Subgroups — C₁₃₇×#33897 #46883283

Order 35072.

580 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3334×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#3283×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2241×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#2236×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#2224×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#2220×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#2208×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#2186×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	C₄×D₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#2169×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#2139×C₁₃₇	C₂	1	2	yes	maximal, complemented
12	C₂×#135×C₁₃₇	C₂²	1	2	yes	—
13	#547×C₁₃₇	—	2	1	no	—
14	#547×C₁₃₇	—	2	1	no	—
15	C₂×SD₃₂×C₁₃₇	C₂²	1	2	yes	—
16	C₂×D₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×M₃₂×C₁₃₇	C₂²	1	2	yes	—
18	#500×C₁₃₇	C₂²	1	1	yes	characteristic
19	#494×C₁₃₇	C₂²	1	1	yes	characteristic
20	#480×C₁₃₇	—	2	2	no	—
21	#474×C₁₃₇	—	2	1	no	—
22	#467×C₁₃₇	C₂²	1	2	yes	—
23	#466×C₁₃₇	C₂²	1	2	yes	—
24	#461×C₁₃₇	—	2	1	no	—
25	#452×C₁₃₇	—	2	2	no	—
26	C₄×D₈×C₁₃₇	C₂²	1	1	yes	characteristic
27	C₄×D₈×C₁₃₇	C₂²	1	1	yes	characteristic
28	C₈×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
29	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
30	#366×C₁₃₇	C₂²	1	1	yes	characteristic
31	#366×C₁₃₇	C₂²	1	2	yes	—
32	C₄⋊C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
33	#358×C₁₃₇	C₂²	1	2	yes	—
34	#358×C₁₃₇	C₂²	1	2	yes	—
35	#358×C₁₃₇	C₂²	1	2	yes	—
36	#357×C₁₃₇	C₂²	1	1	yes	characteristic
37	#357×C₁₃₇	C₂²	1	2	yes	—
38	#357×C₁₃₇	C₂²	1	1	yes	characteristic
39	C₂²⋊C₁₆×C₁₃₇	C₂²	1	2	yes	—
40	C₄×C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
41	C₂×#41×C₁₃₇	—	2	2	no	—
42	C₂×#41×C₁₃₇	—	4	1	no	—
43	#135×C₁₃₇	—	2	4	no	—
44	#135×C₁₃₇	—	4	2	no	—
45	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
46	C₂×Q₁₆×C₁₃₇	C₂³	1	2	yes	—
47	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
48	C₂×D₈×C₁₃₇	C₂³	1	1	yes	characteristic
49	C₂×D₈×C₁₃₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
52	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
53	#123×C₁₃₇	—	4	2	no	—
54	#123×C₁₃₇	—	4	2	no	—
55	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
56	C₂²⋊Q₈×C₁₃₇	—	4	1	no	—
57	#121×C₁₃₇	—	2	2	no	—
58	#121×C₁₃₇	—	4	1	no	—
59	C₄×D₄×C₁₃₇	—	2	1	no	—
60	C₄×D₄×C₁₃₇	—	2	1	no	—
61	C₄×D₄×C₁₃₇	D₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₃₇	—	4	1	no	—
