Subgroups — C₁₃₇×#10311 #46859697

Order 35072.

622 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#487×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#486×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#486×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1990×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1957×C₁₃₇	C₂	1	1	yes	maximal, characteristic
6	#1956×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1273×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
10	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
11	#487×C₁₃₇	—	2	2	no	—
12	#487×C₁₃₇	—	2	2	no	—
13	#486×C₁₃₇	—	2	2	no	—
14	#486×C₁₃₇	—	2	2	no	—
15	#486×C₁₃₇	—	2	2	no	—
16	#486×C₁₃₇	—	2	2	no	—
17	C₂×#103×C₁₃₇	—	2	2	no	—
18	C₂×#103×C₁₃₇	—	2	2	no	—
19	C₂×#102×C₁₃₇	—	2	2	no	—
20	C₂×#102×C₁₃₇	—	2	2	no	—
21	C₂×#102×C₁₃₇	—	2	2	no	—
22	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
25	#384×C₁₃₇	C₂²	1	1	yes	characteristic
26	#340×C₁₃₇	—	2	2	no	—
27	C₂²×Q₈×C₁₃₇	—	2	1	no	—
28	C₂²×Q₈×C₁₃₇	—	2	1	no	—
29	C₂²×D₄×C₁₃₇	—	2	1	no	—
30	C₂²×D₄×C₁₃₇	—	2	1	no	—
31	C₂²×D₄×C₁₃₇	—	2	1	no	—
32	C₂²×C₈×C₁₃₇	D₄	1	2	yes	—
33	C₂²×C₈×C₁₃₇	D₄	1	2	yes	—
34	C₂²×C₈×C₁₃₇	D₄	1	2	yes	—
35	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
36	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
37	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
38	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
39	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
40	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
41	C₄⋊Q₈×C₁₃₇	D₄	1	2	yes	—
42	C₄⋊Q₈×C₁₃₇	D₄	1	2	yes	—
43	#127×C₁₃₇	—	2	1	no	—
44	#127×C₁₃₇	—	2	1	no	—
45	#127×C₁₃₇	—	2	1	no	—
46	#127×C₁₃₇	D₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
54	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
55	#103×C₁₃₇	—	2	8	no	—
56	#103×C₁₃₇	—	4	4	no	—
57	#102×C₁₃₇	—	2	8	no	—
58	#102×C₁₃₇	—	2	8	no	—
59	#102×C₁₃₇	—	4	4	no	—
60	C₄×C₈×C₁₃₇	—	2	1	no	—
61	C₄×C₈×C₁₃₇	—	2	1	no	—
62	C₄×C₈×C₁₃₇	—	2	1	no	—
63	C₄×C₈×C₁₃₇	—	2	1	no	—
64	C₄×C₈×C₁₃₇	—	2	1	no	—
65	C₄×C₈×C₁₃₇	—	2	1	no	—
66	C₂⁴×C₁₃₇	—	4	1	no	—
67	C₂×Q₈×C₁₃₇	—	2	2	no	—
68	C₂×Q₈×C₁₃₇	—	2	2	no	—
69	C₂×Q₈×C₁₃₇	—	4	1	no	—
70	C₂×Q₈×C₁₃₇	—	4	1	no	—
71	C₂×Q₈×C₁₃₇	—	4	2	no	—
72	C₂×Q₈×C₁₃₇	—	4	2	no	—
73	C₂×Q₈×C₁₃₇	—	4	2	no	—
74	C₂×Q₈×C₁₃₇	—	4	2	no	—
75	C₂×D₄×C₁₃₇	—	2	2	no	—
76	C₂×D₄×C₁₃₇	—	2	2	no	—
77	C₂×D₄×C₁₃₇	—	2	2	no	—
78	C₂×D₄×C₁₃₇	—	4	1	no	—
79	C₂×D₄×C₁₃₇	—	4	1	no	—
80	C₂×D₄×C₁₃₇	—	4	1	no	—
81	C₂×D₄×C₁₃₇	—	4	2	no	—
82	C₂×D₄×C₁₃₇	—	4	2	no	—
83	C₂×D₄×C₁₃₇	—	4	2	no	—
84	C₂×D₄×C₁₃₇	—	4	2	no	—
85	C₂×D₄×C₁₃₇	—	4	2	no	—
86	C₂×D₄×C₁₃₇	—	4	2	no	—
87	C₂²×C₄×C₁₃₇	—	4	1	no	—
88	C₂²×C₄×C₁₃₇	—	4	1	no	—
89	C₂²×C₄×C₁₃₇	—	4	1	no	—
90	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
93	C₂×C₈×C₁₃₇	—	2	2	no	—
94	C₂×C₈×C₁₃₇	—	2	2	no	—
95	C₂×C₈×C₁₃₇	—	2	2	no	—
