Subgroups — C₁₃₇×#10072 #46859458

Order 35072.

598 conjugacy classes of subgroups.

The subgroup lattice has 392 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×#474×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2563×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1981×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#333×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄⋊C₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
7	#1279×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×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
11	#487×C₁₃₇	—	2	2	no	—
12	#487×C₁₃₇	—	2	2	no	—
13	#474×C₁₃₇	—	2	2	no	—
14	#474×C₁₃₇	—	2	2	no	—
15	C₂×#107×C₁₃₇	—	2	1	no	—
16	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂×#103×C₁₃₇	—	2	2	no	—
19	C₂×#103×C₁₃₇	—	2	2	no	—
20	C₂×#102×C₁₃₇	—	2	1	no	—
21	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
22	#393×C₁₃₇	—	2	2	no	—
23	#390×C₁₃₇	—	2	1	no	—
24	#382×C₁₃₇	—	2	1	no	—
25	#380×C₁₃₇	—	2	2	no	—
26	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
27	#333×C₁₃₇	—	2	2	no	—
28	D₄⋊C₈×C₁₃₇	—	2	2	no	—
29	C₂²×Q₈×C₁₃₇	—	2	1	no	—
30	C₂²×Q₈×C₁₃₇	D₄	1	2	yes	—
31	C₂²×D₄×C₁₃₇	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₃₇	—	2	1	no	—
33	C₂²×C₈×C₁₃₇	—	2	1	no	—
34	C₂²×C₈×C₁₃₇	—	2	1	no	—
35	C₂²×C₈×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	—	2	1	no	—
42	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
43	C₄⋊Q₈×C₁₃₇	D₄	1	2	yes	—
44	C₄×D₄×C₁₃₇	—	2	1	no	—
45	C₄×D₄×C₁₃₇	—	2	1	no	—
46	C₄×D₄×C₁₃₇	—	2	1	no	—
47	C₄×D₄×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	D₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
54	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
55	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
56	C₂×C₄²×C₁₃₇	—	2	1	no	—
57	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
58	#107×C₁₃₇	—	2	4	no	—
59	C₄⋊C₈×C₁₃₇	—	2	1	no	—
60	C₄⋊C₈×C₁₃₇	—	2	1	no	—
61	C₄⋊C₈×C₁₃₇	—	2	1	no	—
62	C₄⋊C₈×C₁₃₇	D₄	1	2	yes	—
63	#103×C₁₃₇	—	2	8	no	—
64	#103×C₁₃₇	—	4	4	no	—
65	#102×C₁₃₇	—	2	4	no	—
66	C₄×C₈×C₁₃₇	—	2	1	no	—
67	C₄×C₈×C₁₃₇	D₄	1	2	yes	—
68	#95×C₁₃₇	—	2	4	no	—
69	#95×C₁₃₇	—	2	1	no	—
70	C₂⁴×C₁₃₇	—	2	1	no	—
71	C₂×Q₈×C₁₃₇	—	2	2	no	—
72	C₂×Q₈×C₁₃₇	—	2	2	no	—
73	C₂×Q₈×C₁₃₇	—	2	2	no	—
74	C₂×Q₈×C₁₃₇	—	4	4	no	—
75	C₂×Q₈×C₁₃₇	—	4	1	no	—
76	C₂×Q₈×C₁₃₇	—	4	2	no	—
77	C₂×Q₈×C₁₃₇	—	4	2	no	—
78	C₂×D₄×C₁₃₇	—	2	1	no	—
79	C₂×D₄×C₁₃₇	—	2	1	no	—
80	C₂×D₄×C₁₃₇	—	2	1	no	—
81	C₂×D₄×C₁₃₇	—	2	1	no	—
82	C₂×D₄×C₁₃₇	—	2	1	no	—
83	C₂×D₄×C₁₃₇	Q₁₆	1	2	yes	—
84	C₂²×C₄×C₁₃₇	—	2	1	no	—
85	C₂²×C₄×C₁₃₇	—	2	2	no	—
86	C₂²×C₄×C₁₃₇	—	2	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	—	4	2	no	—
91	C₂²×C₄×C₁₃₇	—	4	2	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	C₂×C₈×C₁₃₇	—	2	2	no	—
96	C₂×C₈×C₁₃₇	—	2	2	no	—
97	C₂×C₈×C₁₃₇	—	4	2	no	—
98	C₂×C₈×C₁₃₇	—	4	1	no	—
