Subgroups — C₁₃₇×#10308 #46859694

Order 35072.

686 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#500×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#492×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	C₂²×SD₁₆×C₁₃₇	—	2	2	no	—
9	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
11	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
12	#500×C₁₃₇	—	2	2	no	—
13	#500×C₁₃₇	—	2	2	no	—
14	#492×C₁₃₇	—	2	2	no	—
15	#492×C₁₃₇	—	2	2	no	—
16	#486×C₁₃₇	—	2	2	no	—
17	#486×C₁₃₇	—	2	2	no	—
18	C₂×#107×C₁₃₇	—	2	2	no	—
19	C₂×#103×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	C₂×SD₁₆×C₁₃₇	—	2	8	no	—
33	C₂×SD₁₆×C₁₃₇	—	4	4	no	—
34	C₂×SD₁₆×C₁₃₇	—	4	4	no	—
35	C₂²×C₈×C₁₃₇	D₄	1	2	yes	—
36	C₂²×C₈×C₁₃₇	D₄	1	2	yes	—
37	C₂²×C₈×C₁₃₇	D₄	1	2	yes	—
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	—	2	1	no	—
42	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
43	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
44	C₄⋊Q₈×C₁₃₇	D₄	1	2	yes	—
45	C₄⋊Q₈×C₁₃₇	D₄	1	2	yes	—
46	#127×C₁₃₇	—	2	1	no	—
47	#127×C₁₃₇	—	2	1	no	—
48	#127×C₁₃₇	—	2	1	no	—
49	#127×C₁₃₇	D₄	1	2	yes	—
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×C₄⋊C₄×C₁₃₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
57	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
58	#107×C₁₃₇	—	2	8	no	—
59	#103×C₁₃₇	—	4	4	no	—
60	#102×C₁₃₇	—	2	8	no	—
61	#102×C₁₃₇	—	4	4	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	C₄×C₈×C₁₃₇	—	2	1	no	—
67	C₄×C₈×C₁₃₇	—	2	1	no	—
68	C₂⁴×C₁₃₇	—	4	1	no	—
69	C₂×Q₈×C₁₃₇	—	2	2	no	—
70	C₂×Q₈×C₁₃₇	—	2	2	no	—
71	C₂×Q₈×C₁₃₇	—	4	1	no	—
72	C₂×Q₈×C₁₃₇	—	4	1	no	—
73	C₂×Q₈×C₁₃₇	—	4	2	no	—
74	C₂×Q₈×C₁₃₇	—	4	2	no	—
75	C₂×Q₈×C₁₃₇	—	4	2	no	—
76	C₂×Q₈×C₁₃₇	—	4	2	no	—
77	C₂×D₄×C₁₃₇	—	2	2	no	—
78	C₂×D₄×C₁₃₇	—	2	2	no	—
79	C₂×D₄×C₁₃₇	—	2	2	no	—
80	C₂×D₄×C₁₃₇	—	4	1	no	—
81	C₂×D₄×C₁₃₇	—	4	1	no	—
82	C₂×D₄×C₁₃₇	—	4	1	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	C₂×D₄×C₁₃₇	—	4	2	no	—
88	C₂×D₄×C₁₃₇	—	4	2	no	—
89	C₂²×C₄×C₁₃₇	—	4	1	no	—
90	C₂²×C₄×C₁₃₇	—	4	1	no	—
91	C₂²×C₄×C₁₃₇	—	4	1	no	—
92	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
95	SD₁₆×C₁₃₇	—	4	16	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	C₂×C₈×C₁₃₇	—	2	2	no	—
103	C₂×C₈×C₁₃₇	D₈	1	4	yes	—
104	C₂×C₈×C₁₃₇	SD₁₆	1	4	yes	complemented
105	C₄⋊C₄×C₁₃₇	—	2	2	no	—
106	C₄⋊C₄×C₁₃₇	—	2	2	no	—
107	C₄⋊C₄×C₁₃₇	—	2	2	no	—
108	C₄⋊C₄×C₁₃₇	—	2	2	no	—
109	C₄⋊C₄×C₁₃₇	—	4	1	no	—
110	C₄⋊C₄×C₁₃₇	—	4	1	no	—
111	C₄⋊C₄×C₁₃₇	—	4	1	no	—
112	C₄⋊C₄×C₁₃₇	—	4	1	no	—
113	C₄⋊C₄×C₁₃₇	—	4	2	no	—
114	C₄⋊C₄×C₁₃₇	—	4	2	no	—
115	C₄⋊C₄×C₁₃₇	—	4	2	no	—
116	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₁₃₇	#41	1	1	yes	characteristic
