Group #46860874 — subgroups

Subgroups — C₁₃₇×#11488 #46860874

Order 35072.

418 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 142 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×C₈×D₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2163×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	#1314×C₁₃₇	C₂	1	4	yes	maximal, complemented
4	C₂³×C₈×C₁₃₇	C₄	1	2	yes	—
5	C₂×C₄×D₄×C₁₃₇	C₄	1	1	yes	characteristic
6	C₈×D₄×C₁₃₇	—	2	2	no	—
7	C₈×D₄×C₁₃₇	—	2	2	no	—
8	C₂×C₄⋊C₈×C₁₃₇	C₄	1	1	yes	characteristic
9	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
11	C₄⋊C₁₆×C₁₃₇	—	2	2	no	—
12	C₂²⋊C₁₆×C₁₃₇	C₂²	1	4	yes	—
13	#346×C₁₃₇	—	2	2	no	—
14	C₂²×D₄×C₁₃₇	C₈	1	1	yes	characteristic
15	C₂³×C₄×C₁₃₇	C₂×C₄	1	2	yes	—
16	C₂²×C₈×C₁₃₇	—	2	2	no	—
17	C₂²×C₈×C₁₃₇	—	2	2	no	—
18	C₂²×C₈×C₁₃₇	—	4	4	no	—
19	C₂²×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₃₇	C₂×C₄	1	2	yes	—
21	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
22	C₄×D₄×C₁₃₇	—	2	2	no	—
23	C₄×D₄×C₁₃₇	—	2	2	no	—
24	C₂×C₄⋊C₄×C₁₃₇	C₈	1	1	yes	characteristic
25	C₂×C₂²⋊C₄×C₁₃₇	C₈	1	2	yes	—
26	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
27	C₂×C₁₆×C₁₃₇	—	2	4	no	—
28	C₄⋊C₈×C₁₃₇	—	2	2	no	—
29	C₂²⋊C₈×C₁₃₇	—	2	4	no	—
30	C₄×C₈×C₁₃₇	D₄	1	2	yes	—
31	C₄×C₈×C₁₃₇	D₄	1	2	yes	—
32	C₂⁴×C₁₃₇	C₂×C₈	1	2	yes	—
33	C₂×D₄×C₁₃₇	—	2	4	no	—
34	C₂×D₄×C₁₃₇	—	2	2	no	—
35	C₂²×C₄×C₁₃₇	—	2	2	no	—
36	C₂²×C₄×C₁₃₇	—	2	2	no	—
37	C₂²×C₄×C₁₃₇	—	4	2	no	—
38	C₂²×C₄×C₁₃₇	—	4	2	no	—
39	C₂²×C₄×C₁₃₇	C₂×C₈	1	1	yes	characteristic
40	C₂²×C₄×C₁₃₇	C₂×C₈	1	2	yes	—
41	C₂²×C₄×C₁₃₇	C₂×C₈	1	1	yes	characteristic
42	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₃₇	—	2	2	no	—
44	C₂×C₈×C₁₃₇	—	2	2	no	—
45	C₂×C₈×C₁₃₇	—	4	1	no	—
46	C₂×C₈×C₁₃₇	—	4	4	no	—
47	C₂×C₈×C₁₃₇	—	4	4	no	—
48	C₂×C₈×C₁₃₇	—	4	2	no	—
49	C₂×C₈×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
50	C₂×C₈×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
52	C₄⋊C₄×C₁₃₇	—	2	2	no	—
53	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
54	C₄²×C₁₃₇	C₂²⋊C₄	1	2	yes	—
55	C₄²×C₁₃₇	M₁₆	1	2	yes	—
56	C₁₆×C₁₃₇	—	4	4	no	—
57	C₂³×C₁₃₇	—	2	2	no	—
58	C₂³×C₁₃₇	—	2	2	no	—
59	C₂³×C₁₃₇	—	4	2	no	—
60	C₂³×C₁₃₇	—	4	2	no	—
61	C₂³×C₁₃₇	M₃₂	1	4	yes	—
62	C₂³×C₁₃₇	C₂²×C₈	1	1	yes	characteristic
63	D₄×C₁₃₇	—	2	8	no	—
64	C₂×C₄×C₁₃₇	—	2	2	no	—
65	C₂×C₄×C₁₃₇	—	2	1	no	—
66	C₂×C₄×C₁₃₇	—	2	1	no	—
67	C₂×C₄×C₁₃₇	—	2	2	no	—
68	C₂×C₄×C₁₃₇	—	4	1	no	—
69	C₂×C₄×C₁₃₇	—	4	4	no	—
70	C₂×C₄×C₁₃₇	—	4	2	no	—
71	C₂×C₄×C₁₃₇	—	4	2	no	—
72	C₂×C₄×C₁₃₇	—	4	2	no	—
73	C₂×C₄×C₁₃₇	C₂²⋊C₈	1	2	yes	—
74	C₂×C₄×C₁₃₇	C₂²⋊C₈	1	2	yes	—
75	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₄×C₁₃₇	C₂×M₁₆	1	1	yes	characteristic
77	C₈×C₁₃₇	—	2	2	no	—
78	C₈×C₁₃₇	—	2	1	no	—
79	C₈×C₁₃₇	—	4	2	no	—
80	C₈×C₁₃₇	#100	1	2	yes	—
81	C₂²×C₁₃₇	—	2	1	no	—
82	C₂²×C₁₃₇	—	2	1	no	—
83	C₂²×C₁₃₇	—	2	4	no	—
84	C₂²×C₁₃₇	—	4	4	no	—
85	C₂²×C₁₃₇	—	4	4	no	—
86	C₂²×C₁₃₇	—	4	2	no	—
87	C₂²×C₁₃₇	—	4	2	no	—
88	C₂²×C₁₃₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
89	C₂²×C₁₃₇	C₂×M₃₂	1	2	yes	—
90	C₄×C₁₃₇	—	2	2	no	—
91	C₄×C₁₃₇	—	2	2	no	—
92	C₄×C₁₃₇	—	2	1	no	—
93	C₄×C₁₃₇	—	4	2	no	—
94	C₄×C₁₃₇	#410	1	1	yes	characteristic
95	C₄×C₁₃₇	C₂×#100	1	1	yes	characteristic
96	C₂×C₁₃₇	—	2	2	no	—
97	C₂×C₁₃₇	—	4	4	no	—
98	C₂×C₁₃₇	#1460	1	1	yes	characteristic
