Subgroups — C₁₃₇×#19259 #46868645

Order 35072.

694 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3170×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#3110×C₁₃₇	C₂	1	2	yes	maximal
3	C₂×C₈×D₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1679×C₁₃₇	C₂	1	4	yes	maximal, complemented
5	#1673×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1669×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1568×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1552×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	C₂³×C₈×C₁₃₇	—	2	1	no	—
10	#533×C₁₃₇	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
12	#500×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
13	#494×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
14	#487×C₁₃₇	C₂²	1	2	yes	complemented
15	#484×C₁₃₇	—	2	2	no	—
16	#474×C₁₃₇	C₂²	1	4	yes	—
17	#467×C₁₃₇	—	2	1	no	—
18	#467×C₁₃₇	—	2	1	no	—
19	#461×C₁₃₇	C₂²	1	4	yes	—
20	#450×C₁₃₇	—	2	2	no	—
21	#440×C₁₃₇	—	2	4	no	—
22	C₄×Q₁₆×C₁₃₇	—	2	1	no	—
23	C₄×Q₁₆×C₁₃₇	—	2	1	no	—
24	C₈×D₄×C₁₃₇	—	2	1	no	—
25	C₈×D₄×C₁₃₇	—	2	1	no	—
26	C₈×D₄×C₁₃₇	C₂²	1	2	yes	—
27	C₈×D₄×C₁₃₇	C₂²	1	2	yes	—
28	#432×C₁₃₇	C₂²	1	2	yes	—
29	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₁₃₇	—	2	1	no	—
31	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
32	#335×C₁₃₇	C₂²	1	2	yes	complemented
33	#334×C₁₃₇	C₂²	1	2	yes	complemented
34	#332×C₁₃₇	C₂²	1	4	yes	complemented
35	#332×C₁₃₇	C₂²	1	4	yes	complemented
36	C₂²×D₄×C₁₃₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₃₇	—	2	1	no	—
38	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
39	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
40	C₂×SD₁₆×C₁₃₇	—	2	4	no	—
41	C₂²×C₈×C₁₃₇	—	2	1	no	—
42	C₂²×C₈×C₁₃₇	—	2	2	no	—
43	C₂²×C₈×C₁₃₇	—	2	2	no	—
44	C₂²×C₈×C₁₃₇	—	4	4	no	—
45	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
47	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
48	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
49	#125×C₁₃₇	—	2	2	no	—
50	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
51	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
52	C₄×Q₈×C₁₃₇	—	2	2	no	—
53	C₄×Q₈×C₁₃₇	—	2	2	no	—
54	C₄×D₄×C₁₃₇	—	2	1	no	—
55	C₄×D₄×C₁₃₇	—	2	1	no	—
56	C₄×D₄×C₁₃₇	D₄	1	2	yes	—
57	C₄×D₄×C₁₃₇	C₂³	1	2	yes	—
58	#117×C₁₃₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
60	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
61	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
62	#107×C₁₃₇	—	2	1	no	—
63	#107×C₁₃₇	—	2	1	no	—
64	#107×C₁₃₇	—	2	4	no	—
65	C₄⋊C₈×C₁₃₇	—	2	1	no	—
66	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
67	C₄⋊C₈×C₁₃₇	C₂³	1	4	yes	—
68	#103×C₁₃₇	—	2	2	no	—
69	#103×C₁₃₇	—	2	2	no	—
70	#103×C₁₃₇	—	2	4	no	—
71	#102×C₁₃₇	—	2	4	no	—
72	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
73	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
74	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
75	#97×C₁₃₇	—	2	2	no	—
76	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
77	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
78	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
