Group #46860009 — subgroups

Subgroups — C₁₃₇×#10623 #46860009

Order 35072.

350 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 134 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	#1984×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#1834×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#1803×C₁₃₇	C₂	1	2	yes	maximal
4	#1296×C₁₃₇	C₂	1	2	yes	maximal
5	#1277×C₁₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
8	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
9	C₂×#103×C₁₃₇	—	2	2	no	—
10	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
11	#384×C₁₃₇	C₂²	1	2	yes	—
12	#340×C₁₃₇	—	2	2	no	—
13	#340×C₁₃₇	—	2	2	no	—
14	#336×C₁₃₇	—	2	2	no	—
15	C₂²×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₃₇	—	2	2	no	—
17	C₂²×C₈×C₁₃₇	—	2	1	no	—
18	C₂²×C₈×C₁₃₇	D₄	1	2	yes	—
19	C₄×Q₈×C₁₃₇	—	2	2	no	—
20	C₄×Q₈×C₁₃₇	—	2	2	no	—
21	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
22	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
23	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
24	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
25	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₃₇	—	2	1	no	—
27	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
28	C₄⋊C₈×C₁₃₇	—	2	2	no	—
29	C₄⋊C₈×C₁₃₇	—	2	2	no	—
30	C₄⋊C₈×C₁₃₇	—	2	2	no	—
31	#103×C₁₃₇	—	4	4	no	—
32	C₄×C₈×C₁₃₇	—	2	2	no	—
33	C₂×Q₈×C₁₃₇	—	2	1	no	—
34	C₂×Q₈×C₁₃₇	—	2	2	no	—
35	C₂×Q₈×C₁₃₇	—	2	2	no	—
36	C₂×Q₈×C₁₃₇	D₈	1	2	yes	—
37	C₂²×C₄×C₁₃₇	—	2	1	no	—
38	C₂²×C₄×C₁₃₇	—	2	1	no	—
39	C₂²×C₄×C₁₃₇	—	4	2	no	—
40	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
43	C₂×C₈×C₁₃₇	—	2	2	no	—
44	C₂×C₈×C₁₃₇	—	2	2	no	—
45	C₂×C₈×C₁₃₇	—	2	2	no	—
46	C₂×C₈×C₁₃₇	—	4	2	no	—
47	C₂×C₈×C₁₃₇	—	4	1	no	—
48	C₂×C₈×C₁₃₇	—	4	2	no	—
49	C₂×C₈×C₁₃₇	—	4	2	no	—
50	C₂×C₈×C₁₃₇	—	4	2	no	—
51	C₄⋊C₄×C₁₃₇	—	2	2	no	—
52	C₄⋊C₄×C₁₃₇	—	4	2	no	—
53	C₄⋊C₄×C₁₃₇	—	4	2	no	—
54	C₄⋊C₄×C₁₃₇	—	4	2	no	—
55	C₄⋊C₄×C₁₃₇	—	4	2	no	—
56	C₄⋊C₄×C₁₃₇	—	4	2	no	—
57	C₄⋊C₄×C₁₃₇	—	8	2	no	—
58	C₄²×C₁₃₇	—	4	1	no	—
59	C₄²×C₁₃₇	—	4	1	no	—
60	C₄²×C₁₃₇	#41	1	2	yes	—
61	C₄²×C₁₃₇	#41	1	2	yes	—
62	C₂³×C₁₃₇	#121	1	1	yes	characteristic
63	Q₈×C₁₃₇	—	2	4	no	—
64	Q₈×C₁₃₇	—	4	2	no	—
65	C₂×C₄×C₁₃₇	—	2	2	no	—
66	C₂×C₄×C₁₃₇	—	2	2	no	—