120	C₂³×C₁₃₇	—	4	2	no	—
121	C₂³×C₁₃₇	—	8	1	no	—
122	C₂³×C₁₃₇	—	8	1	no	—
123	C₂³×C₁₃₇	—	8	1	no	—
124	C₂³×C₁₃₇	—	8	1	no	—
125	C₂³×C₁₃₇	—	8	1	no	—
126	C₂³×C₁₃₇	—	8	1	no	—
127	C₂³×C₁₃₇	#127	1	1	yes	characteristic
128	Q₈×C₁₃₇	—	4	4	no	—
129	Q₈×C₁₃₇	—	4	4	no	—
130	Q₈×C₁₃₇	—	8	2	no	—
131	Q₈×C₁₃₇	—	8	2	no	—
132	D₄×C₁₃₇	—	4	4	no	—
133	D₄×C₁₃₇	—	4	4	no	—
134	D₄×C₁₃₇	—	4	4	no	—
135	D₄×C₁₃₇	—	8	2	no	—
136	D₄×C₁₃₇	—	8	2	no	—
137	D₄×C₁₃₇	—	8	2	no	—
138	C₂×C₄×C₁₃₇	—	4	2	no	—
139	C₂×C₄×C₁₃₇	—	4	2	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	—	8	1	no	—
145	C₂×C₄×C₁₃₇	—	8	1	no	—
146	C₂×C₄×C₁₃₇	—	8	1	no	—
147	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
148	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
149	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
150	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
151	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
152	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
153	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
154	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	2	yes	—
155	C₂×C₄×C₁₃₇	#135	1	2	yes	—
156	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
157	C₂×C₄×C₁₃₇	#137	1	2	yes	—
158	C₂×C₄×C₁₃₇	#137	1	2	yes	—
159	C₈×C₁₃₇	—	2	4	no	—
160	C₈×C₁₃₇	—	2	4	no	—
161	C₈×C₁₃₇	—	4	2	no	—
162	C₂²×C₁₃₇	—	8	2	no	—
163	C₂²×C₁₃₇	—	8	2	no	—
164	C₂²×C₁₃₇	—	8	2	no	—
165	C₂²×C₁₃₇	—	16	1	no	—
166	C₂²×C₁₃₇	—	16	1	no	—
167	C₂²×C₁₃₇	—	16	1	no	—
168	C₂²×C₁₃₇	—	16	1	no	—
169	C₂²×C₁₃₇	#392	1	1	yes	characteristic
170	C₂²×C₁₃₇	#492	1	1	yes	characteristic
171	C₂²×C₁₃₇	#493	1	1	yes	characteristic
172	C₂²×C₁₃₇	#495	1	1	yes	characteristic
173	C₂²×C₁₃₇	#496	1	1	yes	characteristic
174	C₂²×C₁₃₇	#497	1	1	yes	characteristic
175	C₂²×C₁₃₇	#497	1	1	yes	characteristic
176	C₄×C₁₃₇	—	8	2	no	—
177	C₄×C₁₃₇	—	8	2	no	—
178	C₄×C₁₃₇	—	16	1	no	—
179	C₄×C₁₃₇	#447	1	2	yes	—
180	C₄×C₁₃₇	#448	1	2	yes	—
181	C₄×C₁₃₇	#452	1	2	yes	—
182	C₄×C₁₃₇	#459	1	2	yes	—
183	C₄×C₁₃₇	#461	1	2	yes	—
184	C₄×C₁₃₇	#464	1	2	yes	—
185	C₂×C₁₃₇	—	16	2	no	—
186	C₂×C₁₃₇	#1706	1	1	yes	characteristic
187	C₂×C₁₃₇	#1714	1	1	yes	characteristic
188	C₂×C₁₃₇	#1719	1	1	yes	characteristic
189	C₂×C₁₃₇	#1722	1	1	yes	characteristic
190	C₂×C₁₃₇	#2011	1	1	yes	characteristic
191	C₂×C₁₃₇	#2013	1	1	yes	characteristic
192	C₂×C₁₃₇	#2015	1	1	yes	characteristic
193	#10308	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₁₃₇	#10308	1	1	yes	characteristic, direct product factor, Sylow
195	C₂×#500	C₂×C₁₃₇	1	1	yes	characteristic, complemented
196	C₂×#492	C₂×C₁₃₇	1	1	yes	characteristic
197	C₂×#486	C₂×C₁₃₇	1	1	yes	characteristic
