Group #46882320 — subgroups

Subgroups — C₁₃₇×#32934 #46882320

Order 35072.

1378 conjugacy classes of subgroups; only the 310 normal subgroups are shown.

normal subgroups only

This group has 1378 conjugacy classes of subgroups — too many to draw. Only its 310 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	C₂²×#131×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#467×C₁₃₇	C₂	1	3	yes	maximal, complemented
3	#2616×C₁₃₇	C₂	1	2	yes	maximal
4	#1894×C₁₃₇	C₂	1	6	yes	maximal, complemented
5	#1808×C₁₃₇	C₂	1	3	yes	maximal, complemented
6	C₂²×#41×C₁₃₇	C₂²	1	1	yes	characteristic
7	C₂²×Q₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
8	C₂×#131×C₁₃₇	—	2	12	no	—
9	C₂²×M₁₆×C₁₃₇	C₂²	1	3	yes	—
10	C₂³×C₈×C₁₃₇	C₂²	1	3	yes	—
11	C₂×C₂²⋊Q₈×C₁₃₇	C₂²	1	6	yes	—
12	#467×C₁₃₇	—	2	12	no	—
13	C₂×#107×C₁₃₇	C₂²	1	3	yes	—
14	C₂×#103×C₁₃₇	C₂²	1	6	yes	—
15	#395×C₁₃₇	—	2	2	no	—
16	#394×C₁₃₇	—	2	6	no	—
17	#380×C₁₃₇	C₂²	1	6	yes	—
18	#340×C₁₃₇	C₂²	1	6	yes	—
19	C₂×#41×C₁₃₇	—	2	6	no	—
20	C₂×#41×C₁₃₇	—	2	6	no	—
21	C₂²×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
22	C₂²×Q₈×C₁₃₇	C₂³	1	2	yes	—
23	C₂²×D₄×C₁₃₇	D₄	1	3	yes	—
24	C₂³×C₄×C₁₃₇	C₂³	1	3	yes	—
25	C₂×Q₁₆×C₁₃₇	—	2	6	no	—
26	#131×C₁₃₇	—	2	32	no	—
27	C₂×M₁₆×C₁₃₇	—	2	6	no	—
28	C₂×M₁₆×C₁₃₇	—	2	12	no	—
29	C₂²×C₈×C₁₃₇	—	2	12	no	—
30	C₂²×C₈×C₁₃₇	D₄	1	12	yes	—
31	C₂²×C₈×C₁₃₇	C₂³	1	3	yes	—
32	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
33	C₂²⋊Q₈×C₁₃₇	—	2	12	no	—
34	C₂²⋊Q₈×C₁₃₇	—	2	12	no	—
35	C₂×C₄⋊C₄×C₁₃₇	—	2	6	no	—
36	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	6	yes	—
37	C₂×C₂²⋊C₄×C₁₃₇	—	2	6	no	—
38	C₂×C₂²⋊C₄×C₁₃₇	—	2	6	no	—
39	#107×C₁₃₇	—	2	6	no	—
40	#103×C₁₃₇	—	2	12	no	—
41	#95×C₁₃₇	—	2	6	no	—
42	C₂⁴×C₁₃₇	C₂×D₄	1	3	yes	—
43	#41×C₁₃₇	—	2	8	no	—
44	#41×C₁₃₇	—	2	24	no	—
45	C₂×Q₈×C₁₃₇	—	2	6	no	—
46	C₂×Q₈×C₁₃₇	—	2	6	no	—
47	C₂×Q₈×C₁₃₇	—	2	6	no	—
48	C₂×D₄×C₁₃₇	—	2	12	no	—
49	C₂×D₄×C₁₃₇	—	2	6	no	—
50	C₂²×C₄×C₁₃₇	—	2	6	no	—
51	C₂²×C₄×C₁₃₇	—	2	6	no	—
52	C₂²×C₄×C₁₃₇	—	2	6	no	—
53	C₂²×C₄×C₁₃₇	—	2	2	no	—
54	C₂²×C₄×C₁₃₇	C₂×D₄	1	3	yes	—
55	C₂²×C₄×C₁₃₇	C₂×D₄	1	6	yes	—
56	C₂²×C₄×C₁₃₇	#41	1	6	yes	—
57	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
58	Q₁₆×C₁₃₇	—	4	4	no	—
59	M₁₆×C₁₃₇	—	2	24	no	—
60	C₂×C₈×C₁₃₇	—	2	6	no	—