96	C₂×C₈×C₁₃₇	—	2	2	no	—
97	C₂×C₈×C₁₃₇	—	2	2	no	—
98	C₂×C₈×C₁₃₇	—	2	2	no	—
99	C₂×C₈×C₁₃₇	—	2	2	no	—
100	C₂×C₈×C₁₃₇	—	2	2	no	—
101	C₂×C₈×C₁₃₇	—	2	2	no	—
102	C₄⋊C₄×C₁₃₇	—	2	2	no	—
103	C₄⋊C₄×C₁₃₇	—	2	2	no	—
104	C₄⋊C₄×C₁₃₇	—	2	2	no	—
105	C₄⋊C₄×C₁₃₇	—	2	2	no	—
106	C₄⋊C₄×C₁₃₇	—	4	1	no	—
107	C₄⋊C₄×C₁₃₇	—	4	1	no	—
108	C₄⋊C₄×C₁₃₇	—	4	1	no	—
109	C₄⋊C₄×C₁₃₇	—	4	1	no	—
110	C₄⋊C₄×C₁₃₇	—	4	2	no	—
111	C₄⋊C₄×C₁₃₇	—	4	2	no	—
112	C₄⋊C₄×C₁₃₇	—	4	2	no	—
113	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₁₃₇	#41	1	1	yes	characteristic
117	C₂³×C₁₃₇	—	4	2	no	—
118	C₂³×C₁₃₇	—	8	1	no	—
119	C₂³×C₁₃₇	—	8	1	no	—
120	C₂³×C₁₃₇	—	8	1	no	—
121	C₂³×C₁₃₇	—	8	1	no	—
122	C₂³×C₁₃₇	—	8	1	no	—
123	C₂³×C₁₃₇	—	8	1	no	—
124	C₂³×C₁₃₇	#127	1	1	yes	characteristic
125	Q₈×C₁₃₇	—	4	4	no	—
126	Q₈×C₁₃₇	—	4	4	no	—
127	Q₈×C₁₃₇	—	8	2	no	—
128	Q₈×C₁₃₇	—	8	2	no	—
129	D₄×C₁₃₇	—	4	4	no	—
130	D₄×C₁₃₇	—	4	4	no	—
131	D₄×C₁₃₇	—	4	4	no	—
132	D₄×C₁₃₇	—	8	2	no	—
133	D₄×C₁₃₇	—	8	2	no	—
134	D₄×C₁₃₇	—	8	2	no	—
135	C₂×C₄×C₁₃₇	—	4	2	no	—
136	C₂×C₄×C₁₃₇	—	4	2	no	—
137	C₂×C₄×C₁₃₇	—	8	1	no	—
138	C₂×C₄×C₁₃₇	—	8	1	no	—
139	C₂×C₄×C₁₃₇	—	8	1	no	—
140	C₂×C₄×C₁₃₇	—	8	1	no	—
141	C₂×C₄×C₁₃₇	—	8	1	no	—
142	C₂×C₄×C₁₃₇	—	8	1	no	—
143	C₂×C₄×C₁₃₇	—	8	1	no	—
144	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
145	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
146	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
147	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
148	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
149	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
150	C₂×C₄×C₁₃₇	#135	1	2	yes	—
151	C₂×C₄×C₁₃₇	#135	1	2	yes	—
152	C₂×C₄×C₁₃₇	#135	1	2	yes	—
153	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
154	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
155	C₂×C₄×C₁₃₇	#137	1	2	yes	—
156	C₈×C₁₃₇	—	4	2	no	—
157	C₈×C₁₃₇	—	4	2	no	—
158	C₈×C₁₃₇	—	4	2	no	—
159	C₂²×C₁₃₇	—	8	2	no	—
160	C₂²×C₁₃₇	—	8	2	no	—
161	C₂²×C₁₃₇	—	8	2	no	—
162	C₂²×C₁₃₇	—	16	1	no	—
163	C₂²×C₁₃₇	—	16	1	no	—
164	C₂²×C₁₃₇	—	16	1	no	—
165	C₂²×C₁₃₇	—	16	1	no	—
166	C₂²×C₁₃₇	#392	1	1	yes	characteristic
167	C₂²×C₁₃₇	#495	1	1	yes	characteristic
168	C₂²×C₁₃₇	#495	1	1	yes	characteristic
169	C₂²×C₁₃₇	#495	1	1	yes	characteristic
170	C₂²×C₁₃₇	#496	1	1	yes	characteristic
171	C₂²×C₁₃₇	#496	1	1	yes	characteristic
172	C₂²×C₁₃₇	#497	1	1	yes	characteristic
173	C₄×C₁₃₇	—	8	2	no	—
174	C₄×C₁₃₇	—	8	2	no	—
175	C₄×C₁₃₇	—	16	1	no	—
176	C₄×C₁₃₇	#449	1	2	yes	—
177	C₄×C₁₃₇	#449	1	2	yes	—
178	C₄×C₁₃₇	#452	1	2	yes	—
179	C₄×C₁₃₇	#463	1	2	yes	—
180	C₄×C₁₃₇	#463	1	2	yes	—
181	C₄×C₁₃₇	#464	1	2	yes	—
182	C₂×C₁₃₇	—	16	2	no	—
183	C₂×C₁₃₇	#1711	1	1	yes	characteristic
184	C₂×C₁₃₇	#1717	1	1	yes	characteristic
185	C₂×C₁₃₇	#1719	1	1	yes	characteristic
186	C₂×C₁₃₇	#1720	1	1	yes	characteristic
187	C₂×C₁₃₇	#2012	1	1	yes	characteristic