198	#1990	C₂×C₁₃₇	1	1	yes	characteristic, complemented
199	#1957	C₂×C₁₃₇	1	1	yes	characteristic
200	#1956	C₂×C₁₃₇	1	1	yes	characteristic, complemented
201	#1273	C₂×C₁₃₇	1	1	yes	characteristic, complemented
202	C₂²×SD₁₆	—	2	2	no	—
203	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
204	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
205	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
206	#500	—	2	2	no	—
207	#500	—	2	2	no	—
208	#492	—	2	2	no	—
209	#492	—	2	2	no	—
210	#486	—	2	2	no	—
211	#486	—	2	2	no	—
212	C₂×#107	—	2	2	no	—
213	C₂×#103	—	2	2	no	—
214	C₂×#102	—	2	2	no	—
215	C₂×#102	—	2	2	no	—
216	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
217	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
218	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
219	#384	C₂²×C₁₃₇	1	1	yes	characteristic
220	#340	—	2	2	no	—
221	C₂²×Q₈	—	2	1	no	—
222	C₂²×Q₈	—	2	1	no	—
223	C₂²×D₄	—	2	1	no	—
224	C₂²×D₄	—	2	1	no	—
225	C₂²×D₄	—	2	1	no	—
226	C₂×SD₁₆	—	2	8	no	—
227	C₂×SD₁₆	—	4	4	no	—
228	C₂×SD₁₆	—	4	4	no	—
229	C₂²×C₈	D₄×C₁₃₇	1	2	yes	—
230	C₂²×C₈	D₄×C₁₃₇	1	2	yes	—
231	C₂²×C₈	D₄×C₁₃₇	1	2	yes	—
232	C₄⋊Q₈	—	2	1	no	—
233	C₄⋊Q₈	—	2	1	no	—
234	C₄⋊Q₈	—	2	1	no	—
235	C₄⋊Q₈	—	2	1	no	—
236	C₄⋊Q₈	—	2	1	no	—
237	C₄⋊Q₈	—	2	1	no	—
238	C₄⋊Q₈	D₄×C₁₃₇	1	2	yes	—
239	C₄⋊Q₈	D₄×C₁₃₇	1	2	yes	—
240	#127	—	2	1	no	—
241	#127	—	2	1	no	—
242	#127	—	2	1	no	—
243	#127	D₄×C₁₃₇	1	2	yes	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
252	#107	—	2	8	no	—
253	#103	—	4	4	no	—
254	#102	—	2	8	no	—
255	#102	—	4	4	no	—
256	C₄×C₈	—	2	1	no	—
257	C₄×C₈	—	2	1	no	—
258	C₄×C₈	—	2	1	no	—
259	C₄×C₈	—	2	1	no	—
260	C₄×C₈	—	2	1	no	—
261	C₄×C₈	—	2	1	no	—
262	C₂⁴	—	4	1	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	4	1	no	—
266	C₂×Q₈	—	4	1	no	—
267	C₂×Q₈	—	4	2	no	—
268	C₂×Q₈	—	4	2	no	—
269	C₂×Q₈	—	4	2	no	—
270	C₂×Q₈	—	4	2	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	4	1	no	—
275	C₂×D₄	—	4	1	no	—
276	C₂×D₄	—	4	1	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	—	4	2	no	—
282	C₂×D₄	—	4	2	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
289	SD₁₆	—	4	16	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	D₈×C₁₃₇	1	4	yes	—
298	C₂×C₈	SD₁₆×C₁₃₇	1	4	yes	complemented
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
311	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
312	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
313	C₄²	#41×C₁₃₇	1	1	yes	characteristic
314	C₂³	—	4	2	no	—
315	C₂³	—	8	1	no	—
316	C₂³	—	8	1	no	—
317	C₂³	—	8	1	no	—
318	C₂³	—	8	1	no	—
319	C₂³	—	8	1	no	—
320	C₂³	—	8	1	no	—
321	C₂³	#127×C₁₃₇	1	1	yes	characteristic
322	Q₈	—	4	4	no	—
323	Q₈	—	4	4	no	—