61	C₂×C₈×C₁₃₇	—	2	24	no	—
62	C₂×C₈×C₁₃₇	C₂×D₄	1	6	yes	—
63	C₂×C₈×C₁₃₇	C₂×D₄	1	6	yes	—
64	C₄⋊C₄×C₁₃₇	—	2	6	no	—
65	C₄⋊C₄×C₁₃₇	—	2	6	no	—
66	C₄⋊C₄×C₁₃₇	—	4	12	no	—
67	C₂²⋊C₄×C₁₃₇	—	4	12	no	—
68	C₂²⋊C₄×C₁₃₇	—	8	6	no	—
69	C₂³×C₁₃₇	—	2	6	no	—
70	C₂³×C₁₃₇	—	2	3	no	—
71	C₂³×C₁₃₇	—	2	6	no	—
72	C₂³×C₁₃₇	—	2	3	no	—
73	C₂³×C₁₃₇	#121	1	6	yes	—
74	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
75	Q₈×C₁₃₇	—	2	8	no	—
76	Q₈×C₁₃₇	—	4	2	no	—
77	Q₈×C₁₃₇	—	4	6	no	—
78	D₄×C₁₃₇	—	2	24	no	—
79	C₂×C₄×C₁₃₇	—	2	6	no	—
80	C₂×C₄×C₁₃₇	—	2	6	no	—
81	C₂×C₄×C₁₃₇	—	2	6	no	—
82	C₂×C₄×C₁₃₇	—	2	12	no	—
83	C₂×C₄×C₁₃₇	—	4	6	no	—
84	C₂×C₄×C₁₃₇	—	4	6	no	—
85	C₂×C₄×C₁₃₇	—	4	6	no	—
86	C₂×C₄×C₁₃₇	—	4	6	no	—
87	C₂×C₄×C₁₃₇	#121	1	6	yes	—
88	C₂×C₄×C₁₃₇	C₂²×D₄	1	3	yes	—
89	C₂×C₄×C₁₃₇	C₂×#41	1	3	yes	—
90	C₈×C₁₃₇	—	2	6	no	—
91	C₈×C₁₃₇	#120	1	4	yes	—
92	C₂²×C₁₃₇	—	2	6	no	—
93	C₂²×C₁₃₇	—	2	6	no	—
94	C₂²×C₁₃₇	—	2	6	no	—
95	C₂²×C₁₃₇	—	4	6	no	—
96	C₂²×C₁₃₇	—	4	6	no	—
97	C₂²×C₁₃₇	C₂×#121	1	3	yes	—
98	C₂²×C₁₃₇	#576	1	1	yes	characteristic
99	C₂²×C₁₃₇	#578	1	3	yes	—
100	C₄×C₁₃₇	—	2	6	no	—
101	C₄×C₁₃₇	—	8	2	no	—
102	C₄×C₁₃₇	—	8	6	no	—
103	C₄×C₁₃₇	C₂×#120	1	1	yes	characteristic
104	C₄×C₁₃₇	#525	1	3	yes	—
105	C₂×C₁₃₇	—	4	6	no	—
106	C₂×C₁₃₇	#2847	1	1	yes	characteristic
107	C₂×C₁₃₇	#3059	1	3	yes	—
108	C₂×C₁₃₇	#3061	1	3	yes	—
109	#32934	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₁₃₇	#32934	1	1	yes	characteristic, direct product factor, Sylow
111	C₂²×#131	C₂×C₁₃₇	1	1	yes	characteristic
112	C₂×#467	C₂×C₁₃₇	1	3	yes	complemented
113	#2616	C₂×C₁₃₇	1	2	yes	—
114	#1894	C₂×C₁₃₇	1	6	yes	complemented
115	#1808	C₂×C₁₃₇	1	3	yes	complemented
116	C₂²×#41	C₂²×C₁₃₇	1	1	yes	characteristic
117	C₂²×Q₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
118	C₂×#131	—	2	12	no	—
119	C₂²×M₁₆	C₂²×C₁₃₇	1	3	yes	—
120	C₂³×C₈	C₂²×C₁₃₇	1	3	yes	—
121	C₂×C₂²⋊Q₈	C₂²×C₁₃₇	1	6	yes	—
122	#467	—	2	12	no	—
123	C₂×#107	C₂²×C₁₃₇	1	3	yes	—
124	C₂×#103	C₂²×C₁₃₇	1	6	yes	—
125	#395	—	2	2	no	—
126	#394	—	2	6	no	—
127	#380	C₂²×C₁₃₇	1	6	yes	—
128	#340	C₂²×C₁₃₇	1	6	yes	—
129	C₂×#41	—	2	6	no	—
130	C₂×#41	—	2	6	no	—
131	C₂²×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
132	C₂²×Q₈	C₂³×C₁₃₇	1	2	yes	—
133	C₂²×D₄	D₄×C₁₃₇	1	3	yes	—
