Subgroups — C₁₃₇×#28778 #46878164

Order 35072.

702 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2441×C₁₃₇	C₂	1	2	yes	maximal
2	#2083×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	#2059×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#1992×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1944×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1854×C₁₃₇	C₂	1	2	yes	maximal
7	#1808×C₁₃₇	C₂	1	1	yes	maximal, characteristic
8	#1752×C₁₃₇	C₂	1	1	yes	maximal, characteristic
9	#1735×C₁₃₇	C₂	1	1	yes	maximal, characteristic
10	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
11	C₂×#125×C₁₃₇	C₂²	1	2	yes	—
12	C₂×#117×C₁₃₇	C₂²	1	2	yes	—
13	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
14	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
15	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
18	#399×C₁₃₇	—	2	2	no	—
19	#396×C₁₃₇	—	2	2	no	—
20	#389×C₁₃₇	—	2	2	no	—
21	#389×C₁₃₇	C₂²	1	2	yes	—
22	#389×C₁₃₇	C₂²	1	2	yes	—
23	#387×C₁₃₇	—	2	2	no	—
24	#384×C₁₃₇	C₂²	1	2	yes	—
25	#380×C₁₃₇	C₂²	1	2	yes	—
26	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
27	#340×C₁₃₇	C₂²	1	1	yes	characteristic
28	#340×C₁₃₇	C₂²	1	2	yes	—
29	#340×C₁₃₇	C₂²	1	1	yes	characteristic
30	#340×C₁₃₇	C₂²	1	1	yes	characteristic
31	#340×C₁₃₇	C₂²	1	1	yes	characteristic
32	#340×C₁₃₇	C₂²	1	2	yes	—
33	#340×C₁₃₇	C₂²	1	2	yes	—
34	#336×C₁₃₇	C₂²	1	2	yes	—
35	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₁₃₇	—	4	2	no	—
37	C₂²×C₈×C₁₃₇	Q₈	1	4	yes	—
38	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
41	#125×C₁₃₇	—	2	4	no	—
42	#125×C₁₃₇	—	4	2	no	—
43	#117×C₁₃₇	—	2	4	no	—
44	#117×C₁₃₇	—	4	2	no	—
45	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
55	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₁₃₇	D₄	1	2	yes	—
58	C₂×C₄²×C₁₃₇	—	2	2	no	—
59	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
60	#107×C₁₃₇	—	4	2	no	—
61	#107×C₁₃₇	—	4	2	no	—
62	#106×C₁₃₇	—	2	4	no	—
63	C₂²⋊C₈×C₁₃₇	Q₈	1	4	yes	—
64	#97×C₁₃₇	—	4	2	no	—
65	#95×C₁₃₇	—	2	2	no	—
66	#95×C₁₃₇	—	2	2	no	—
67	#95×C₁₃₇	—	2	2	no	—
68	#95×C₁₃₇	D₄	1	1	yes	characteristic
69	#95×C₁₃₇	D₄	1	1	yes	characteristic
70	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₃₇	—	2	2	no	—
72	C₂²×C₄×C₁₃₇	—	2	2	no	—
73	C₂²×C₄×C₁₃₇	—	2	2	no	—
74	C₂²×C₄×C₁₃₇	—	2	2	no	—
75	C₂²×C₄×C₁₃₇	—	2	2	no	—
76	C₂²×C₄×C₁₃₇	—	2	2	no	—
77	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
78	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
81	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
82	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
83	C₂×C₈×C₁₃₇	—	2	2	no	—
84	C₂×C₈×C₁₃₇	—	2	2	no	—
85	C₂×C₈×C₁₃₇	—	2	2	no	—