64	SD₃₂×C₁₃₇	—	4	2	no	—
65	D₁₆×C₁₃₇	—	2	2	no	—
66	M₃₂×C₁₃₇	—	4	2	no	—
67	C₂×C₁₆×C₁₃₇	C₂³	1	2	yes	—
68	C₂×C₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
69	C₂×C₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
70	#107×C₁₃₇	—	2	2	no	—
71	#107×C₁₃₇	—	2	1	no	—
72	#107×C₁₃₇	C₂³	1	1	yes	characteristic
73	#107×C₁₃₇	C₂³	1	1	yes	characteristic
74	#107×C₁₃₇	C₂³	1	2	yes	—
75	C₄⋊C₈×C₁₃₇	D₄	1	1	yes	characteristic
76	#103×C₁₃₇	—	2	2	no	—
77	#102×C₁₃₇	—	2	1	no	—
78	#102×C₁₃₇	—	2	1	no	—
79	#102×C₁₃₇	—	2	2	no	—
80	C₂²⋊C₈×C₁₃₇	D₄	1	2	yes	—
81	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
82	#41×C₁₃₇	—	4	4	no	—
83	#41×C₁₃₇	—	8	2	no	—
84	#41×C₁₃₇	—	8	4	no	—
85	C₂×Q₈×C₁₃₇	—	2	2	no	—
86	C₂×Q₈×C₁₃₇	—	4	1	no	—
87	C₂×D₄×C₁₃₇	—	2	1	no	—
88	C₂×D₄×C₁₃₇	—	2	1	no	—
89	C₂×D₄×C₁₃₇	—	4	2	no	—
90	C₂×D₄×C₁₃₇	—	4	2	no	—
91	C₂×D₄×C₁₃₇	D₈	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₇	—	4	2	no	—
93	C₂²×C₄×C₁₃₇	—	4	1	no	—
94	C₂²×C₄×C₁₃₇	—	4	2	no	—
95	C₂²×C₄×C₁₃₇	—	4	1	no	—
96	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
97	Q₁₆×C₁₃₇	—	2	2	no	—
98	Q₁₆×C₁₃₇	—	2	2	no	—
99	Q₁₆×C₁₃₇	—	8	1	no	—
100	SD₁₆×C₁₃₇	—	4	4	no	—
101	D₈×C₁₃₇	—	2	1	no	—
102	D₈×C₁₃₇	—	2	1	no	—
103	D₈×C₁₃₇	—	2	1	no	—
104	D₈×C₁₃₇	#41	1	2	yes	complemented
105	C₂×C₈×C₁₃₇	—	2	2	no	—
106	C₂×C₈×C₁₃₇	—	2	2	no	—
107	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₁₃₇	C₂⁴	1	1	yes	characteristic
110	C₄⋊C₄×C₁₃₇	—	2	1	no	—
111	C₄⋊C₄×C₁₃₇	—	2	1	no	—
112	C₄⋊C₄×C₁₃₇	—	2	2	no	—
113	C₄⋊C₄×C₁₃₇	—	4	2	no	—
114	C₄⋊C₄×C₁₃₇	—	4	1	no	—
115	C₄⋊C₄×C₁₃₇	—	4	2	no	—
116	C₄⋊C₄×C₁₃₇	—	4	1	no	—
117	C₄⋊C₄×C₁₃₇	—	4	1	no	—
118	C₄⋊C₄×C₁₃₇	D₈	1	1	yes	characteristic
119	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
120	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
121	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
122	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
123	C₂²⋊C₄×C₁₃₇	D₈	1	2	yes	—
124	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
125	C₁₆×C₁₃₇	—	2	1	no	—
126	C₁₆×C₁₃₇	—	2	1	no	—
127	C₁₆×C₁₃₇	—	2	2	no	—
128	C₂³×C₁₃₇	—	4	1	no	—
129	C₂³×C₁₃₇	—	4	1	no	—
130	C₂³×C₁₃₇	C₂×D₈	1	2	yes	—
131	Q₈×C₁₃₇	—	4	2	no	—
132	Q₈×C₁₃₇	—	4	2	no	—
133	Q₈×C₁₃₇	—	8	2	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	D₄×C₁₃₇	—	4	1	no	—
139	D₄×C₁₃₇	—	8	4	no	—
140	D₄×C₁₃₇	—	8	4	no	—
141	C₂×C₄×C₁₃₇	—	2	2	no	—
142	C₂×C₄×C₁₃₇	—	2	2	no	—
143	C₂×C₄×C₁₃₇	—	4	1	no	—
144	C₂×C₄×C₁₃₇	—	4	1	no	—
145	C₂×C₄×C₁₃₇	—	4	2	no	—
146	C₂×C₄×C₁₃₇	—	4	2	no	—
147	C₂×C₄×C₁₃₇	—	8	4	no	—
148	C₂×C₄×C₁₃₇	—	8	4	no	—
149	C₂×C₄×C₁₃₇	—	8	2	no	—