79	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
80	C₂⁴×C₁₃₇	—	2	1	no	—
81	C₂×Q₈×C₁₃₇	—	2	2	no	—
82	C₂×Q₈×C₁₃₇	—	2	2	no	—
83	C₂×D₄×C₁₃₇	—	2	4	no	—
84	C₂×D₄×C₁₃₇	—	2	1	no	—
85	C₂×D₄×C₁₃₇	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₁₃₇	—	2	1	no	—
87	C₂²×C₄×C₁₃₇	—	2	2	no	—
88	C₂²×C₄×C₁₃₇	—	2	2	no	—
89	C₂²×C₄×C₁₃₇	—	4	2	no	—
90	C₂²×C₄×C₁₃₇	—	4	2	no	—
91	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
94	Q₁₆×C₁₃₇	—	4	2	no	—
95	Q₁₆×C₁₃₇	—	4	2	no	—
96	SD₁₆×C₁₃₇	—	4	8	no	—
97	C₂×C₈×C₁₃₇	—	2	2	no	—
98	C₂×C₈×C₁₃₇	—	2	4	no	—
99	C₂×C₈×C₁₃₇	—	2	2	no	—
100	C₂×C₈×C₁₃₇	—	4	1	no	—
101	C₂×C₈×C₁₃₇	—	4	4	no	—
102	C₂×C₈×C₁₃₇	—	4	2	no	—
103	C₂×C₈×C₁₃₇	—	4	4	no	—
104	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
105	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
106	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
107	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
108	C₄⋊C₄×C₁₃₇	—	2	1	no	—
109	C₄⋊C₄×C₁₃₇	—	2	2	no	—
110	C₄⋊C₄×C₁₃₇	—	2	2	no	—
111	C₄⋊C₄×C₁₃₇	—	2	2	no	—
112	C₄⋊C₄×C₁₃₇	—	2	2	no	—
113	C₄⋊C₄×C₁₃₇	—	4	2	no	—
114	C₄⋊C₄×C₁₃₇	—	4	2	no	—
115	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
116	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
117	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
118	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
119	C₄²×C₁₃₇	—	4	2	no	—
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	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
124	C₂³×C₁₃₇	—	2	4	no	—
125	C₂³×C₁₃₇	—	2	2	no	—
126	C₂³×C₁₃₇	—	4	2	no	—
127	C₂³×C₁₃₇	—	4	2	no	—
128	C₂³×C₁₃₇	#121	1	1	yes	characteristic
129	Q₈×C₁₃₇	—	4	4	no	—
130	Q₈×C₁₃₇	—	4	2	no	—
131	Q₈×C₁₃₇	—	4	2	no	—
132	D₄×C₁₃₇	—	2	4	no	—
133	D₄×C₁₃₇	—	2	2	no	—
134	D₄×C₁₃₇	#135	1	4	yes	—
135	C₂×C₄×C₁₃₇	—	2	2	no	—
136	C₂×C₄×C₁₃₇	—	2	2	no	—
137	C₂×C₄×C₁₃₇	—	2	1	no	—
138	C₂×C₄×C₁₃₇	—	2	1	no	—
139	C₂×C₄×C₁₃₇	—	2	2	no	—
140	C₂×C₄×C₁₃₇	—	4	4	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	#121	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	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
152	C₈×C₁₃₇	—	2	1	no	—
153	C₈×C₁₃₇	—	2	1	no	—
154	C₈×C₁₃₇	—	2	1	no	—
155	C₈×C₁₃₇	—	4	4	no	—
156	C₈×C₁₃₇	—	4	2	no	—
157	C₈×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
158	C₂²×C₁₃₇	—	2	1	no	—
159	C₂²×C₁₃₇	—	2	1	no	—
160	C₂²×C₁₃₇	—	2	4	no	—
161	C₂²×C₁₃₇	—	4	8	no	—
162	C₂²×C₁₃₇	—	4	2	no	—
163	C₂²×C₁₃₇	—	4	2	no	—
164	C₂²×C₁₃₇	#473	1	2	yes	—
165	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
166	C₄×C₁₃₇	—	2	1	no	—
167	C₄×C₁₃₇	—	2	1	no	—
168	C₄×C₁₃₇	—	2	1	no	—
169	C₄×C₁₃₇	—	2	1	no	—
170	C₄×C₁₃₇	—	4	2	no	—
171	C₄×C₁₃₇	—	8	2	no	—
172	C₄×C₁₃₇	—	8	2	no	—
173	C₄×C₁₃₇	C₂×#135	1	2	yes	—
174	C₄×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₄×C₁₃₇	#575	1	1	yes	characteristic
176	C₂×C₁₃₇	—	2	2	no	—
177	C₂×C₁₃₇	—	4	4	no	—
178	C₂×C₁₃₇	#3036	1	1	yes	characteristic
179	C₂×C₁₃₇	#3050	1	1	yes	characteristic
180	C₂×C₁₃₇	C₂×#473	1	1	yes	characteristic
181	#19259	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₁₃₇	#19259	1	1	yes	characteristic, direct product factor, Sylow
