	no	—
190	C₂×C₄	—	8	1	no	—
191	C₂×C₄	—	8	2	no	—
192	C₂×C₄	—	8	1	no	—
193	C₂×C₄	—	8	2	no	—
194	C₂×C₄	—	8	1	no	—
195	C₂×C₄	—	8	2	no	—
196	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
197	C₂×C₄	#120×C₆₇	1	2	yes	—
198	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
199	C₂×C₄	#121×C₆₇	1	2	yes	—
200	C₂×C₄	C₂×SD₁₆×C₆₇	1	2	yes	—
201	C₂×C₄	#135×C₆₇	1	4	yes	—
202	C₂×C₄	#137×C₆₇	1	2	yes	—
203	C₂×C₄	#137×C₆₇	1	4	yes	—
204	C₈	—	2	4	no	—
205	C₈	—	4	4	no	—
206	C₂²	#392×C₆₇	1	1	yes	characteristic
207	C₂²	#492×C₆₇	1	1	yes	characteristic
208	C₂²	#495×C₆₇	1	2	yes	—
209	C₂²	#497×C₆₇	1	1	yes	characteristic
210	C₂²	#497×C₆₇	1	2	yes	—
211	C₄	—	8	2	no	—
212	C₄	—	8	4	no	—
213	C₄	—	16	1	no	—
214	C₄	#448×C₆₇	1	2	yes	—
215	C₄	#452×C₆₇	1	4	yes	—
216	C₄	#461×C₆₇	1	2	yes	—
217	C₄	#464×C₆₇	1	4	yes	—
218	C₂	C₆₇×#1708	1	1	yes	characteristic
219	C₂	C₆₇×#1716	1	1	yes	characteristic
220	C₂	C₆₇×#1718	1	2	yes	—
221	C₂	C₆₇×#2013	1	1	yes	characteristic
222	C₂	C₆₇×#2015	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#498×C₆₇