150	C₂×C₄×C₁₃₇	—	8	2	no	—
151	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
152	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
153	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
154	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
155	C₈×C₁₃₇	—	2	2	no	—
156	C₈×C₁₃₇	—	2	1	no	—
157	C₈×C₁₃₇	C₂×#41	1	1	yes	characteristic
158	C₈×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
159	C₂²×C₁₃₇	—	2	2	no	—
160	C₂²×C₁₃₇	—	2	2	no	—
161	C₂²×C₁₃₇	—	2	2	no	—
162	C₂²×C₁₃₇	—	4	2	no	—
163	C₂²×C₁₃₇	—	8	1	no	—
164	C₂²×C₁₃₇	—	8	1	no	—
165	C₂²×C₁₃₇	—	8	1	no	—
166	C₂²×C₁₃₇	—	8	1	no	—
167	C₂²×C₁₃₇	—	8	1	no	—
168	C₂²×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
169	C₄×C₁₃₇	—	2	1	no	—
170	C₄×C₁₃₇	—	2	2	no	—
171	C₄×C₁₃₇	—	8	1	no	—
172	C₄×C₁₃₇	—	8	1	no	—
173	C₄×C₁₃₇	—	8	2	no	—
174	C₄×C₁₃₇	—	8	2	no	—
175	C₄×C₁₃₇	#509	1	2	yes	—
176	C₄×C₁₃₇	#546	1	1	yes	characteristic
177	C₄×C₁₃₇	#577	1	1	yes	characteristic
178	C₂×C₁₃₇	—	4	2	no	—
179	C₂×C₁₃₇	—	8	2	no	—
180	C₂×C₁₃₇	—	16	1	no	—
181	C₂×C₁₃₇	#3294	1	1	yes	characteristic
182	C₂×C₁₃₇	C₂×#509	1	1	yes	characteristic
183	C₂×C₁₃₇	#3417	1	1	yes	characteristic
184	#33897	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₁₃₇	#33897	1	1	yes	characteristic, direct product factor, Sylow
186	#3334	C₂×C₁₃₇	1	1	yes	characteristic, complemented
187	#3283	C₂×C₁₃₇	1	1	yes	characteristic, complemented
188	#2241	C₂×C₁₃₇	1	1	yes	characteristic, complemented
189	#2236	C₂×C₁₃₇	1	2	yes	complemented
190	#2224	C₂×C₁₃₇	1	1	yes	characteristic, complemented
191	#2220	C₂×C₁₃₇	1	2	yes	complemented
192	#2208	C₂×C₁₃₇	1	1	yes	characteristic, complemented
193	#2186	C₂×C₁₃₇	1	2	yes	complemented
194	C₄×D₁₆	C₂×C₁₃₇	1	1	yes	characteristic, complemented
195	#2169	C₂×C₁₃₇	1	1	yes	characteristic, complemented
196	#2139	C₂×C₁₃₇	1	2	yes	complemented
197	C₂×#135	C₂²×C₁₃₇	1	2	yes	—
198	#547	—	2	1	no	—
199	#547	—	2	1	no	—
200	C₂×SD₃₂	C₂²×C₁₃₇	1	2	yes	—
201	C₂×D₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
202	C₂×M₃₂	C₂²×C₁₃₇	1	2	yes	—
203	#500	C₂²×C₁₃₇	1	1	yes	characteristic
204	#494	C₂²×C₁₃₇	1	1	yes	characteristic
205	#480	—	2	2	no	—
206	#474	—	2	1	no	—
207	#467	C₂²×C₁₃₇	1	2	yes	—
208	#466	C₂²×C₁₃₇	1	2	yes	—
209	#461	—	2	1	no	—
210	#452	—	2	2	no	—
211	C₄×D₈	C₂²×C₁₃₇	1	1	yes	characteristic
212	C₄×D₈	C₂²×C₁₃₇	1	1	yes	characteristic
213	C₈×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
214	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
215	#366	C₂²×C₁₃₇	1	1	yes	characteristic
216	#366	C₂²×C₁₃₇	1	2	yes	—