134	C₂³×C₄	C₂³×C₁₃₇	1	3	yes	—
135	C₂×Q₁₆	—	2	6	no	—
136	#131	—	2	32	no	—
137	C₂×M₁₆	—	2	6	no	—
138	C₂×M₁₆	—	2	12	no	—
139	C₂²×C₈	—	2	12	no	—
140	C₂²×C₈	D₄×C₁₃₇	1	12	yes	—
141	C₂²×C₈	C₂³×C₁₃₇	1	3	yes	—
142	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
143	C₂²⋊Q₈	—	2	12	no	—
144	C₂²⋊Q₈	—	2	12	no	—
145	C₂×C₄⋊C₄	—	2	6	no	—
146	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	6	yes	—
147	C₂×C₂²⋊C₄	—	2	6	no	—
148	C₂×C₂²⋊C₄	—	2	6	no	—
149	#107	—	2	6	no	—
150	#103	—	2	12	no	—
151	#95	—	2	6	no	—
152	C₂⁴	C₂×D₄×C₁₃₇	1	3	yes	—
153	#41	—	2	8	no	—
154	#41	—	2	24	no	—
155	C₂×Q₈	—	2	6	no	—
156	C₂×Q₈	—	2	6	no	—
157	C₂×Q₈	—	2	6	no	—
158	C₂×D₄	—	2	12	no	—
159	C₂×D₄	—	2	6	no	—
160	C₂²×C₄	—	2	6	no	—
161	C₂²×C₄	—	2	6	no	—
162	C₂²×C₄	—	2	6	no	—
163	C₂²×C₄	—	2	2	no	—
164	C₂²×C₄	C₂×D₄×C₁₃₇	1	3	yes	—
165	C₂²×C₄	C₂×D₄×C₁₃₇	1	6	yes	—
166	C₂²×C₄	#41×C₁₃₇	1	6	yes	—
167	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
168	Q₁₆	—	4	4	no	—
169	M₁₆	—	2	24	no	—
170	C₂×C₈	—	2	6	no	—
171	C₂×C₈	—	2	24	no	—
172	C₂×C₈	C₂×D₄×C₁₃₇	1	6	yes	—
173	C₂×C₈	C₂×D₄×C₁₃₇	1	6	yes	—
174	C₄⋊C₄	—	2	6	no	—
175	C₄⋊C₄	—	2	6	no	—
176	C₄⋊C₄	—	4	12	no	—
177	C₂²⋊C₄	—	4	12	no	—
178	C₂²⋊C₄	—	8	6	no	—
179	C₂³	—	2	6	no	—
180	C₂³	—	2	3	no	—
181	C₂³	—	2	6	no	—
182	C₂³	—	2	3	no	—
183	C₂³	#121×C₁₃₇	1	6	yes	—
184	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
185	Q₈	—	2	8	no	—
186	Q₈	—	4	2	no	—
187	Q₈	—	4	6	no	—
188	D₄	—	2	24	no	—
189	C₂×C₄	—	2	6	no	—
190	C₂×C₄	—	2	6	no	—
191	C₂×C₄	—	2	6	no	—
192	C₂×C₄	—	2	12	no	—
193	C₂×C₄	—	4	6	no	—
194	C₂×C₄	—	4	6	no	—
195	C₂×C₄	—	4	6	no	—
196	C₂×C₄	—	4	6	no	—
197	C₂×C₄	#121×C₁₃₇	1	6	yes	—
198	C₂×C₄	C₂²×D₄×C₁₃₇	1	3	yes	—
199	C₂×C₄	C₂×#41×C₁₃₇	1	3	yes	—
200	C₈	—	2	6	no	—
201	C₈	#120×C₁₃₇	1	4	yes	—
202	C₂²	—	2	6	no	—
203	C₂²	—	2	6	no	—
204	C₂²	—	2	6	no	—
205	C₂²	—	4	6	no	—
206	C₂²	—	4	6	no	—
207	C₂²	C₂×#121×C₁₃₇	1	3	yes	—
208	C₂²	#576×C₁₃₇	1	1	yes	characteristic
209	C₂²	#578×C₁₃₇	1	3	yes	—
210	C₄	—	2	6	no	—
211	C₄	—	8	6	no	—
212	C₄	—	8	2	no	—
213	C₄	C₂×#120×C₁₃₇	1	1	yes	characteristic
214	C₄	#525×C₁₃₇	1	3	yes	—
215	C₂	—	4	6	no	—
216	C₂	#2847×C₁₃₇	1	1	yes	characteristic
217	C₂	#3059×C₁₃₇	1	3	yes	—
218	C₂	#3061×C₁₃₇	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#131×C₁₃₇