188	C₂×C₁₃₇	#2012	1	1	yes	characteristic
189	C₂×C₁₃₇	#2015	1	1	yes	characteristic
190	#10311	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₁₃₇	#10311	1	1	yes	characteristic, direct product factor, Sylow
192	C₂×#487	C₂×C₁₃₇	1	1	yes	characteristic, complemented
193	C₂×#486	C₂×C₁₃₇	1	1	yes	characteristic
194	C₂×#486	C₂×C₁₃₇	1	1	yes	characteristic
195	#1990	C₂×C₁₃₇	1	1	yes	characteristic, complemented
196	#1957	C₂×C₁₃₇	1	1	yes	characteristic
197	#1956	C₂×C₁₃₇	1	1	yes	characteristic, complemented
198	#1273	C₂×C₁₃₇	1	1	yes	characteristic, complemented
199	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
200	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
201	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
202	#487	—	2	2	no	—
203	#487	—	2	2	no	—
204	#486	—	2	2	no	—
205	#486	—	2	2	no	—
206	#486	—	2	2	no	—
207	#486	—	2	2	no	—
208	C₂×#103	—	2	2	no	—
209	C₂×#103	—	2	2	no	—
210	C₂×#102	—	2	2	no	—
211	C₂×#102	—	2	2	no	—
212	C₂×#102	—	2	2	no	—
213	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
214	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
215	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
216	#384	C₂²×C₁₃₇	1	1	yes	characteristic
217	#340	—	2	2	no	—
218	C₂²×Q₈	—	2	1	no	—
219	C₂²×Q₈	—	2	1	no	—
220	C₂²×D₄	—	2	1	no	—
221	C₂²×D₄	—	2	1	no	—
222	C₂²×D₄	—	2	1	no	—
223	C₂²×C₈	D₄×C₁₃₇	1	2	yes	—
224	C₂²×C₈	D₄×C₁₃₇	1	2	yes	—
225	C₂²×C₈	D₄×C₁₃₇	1	2	yes	—
226	C₄⋊Q₈	—	2	1	no	—
227	C₄⋊Q₈	—	2	1	no	—
228	C₄⋊Q₈	—	2	1	no	—
229	C₄⋊Q₈	—	2	1	no	—
230	C₄⋊Q₈	—	2	1	no	—
231	C₄⋊Q₈	—	2	1	no	—
232	C₄⋊Q₈	D₄×C₁₃₇	1	2	yes	—
233	C₄⋊Q₈	D₄×C₁₃₇	1	2	yes	—
234	#127	—	2	1	no	—
235	#127	—	2	1	no	—
236	#127	—	2	1	no	—
237	#127	D₄×C₁₃₇	1	2	yes	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
246	#103	—	2	8	no	—
247	#103	—	4	4	no	—
248	#102	—	2	8	no	—
249	#102	—	2	8	no	—
250	#102	—	4	4	no	—
251	C₄×C₈	—	2	1	no	—
252	C₄×C₈	—	2	1	no	—
253	C₄×C₈	—	2	1	no	—
254	C₄×C₈	—	2	1	no	—
255	C₄×C₈	—	2	1	no	—
256	C₄×C₈	—	2	1	no	—
257	C₂⁴	—	4	1	no	—
258	C₂×Q₈	—	2	2	no	—
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	—	4	1	no	—
261	C₂×Q₈	—	4	1	no	—
262	C₂×Q₈	—	4	2	no	—
263	C₂×Q₈	—	4	2	no	—
264	C₂×Q₈	—	4	2	no	—
265	C₂×Q₈	—	4	2	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	4	1	no	—
270	C₂×D₄	—	4	1	no	—
271	C₂×D₄	—	4	1	no	—
272	C₂×D₄	—	4	2	no	—
273	C₂×D₄	—	4	2	no	—
274	C₂×D₄	—	4	2	no	—
275	C₂×D₄	—	4	2	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	4	1	no	—
298	C₄⋊C₄	—	4	1	no	—
299	C₄⋊C₄	—	4	1	no	—
300	C₄⋊C₄	—	4	1	no	—
301	C₄⋊C₄	—	4	2	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
305	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
306	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
307	C₄²	#41×C₁₃₇	1	1	yes	characteristic
308	C₂³	—	4	2	no	—
309	C₂³	—	8	1	no	—
310	C₂³	—	8	1	no	—