183	#3170	C₂×C₁₃₇	1	1	yes	characteristic, complemented
184	#3110	C₂×C₁₃₇	1	2	yes	—
185	C₂×C₈×D₄	C₂×C₁₃₇	1	1	yes	characteristic
186	#1679	C₂×C₁₃₇	1	4	yes	complemented
187	#1673	C₂×C₁₃₇	1	2	yes	complemented
188	#1669	C₂×C₁₃₇	1	2	yes	complemented
189	#1568	C₂×C₁₃₇	1	1	yes	characteristic, complemented
190	#1552	C₂×C₁₃₇	1	2	yes	complemented
191	C₂³×C₈	—	2	1	no	—
192	#533	C₂²×C₁₃₇	1	2	yes	—
193	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
194	#500	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
195	#494	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
196	#487	C₂²×C₁₃₇	1	2	yes	complemented
197	#484	—	2	2	no	—
198	#474	C₂²×C₁₃₇	1	4	yes	—
199	#467	—	2	1	no	—
200	#467	—	2	1	no	—
201	#461	C₂²×C₁₃₇	1	4	yes	—
202	#450	—	2	2	no	—
203	#440	—	2	4	no	—
204	C₄×Q₁₆	—	2	1	no	—
205	C₄×Q₁₆	—	2	1	no	—
206	C₈×D₄	—	2	1	no	—
207	C₈×D₄	—	2	1	no	—
208	C₈×D₄	C₂²×C₁₃₇	1	2	yes	—
209	C₈×D₄	C₂²×C₁₃₇	1	2	yes	—
210	#432	C₂²×C₁₃₇	1	2	yes	—
211	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
212	C₂×C₂²⋊C₈	—	2	1	no	—
213	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
214	#335	C₂²×C₁₃₇	1	2	yes	complemented
215	#334	C₂²×C₁₃₇	1	2	yes	complemented
216	#332	C₂²×C₁₃₇	1	4	yes	complemented
217	#332	C₂²×C₁₃₇	1	4	yes	complemented
218	C₂²×D₄	D₄×C₁₃₇	1	1	yes	characteristic
219	C₂³×C₄	—	2	1	no	—
220	C₂×Q₁₆	—	2	1	no	—
221	C₂×Q₁₆	—	2	1	no	—
222	C₂×SD₁₆	—	2	4	no	—
223	C₂²×C₈	—	2	1	no	—
224	C₂²×C₈	—	2	2	no	—
225	C₂²×C₈	—	2	2	no	—
226	C₂²×C₈	—	4	4	no	—
227	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
228	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
229	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
230	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
231	#125	—	2	2	no	—
232	C₂²⋊Q₈	—	2	2	no	—
233	C₂²⋊Q₈	—	2	2	no	—
234	C₄×Q₈	—	2	2	no	—
235	C₄×Q₈	—	2	2	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	D₄×C₁₃₇	1	2	yes	—
239	C₄×D₄	C₂³×C₁₃₇	1	2	yes	—
240	#117	—	2	2	no	—
241	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
242	C₂×C₂²⋊C₄	—	2	1	no	—
243	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
244	#107	—	2	1	no	—
245	#107	—	2	1	no	—
246	#107	—	2	4	no	—
247	C₄⋊C₈	—	2	1	no	—
248	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
249	C₄⋊C₈	C₂³×C₁₃₇	1	4	yes	—
250	#103	—	2	2	no	—
251	#103	—	2	2	no	—
252	#103	—	2	4	no	—
253	#102	—	2	4	no	—
254	C₂²⋊C₈	—	2	2	no	—
255	C₂²⋊C₈	—	2	2	no	—
256	C₂²⋊C₈	—	2	2	no	—
257	#97	—	2	2	no	—
258	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
259	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
260	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
261	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
262	C₂⁴	—	2	1	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×D₄	—	2	4	no	—
266	C₂×D₄	—	2	1	no	—
267	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
275	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
276	Q₁₆	—	4	2	no	—
277	Q₁₆	—	4	2	no	—
278	SD₁₆	—	4	8	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	4	1	no	—
283	C₂×C₈	—	4	4	no	—
284	C₂×C₈	—	4	2	no	—
285	C₂×C₈	—	4	4	no	—
286	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