C₂

yes

maximal, characteristic

C₂×#467×C₁₃₇

C₂

yes

maximal, complemented

#2616×C₁₃₇

C₂

yes

maximal

#1894×C₁₃₇

C₂

yes

maximal, complemented

#1808×C₁₃₇

C₂

yes

maximal, complemented

C₂²×#41×C₁₃₇

C₂²

yes

characteristic

C₂²×Q₁₆×C₁₃₇

C₂²

yes

characteristic

C₂×#131×C₁₃₇

—

C₂²×M₁₆×C₁₃₇

C₂²

yes

—

C₂³×C₈×C₁₃₇

C₂²

yes

—

C₂×C₂²⋊Q₈×C₁₃₇

C₂²

yes

—

#467×C₁₃₇

—

C₂×#107×C₁₃₇

C₂²

yes

—

C₂×#103×C₁₃₇

C₂²

yes

—

#395×C₁₃₇

—

#394×C₁₃₇

—

#380×C₁₃₇

C₂²

yes

—

#340×C₁₃₇

C₂²

yes

—

C₂×#41×C₁₃₇

—

C₂×#41×C₁₃₇

—

C₂²×Q₈×C₁₃₇

D₄

yes

characteristic

C₂²×Q₈×C₁₃₇

C₂³

yes

—

C₂²×D₄×C₁₃₇

D₄

yes

—

C₂³×C₄×C₁₃₇

C₂³

yes

—

C₂×Q₁₆×C₁₃₇

—

#131×C₁₃₇

—

C₂×M₁₆×C₁₃₇

—

C₂×M₁₆×C₁₃₇

—

C₂²×C₈×C₁₃₇

—

C₂²×C₈×C₁₃₇

D₄

yes

—

C₂²×C₈×C₁₃₇

C₂³

yes

—

C₂²×C₈×C₁₃₇

C₂³

yes

characteristic

C₂²⋊Q₈×C₁₃₇

—

C₂²⋊Q₈×C₁₃₇

—

C₂×C₄⋊C₄×C₁₃₇

—

C₂×C₄⋊C₄×C₁₃₇

C₂³

yes

—

C₂×C₂²⋊C₄×C₁₃₇

—

C₂×C₂²⋊C₄×C₁₃₇

—

#107×C₁₃₇

—

#103×C₁₃₇

—

#95×C₁₃₇

—

C₂⁴×C₁₃₇

C₂×D₄

yes

—

#41×C₁₃₇

—

#41×C₁₃₇

—

C₂×Q₈×C₁₃₇

—

C₂×Q₈×C₁₃₇

—

C₂×Q₈×C₁₃₇

—

C₂×D₄×C₁₃₇

—

C₂×D₄×C₁₃₇

—

C₂²×C₄×C₁₃₇

—

C₂²×C₄×C₁₃₇

—

C₂²×C₄×C₁₃₇

—

C₂²×C₄×C₁₃₇

—

C₂²×C₄×C₁₃₇

C₂×D₄

yes

—

C₂²×C₄×C₁₃₇

C₂×D₄

yes

—

C₂²×C₄×C₁₃₇

#41

yes

—

C₂²×C₄×C₁₃₇

C₂⁴

yes

characteristic

Q₁₆×C₁₃₇

—

M₁₆×C₁₃₇

—

C₂×C₈×C₁₃₇

—

C₂×C₈×C₁₃₇

—

C₂×C₈×C₁₃₇

C₂×D₄

yes

—

C₂×C₈×C₁₃₇

C₂×D₄

yes

—

C₄⋊C₄×C₁₃₇

—

C₄⋊C₄×C₁₃₇

—

C₄⋊C₄×C₁₃₇

—

C₂²⋊C₄×C₁₃₇

—

C₂²⋊C₄×C₁₃₇

—

C₂³×C₁₃₇

—

C₂³×C₁₃₇

—

C₂³×C₁₃₇

—

C₂³×C₁₃₇

—

C₂³×C₁₃₇

#121

yes

—

C₂³×C₁₃₇

C₂²×D₄

yes

characteristic

Q₈×C₁₃₇

—

Q₈×C₁₃₇

—

Q₈×C₁₃₇

—

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

#121

yes

—

C₂×C₄×C₁₃₇

C₂²×D₄

yes

—

C₂×C₄×C₁₃₇

C₂×#41

yes

—

C₈×C₁₃₇

—

C₈×C₁₃₇

#120

yes

—

C₂²×C₁₃₇

—

C₂²×C₁₃₇

—

C₂²×C₁₃₇

—

C₂²×C₁₃₇

—

C₂²×C₁₃₇

—

C₂²×C₁₃₇

C₂×#121

yes

—

C₂²×C₁₃₇

#576

yes

characteristic

C₂²×C₁₃₇

#578

yes

—

100

C₄×C₁₃₇

—

101

C₄×C₁₃₇

—

102

C₄×C₁₃₇

