Subgroups — C₁₃₇×#7884 #46857270

Order 35072.

572 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2920×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#431×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#431×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1278×C₁₃₇	C₂	1	4	yes	maximal, complemented
5	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
6	#432×C₁₃₇	—	2	1	no	—
7	#432×C₁₃₇	—	2	1	no	—
8	#431×C₁₃₇	—	2	1	no	—
9	#431×C₁₃₇	—	2	1	no	—
10	#431×C₁₃₇	—	2	1	no	—
11	#431×C₁₃₇	—	2	1	no	—
12	#431×C₁₃₇	—	2	1	no	—
13	#431×C₁₃₇	—	2	1	no	—
14	#431×C₁₃₇	C₄	1	2	yes	—
15	#431×C₁₃₇	C₄	1	2	yes	—
16	#431×C₁₃₇	C₄	1	2	yes	—
17	#431×C₁₃₇	C₂²	1	2	yes	—
18	#423×C₁₃₇	C₄	1	2	yes	—
19	C₂×C₄⋊C₈×C₁₃₇	—	2	1	no	—
20	C₂×C₄⋊C₈×C₁₃₇	C₄	1	2	yes	—
21	#407×C₁₃₇	C₄	1	2	yes	—
22	C₂×C₂²⋊C₈×C₁₃₇	—	2	1	no	—
23	C₂×C₂²⋊C₈×C₁₃₇	—	2	1	no	—
24	C₄×M₁₆×C₁₃₇	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃₇	—	2	1	no	—
26	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
27	C₂³×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₃₇	Q₈	1	1	yes	characteristic
30	C₂×M₁₆×C₁₃₇	C₂×C₄	1	4	yes	—
31	C₂²×C₈×C₁₃₇	—	2	2	no	—
32	C₂²×C₈×C₁₃₇	—	2	2	no	—
33	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₃₇	Q₈	1	1	yes	characteristic
44	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
45	C₄⋊C₈×C₁₃₇	—	2	2	no	—
46	C₄⋊C₈×C₁₃₇	—	2	2	no	—
47	C₄⋊C₈×C₁₃₇	—	2	2	no	—
48	C₄⋊C₈×C₁₃₇	—	2	2	no	—
49	C₄⋊C₈×C₁₃₇	—	2	2	no	—
50	C₄⋊C₈×C₁₃₇	C₂×C₄	1	4	yes	—
51	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
52	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
53	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
54	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
55	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
56	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
57	#97×C₁₃₇	—	2	2	no	—
58	C₄×C₈×C₁₃₇	—	2	2	no	—
59	C₄×C₈×C₁₃₇	—	2	2	no	—
60	C₄×C₈×C₁₃₇	—	2	2	no	—
61	C₄×C₈×C₁₃₇	—	2	2	no	—
62	C₄×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
63	C₂⁴×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₃₇	—	2	4	no	—
65	C₂²×C₄×C₁₃₇	—	2	4	no	—
66	C₂²×C₄×C₁₃₇	—	4	2	no	—
67	C₂²×C₄×C₁₃₇	C₄²	1	1	yes	characteristic
68	C₂²×C₄×C₁₃₇	C₄²	1	1	yes	characteristic
69	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
85	M₁₆×C₁₃₇	—	2	8	no	—
86	C₂×C₈×C₁₃₇	—	2	4	no	—
87	C₂×C₈×C₁₃₇	—	2	4	no	—
88	C₂×C₈×C₁₃₇	—	2	4	no	—
89	C₂×C₈×C₁₃₇	—	4	4	no	—
90	C₂×C₈×C₁₃₇	—	4	4	no	—
91	C₄²×C₁₃₇	C₄²	1	1	yes	characteristic
92	C₄²×C₁₃₇	C₄²	1	1	yes	characteristic
93	C₄²×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
94	C₄²×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
95	C₄²×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
96	C₄²×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
107	C₂³×C₁₃₇	—	2	2	no	—
108	C₂³×C₁₃₇	—	2	2	no	—
109	C₂³×C₁₃₇	—	4	1	no	—
110	C₂³×C₁₃₇	#95	1	1	yes	characteristic