99	C₂×C₁₃₇	#2112	1	1	yes	characteristic
100	C₂×C₁₃₇	#2115	1	1	yes	characteristic
101	#11488	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₁₃₇	#11488	1	1	yes	characteristic, direct product factor, Sylow
103	C₂×C₈×D₄	C₂×C₁₃₇	1	1	yes	characteristic
104	#2163	C₂×C₁₃₇	1	2	yes	complemented
105	#1314	C₂×C₁₃₇	1	4	yes	complemented
106	C₂³×C₈	C₄×C₁₃₇	1	2	yes	—
107	C₂×C₄×D₄	C₄×C₁₃₇	1	1	yes	characteristic
108	C₈×D₄	—	2	2	no	—
109	C₈×D₄	—	2	2	no	—
110	C₂×C₄⋊C₈	C₄×C₁₃₇	1	1	yes	characteristic
111	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
112	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
113	C₄⋊C₁₆	—	2	2	no	—
114	C₂²⋊C₁₆	C₂²×C₁₃₇	1	4	yes	—
115	#346	—	2	2	no	—
116	C₂²×D₄	C₈×C₁₃₇	1	1	yes	characteristic
117	C₂³×C₄	C₂×C₄×C₁₃₇	1	2	yes	—
118	C₂²×C₈	—	2	2	no	—
119	C₂²×C₈	—	2	2	no	—
120	C₂²×C₈	—	4	4	no	—
121	C₂²×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
122	C₂²×C₈	C₂×C₄×C₁₃₇	1	2	yes	—
123	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
124	C₄×D₄	—	2	2	no	—
125	C₄×D₄	—	2	2	no	—
126	C₂×C₄⋊C₄	C₈×C₁₃₇	1	1	yes	characteristic
127	C₂×C₂²⋊C₄	C₈×C₁₃₇	1	2	yes	—
128	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
129	C₂×C₁₆	—	2	4	no	—
130	C₄⋊C₈	—	2	2	no	—
131	C₂²⋊C₈	—	2	4	no	—
132	C₄×C₈	D₄×C₁₃₇	1	2	yes	—
133	C₄×C₈	D₄×C₁₃₇	1	2	yes	—
134	C₂⁴	C₂×C₈×C₁₃₇	1	2	yes	—
135	C₂×D₄	—	2	4	no	—
136	C₂×D₄	—	2	2	no	—
137	C₂²×C₄	—	2	2	no	—
138	C₂²×C₄	—	2	2	no	—
139	C₂²×C₄	—	4	2	no	—
140	C₂²×C₄	—	4	2	no	—
141	C₂²×C₄	C₂×C₈×C₁₃₇	1	1	yes	characteristic
142	C₂²×C₄	C₂×C₈×C₁₃₇	1	2	yes	—
143	C₂²×C₄	C₂×C₈×C₁₃₇	1	1	yes	characteristic
144	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
145	C₂×C₈	—	2	2	no	—
146	C₂×C₈	—	2	2	no	—
147	C₂×C₈	—	4	1	no	—
148	C₂×C₈	—	4	4	no	—
149	C₂×C₈	—	4	4	no	—
150	C₂×C₈	—	4	2	no	—
151	C₂×C₈	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
152	C₂×C₈	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
153	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
154	C₄⋊C₄	—	2	2	no	—
155	C₂²⋊C₄	—	2	4	no	—
156	C₄²	C₂²⋊C₄×C₁₃₇	1	2	yes	—
157	C₄²	M₁₆×C₁₃₇	1	2	yes	—
158	C₁₆	—	4	4	no	—
159	C₂³	—	2	2	no	—
160	C₂³	—	2	2	no	—
161	C₂³	—	4	2	no	—
162	C₂³	—	4	2	no	—
163	C₂³	M₃₂×C₁₃₇	1	4	yes	—
164	C₂³	C₂²×C₈×C₁₃₇	1	1	yes	characteristic
165	D₄	—	2	8	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	2	1	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	4	1	no	—
171	C₂×C₄	—	4	4	no	—
172	C₂×C₄	—	4	2	no	—
173	C₂×C₄	—	4	2	no	—
174	C₂×C₄	—	4	2	no	—
175	C₂×C₄	C₂²⋊C₈×C₁₃₇	1	2	yes	—
176	C₂×C₄	C₂²⋊C₈×C₁₃₇	1	2	yes	—
177	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
178	C₂×C₄	C₂×M₁₆×C₁₃₇	1	1	yes	characteristic
179	C₈	—	2	2	no	—
180	C₈	—	2	1	no	—
181	C₈	—	4	2	no	—
182	C₈	#100×C₁₃₇	1	2	yes	—
183	C₂²	—	2	1	no	—
184	C₂²	—	2	1	no	—
185	C₂²	—	2	4	no	—
186	C₂²	—	4	4	no	—
187	C₂²	—	4	4	no	—
188	C₂²	—	4	2	no	—
189	C₂²	—	4	2	no	—
190	C₂²	C₂×C₂²⋊C₈×C₁₃₇	1	1	yes	characteristic
191	C₂²	C₂×M₃₂×C₁₃₇	1	2	yes	—
192	C₄	—	2	2	no	—
193	C₄	—	2	2	no	—
194	C₄	—	2	1	no	—
195	C₄	—	4	2	no	—
196	C₄	#410×C₁₃₇	1	1	yes	characteristic
197	C₄	C₂×#100×C₁₃₇	1	1	yes	characteristic
198	C₂	—	2	2	no	—
199	C₂	—	4	4	no	—
200	C₂	#1460×C₁₃₇	1	1	yes	characteristic
201	C₂	#2112×C₁₃₇	1	1	yes	characteristic
202	C₂	#2115×C₁₃₇	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×D₄×C₁₃₇