217	C₄⋊C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
218	#358	C₂²×C₁₃₇	1	2	yes	—
219	#358	C₂²×C₁₃₇	1	2	yes	—
220	#358	C₂²×C₁₃₇	1	2	yes	—
221	#357	C₂²×C₁₃₇	1	1	yes	characteristic
222	#357	C₂²×C₁₃₇	1	2	yes	—
223	#357	C₂²×C₁₃₇	1	1	yes	characteristic
224	C₂²⋊C₁₆	C₂²×C₁₃₇	1	2	yes	—
225	C₄×C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
226	C₂×#41	—	2	2	no	—
227	C₂×#41	—	4	1	no	—
228	#135	—	2	4	no	—
229	#135	—	4	2	no	—
230	C₂×Q₁₆	—	2	1	no	—
231	C₂×Q₁₆	C₂³×C₁₃₇	1	2	yes	—
232	C₂×SD₁₆	—	2	2	no	—
233	C₂×D₈	C₂³×C₁₃₇	1	1	yes	characteristic
234	C₂×D₈	C₂³×C₁₃₇	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
236	C₄⋊Q₈	—	2	1	no	—
237	C₄⋊Q₈	—	2	1	no	—
238	#123	—	4	2	no	—
239	#123	—	4	2	no	—
240	C₂²⋊Q₈	—	2	2	no	—
241	C₂²⋊Q₈	—	4	1	no	—
242	#121	—	2	2	no	—
243	#121	—	4	1	no	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	D₄×C₁₃₇	1	1	yes	characteristic
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	4	1	no	—
249	SD₃₂	—	4	2	no	—
250	D₁₆	—	2	2	no	—
251	M₃₂	—	4	2	no	—
252	C₂×C₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
253	C₂×C₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
254	C₂×C₁₆	C₂³×C₁₃₇	1	2	yes	—
255	#107	—	2	2	no	—
256	#107	—	2	1	no	—
257	#107	C₂³×C₁₃₇	1	1	yes	characteristic
258	#107	C₂³×C₁₃₇	1	2	yes	—
259	#107	C₂³×C₁₃₇	1	1	yes	characteristic
260	C₄⋊C₈	D₄×C₁₃₇	1	1	yes	characteristic
261	#103	—	2	2	no	—
262	#102	—	2	1	no	—
263	#102	—	2	1	no	—
264	#102	—	2	2	no	—
265	C₂²⋊C₈	D₄×C₁₃₇	1	2	yes	—
266	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
267	#41	—	4	4	no	—
268	#41	—	8	2	no	—
269	#41	—	8	4	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	4	1	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	4	2	no	—
275	C₂×D₄	—	4	2	no	—
276	C₂×D₄	D₈×C₁₃₇	1	1	yes	characteristic
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
282	Q₁₆	—	2	2	no	—
283	Q₁₆	—	2	2	no	—
284	Q₁₆	—	8	1	no	—
285	SD₁₆	—	4	4	no	—
286	D₈	—	2	1	no	—
287	D₈	—	2	1	no	—
288	D₈	—	2	1	no	—
289	D₈	#41×C₁₃₇	1	2	yes	complemented
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
293	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
294	C₂×C₈	C₂⁴×C₁₃₇	1	1	yes	characteristic
295	C₄⋊C₄	—	2	1	no	—
296	C₄⋊C₄	—	2	1	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	4	2	no	—
299	C₄⋊C₄	—	4	1	no	—
300	C₄⋊C₄	—	4	2	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	D₈×C₁₃₇	1	1	yes	characteristic
304	C₂²⋊C₄	—	4	2	no	—
305	C₂²⋊C₄	—	4	1	no	—
306	C₂²⋊C₄	—	4	1	no	—
307	C₂²⋊C₄	—	4	2	no	—
308	C₂²⋊C₄	D₈×C₁₃₇	1	2	yes	—
309	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