111	C₂³×C₁₃₇	#95	1	1	yes	characteristic
112	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₄×C₁₃₇	—	2	2	no	—
114	C₂×C₄×C₁₃₇	—	2	2	no	—
115	C₂×C₄×C₁₃₇	—	2	2	no	—
116	C₂×C₄×C₁₃₇	—	2	2	no	—
117	C₂×C₄×C₁₃₇	—	2	2	no	—
118	C₂×C₄×C₁₃₇	—	2	2	no	—
119	C₂×C₄×C₁₃₇	—	2	2	no	—
120	C₂×C₄×C₁₃₇	—	2	2	no	—
121	C₂×C₄×C₁₃₇	—	2	2	no	—
122	C₂×C₄×C₁₃₇	—	2	2	no	—
123	C₂×C₄×C₁₃₇	—	2	2	no	—
124	C₂×C₄×C₁₃₇	—	2	2	no	—
125	C₂×C₄×C₁₃₇	—	2	2	no	—
126	C₂×C₄×C₁₃₇	—	4	1	no	—
127	C₂×C₄×C₁₃₇	—	4	1	no	—
128	C₂×C₄×C₁₃₇	—	4	1	no	—
129	C₂×C₄×C₁₃₇	#95	1	1	yes	characteristic
130	C₂×C₄×C₁₃₇	#95	1	1	yes	characteristic
131	C₂×C₄×C₁₃₇	#95	1	1	yes	characteristic
132	C₂×C₄×C₁₃₇	#95	1	1	yes	characteristic
133	C₂×C₄×C₁₃₇	#95	1	1	yes	characteristic
134	C₂×C₄×C₁₃₇	#95	1	1	yes	characteristic
135	C₂×C₄×C₁₃₇	#108	1	4	yes	—
136	C₂×C₄×C₁₃₇	C₂×C₄²	1	1	yes	characteristic
137	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₃₇	#131	1	4	yes	—
143	C₈×C₁₃₇	—	4	4	no	—
144	C₈×C₁₃₇	—	4	4	no	—
145	C₈×C₁₃₇	—	4	4	no	—
146	C₂²×C₁₃₇	—	2	1	no	—
147	C₂²×C₁₃₇	—	2	1	no	—
148	C₂²×C₁₃₇	—	2	1	no	—
149	C₂²×C₁₃₇	—	2	1	no	—
150	C₂²×C₁₃₇	—	2	1	no	—
151	C₂²×C₁₃₇	—	2	1	no	—
152	C₂²×C₁₃₇	—	2	1	no	—
153	C₂²×C₁₃₇	—	4	4	no	—
154	C₂²×C₁₃₇	#341	1	2	yes	—
155	C₂²×C₁₃₇	C₂×#95	1	1	yes	characteristic
156	C₂²×C₁₃₇	#424	1	2	yes	—
157	C₄×C₁₃₇	—	2	1	no	—
158	C₄×C₁₃₇	—	2	1	no	—
159	C₄×C₁₃₇	—	2	1	no	—
160	C₄×C₁₃₇	—	2	1	no	—
161	C₄×C₁₃₇	—	2	1	no	—
162	C₄×C₁₃₇	—	2	1	no	—
163	C₄×C₁₃₇	—	2	1	no	—
164	C₄×C₁₃₇	#341	1	2	yes	—
165	C₄×C₁₃₇	#405	1	2	yes	—
166	C₄×C₁₃₇	#408	1	2	yes	—
167	C₄×C₁₃₇	#421	1	2	yes	—
168	C₄×C₁₃₇	C₂×#108	1	2	yes	—
169	C₂×C₁₃₇	—	2	2	no	—
170	C₂×C₁₃₇	—	2	2	no	—
171	C₂×C₁₃₇	—	4	1	no	—
172	C₂×C₁₃₇	#1729	1	1	yes	characteristic
173	C₂×C₁₃₇	#1733	1	1	yes	characteristic
174	C₂×C₁₃₇	C₂×#341	1	1	yes	characteristic
175	#7884	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₁₃₇	#7884	1	1	yes	characteristic, direct product factor, Sylow
177	#2920	C₂×C₁₃₇	1	1	yes	characteristic
178	C₂×#431	C₂×C₁₃₇	1	1	yes	characteristic
179	C₂×#431	C₂×C₁₃₇	1	1	yes	characteristic
180	#1278	C₂×C₁₃₇	1	4	yes	complemented
181	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
182	#432	—	2	1	no	—
183	#432	—	2	1	no	—
184	#431	—	2	1	no	—
185	#431	—	2	1	no	—
186	#431	—	2	1	no	—
187	#431	—	2	1	no	—
188	#431	—	2	1	no	—
189	#431	—	2	1	no	—
190	#431	C₄×C₁₃₇	1	2	yes	—
191	#431	C₄×C₁₃₇	1	2	yes	—
192	#431	C₄×C₁₃₇	1	2	yes	—
193	#431	C₂²×C₁₃₇	1	2	yes	—
194	#423	C₄×C₁₃₇	1	2	yes	—
195	C₂×C₄⋊C₈	—	2	1	no	—
196	C₂×C₄⋊C₈	C₄×C₁₃₇	1	2	yes	—
197	#407	C₄×C₁₃₇	1	2	yes	—
198	C₂×C₂²⋊C₈	—	2	1	no	—
199	C₂×C₂²⋊C₈	—	2	1	no	—
200	C₄×M₁₆	C₂²×C₁₃₇	1	2	yes	—
201	C₂×C₄×C₈	—	2	1	no	—
202	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
203	C₂³×C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
204	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
205	C₂³×C₄	Q₈×C₁₃₇	1	1	yes	characteristic
206	C₂×M₁₆	C₂×C₄×C₁₃₇	1	4	yes	—