99	C₂×C₈×C₁₃₇	—	4	1	no	—
100	C₂×C₈×C₁₃₇	—	4	1	no	—
101	C₂×C₈×C₁₃₇	—	4	2	no	—
102	C₄⋊C₄×C₁₃₇	—	2	2	no	—
103	C₄⋊C₄×C₁₃₇	—	2	2	no	—
104	C₄⋊C₄×C₁₃₇	—	2	1	no	—
105	C₄⋊C₄×C₁₃₇	—	2	1	no	—
106	C₄⋊C₄×C₁₃₇	—	2	2	no	—
107	C₄⋊C₄×C₁₃₇	—	2	2	no	—
108	C₄⋊C₄×C₁₃₇	—	4	1	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	1	no	—
114	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
115	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
116	C₂²⋊C₄×C₁₃₇	—	8	4	no	—
117	C₄²×C₁₃₇	—	4	1	no	—
118	C₄²×C₁₃₇	—	4	1	no	—
119	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₃₇	#41	1	1	yes	characteristic
123	C₂³×C₁₃₇	—	2	2	no	—
124	C₂³×C₁₃₇	—	4	1	no	—
125	C₂³×C₁₃₇	—	4	2	no	—
126	C₂³×C₁₃₇	—	4	1	no	—
127	C₂³×C₁₃₇	—	4	2	no	—
128	C₂³×C₁₃₇	#120	1	1	yes	characteristic
129	Q₈×C₁₃₇	—	4	4	no	—
130	Q₈×C₁₃₇	—	4	4	no	—
131	Q₈×C₁₃₇	—	8	2	no	—
132	Q₈×C₁₃₇	—	8	1	no	—
133	Q₈×C₁₃₇	—	8	1	no	—
134	D₄×C₁₃₇	—	2	2	no	—
135	D₄×C₁₃₇	—	2	2	no	—
136	D₄×C₁₃₇	—	4	1	no	—
137	D₄×C₁₃₇	—	4	1	no	—
138	C₂×C₄×C₁₃₇	—	2	2	no	—
139	C₂×C₄×C₁₃₇	—	4	1	no	—
140	C₂×C₄×C₁₃₇	—	4	2	no	—
141	C₂×C₄×C₁₃₇	—	4	2	no	—
142	C₂×C₄×C₁₃₇	—	4	2	no	—
143	C₂×C₄×C₁₃₇	—	4	2	no	—
144	C₂×C₄×C₁₃₇	—	4	2	no	—
145	C₂×C₄×C₁₃₇	—	4	2	no	—
146	C₂×C₄×C₁₃₇	—	4	4	no	—
147	C₂×C₄×C₁₃₇	—	8	2	no	—
148	C₂×C₄×C₁₃₇	—	8	2	no	—
149	C₂×C₄×C₁₃₇	—	8	1	no	—
150	C₂×C₄×C₁₃₇	—	8	1	no	—
151	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
152	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
153	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
154	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
155	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
156	C₂×C₄×C₁₃₇	#127	1	1	yes	characteristic
157	C₂×C₄×C₁₃₇	C₂×Q₁₆	1	1	yes	characteristic
158	C₂×C₄×C₁₃₇	#135	1	1	yes	characteristic
159	C₂×C₄×C₁₃₇	#135	1	2	yes	—
160	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
161	C₂×C₄×C₁₃₇	#137	1	1	yes	characteristic
162	C₂×C₄×C₁₃₇	#137	1	1	yes	characteristic
163	C₈×C₁₃₇	—	4	2	no	—
164	C₈×C₁₃₇	—	4	2	no	—
165	C₈×C₁₃₇	—	8	1	no	—
166	C₂²×C₁₃₇	—	4	4	no	—
167	C₂²×C₁₃₇	—	4	2	no	—
168	C₂²×C₁₃₇	—	8	2	no	—
169	C₂²×C₁₃₇	—	8	1	no	—
170	C₂²×C₁₃₇	—	8	1	no	—
171	C₂²×C₁₃₇	#392	1	1	yes	characteristic
172	C₂²×C₁₃₇	#449	1	2	yes	—
173	C₂²×C₁₃₇	#451	1	1	yes	characteristic
174	C₂²×C₁₃₇	#452	1	1	yes	characteristic
175	C₂²×C₁₃₇	#455	1	2	yes	—
176	C₄×C₁₃₇	—	2	1	no	—
177	C₄×C₁₃₇	—	2	1	no	—
178	C₄×C₁₃₇	—	8	2	no	—
179	C₄×C₁₃₇	—	8	2	no	—
180	C₄×C₁₃₇	—	8	1	no	—
181	C₄×C₁₃₇	—	8	2	no	—
182	C₄×C₁₃₇	#451	1	1	yes	characteristic
183	C₄×C₁₃₇	#452	1	1	yes	characteristic
184	C₄×C₁₃₇	#463	1	2	yes	—
185	C₄×C₁₃₇	#467	1	1	yes	characteristic
186	C₄×C₁₃₇	#470	1	1	yes	characteristic
187	C₄×C₁₃₇	#495	1	1	yes	characteristic
188	C₄×C₁₃₇	#496	1	1	yes	characteristic
189	C₂×C₁₃₇	—	8	2	no	—
190	C₂×C₁₃₇	#1644	1	2	yes	—
191	C₂×C₁₃₇	#1646	1	2	yes	—