86	C₂×C₈×C₁₃₇	—	2	2	no	—
87	C₂×C₈×C₁₃₇	—	4	4	no	—
88	C₂×C₈×C₁₃₇	C₂×Q₈	1	4	yes	—
89	C₂×C₈×C₁₃₇	C₂×Q₈	1	2	yes	—
90	C₂×C₈×C₁₃₇	C₂×Q₈	1	2	yes	—
91	C₄⋊C₄×C₁₃₇	—	2	2	no	—
92	C₄⋊C₄×C₁₃₇	—	2	2	no	—
93	C₄⋊C₄×C₁₃₇	—	2	2	no	—
94	C₄⋊C₄×C₁₃₇	—	2	2	no	—
95	C₄⋊C₄×C₁₃₇	—	2	2	no	—
96	C₄⋊C₄×C₁₃₇	—	2	2	no	—
97	C₄⋊C₄×C₁₃₇	—	2	2	no	—
98	C₄⋊C₄×C₁₃₇	—	4	4	no	—
99	C₄⋊C₄×C₁₃₇	—	4	4	no	—
100	C₄⋊C₄×C₁₃₇	—	4	4	no	—
101	C₄⋊C₄×C₁₃₇	—	4	4	no	—
102	C₄⋊C₄×C₁₃₇	—	8	2	no	—
103	C₄⋊C₄×C₁₃₇	—	8	2	no	—
104	C₄⋊C₄×C₁₃₇	#41	1	4	yes	—
105	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
106	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
107	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
108	C₄²×C₁₃₇	—	2	2	no	—
109	C₄²×C₁₃₇	—	2	2	no	—
110	C₄²×C₁₃₇	—	4	4	no	—
111	C₂³×C₁₃₇	—	2	2	no	—
112	C₂³×C₁₃₇	—	2	2	no	—
113	C₂³×C₁₃₇	—	2	1	no	—
114	C₂³×C₁₃₇	—	2	1	no	—
115	C₂³×C₁₃₇	C₄⋊Q₈	1	2	yes	—
116	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
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	4	no	—
121	C₂×C₄×C₁₃₇	—	2	2	no	—
122	C₂×C₄×C₁₃₇	—	2	2	no	—
123	C₂×C₄×C₁₃₇	—	2	4	no	—
124	C₂×C₄×C₁₃₇	—	2	2	no	—
125	C₂×C₄×C₁₃₇	—	2	2	no	—
126	C₂×C₄×C₁₃₇	—	2	2	no	—
127	C₂×C₄×C₁₃₇	—	2	2	no	—
128	C₂×C₄×C₁₃₇	—	4	2	no	—
129	C₂×C₄×C₁₃₇	—	4	2	no	—
130	C₂×C₄×C₁₃₇	—	4	2	no	—
131	C₂×C₄×C₁₃₇	—	4	2	no	—
132	C₂×C₄×C₁₃₇	—	4	2	no	—
133	C₂×C₄×C₁₃₇	—	4	2	no	—
134	C₂×C₄×C₁₃₇	—	4	2	no	—
135	C₂×C₄×C₁₃₇	—	4	2	no	—
136	C₂×C₄×C₁₃₇	—	4	2	no	—
137	C₂×C₄×C₁₃₇	—	4	2	no	—
138	C₂×C₄×C₁₃₇	—	4	2	no	—
139	C₂×C₄×C₁₃₇	C₄⋊Q₈	1	2	yes	—
140	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
141	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
142	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
143	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
144	C₈×C₁₃₇	—	2	2	no	—
145	C₈×C₁₃₇	—	2	2	no	—
146	C₈×C₁₃₇	—	2	4	no	—
147	C₂²×C₁₃₇	—	2	2	no	—
148	C₂²×C₁₃₇	—	2	2	no	—
149	C₂²×C₁₃₇	—	2	2	no	—
150	C₂²×C₁₃₇	—	4	2	no	—
151	C₂²×C₁₃₇	—	4	2	no	—
152	C₂²×C₁₃₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
153	C₂²×C₁₃₇	#546	1	2	yes	—
154	C₂²×C₁₃₇	#575	1	2	yes	—
155	C₂²×C₁₃₇	#576	1	1	yes	characteristic
156	C₂²×C₁₃₇	#578	1	1	yes	characteristic
157	C₄×C₁₃₇	—	2	2	no	—
158	C₄×C₁₃₇	—	4	2	no	—
159	C₄×C₁₃₇	—	4	2	no	—
160	C₄×C₁₃₇	—	4	4	no	—
161	C₄×C₁₃₇	—	8	2	no	—
162	C₄×C₁₃₇	—	8	2	no	—
163	C₄×C₁₃₇	—	8	2	no	—
164	C₄×C₁₃₇	#533	1	1	yes	characteristic
165	C₄×C₁₃₇	#543	1	1	yes	characteristic
166	C₄×C₁₃₇	#554	1	2	yes	—
167	C₂×C₁₃₇	—	4	2	no	—
168	C₂×C₁₃₇	#2549	1	1	yes	characteristic
169	C₂×C₁₃₇	#3162	1	1	yes	characteristic
170	C₂×C₁₃₇	#3164	1	1	yes	characteristic
171	C₂×C₁₃₇	#3309	1	2	yes	—
172	C₂×C₁₃₇	#3315	1	2	yes	—