C₂

yes

maximal, characteristic

#2163×C₁₃₇

C₂

yes

maximal, complemented

#1314×C₁₃₇

C₂

yes

maximal, complemented

C₂³×C₈×C₁₃₇

C₄

yes

—

C₂×C₄×D₄×C₁₃₇

C₄

yes

characteristic

C₈×D₄×C₁₃₇

—

C₈×D₄×C₁₃₇

—

C₂×C₄⋊C₈×C₁₃₇

C₄

yes

characteristic

C₂×C₂²⋊C₈×C₁₃₇

C₂²

yes

—

C₂×C₄×C₈×C₁₃₇

C₂²

yes

characteristic

C₄⋊C₁₆×C₁₃₇

—

C₂²⋊C₁₆×C₁₃₇

C₂²

yes

—

#346×C₁₃₇

—

C₂²×D₄×C₁₃₇

C₈

yes

characteristic

C₂³×C₄×C₁₃₇

C₂×C₄

yes

—

C₂²×C₈×C₁₃₇

—

C₂²×C₈×C₁₃₇

—

C₂²×C₈×C₁₃₇

—

C₂²×C₈×C₁₃₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₃₇

C₂×C₄

yes

—

C₂²×C₈×C₁₃₇

C₂³

yes

characteristic

C₄×D₄×C₁₃₇

—

C₄×D₄×C₁₃₇

—

C₂×C₄⋊C₄×C₁₃₇

C₈

yes

characteristic

C₂×C₂²⋊C₄×C₁₃₇

C₈

yes

—

C₂×C₄²×C₁₃₇

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₃₇

—

C₄⋊C₈×C₁₃₇

—

C₂²⋊C₈×C₁₃₇

—

C₄×C₈×C₁₃₇

D₄

yes

—

C₄×C₈×C₁₃₇

D₄

yes

—

C₂⁴×C₁₃₇

C₂×C₈

yes

—

C₂×D₄×C₁₃₇

—

C₂×D₄×C₁₃₇

—

C₂²×C₄×C₁₃₇

—

C₂²×C₄×C₁₃₇

—

C₂²×C₄×C₁₃₇

—

C₂²×C₄×C₁₃₇

—

C₂²×C₄×C₁₃₇

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₃₇

C₂×C₈

yes

—

C₂²×C₄×C₁₃₇

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₃₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₃₇

—

C₂×C₈×C₁₃₇

—

C₂×C₈×C₁₃₇

—

C₂×C₈×C₁₃₇

—

C₂×C₈×C₁₃₇

—

C₂×C₈×C₁₃₇

—

C₂×C₈×C₁₃₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₃₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₃₇