67	C₂×C₄×C₁₃₇	—	4	1	no	—
68	C₂×C₄×C₁₃₇	—	4	1	no	—
69	C₂×C₄×C₁₃₇	—	4	1	no	—
70	C₂×C₄×C₁₃₇	—	4	2	no	—
71	C₂×C₄×C₁₃₇	—	8	2	no	—
72	C₂×C₄×C₁₃₇	—	8	2	no	—
73	C₂×C₄×C₁₃₇	—	8	2	no	—
74	C₂×C₄×C₁₃₇	#123	1	2	yes	—
75	C₂×C₄×C₁₃₇	#123	1	1	yes	characteristic
76	C₂×C₄×C₁₃₇	#124	1	1	yes	characteristic
77	C₂×C₄×C₁₃₇	#126	1	2	yes	—
78	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
79	C₂×C₄×C₁₃₇	#135	1	1	yes	characteristic
80	C₂×C₄×C₁₃₇	#135	1	2	yes	—
81	C₂×C₄×C₁₃₇	#137	1	2	yes	—
82	C₂×C₄×C₁₃₇	#137	1	2	yes	—
83	C₈×C₁₃₇	—	4	2	no	—
84	C₈×C₁₃₇	—	8	2	no	—
85	C₈×C₁₃₇	—	8	1	no	—
86	C₂²×C₁₃₇	#397	1	1	yes	characteristic
87	C₂²×C₁₃₇	#464	1	2	yes	—
88	C₂²×C₁₃₇	#466	1	1	yes	characteristic
89	C₂²×C₁₃₇	#470	1	1	yes	characteristic
90	C₂²×C₁₃₇	#471	1	2	yes	—
91	C₄×C₁₃₇	—	2	2	no	—
92	C₄×C₁₃₇	—	4	2	no	—
93	C₄×C₁₃₇	—	8	1	no	—
94	C₄×C₁₃₇	—	16	2	no	—
95	C₄×C₁₃₇	#480	1	2	yes	—
96	C₄×C₁₃₇	#485	1	2	yes	—
97	C₄×C₁₃₇	#485	1	2	yes	—
98	C₄×C₁₃₇	#488	1	1	yes	characteristic
99	C₄×C₁₃₇	#491	1	1	yes	characteristic
100	C₂×C₁₃₇	#1682	1	2	yes	—
101	C₂×C₁₃₇	#1704	1	2	yes	—
102	C₂×C₁₃₇	#2074	1	1	yes	characteristic
103	C₂×C₁₃₇	#2075	1	1	yes	characteristic
104	C₂×C₁₃₇	#2079	1	1	yes	characteristic
105	#10623	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₁₃₇	#10623	1	1	yes	characteristic, direct product factor, Sylow
107	#1984	C₂×C₁₃₇	1	1	yes	characteristic
108	#1834	C₂×C₁₃₇	1	1	yes	characteristic
109	#1803	C₂×C₁₃₇	1	2	yes	—
110	#1296	C₂×C₁₃₇	1	2	yes	—
111	#1277	C₂×C₁₃₇	1	1	yes	characteristic
112	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
113	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
114	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
115	C₂×#103	—	2	2	no	—
116	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
117	#384	C₂²×C₁₃₇	1	2	yes	—
118	#340	—	2	2	no	—
119	#340	—	2	2	no	—
120	#336	—	2	2	no	—
121	C₂²×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
122	C₂²×C₈	—	2	1	no	—
123	C₂²×C₈	—	2	2	no	—
124	C₂²×C₈	D₄×C₁₃₇	1	2	yes	—
125	C₄×Q₈	—	2	2	no	—
126	C₄×Q₈	—	2	2	no	—
127	C₂×C₄⋊C₄	—	2	1	no	—
128	C₂×C₄⋊C₄	—	2	2	no	—
129	C₂×C₄⋊C₄	—	2	2	no	—
130	C₂×C₄⋊C₄	—	2	2	no	—
131	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
132	C₂×C₄²	—	2	1	no	—