173	#28778	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₁₃₇	#28778	1	1	yes	characteristic, direct product factor, Sylow
175	#2441	C₂×C₁₃₇	1	2	yes	—
176	#2083	C₂×C₁₃₇	1	2	yes	complemented
177	#2059	C₂×C₁₃₇	1	2	yes	complemented
178	#1992	C₂×C₁₃₇	1	2	yes	complemented
179	#1944	C₂×C₁₃₇	1	2	yes	complemented
180	#1854	C₂×C₁₃₇	1	2	yes	—
181	#1808	C₂×C₁₃₇	1	1	yes	characteristic
182	#1752	C₂×C₁₃₇	1	1	yes	characteristic
183	#1735	C₂×C₁₃₇	1	1	yes	characteristic
184	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
185	C₂×#125	C₂²×C₁₃₇	1	2	yes	—
186	C₂×#117	C₂²×C₁₃₇	1	2	yes	—
187	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
188	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
189	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
190	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
191	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
192	#399	—	2	2	no	—
193	#396	—	2	2	no	—
194	#389	—	2	2	no	—
195	#389	C₂²×C₁₃₇	1	2	yes	—
196	#389	C₂²×C₁₃₇	1	2	yes	—
197	#387	—	2	2	no	—
198	#384	C₂²×C₁₃₇	1	2	yes	—
199	#380	C₂²×C₁₃₇	1	2	yes	—
200	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
201	#340	C₂²×C₁₃₇	1	1	yes	characteristic
202	#340	C₂²×C₁₃₇	1	2	yes	—
203	#340	C₂²×C₁₃₇	1	1	yes	characteristic
204	#340	C₂²×C₁₃₇	1	1	yes	characteristic
205	#340	C₂²×C₁₃₇	1	1	yes	characteristic
206	#340	C₂²×C₁₃₇	1	2	yes	—
207	#340	C₂²×C₁₃₇	1	2	yes	—
208	#336	C₂²×C₁₃₇	1	2	yes	—
209	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
210	C₂²×C₈	—	4	2	no	—
211	C₂²×C₈	Q₈×C₁₃₇	1	4	yes	—
212	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
213	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
214	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
215	#125	—	2	4	no	—
216	#125	—	4	2	no	—
217	#117	—	2	4	no	—
218	#117	—	4	2	no	—
219	C₂×C₄⋊C₄	—	2	2	no	—
220	C₂×C₄⋊C₄	—	2	2	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
226	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
227	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
228	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
229	C₂×C₂²⋊C₄	—	2	2	no	—
230	C₂×C₂²⋊C₄	—	2	2	no	—
231	C₂×C₂²⋊C₄	D₄×C₁₃₇	1	2	yes	—
232	C₂×C₄²	—	2	2	no	—
233	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
234	#107	—	4	2	no	—
235	#107	—	4	2	no	—
236	#106	—	2	4	no	—
237	C₂²⋊C₈	Q₈×C₁₃₇	1	4	yes	—
238	#97	—	4	2	no	—
239	#95	—	2	2	no	—
240	#95	—	2	2	no	—
241	#95	—	2	2	no	—
242	#95	D₄×C₁₃₇	1	1	yes	characteristic
243	#95	D₄×C₁₃₇	1	1	yes	characteristic
244	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
252	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
253	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