207	C₂²×C₈	—	2	2	no	—
208	C₂²×C₈	—	2	2	no	—
209	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
210	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
211	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
212	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
213	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
214	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
215	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
216	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
217	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
218	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
219	C₂×C₄²	Q₈×C₁₃₇	1	1	yes	characteristic
220	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
221	C₄⋊C₈	—	2	2	no	—
222	C₄⋊C₈	—	2	2	no	—
223	C₄⋊C₈	—	2	2	no	—
224	C₄⋊C₈	—	2	2	no	—
225	C₄⋊C₈	—	2	2	no	—
226	C₄⋊C₈	C₂×C₄×C₁₃₇	1	4	yes	—
227	C₂²⋊C₈	—	2	2	no	—
228	C₂²⋊C₈	—	2	2	no	—
229	C₂²⋊C₈	—	2	2	no	—
230	C₂²⋊C₈	—	2	2	no	—
231	C₂²⋊C₈	—	2	2	no	—
232	C₂²⋊C₈	—	2	2	no	—
233	#97	—	2	2	no	—
234	C₄×C₈	—	2	2	no	—
235	C₄×C₈	—	2	2	no	—
236	C₄×C₈	—	2	2	no	—
237	C₄×C₈	—	2	2	no	—
238	C₄×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
239	C₂⁴	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
240	C₂²×C₄	—	2	4	no	—
241	C₂²×C₄	—	2	4	no	—
242	C₂²×C₄	—	4	2	no	—
243	C₂²×C₄	C₄²×C₁₃₇	1	1	yes	characteristic
244	C₂²×C₄	C₄²×C₁₃₇	1	1	yes	characteristic
245	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
246	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
247	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
248	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
249	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
250	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
251	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
252	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
253	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
254	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
255	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
256	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
257	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
258	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
259	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
260	C₂²×C₄	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
261	M₁₆	—	2	8	no	—
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	—	2	4	no	—
264	C₂×C₈	—	2	4	no	—
265	C₂×C₈	—	4	4	no	—
266	C₂×C₈	—	4	4	no	—
267	C₄²	C₄²×C₁₃₇	1	1	yes	characteristic
268	C₄²	C₄²×C₁₃₇	1	1	yes	characteristic
269	C₄²	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
270	C₄²	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
271	C₄²	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
272	C₄²	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
273	C₄²	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