133	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
134	C₄⋊C₈	—	2	2	no	—
135	C₄⋊C₈	—	2	2	no	—
136	C₄⋊C₈	—	2	2	no	—
137	#103	—	4	4	no	—
138	C₄×C₈	—	2	2	no	—
139	C₂×Q₈	—	2	1	no	—
140	C₂×Q₈	—	2	2	no	—
141	C₂×Q₈	—	2	2	no	—
142	C₂×Q₈	D₈×C₁₃₇	1	2	yes	—
143	C₂²×C₄	—	2	1	no	—
144	C₂²×C₄	—	2	1	no	—
145	C₂²×C₄	—	4	2	no	—
146	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
147	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
148	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
149	C₂×C₈	—	2	2	no	—
150	C₂×C₈	—	2	2	no	—
151	C₂×C₈	—	2	2	no	—
152	C₂×C₈	—	4	2	no	—
153	C₂×C₈	—	4	1	no	—
154	C₂×C₈	—	4	2	no	—
155	C₂×C₈	—	4	2	no	—
156	C₂×C₈	—	4	2	no	—
157	C₄⋊C₄	—	2	2	no	—
158	C₄⋊C₄	—	4	2	no	—
159	C₄⋊C₄	—	4	2	no	—
160	C₄⋊C₄	—	4	2	no	—
161	C₄⋊C₄	—	4	2	no	—
162	C₄⋊C₄	—	4	2	no	—
163	C₄⋊C₄	—	8	2	no	—
164	C₄²	—	4	1	no	—
165	C₄²	—	4	1	no	—
166	C₄²	#41×C₁₃₇	1	2	yes	—
167	C₄²	#41×C₁₃₇	1	2	yes	—
168	C₂³	#121×C₁₃₇	1	1	yes	characteristic
169	Q₈	—	2	4	no	—
170	Q₈	—	4	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	4	1	no	—
174	C₂×C₄	—	4	1	no	—
175	C₂×C₄	—	4	1	no	—
176	C₂×C₄	—	4	2	no	—
177	C₂×C₄	—	8	2	no	—
178	C₂×C₄	—	8	2	no	—
179	C₂×C₄	—	8	2	no	—
180	C₂×C₄	#123×C₁₃₇	1	2	yes	—
181	C₂×C₄	#123×C₁₃₇	1	1	yes	characteristic
182	C₂×C₄	#124×C₁₃₇	1	1	yes	characteristic
183	C₂×C₄	#126×C₁₃₇	1	2	yes	—
184	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
185	C₂×C₄	#135×C₁₃₇	1	1	yes	characteristic
186	C₂×C₄	#135×C₁₃₇	1	2	yes	—
187	C₂×C₄	#137×C₁₃₇	1	2	yes	—
188	C₂×C₄	#137×C₁₃₇	1	2	yes	—
189	C₈	—	4	2	no	—
190	C₈	—	8	2	no	—
191	C₈	—	8	1	no	—
192	C₂²	#397×C₁₃₇	1	1	yes	characteristic
193	C₂²	#464×C₁₃₇	1	2	yes	—
194	C₂²	#466×C₁₃₇	1	1	yes	characteristic
195	C₂²	#470×C₁₃₇	1	1	yes	characteristic
196	C₂²	#471×C₁₃₇	1	2	yes	—
197	C₄	—	2	2	no	—
198	C₄	—	4	2	no	—
199	C₄	—	8	1	no	—
200	C₄	—	16	2	no	—
201	C₄	#480×C₁₃₇	1	2	yes	—
202	C₄	#485×C₁₃₇	1	2	yes	—
203	C₄	#485×C₁₃₇	1	2	yes	—
204	C₄	#488×C₁₃₇	1	1	yes	characteristic
205	C₄	#491×C₁₃₇	1	1	yes	characteristic
206	C₂	#1682×C₁₃₇	1	2	yes	—
207	C₂	#1704×C₁₃₇	1	2	yes	—
208	C₂	#2074×C₁₃₇	1	1	yes	characteristic
209	C₂	#2075×C₁₃₇	1	1	yes	characteristic
210	C₂	#2079×C₁₃₇	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#1984×C₁₃₇