324	Q₈	—	8	2	no	—
325	Q₈	—	8	2	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	4	no	—
328	D₄	—	4	4	no	—
329	D₄	—	8	2	no	—
330	D₄	—	8	2	no	—
331	D₄	—	8	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	8	1	no	—
335	C₂×C₄	—	8	1	no	—
336	C₂×C₄	—	8	1	no	—
337	C₂×C₄	—	8	1	no	—
338	C₂×C₄	—	8	1	no	—
339	C₂×C₄	—	8	1	no	—
340	C₂×C₄	—	8	1	no	—
341	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
342	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
343	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
344	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
345	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
346	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
347	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
348	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	2	yes	—
349	C₂×C₄	#135×C₁₃₇	1	2	yes	—
350	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
351	C₂×C₄	#137×C₁₃₇	1	2	yes	—
352	C₂×C₄	#137×C₁₃₇	1	2	yes	—
353	C₈	—	2	4	no	—
354	C₈	—	2	4	no	—
355	C₈	—	4	2	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	8	2	no	—
359	C₂²	—	16	1	no	—
360	C₂²	—	16	1	no	—
361	C₂²	—	16	1	no	—
362	C₂²	—	16	1	no	—
363	C₂²	#392×C₁₃₇	1	1	yes	characteristic
364	C₂²	#492×C₁₃₇	1	1	yes	characteristic
365	C₂²	#493×C₁₃₇	1	1	yes	characteristic
366	C₂²	#495×C₁₃₇	1	1	yes	characteristic
367	C₂²	#496×C₁₃₇	1	1	yes	characteristic
368	C₂²	#497×C₁₃₇	1	1	yes	characteristic
369	C₂²	#497×C₁₃₇	1	1	yes	characteristic
370	C₄	—	8	2	no	—
371	C₄	—	8	2	no	—
372	C₄	—	16	1	no	—
373	C₄	#447×C₁₃₇	1	2	yes	—
374	C₄	#448×C₁₃₇	1	2	yes	—
375	C₄	#452×C₁₃₇	1	2	yes	—
376	C₄	#459×C₁₃₇	1	2	yes	—
377	C₄	#461×C₁₃₇	1	2	yes	—
378	C₄	#464×C₁₃₇	1	2	yes	—
379	C₂	—	16	2	no	—
380	C₂	#1706×C₁₃₇	1	1	yes	characteristic
381	C₂	#1714×C₁₃₇	1	1	yes	characteristic
382	C₂	#1719×C₁₃₇	1	1	yes	characteristic
383	C₂	#1722×C₁₃₇	1	1	yes	characteristic
384	C₂	#2011×C₁₃₇	1	1	yes	characteristic
385	C₂	#2013×C₁₃₇	1	1	yes	characteristic
386	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×#500×C₁₃₇	C₂	semidirect
4. #1990×C₁₃₇	C₂	semidirect
6. #1956×C₁₃₇	C₂	semidirect
7. #1273×C₁₃₇	C₂	semidirect
104. C₂×C₈×C₁₃₇	SD₁₆	semidirect
193. #10308	C₁₃₇	direct (N × H)
194. C₁₃₇	#10308	direct (N × H)
195. C₂×#500	C₂×C₁₃₇	semidirect
198. #1990	C₂×C₁₃₇	semidirect
200. #1956	C₂×C₁₃₇	semidirect
201. #1273	C₂×C₁₃₇	semidirect
298. C₂×C₈	SD₁₆×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#500×C₁₃₇	2
C₂×#492×C₁₃₇	2
C₂×#486×C₁₃₇	2
#1990×C₁₃₇	2
#1957×C₁₃₇	2
#1956×C₁₃₇	2
#1273×C₁₃₇	2
#10308	137

Subgroups — C137×#10308 #46859694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#10308 #46859694