311	C₂³	—	8	1	no	—
312	C₂³	—	8	1	no	—
313	C₂³	—	8	1	no	—
314	C₂³	—	8	1	no	—
315	C₂³	#127×C₁₃₇	1	1	yes	characteristic
316	Q₈	—	4	4	no	—
317	Q₈	—	4	4	no	—
318	Q₈	—	8	2	no	—
319	Q₈	—	8	2	no	—
320	D₄	—	4	4	no	—
321	D₄	—	4	4	no	—
322	D₄	—	4	4	no	—
323	D₄	—	8	2	no	—
324	D₄	—	8	2	no	—
325	D₄	—	8	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	8	1	no	—
329	C₂×C₄	—	8	1	no	—
330	C₂×C₄	—	8	1	no	—
331	C₂×C₄	—	8	1	no	—
332	C₂×C₄	—	8	1	no	—
333	C₂×C₄	—	8	1	no	—
334	C₂×C₄	—	8	1	no	—
335	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
336	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
337	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
338	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
339	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
340	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
341	C₂×C₄	#135×C₁₃₇	1	2	yes	—
342	C₂×C₄	#135×C₁₃₇	1	2	yes	—
343	C₂×C₄	#135×C₁₃₇	1	2	yes	—
344	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
345	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
346	C₂×C₄	#137×C₁₃₇	1	2	yes	—
347	C₈	—	4	2	no	—
348	C₈	—	4	2	no	—
349	C₈	—	4	2	no	—
350	C₂²	—	8	2	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	8	2	no	—
353	C₂²	—	16	1	no	—
354	C₂²	—	16	1	no	—
355	C₂²	—	16	1	no	—
356	C₂²	—	16	1	no	—
357	C₂²	#392×C₁₃₇	1	1	yes	characteristic
358	C₂²	#495×C₁₃₇	1	1	yes	characteristic
359	C₂²	#495×C₁₃₇	1	1	yes	characteristic
360	C₂²	#495×C₁₃₇	1	1	yes	characteristic
361	C₂²	#496×C₁₃₇	1	1	yes	characteristic
362	C₂²	#496×C₁₃₇	1	1	yes	characteristic
363	C₂²	#497×C₁₃₇	1	1	yes	characteristic
364	C₄	—	8	2	no	—
365	C₄	—	8	2	no	—
366	C₄	—	16	1	no	—
367	C₄	#449×C₁₃₇	1	2	yes	—
368	C₄	#449×C₁₃₇	1	2	yes	—
369	C₄	#452×C₁₃₇	1	2	yes	—
370	C₄	#463×C₁₃₇	1	2	yes	—
371	C₄	#463×C₁₃₇	1	2	yes	—
372	C₄	#464×C₁₃₇	1	2	yes	—
373	C₂	—	16	2	no	—
374	C₂	#1711×C₁₃₇	1	1	yes	characteristic
375	C₂	#1717×C₁₃₇	1	1	yes	characteristic
376	C₂	#1719×C₁₃₇	1	1	yes	characteristic
377	C₂	#1720×C₁₃₇	1	1	yes	characteristic
378	C₂	#2012×C₁₃₇	1	1	yes	characteristic
379	C₂	#2012×C₁₃₇	1	1	yes	characteristic
380	C₂	#2015×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₇	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₇
prime radical	C₂×#127×C₁₃₇	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#487×C₁₃₇	C₂	semidirect
4. #1990×C₁₃₇	C₂	semidirect
6. #1956×C₁₃₇	C₂	semidirect
7. #1273×C₁₃₇	C₂	semidirect
190. #10311	C₁₃₇	direct (N × H)
191. C₁₃₇	#10311	direct (N × H)
192. C₂×#487	C₂×C₁₃₇	semidirect
195. #1990	C₂×C₁₃₇	semidirect
197. #1956	C₂×C₁₃₇	semidirect
198. #1273	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#487×C₁₃₇	2
C₂×#486×C₁₃₇	2
#1990×C₁₃₇	2
#1957×C₁₃₇	2
#1956×C₁₃₇	2
#1273×C₁₃₇	2
#10311	137

Subgroups — C137×#10311 #46859697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#10311 #46859697