C₂

yes

maximal, characteristic

#1834×C₁₃₇

C₂

yes

maximal, characteristic

#1803×C₁₃₇

C₂

yes

maximal

#1296×C₁₃₇

C₂

yes

maximal

#1277×C₁₃₇

C₂

yes

maximal, characteristic

C₂×C₄×Q₈×C₁₃₇

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₁₃₇

C₂²

yes

—

C₂×C₄⋊C₈×C₁₃₇

C₂²

yes

characteristic

C₂×#103×C₁₃₇

—

C₂×C₄×C₈×C₁₃₇

C₂²

yes

characteristic

#384×C₁₃₇

C₂²

yes

—

#340×C₁₃₇

—

#340×C₁₃₇

—

#336×C₁₃₇

—

C₂²×Q₈×C₁₃₇

D₄

yes

characteristic

C₂²×C₈×C₁₃₇

—

C₂²×C₈×C₁₃₇

—

C₂²×C₈×C₁₃₇

D₄

yes

—

C₄×Q₈×C₁₃₇

—

C₄×Q₈×C₁₃₇

—

C₂×C₄⋊C₄×C₁₃₇

—

C₂×C₄⋊C₄×C₁₃₇

—

C₂×C₄⋊C₄×C₁₃₇

—

C₂×C₄⋊C₄×C₁₃₇

—

C₂×C₄⋊C₄×C₁₃₇

D₄

yes

characteristic

C₂×C₄²×C₁₃₇

—

C₂×C₄²×C₁₃₇

C₂³

yes

characteristic

C₄⋊C₈×C₁₃₇

—

C₄⋊C₈×C₁₃₇

—

C₄⋊C₈×C₁₃₇

—

#103×C₁₃₇

—

C₄×C₈×C₁₃₇

—

C₂×Q₈×C₁₃₇

—

C₂×Q₈×C₁₃₇

—

C₂×Q₈×C₁₃₇

—

C₂×Q₈×C₁₃₇

D₈

yes

—

C₂²×C₄×C₁₃₇

—

C₂²×C₄×C₁₃₇

—

C₂²×C₄×C₁₃₇

—

C₂²×C₄×C₁₃₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃₇

#41

yes

characteristic

C₂×C₈×C₁₃₇

—

C₂×C₈×C₁₃₇

—

C₂×C₈×C₁₃₇

—

C₂×C₈×C₁₃₇

—

C₂×C₈×C₁₃₇

—

C₂×C₈×C₁₃₇

—

C₂×C₈×C₁₃₇

—

C₂×C₈×C₁₃₇

—

C₄⋊C₄×C₁₃₇

—

C₄⋊C₄×C₁₃₇

—

C₄⋊C₄×C₁₃₇

—

C₄⋊C₄×C₁₃₇

—

C₄⋊C₄×C₁₃₇

—

C₄⋊C₄×C₁₃₇

—

C₄⋊C₄×C₁₃₇

—

C₄²×C₁₃₇

—

C₄²×C₁₃₇

—

C₄²×C₁₃₇

#41

yes

—

C₄²×C₁₃₇

#41

yes

—

C₂³×C₁₃₇

#121

yes

characteristic

Q₈×C₁₃₇

—

Q₈×C₁₃₇

—

C₂×C₄×C₁₃₇

—

C₂×C₄×C₁₃₇

—

C₂×C₄×C₁₃₇

—

C₂×C₄×C₁₃₇

—

C₂×C₄×C₁₃₇

—

C₂×C₄×C₁₃₇

—

C₂×C₄×C₁₃₇

—

C₂×C₄×C₁₃₇

—

C₂×C₄×C₁₃₇

—

C₂×C₄×C₁₃₇

#123

yes

—

C₂×C₄×C₁₃₇

yes

C₂×C₄×C₁₃₇

yes

C₂×C₄×C₁₃₇

yes

—

C₂×C₄×C₁₃₇

C₂×D₈

yes

C₂×C₄×C₁₃₇

yes

C₂×C₄×C₁₃₇

yes

—

C₂×C₄×C₁₃₇

#137

yes

—

C₂×C₄×C₁₃₇

#137

yes

—

C₈×C₁₃₇

—

C₈×C₁₃₇

—

C₈×C₁₃₇

—

C₂²×C₁₃₇

#397

yes

characteristic

C₂²×C₁₃₇

#464

yes

—

C₂²×C₁₃₇

yes

C₂²×C₁₃₇

yes

C₂²×C₁₃₇

yes

—

C₄×C₁₃₇

—

C₄×C₁₃₇

—

C₄×C₁₃₇

—

C₄×C₁₃₇

—

C₄×C₁₃₇

#480

yes

—

C₄×C₁₃₇

#485

yes

—

C₄×C₁₃₇

#485

yes

—

C₄×C₁₃₇

yes

C₄×C₁₃₇

yes

100

C₂×C₁₃₇

#1682

yes

—

101

C₂×C₁₃₇

#1704

yes

—

102

C₂×C₁₃₇

#2074

yes

characteristic

103

C₂×C₁₃₇

#2075

yes

characteristic

104

C₂×C₁₃₇

#2079

yes

characteristic

105

#10623

C₁₃₇

yes

maximal, characteristic, direct product factor, Sylow

106

C₁₃₇

#10623

yes

characteristic, direct product factor, Sylow

107

#1984

C₂×C₁₃₇

yes

characteristic

108

#1834

C₂×C₁₃₇

yes

characteristic

109

#1803

C₂×C₁₃₇

yes

—

110

#1296

C₂×C₁₃₇

yes

—

111

#1277

C₂×C₁₃₇

yes

characteristic

112

C₂×C₄×Q₈

C₂²×C₁₃₇

yes

characteristic

113

C₂×C₄⋊C₈

C₂²×C₁₃₇

yes

—

114

C₂×C₄⋊C₈

C₂²×C₁₃₇

yes

characteristic

115

C₂×#103

—

116

C₂×C₄×C₈

C₂²×C₁₃₇

yes

characteristic

117

#384

C₂²×C₁₃₇

yes

—

118

#340

—

119

#340

—

120

#336

—

121

C₂²×Q₈

D₄×C₁₃₇

yes