287	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
288	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
289	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	4	2	no	—
296	C₄⋊C₄	—	4	2	no	—
297	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
298	C₂²⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	2	2	no	—
300	C₂²⋊C₄	—	4	2	no	—
301	C₄²	—	4	2	no	—
302	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
303	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
304	C₄²	#41×C₁₃₇	1	1	yes	characteristic
305	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
306	C₂³	—	2	4	no	—
307	C₂³	—	2	2	no	—
308	C₂³	—	4	2	no	—
309	C₂³	—	4	2	no	—
310	C₂³	#121×C₁₃₇	1	1	yes	characteristic
311	Q₈	—	4	4	no	—
312	Q₈	—	4	2	no	—
313	Q₈	—	4	2	no	—
314	D₄	—	2	4	no	—
315	D₄	—	2	2	no	—
316	D₄	#135×C₁₃₇	1	4	yes	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
329	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
330	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
331	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
332	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
333	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
334	C₈	—	2	1	no	—
335	C₈	—	2	1	no	—
336	C₈	—	2	1	no	—
337	C₈	—	4	4	no	—
338	C₈	—	4	2	no	—
339	C₈	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	4	8	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	2	no	—
346	C₂²	#473×C₁₃₇	1	2	yes	—
347	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	4	2	no	—
353	C₄	—	8	2	no	—
354	C₄	—	8	2	no	—
355	C₄	C₂×#135×C₁₃₇	1	2	yes	—
356	C₄	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
357	C₄	#575×C₁₃₇	1	1	yes	characteristic
358	C₂	—	2	2	no	—
359	C₂	—	4	4	no	—
360	C₂	#3036×C₁₃₇	1	1	yes	characteristic
361	C₂	#3050×C₁₃₇	1	1	yes	characteristic
362	C₂	C₂×#473×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
prime radical	C₂²×D₄×C₁₃₇	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₂×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3170×C₁₃₇	C₂	semidirect
4. #1679×C₁₃₇	C₂	semidirect
5. #1673×C₁₃₇	C₂	semidirect
6. #1669×C₁₃₇	C₂	semidirect
7. #1568×C₁₃₇	C₂	semidirect
8. #1552×C₁₃₇	C₂	semidirect
12. #500×C₁₃₇	C₂²	semidirect
13. #494×C₁₃₇	C₂²	semidirect
14. #487×C₁₃₇	C₂²	semidirect
32. #335×C₁₃₇	C₂²	semidirect
33. #334×C₁₃₇	C₂²	semidirect
34. #332×C₁₃₇	C₂²	semidirect
35. #332×C₁₃₇	C₂²	semidirect
181. #19259	C₁₃₇	direct (N × H)
182. C₁₃₇	#19259	direct (N × H)
183. #3170	C₂×C₁₃₇	semidirect
186. #1679	C₂×C₁₃₇	semidirect
187. #1673	C₂×C₁₃₇	semidirect
188. #1669	C₂×C₁₃₇	semidirect
189. #1568	C₂×C₁₃₇	semidirect
190. #1552	C₂×C₁₃₇	semidirect
194. #500	C₂²×C₁₃₇	semidirect
195. #494	C₂²×C₁₃₇	semidirect
196. #487	C₂²×C₁₃₇	semidirect
214. #335	C₂²×C₁₃₇	semidirect
215. #334	C₂²×C₁₃₇	semidirect
216. #332	C₂²×C₁₃₇	semidirect
217. #332	C₂²×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3170×C₁₃₇	2
#3110×C₁₃₇	2
C₂×C₈×D₄×C₁₃₇	2
#1679×C₁₃₇	2
#1673×C₁₃₇	2
#1669×C₁₃₇	2
#1568×C₁₃₇	2
#1552×C₁₃₇	2
#19259	137

Subgroups — C137×#19259 #46868645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#19259 #46868645