192	C₂×C₁₃₇	#2001	1	1	yes	characteristic
193	C₂×C₁₃₇	#2004	1	1	yes	characteristic
194	C₂×C₁₃₇	#2012	1	1	yes	characteristic
195	#10072	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₁₃₇	#10072	1	1	yes	characteristic, direct product factor, Sylow
197	C₂×#487	C₂×C₁₃₇	1	1	yes	characteristic, complemented
198	C₂×#474	C₂×C₁₃₇	1	1	yes	characteristic
199	#2563	C₂×C₁₃₇	1	1	yes	characteristic
200	#1981	C₂×C₁₃₇	1	1	yes	characteristic, complemented
201	C₂×#333	C₂×C₁₃₇	1	1	yes	characteristic, complemented
202	C₂×D₄⋊C₈	C₂×C₁₃₇	1	1	yes	characteristic
203	#1279	C₂×C₁₃₇	1	1	yes	characteristic, complemented
204	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
205	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
206	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
207	#487	—	2	2	no	—
208	#487	—	2	2	no	—
209	#474	—	2	2	no	—
210	#474	—	2	2	no	—
211	C₂×#107	—	2	1	no	—
212	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
213	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
214	C₂×#103	—	2	2	no	—
215	C₂×#103	—	2	2	no	—
216	C₂×#102	—	2	1	no	—
217	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
218	#393	—	2	2	no	—
219	#390	—	2	1	no	—
220	#382	—	2	1	no	—
221	#380	—	2	2	no	—
222	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
223	#333	—	2	2	no	—
224	D₄⋊C₈	—	2	2	no	—
225	C₂²×Q₈	—	2	1	no	—
226	C₂²×Q₈	D₄×C₁₃₇	1	2	yes	—
227	C₂²×D₄	D₄×C₁₃₇	1	1	yes	characteristic
228	C₂³×C₄	—	2	1	no	—
229	C₂²×C₈	—	2	1	no	—
230	C₂²×C₈	—	2	1	no	—
231	C₂²×C₈	—	2	1	no	—
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	—	2	1	no	—
239	C₄⋊Q₈	D₄×C₁₃₇	1	2	yes	—
240	C₄×D₄	—	2	1	no	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
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	D₄×C₁₃₇	1	1	yes	characteristic
249	C₂×C₄⋊C₄	D₄×C₁₃₇	1	2	yes	—
250	C₂×C₂²⋊C₄	—	2	1	no	—
251	C₂×C₂²⋊C₄	—	2	4	no	—
252	C₂×C₄²	—	2	1	no	—
253	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
254	#107	—	2	4	no	—
255	C₄⋊C₈	—	2	1	no	—
256	C₄⋊C₈	—	2	1	no	—
257	C₄⋊C₈	—	2	1	no	—
258	C₄⋊C₈	D₄×C₁₃₇	1	2	yes	—
259	#103	—	2	8	no	—
260	#103	—	4	4	no	—
261	#102	—	2	4	no	—
262	C₄×C₈	—	2	1	no	—
263	C₄×C₈	D₄×C₁₃₇	1	2	yes	—
264	#95	—	2	4	no	—
265	#95	—	2	1	no	—
266	C₂⁴	—	2	1	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	4	4	no	—
271	C₂×Q₈	—	4	1	no	—
272	C₂×Q₈	—	4	2	no	—
273	C₂×Q₈	—	4	2	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	2	1	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	Q₁₆×C₁₃₇	1	2	yes	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	4	2	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	—	4	1	no	—
296	C₂×C₈	—	4	1	no	—
297	C₂×C₈	—	4	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₂²⋊C₄	—	4	1	no	—
311	C₂²⋊C₄	—	4	1	no	—
312	C₂²⋊C₄	—	8	4	no	—
313	C₄²	—	4	1	no	—
314	C₄²	—	4	1	no	—
315	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