254	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
255	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
256	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	4	4	no	—
262	C₂×C₈	C₂×Q₈×C₁₃₇	1	4	yes	—
263	C₂×C₈	C₂×Q₈×C₁₃₇	1	2	yes	—
264	C₂×C₈	C₂×Q₈×C₁₃₇	1	2	yes	—
265	C₄⋊C₄	—	2	2	no	—
266	C₄⋊C₄	—	2	2	no	—
267	C₄⋊C₄	—	2	2	no	—
268	C₄⋊C₄	—	2	2	no	—
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	—	2	2	no	—
271	C₄⋊C₄	—	2	2	no	—
272	C₄⋊C₄	—	4	4	no	—
273	C₄⋊C₄	—	4	4	no	—
274	C₄⋊C₄	—	4	4	no	—
275	C₄⋊C₄	—	4	4	no	—
276	C₄⋊C₄	—	8	2	no	—
277	C₄⋊C₄	—	8	2	no	—
278	C₄⋊C₄	#41×C₁₃₇	1	4	yes	—
279	C₂²⋊C₄	—	4	2	no	—
280	C₂²⋊C₄	—	4	4	no	—
281	C₂²⋊C₄	—	8	2	no	—
282	C₄²	—	2	2	no	—
283	C₄²	—	2	2	no	—
284	C₄²	—	4	4	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	2	no	—
287	C₂³	—	2	1	no	—
288	C₂³	—	2	1	no	—
289	C₂³	C₄⋊Q₈×C₁₃₇	1	2	yes	—
290	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	4	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	2	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	C₄⋊Q₈×C₁₃₇	1	2	yes	—
314	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
315	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
316	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
317	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
318	C₈	—	2	2	no	—
319	C₈	—	2	2	no	—
320	C₈	—	2	4	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	4	2	no	—
325	C₂²	—	4	2	no	—
326	C₂²	C₂×C₄⋊Q₈×C₁₃₇	1	1	yes	characteristic
327	C₂²	#546×C₁₃₇	1	2	yes	—
328	C₂²	#575×C₁₃₇	1	2	yes	—
329	C₂²	#576×C₁₃₇	1	1	yes	characteristic
330	C₂²	#578×C₁₃₇	1	1	yes	characteristic
331	C₄	—	2	2	no	—
332	C₄	—	4	2	no	—
333	C₄	—	4	2	no	—
334	C₄	—	4	4	no	—
335	C₄	—	8	2	no	—
336	C₄	—	8	2	no	—
337	C₄	—	8	2	no	—
338	C₄	#533×C₁₃₇	1	1	yes	characteristic
339	C₄	#543×C₁₃₇	1	1	yes	characteristic
340	C₄	#554×C₁₃₇	1	2	yes	—
341	C₂	—	4	2	no	—
342	C₂	#2549×C₁₃₇	1	1	yes	characteristic
343	C₂	#3162×C₁₃₇	1	1	yes	characteristic
344	C₂	#3164×C₁₃₇	1	1	yes	characteristic
345	C₂	#3309×C₁₃₇	1	2	yes	—
346	C₂	#3315×C₁₃₇	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. #2083×C₁₃₇	C₂	semidirect
3. #2059×C₁₃₇	C₂	semidirect
4. #1992×C₁₃₇	C₂	semidirect
5. #1944×C₁₃₇	C₂	semidirect
173. #28778	C₁₃₇	direct (N × H)
174. C₁₃₇	#28778	direct (N × H)
176. #2083	C₂×C₁₃₇	semidirect
177. #2059	C₂×C₁₃₇	semidirect
178. #1992	C₂×C₁₃₇	semidirect
179. #1944	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#2441×C₁₃₇	2
#2083×C₁₃₇	2
#2059×C₁₃₇	2
#1992×C₁₃₇	2
#1944×C₁₃₇	2
#1854×C₁₃₇	2
#1808×C₁₃₇	2
#1752×C₁₃₇	2
#1735×C₁₃₇	2
#28778	137

Subgroups — C137×#28778 #46878164

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28778 #46878164