characteristic

122

C₂²×C₈

—

123

C₂²×C₈

—

124

C₂²×C₈

D₄×C₁₃₇

yes

—

125

C₄×Q₈

—

126

C₄×Q₈

—

127

C₂×C₄⋊C₄

—

128

C₂×C₄⋊C₄

—

129

C₂×C₄⋊C₄

—

130

C₂×C₄⋊C₄

—

131

C₂×C₄⋊C₄

D₄×C₁₃₇

yes

characteristic

132

C₂×C₄²

—

133

C₂×C₄²

C₂³×C₁₃₇

yes

characteristic

134

C₄⋊C₈

—

135

C₄⋊C₈

—

136

C₄⋊C₈

—

137

#103

—

138

C₄×C₈

—

139

C₂×Q₈

—

140

C₂×Q₈

—

141

C₂×Q₈

—

142

C₂×Q₈

D₈×C₁₃₇

yes

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

C₂×D₄×C₁₃₇

yes

characteristic

147

C₂²×C₄

C₂×D₄×C₁₃₇

yes

characteristic

148

C₂²×C₄

#41×C₁₃₇

yes

characteristic

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄⋊C₄

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄²

—

165

C₄²

—

166

C₄²

#41×C₁₃₇

yes

—

167

C₄²

#41×C₁₃₇

yes

—

168

C₂³

#121×C₁₃₇

yes

characteristic

169

Q₈

—

170

Q₈

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

#123×C₁₃₇

yes

—

181

C₂×C₄

#123×C₁₃₇

yes

characteristic

182

C₂×C₄

#124×C₁₃₇

yes

characteristic

183

C₂×C₄

#126×C₁₃₇

yes

—

184

C₂×C₄

C₂×D₈×C₁₃₇

yes

characteristic

185

C₂×C₄

#135×C₁₃₇

yes

characteristic

186

C₂×C₄

#135×C₁₃₇

yes

—

187

C₂×C₄

#137×C₁₃₇

yes

—

188

C₂×C₄

#137×C₁₃₇

yes

—

189

C₈

—

190

C₈

—

191

C₈

—

192

C₂²

#397×C₁₃₇

yes

characteristic

193

C₂²

#464×C₁₃₇

yes

—

194

C₂²

#466×C₁₃₇

yes

characteristic

195

C₂²

#470×C₁₃₇

yes

characteristic

196

C₂²

#471×C₁₃₇

yes

—

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

—

201

C₄

#480×C₁₃₇

yes

—

202

C₄

#485×C₁₃₇

yes

—

203

C₄

#485×C₁₃₇

yes

—

204

C₄

#488×C₁₃₇

yes

characteristic

205

C₄

#491×C₁₃₇

yes

characteristic

206

C₂

#1682×C₁₃₇

yes

—

207

C₂

#1704×C₁₃₇

yes

—

208

C₂

#2074×C₁₃₇

yes

characteristic

209

C₂

#2075×C₁₃₇

yes

characteristic

210

C₂

#2079×C₁₃₇

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃₇	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₇
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂×C₄²×C₁₃₇ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₁₃₇

#121

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₃₇

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃₇ ◁ C₂×C₄²×C₁₃₇ ◁ G

N	H ≅ G/N	type
105. #10623	C₁₃₇	direct (N × H)
106. C₁₃₇	#10623	direct (N × H)

H ≅ G/N

type

105. #10623

C₁₃₇

direct (N × H)

106. C₁₃₇

#10623

direct (N × H)

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

subgroup	index
#1984×C₁₃₇	2
#1834×C₁₃₇	2
#1803×C₁₃₇	2
#1296×C₁₃₇	2
#1277×C₁₃₇	2
#10623	137

subgroup

index

#1984×C₁₃₇

#1834×C₁₃₇

#1803×C₁₃₇

#1296×C₁₃₇

#1277×C₁₃₇

#10623

137

Subgroups — C₁₃₇×#10623 #46860009

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C137×#10623 #46860009

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#10623 #46860009