C₂×D₄

yes

—

C₄⋊C₄×C₁₃₇

—

C₂²⋊C₄×C₁₃₇

—

C₄²×C₁₃₇

C₂²⋊C₄

yes

—

C₄²×C₁₃₇

M₁₆

yes

—

C₁₆×C₁₃₇

—

C₂³×C₁₃₇

—

C₂³×C₁₃₇

—

C₂³×C₁₃₇

—

C₂³×C₁₃₇

—

C₂³×C₁₃₇

M₃₂

yes

—

C₂³×C₁₃₇

C₂²×C₈

yes

characteristic

D₄×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

C₂²⋊C₈

yes

—

C₂×C₄×C₁₃₇

C₂²⋊C₈

yes

—

C₂×C₄×C₁₃₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃₇

C₂×M₁₆

yes

characteristic

C₈×C₁₃₇

—

C₈×C₁₃₇

—

C₈×C₁₃₇

—

C₈×C₁₃₇

#100

yes

—

C₂²×C₁₃₇

—

C₂²×C₁₃₇

—

C₂²×C₁₃₇

—

C₂²×C₁₃₇

—

C₂²×C₁₃₇

—

C₂²×C₁₃₇

—

C₂²×C₁₃₇

—

C₂²×C₁₃₇

C₂×C₂²⋊C₈

yes

characteristic

C₂²×C₁₃₇

C₂×M₃₂

yes

—

C₄×C₁₃₇

—

C₄×C₁₃₇

—

C₄×C₁₃₇

—

C₄×C₁₃₇

—

C₄×C₁₃₇

yes

C₄×C₁₃₇

yes

C₂×C₁₃₇

—

C₂×C₁₃₇

—

C₂×C₁₃₇

yes

C₂×C₁₃₇

yes

100

C₂×C₁₃₇

#2115

yes

characteristic

101

#11488

C₁₃₇

yes

maximal, characteristic, direct product factor, Sylow

102

C₁₃₇

#11488

yes

characteristic, direct product factor, Sylow

103

C₂×C₈×D₄

C₂×C₁₃₇

yes

characteristic

104

#2163

C₂×C₁₃₇

yes

complemented

105

#1314

C₂×C₁₃₇

yes

complemented

106

C₂³×C₈

C₄×C₁₃₇

yes

—

107

C₂×C₄×D₄

C₄×C₁₃₇

yes

characteristic

108

C₈×D₄

—

109

C₈×D₄

—

110

C₂×C₄⋊C₈

C₄×C₁₃₇

yes

characteristic

111

C₂×C₂²⋊C₈

C₂²×C₁₃₇

yes

—

112

C₂×C₄×C₈

C₂²×C₁₃₇

yes

characteristic

113

C₄⋊C₁₆

—

114

C₂²⋊C₁₆

C₂²×C₁₃₇

yes

—

115

#346

—

116

C₂²×D₄

C₈×C₁₃₇

yes

characteristic

117

C₂³×C₄

C₂×C₄×C₁₃₇

yes

—

118

C₂²×C₈

—

119

C₂²×C₈

—

120

C₂²×C₈

—

121

C₂²×C₈

C₂×C₄×C₁₃₇

yes

characteristic

122

C₂²×C₈

C₂×C₄×C₁₃₇

yes

—

123

C₂²×C₈

C₂³×C₁₃₇

yes

characteristic

124

C₄×D₄

—

125

C₄×D₄

—

126

C₂×C₄⋊C₄

C₈×C₁₃₇

yes

characteristic

127

C₂×C₂²⋊C₄

C₈×C₁₃₇

yes

—

128

C₂×C₄²

C₂×C₄×C₁₃₇

yes

characteristic

129

C₂×C₁₆

—

130

C₄⋊C₈

—

131

C₂²⋊C₈

—

132

C₄×C₈

D₄×C₁₃₇

yes

—

133

C₄×C₈

D₄×C₁₃₇

yes

—

134

C₂⁴

C₂×C₈×C₁₃₇

yes

—

135

C₂×D₄

—

136

C₂×D₄

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

C₂×C₈×C₁₃₇

yes

characteristic

142

C₂²×C₄

C₂×C₈×C₁₃₇

yes

—

143

C₂²×C₄

C₂×C₈×C₁₃₇

yes

characteristic

144

C₂²×C₄

C₂²×C₄×C₁₃₇

yes

characteristic

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

C₂²⋊C₄×C₁₃₇

yes

characteristic

152

C₂×C₈

C₂²⋊C₄×C₁₃₇

yes