274	C₄²	C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
275	C₄²	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
276	C₄²	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
277	C₄²	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
278	C₄²	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
279	C₄²	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
280	C₄²	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
281	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
282	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
283	C₂³	—	2	2	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	4	1	no	—
286	C₂³	#95×C₁₃₇	1	1	yes	characteristic
287	C₂³	#95×C₁₃₇	1	1	yes	characteristic
288	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	4	1	no	—
303	C₂×C₄	—	4	1	no	—
304	C₂×C₄	—	4	1	no	—
305	C₂×C₄	#95×C₁₃₇	1	1	yes	characteristic
306	C₂×C₄	#95×C₁₃₇	1	1	yes	characteristic
307	C₂×C₄	#95×C₁₃₇	1	1	yes	characteristic
308	C₂×C₄	#95×C₁₃₇	1	1	yes	characteristic
309	C₂×C₄	#95×C₁₃₇	1	1	yes	characteristic
310	C₂×C₄	#95×C₁₃₇	1	1	yes	characteristic
311	C₂×C₄	#108×C₁₃₇	1	4	yes	—
312	C₂×C₄	C₂×C₄²×C₁₃₇	1	1	yes	characteristic
313	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
314	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
315	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
316	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
317	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
318	C₂×C₄	#131×C₁₃₇	1	4	yes	—
319	C₈	—	4	4	no	—
320	C₈	—	4	4	no	—
321	C₈	—	4	4	no	—
322	C₂²	—	2	1	no	—
323	C₂²	—	2	1	no	—
324	C₂²	—	2	1	no	—
325	C₂²	—	2	1	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	2	1	no	—
328	C₂²	—	2	1	no	—
329	C₂²	—	4	4	no	—
330	C₂²	#341×C₁₃₇	1	2	yes	—
331	C₂²	C₂×#95×C₁₃₇	1	1	yes	characteristic
332	C₂²	#424×C₁₃₇	1	2	yes	—
333	C₄	—	2	1	no	—
334	C₄	—	2	1	no	—
335	C₄	—	2	1	no	—
336	C₄	—	2	1	no	—
337	C₄	—	2	1	no	—
338	C₄	—	2	1	no	—
339	C₄	—	2	1	no	—
340	C₄	#341×C₁₃₇	1	2	yes	—
341	C₄	#405×C₁₃₇	1	2	yes	—
342	C₄	#408×C₁₃₇	1	2	yes	—
343	C₄	#421×C₁₃₇	1	2	yes	—
344	C₄	C₂×#108×C₁₃₇	1	2	yes	—
345	C₂	—	2	2	no	—
346	C₂	—	2	2	no	—
347	C₂	—	4	1	no	—
348	C₂	#1729×C₁₃₇	1	1	yes	characteristic
349	C₂	#1733×C₁₃₇	1	1	yes	characteristic
350	C₂	C₂×#341×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₁₃₇	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₃₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₇
socle	C₂²×C₁₃₇	C₂×#95
prime radical	C₂⁴×C₁₃₇	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₃₇ ◁ C₂²×C₄²×C₁₃₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. #1278×C₁₃₇	C₂	semidirect
175. #7884	C₁₃₇	direct (N × H)
176. C₁₃₇	#7884	direct (N × H)
180. #1278	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#2920×C₁₃₇	2
C₂×#431×C₁₃₇	2
#1278×C₁₃₇	2
#7884	137

Subgroups — C137×#7884 #46857270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#7884 #46857270