—

103

C₄×C₁₃₇

C₂×#120

yes

characteristic

104

C₄×C₁₃₇

#525

yes

—

105

C₂×C₁₃₇

—

106

C₂×C₁₃₇

#2847

yes

characteristic

107

C₂×C₁₃₇

#3059

yes

—

108

C₂×C₁₃₇

#3061

yes

—

109

#32934

C₁₃₇

yes

maximal, characteristic, direct product factor, Sylow

110

C₁₃₇

#32934

yes

characteristic, direct product factor, Sylow

111

C₂²×#131

C₂×C₁₃₇

yes

characteristic

112

C₂×#467

C₂×C₁₃₇

yes

complemented

113

#2616

C₂×C₁₃₇

yes

—

114

#1894

C₂×C₁₃₇

yes

complemented

115

#1808

C₂×C₁₃₇

yes

complemented

116

C₂²×#41

C₂²×C₁₃₇

yes

characteristic

117

C₂²×Q₁₆

C₂²×C₁₃₇

yes

characteristic

118

C₂×#131

—

119

C₂²×M₁₆

C₂²×C₁₃₇

yes

—

120

C₂³×C₈

C₂²×C₁₃₇

yes

—

121

C₂×C₂²⋊Q₈

C₂²×C₁₃₇

yes

—

122

#467

—

123

C₂×#107

C₂²×C₁₃₇

yes

—

124

C₂×#103

C₂²×C₁₃₇

yes

—

125

#395

—

126

#394

—

127

#380

C₂²×C₁₃₇

yes

—

128

#340

C₂²×C₁₃₇

yes

—

129

C₂×#41

—

130

C₂×#41

—

131

C₂²×Q₈

D₄×C₁₃₇

yes

characteristic

132

C₂²×Q₈

C₂³×C₁₃₇

yes

—

133

C₂²×D₄

D₄×C₁₃₇

yes

—

134

C₂³×C₄

C₂³×C₁₃₇

yes

—

135

C₂×Q₁₆

—

136

#131

—

137

C₂×M₁₆

—

138

C₂×M₁₆

—

139

C₂²×C₈

—

140

C₂²×C₈

D₄×C₁₃₇

yes

—

141

C₂²×C₈

C₂³×C₁₃₇

yes

—

142

C₂²×C₈

C₂³×C₁₃₇

yes

characteristic

143

C₂²⋊Q₈

—

144

C₂²⋊Q₈

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

C₂³×C₁₃₇

yes

—

147

C₂×C₂²⋊C₄

—

148

C₂×C₂²⋊C₄

—

149

#107

—

150

#103

—

151

#95

—

152

C₂⁴

C₂×D₄×C₁₃₇

yes

—

153

#41

—

154

#41

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂×D₄

—

159

C₂×D₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

C₂×D₄×C₁₃₇

yes

—

165

C₂²×C₄

C₂×D₄×C₁₃₇

yes

—

166

C₂²×C₄

#41×C₁₃₇

yes

—

167

C₂²×C₄

C₂⁴×C₁₃₇

yes

characteristic

168

Q₁₆

—

169

M₁₆

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

C₂×D₄×C₁₃₇

yes

—

173

C₂×C₈

C₂×D₄×C₁₃₇

yes

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₂²⋊C₄

—

178

C₂²⋊C₄

—

179

C₂³

—

180

C₂³

—

181

C₂³

—

182

C₂³

—