310	C₁₆	—	2	1	no	—
311	C₁₆	—	2	1	no	—
312	C₁₆	—	2	2	no	—
313	C₂³	—	4	1	no	—
314	C₂³	—	4	1	no	—
315	C₂³	C₂×D₈×C₁₃₇	1	2	yes	—
316	Q₈	—	4	2	no	—
317	Q₈	—	4	2	no	—
318	Q₈	—	8	2	no	—
319	D₄	—	2	2	no	—
320	D₄	—	2	2	no	—
321	D₄	—	4	1	no	—
322	D₄	—	4	1	no	—
323	D₄	—	4	1	no	—
324	D₄	—	8	4	no	—
325	D₄	—	8	4	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	8	4	no	—
333	C₂×C₄	—	8	4	no	—
334	C₂×C₄	—	8	2	no	—
335	C₂×C₄	—	8	2	no	—
336	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
337	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
338	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
340	C₈	—	2	2	no	—
341	C₈	—	2	1	no	—
342	C₈	C₂×#41×C₁₃₇	1	1	yes	characteristic
343	C₈	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
344	C₂²	—	2	2	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	4	2	no	—
348	C₂²	—	8	1	no	—
349	C₂²	—	8	1	no	—
350	C₂²	—	8	1	no	—
351	C₂²	—	8	1	no	—
352	C₂²	—	8	1	no	—
353	C₂²	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	2	1	no	—
356	C₄	—	8	2	no	—
357	C₄	—	8	1	no	—
358	C₄	—	8	2	no	—
359	C₄	—	8	1	no	—
360	C₄	#509×C₁₃₇	1	2	yes	—
361	C₄	#546×C₁₃₇	1	1	yes	characteristic
362	C₄	#577×C₁₃₇	1	1	yes	characteristic
363	C₂	—	4	2	no	—
364	C₂	—	8	2	no	—
365	C₂	—	16	1	no	—
366	C₂	#3294×C₁₃₇	1	1	yes	characteristic
367	C₂	C₂×#509×C₁₃₇	1	1	yes	characteristic
368	C₂	#3417×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₄×D₄×C₁₃₇ ◁ C₈×D₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3334×C₁₃₇	C₂	semidirect
2. #3283×C₁₃₇	C₂	semidirect
3. #2241×C₁₃₇	C₂	semidirect
4. #2236×C₁₃₇	C₂	semidirect
5. #2224×C₁₃₇	C₂	semidirect
6. #2220×C₁₃₇	C₂	semidirect
7. #2208×C₁₃₇	C₂	semidirect
8. #2186×C₁₃₇	C₂	semidirect
9. C₄×D₁₆×C₁₃₇	C₂	semidirect
10. #2169×C₁₃₇	C₂	semidirect
11. #2139×C₁₃₇	C₂	semidirect
104. D₈×C₁₃₇	#41	semidirect
184. #33897	C₁₃₇	direct (N × H)
185. C₁₃₇	#33897	direct (N × H)
186. #3334	C₂×C₁₃₇	semidirect
187. #3283	C₂×C₁₃₇	semidirect
188. #2241	C₂×C₁₃₇	semidirect
189. #2236	C₂×C₁₃₇	semidirect
190. #2224	C₂×C₁₃₇	semidirect
191. #2220	C₂×C₁₃₇	semidirect
192. #2208	C₂×C₁₃₇	semidirect
193. #2186	C₂×C₁₃₇	semidirect
194. C₄×D₁₆	C₂×C₁₃₇	semidirect
195. #2169	C₂×C₁₃₇	semidirect
196. #2139	C₂×C₁₃₇	semidirect
289. D₈	#41×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3334×C₁₃₇	2
#3283×C₁₃₇	2
#2241×C₁₃₇	2
#2236×C₁₃₇	2
#2224×C₁₃₇	2
#2220×C₁₃₇	2
#2208×C₁₃₇	2
#2186×C₁₃₇	2
C₄×D₁₆×C₁₃₇	2
#2169×C₁₃₇	2
#2139×C₁₃₇	2
#33897	137

Subgroups — C137×#33897 #46883283

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#33897 #46883283