316	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
317	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
318	C₄²	#41×C₁₃₇	1	1	yes	characteristic
319	C₂³	—	2	2	no	—
320	C₂³	—	4	1	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	4	1	no	—
323	C₂³	—	4	2	no	—
324	C₂³	#120×C₁₃₇	1	1	yes	characteristic
325	Q₈	—	4	4	no	—
326	Q₈	—	4	4	no	—
327	Q₈	—	8	2	no	—
328	Q₈	—	8	1	no	—
329	Q₈	—	8	1	no	—
330	D₄	—	2	2	no	—
331	D₄	—	2	2	no	—
332	D₄	—	4	1	no	—
333	D₄	—	4	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	8	2	no	—
344	C₂×C₄	—	8	2	no	—
345	C₂×C₄	—	8	1	no	—
346	C₂×C₄	—	8	1	no	—
347	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
348	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
349	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
350	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
351	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
352	C₂×C₄	#127×C₁₃₇	1	1	yes	characteristic
353	C₂×C₄	C₂×Q₁₆×C₁₃₇	1	1	yes	characteristic
354	C₂×C₄	#135×C₁₃₇	1	1	yes	characteristic
355	C₂×C₄	#135×C₁₃₇	1	2	yes	—
356	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
357	C₂×C₄	#137×C₁₃₇	1	1	yes	characteristic
358	C₂×C₄	#137×C₁₃₇	1	1	yes	characteristic
359	C₈	—	4	2	no	—
360	C₈	—	4	2	no	—
361	C₈	—	8	1	no	—
362	C₂²	—	4	4	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	8	2	no	—
365	C₂²	—	8	1	no	—
366	C₂²	—	8	1	no	—
367	C₂²	#392×C₁₃₇	1	1	yes	characteristic
368	C₂²	#449×C₁₃₇	1	2	yes	—
369	C₂²	#451×C₁₃₇	1	1	yes	characteristic
370	C₂²	#452×C₁₃₇	1	1	yes	characteristic
371	C₂²	#455×C₁₃₇	1	2	yes	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	8	2	no	—
375	C₄	—	8	2	no	—
376	C₄	—	8	1	no	—
377	C₄	—	8	2	no	—
378	C₄	#451×C₁₃₇	1	1	yes	characteristic
379	C₄	#452×C₁₃₇	1	1	yes	characteristic
380	C₄	#463×C₁₃₇	1	2	yes	—
381	C₄	#467×C₁₃₇	1	1	yes	characteristic
382	C₄	#470×C₁₃₇	1	1	yes	characteristic
383	C₄	#495×C₁₃₇	1	1	yes	characteristic
384	C₄	#496×C₁₃₇	1	1	yes	characteristic
385	C₂	—	8	2	no	—
386	C₂	#1644×C₁₃₇	1	2	yes	—
387	C₂	#1646×C₁₃₇	1	2	yes	—
388	C₂	#2001×C₁₃₇	1	1	yes	characteristic
389	C₂	#2004×C₁₃₇	1	1	yes	characteristic
390	C₂	#2012×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₇	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₇
prime radical	C₂²×D₄×C₁₃₇	D₄
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. #1981×C₁₃₇	C₂	semidirect
5. C₂×#333×C₁₃₇	C₂	semidirect
7. #1279×C₁₃₇	C₂	semidirect
195. #10072	C₁₃₇	direct (N × H)
196. C₁₃₇	#10072	direct (N × H)
197. C₂×#487	C₂×C₁₃₇	semidirect
200. #1981	C₂×C₁₃₇	semidirect
201. C₂×#333	C₂×C₁₃₇	semidirect
203. #1279	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×#474×C₁₃₇	2
#2563×C₁₃₇	2
#1981×C₁₃₇	2
C₂×#333×C₁₃₇	2
C₂×D₄⋊C₈×C₁₃₇	2
#1279×C₁₃₇	2
#10072	137

Subgroups — C137×#10072 #46859458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#10072 #46859458