C₂

yes

maximal, characteristic

C₂×#487×C₆₇

C₂

yes

maximal

C₆₇×#1990

C₂

yes

maximal

C₆₇×#1956

C₂

yes

maximal, characteristic

C₆₇×#1273

C₂

yes

maximal, characteristic

C₂×C₄⋊Q₈×C₆₇

C₂²

yes

—

C₂×C₄⋊Q₈×C₆₇

C₂²

yes

characteristic

#498×C₆₇

—

#487×C₆₇

—

#487×C₆₇

—

C₂×#106×C₆₇

—

C₂×#103×C₆₇

—

C₂×#103×C₆₇

—

C₂×C₄×C₈×C₆₇

C₂²

yes

—

C₂×C₄×C₈×C₆₇

C₂²

yes

characteristic

#384×C₆₇

C₂²

yes

characteristic

#340×C₆₇

—

C₂²×Q₈×C₆₇

—

C₂²×Q₈×C₆₇

—

C₂²×C₈×C₆₇

D₄

yes

—

C₂²×C₈×C₆₇

D₄

yes

—

C₄⋊Q₈×C₆₇

—

C₄⋊Q₈×C₆₇

—

C₄⋊Q₈×C₆₇

—

C₄⋊Q₈×C₆₇

—

C₄⋊Q₈×C₆₇

—

C₄⋊Q₈×C₆₇

D₄

yes

—

C₄⋊Q₈×C₆₇

D₄

yes

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₄²×C₆₇

C₂³

yes

characteristic

#106×C₆₇

—

#103×C₆₇

—

#103×C₆₇

—

C₄×C₈×C₆₇

—

C₄×C₈×C₆₇

—

C₄×C₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₇

C₂×D₄

yes

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

SD₁₆

yes

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄²×C₆₇

C₂×D₄

yes

—

C₄²×C₆₇

C₂×D₄

yes

C₄²×C₆₇

yes

C₂³×C₆₇

yes

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

—

C₂×C₄×C₆₇

#120

yes

characteristic

C₂×C₄×C₆₇

#120

yes

—

C₂×C₄×C₆₇

#121

yes

characteristic

C₂×C₄×C₆₇

#121

yes

—

C₂×C₄×C₆₇

C₂×SD₁₆

yes

—

C₂×C₄×C₆₇

#135

yes

—

C₂×C₄×C₆₇

#137

yes

—

C₂×C₄×C₆₇

#137

yes

—

C₈×C₆₇

—

C₈×C₆₇

—

C₂²×C₆₇

yes

C₂²×C₆₇

yes

C₂²×C₆₇

yes

—

C₂²×C₆₇

#497

yes

—

C₂²×C₆₇

#497

yes

characteristic

C₄×C₆₇

—

100

C₄×C₆₇

—

101

C₄×C₆₇

—

102

C₄×C₆₇

#448

yes

—

103

C₄×C₆₇

#452

yes

—

104

C₄×C₆₇

#461

yes

—

105

C₄×C₆₇

#464

yes

—

106

#10317

C₆₇

yes

maximal, characteristic, direct product factor, Sylow

107

C₂×C₆₇

#1708

yes

characteristic

108

C₂×C₆₇

#1716

yes

characteristic

109

C₂×C₆₇

#1718

yes

—

110

C₂×C₆₇

#2013

yes

characteristic

111

C₂×C₆₇

#2015

yes

—

112

C₂×#498

C₂×C₆₇

yes

characteristic

113

C₂×#487

C₂×C₆₇

yes

—

114

#1990

C₂×C₆₇

yes

—

115

#1956

C₂×C₆₇

yes

characteristic

116

#1273

C₂×C₆₇

yes

characteristic

117

C₆₇

#10317

yes

characteristic, direct product factor, Sylow

118

C₂×C₄⋊Q₈

C₂²×C₆₇

yes

characteristic

119

C₂×C₄⋊Q₈

C₂²×C₆₇

yes

—

120

#498

—

121

#487

—

122

#487

—

123

C₂×#106

—

124

C₂×#103

—

125

C₂×#103

—

126

C₂×C₄×C₈

C₂²×C₆₇

yes

—

127

C₂×C₄×C₈

C₂²×C₆₇

yes

characteristic

128

#384

C₂²×C₆₇

yes

characteristic

129

#340

—

130

C₂²×Q₈

—

131

C₂²×Q₈

—

132

C₂²×C₈

D₄×C₆₇

yes

—

133

C₂²×C₈

D₄×C₆₇

yes

—

134

C₄⋊Q₈

—

135

C₄⋊Q₈

—

136

C₄⋊Q₈

—

137

C₄⋊Q₈

—

138

C₄⋊Q₈

—

139

C₄⋊Q₈

D₄×C₆₇

yes

—

140

C₄⋊Q₈

D₄×C₆₇

yes

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄²

C₂³×C₆₇

yes

characteristic

147

#106

—

148

#103

—

149

#103

—

150

C₄×C₈

—

151

C₄×C₈

—

152

C₄×C₈

—

153

C₂×Q₈

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

C₂×D₄×C₆₇

yes

characteristic

165

C₂²×C₄

C₂×D₄×C₆₇

yes

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

SD₁₆×C₆₇

yes

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄²

C₂×D₄×C₆₇

yes

—

181

C₄²

C₂×D₄×C₆₇

yes

characteristic

182

C₄²

#41×C₆₇

yes

characteristic

183

C₂³

#127×C₆₇

yes

characteristic

184

Q₈

—

185

Q₈

—

186

Q₈

—

187

Q₈

—

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

#120×C₆₇

yes

characteristic

197

C₂×C₄

#120×C₆₇

yes

—

198

C₂×C₄

#121×C₆₇

yes

characteristic

199

C₂×C₄

#121×C₆₇

yes

—

200

C₂×C₄

C₂×SD₁₆×C₆₇

yes

—

201

C₂×C₄

#135×C₆₇

yes

—

202

C₂×C₄

#137×C₆₇

yes

—

203

C₂×C₄

#137×C₆₇

yes

—

204

C₈

—

205

C₈

—

206

C₂²

#392×C₆₇

yes

characteristic

207

C₂²

#492×C₆₇

yes

characteristic

208

C₂²

#495×C₆₇

yes

—

209

C₂²

#497×C₆₇

yes

characteristic

210

C₂²

#497×C₆₇

yes

—

211

C₄

—

212

C₄

—

213

C₄

—

214

C₄

#448×C₆₇

yes

—

215

C₄

#452×C₆₇

yes

—

216

C₄

#461×C₆₇

yes

—

217

C₄

#464×C₆₇

yes

—

218

C₂

C₆₇×#1708

yes

characteristic

219

C₂

C₆₇×#1716

yes

characteristic

220

C₂

C₆₇×#1718

yes

—

221

C₂

C₆₇×#2013

yes

characteristic

222

C₂

C₆₇×#2015

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₆₇	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₆₇
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×C₄²×C₆₇ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₆₇

#127

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₆₇

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₆₇ ◁ C₂×C₄²×C₆₇ ◁ G

N	H ≅ G/N	type
106. #10317	C₆₇	direct (N × H)
117. C₆₇	#10317	direct (N × H)

H ≅ G/N

type

106. #10317

C₆₇

direct (N × H)

117. C₆₇

#10317

direct (N × H)

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

subgroup	index
C₂×#498×C₆₇	2
C₂×#487×C₆₇	2
C₆₇×#1990	2
C₆₇×#1956	2
C₆₇×#1273	2
#10317	67

subgroup

index

C₂×#498×C₆₇

C₂×#487×C₆₇

C₆₇×#1990

C₆₇×#1956

C₆₇×#1273

#10317

Subgroups — C₆₇×#10317 #30689568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C67×#10317 #30689568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#10317 #30689568