183

C₂³

#121×C₁₃₇

yes

—

184

C₂³

C₂²×D₄×C₁₃₇

yes

characteristic

185

Q₈

—

186

Q₈

—

187

Q₈

—

188

D₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

#121×C₁₃₇

yes

—

198

C₂×C₄

C₂²×D₄×C₁₃₇

yes

—

199

C₂×C₄

C₂×#41×C₁₃₇

yes

—

200

C₈

—

201

C₈

#120×C₁₃₇

yes

—

202

C₂²

—

203

C₂²

—

204

C₂²

—

205

C₂²

—

206

C₂²

—

207

C₂²

C₂×#121×C₁₃₇

yes

—

208

C₂²

#576×C₁₃₇

yes

characteristic

209

C₂²

#578×C₁₃₇

yes

—

210

C₄

—

211

C₄

—

212

C₄

—

213

C₄

C₂×#120×C₁₃₇

yes

characteristic

214

C₄

#525×C₁₃₇

yes

—

215

C₂

—

216

C₂

#2847×C₁₃₇

yes

characteristic

217

C₂

#3059×C₁₃₇

yes

—

218

C₂

#3061×C₁₃₇

yes

—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂²×#41×C₁₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂²×#41×C₁₃₇ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₃₇

C₂²×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂⁴×C₁₃₇

prime radical

C₂²×#41×C₁₃₇

C₂²

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃₇ ◁ C₂²×#41×C₁₃₇ ◁ G

N	H ≅ G/N	type
2. C₂×#467×C₁₃₇	C₂	semidirect
4. #1894×C₁₃₇	C₂	semidirect
5. #1808×C₁₃₇	C₂	semidirect
109. #32934	C₁₃₇	direct (N × H)
110. C₁₃₇	#32934	direct (N × H)
112. C₂×#467	C₂×C₁₃₇	semidirect
114. #1894	C₂×C₁₃₇	semidirect
115. #1808	C₂×C₁₃₇	semidirect

H ≅ G/N

type

2. C₂×#467×C₁₃₇

C₂

semidirect

4. #1894×C₁₃₇

C₂

semidirect

5. #1808×C₁₃₇

C₂

semidirect

109. #32934

C₁₃₇

direct (N × H)

110. C₁₃₇

#32934

direct (N × H)

112. C₂×#467

C₂×C₁₃₇

semidirect

114. #1894

C₂×C₁₃₇

semidirect

115. #1808

C₂×C₁₃₇

semidirect

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

subgroup	index
C₂²×#131×C₁₃₇	2
C₂×#467×C₁₃₇	2
#2616×C₁₃₇	2
#1894×C₁₃₇	2
#1808×C₁₃₇	2
#32934	137

subgroup

index

C₂²×#131×C₁₃₇

C₂×#467×C₁₃₇

#2616×C₁₃₇

#1894×C₁₃₇

#1808×C₁₃₇

#32934

137

Subgroups — C₁₃₇×#32934 #46882320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C137×#32934 #46882320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#32934 #46882320