characteristic

153

C₂×C₈

C₂×D₄×C₁₃₇

yes

—

154

C₄⋊C₄

—

155

C₂²⋊C₄

—

156

C₄²

C₂²⋊C₄×C₁₃₇

yes

—

157

C₄²

M₁₆×C₁₃₇

yes

—

158

C₁₆

—

159

C₂³

—

160

C₂³

—

161

C₂³

—

162

C₂³

—

163

C₂³

M₃₂×C₁₃₇

yes

—

164

C₂³

C₂²×C₈×C₁₃₇

yes

characteristic

165

D₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

C₂²⋊C₈×C₁₃₇

yes

—

176

C₂×C₄

C₂²⋊C₈×C₁₃₇

yes

—

177

C₂×C₄

C₂×C₂²⋊C₄×C₁₃₇

yes

characteristic

178

C₂×C₄

C₂×M₁₆×C₁₃₇

yes

characteristic

179

C₈

—

180

C₈

—

181

C₈

—

182

C₈

#100×C₁₃₇

yes

—

183

C₂²

—

184

C₂²

—

185

C₂²

—

186

C₂²

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

C₂×C₂²⋊C₈×C₁₃₇

yes

characteristic

191

C₂²

C₂×M₃₂×C₁₃₇

yes

—

192

C₄

—

193

C₄

—

194

C₄

—

195

C₄

—

196

C₄

#410×C₁₃₇

yes

characteristic

197

C₄

C₂×#100×C₁₃₇

yes

characteristic

198

C₂

—

199

C₂

—

200

C₂

#1460×C₁₃₇

yes

characteristic

201

C₂

#2112×C₁₃₇

yes

characteristic

202

C₂

#2115×C₁₃₇

yes

characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₈×C₁₃₇
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃₇
socle	C₂²×C₁₃₇	C₂×C₂²⋊C₈
prime radical	C₂²×D₄×C₁₃₇	C₈
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₇ ◁ C₂×C₄×C₈×C₁₃₇ ◁ G

subgroup

G/H

center

C₂×C₄×C₁₃₇

C₂×C₂²⋊C₄

commutator

C₂³

C₂²×C₈×C₁₃₇

Frattini, cosocle

C₂²×C₈

C₂³×C₁₃₇

socle

C₂²×C₁₃₇

C₂×C₂²⋊C₈

prime radical

C₂²×D₄×C₁₃₇

C₈

LCS

G ▷ C₂³ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₁₃₇ ◁ C₂×C₄×C₈×C₁₃₇ ◁ G

N	H ≅ G/N	type
2. #2163×C₁₃₇	C₂	semidirect
3. #1314×C₁₃₇	C₂	semidirect
101. #11488	C₁₃₇	direct (N × H)
102. C₁₃₇	#11488	direct (N × H)
104. #2163	C₂×C₁₃₇	semidirect
105. #1314	C₂×C₁₃₇	semidirect

H ≅ G/N

type

2. #2163×C₁₃₇

C₂

semidirect

3. #1314×C₁₃₇

C₂

semidirect

101. #11488

C₁₃₇

direct (N × H)

102. C₁₃₇

#11488

direct (N × H)

104. #2163

C₂×C₁₃₇

semidirect

105. #1314

C₂×C₁₃₇

semidirect

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

subgroup	index
C₂×C₈×D₄×C₁₃₇	2
#2163×C₁₃₇	2
#1314×C₁₃₇	2
#11488	137

subgroup

index

C₂×C₈×D₄×C₁₃₇

#2163×C₁₃₇

#1314×C₁₃₇

#11488

137

Subgroups — C₁₃₇×#11488 #46860874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C137×#11488 #46860874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#11488 #46860874