Subgroups — C₁₃₇×#33617 #46883003

Order 35072.

642 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#508×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#504×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#3067×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#2223×C₁₃₇	C₂	1	4	yes	maximal, complemented
5	#2222×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2221×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	C₂×#368×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#2148×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#575×C₁₃₇	—	2	2	no	—
10	C₂×#135×C₁₃₇	C₂²	1	2	yes	—
11	C₂×#131×C₁₃₇	C₂²	1	1	yes	characteristic
12	#508×C₁₃₇	—	2	1	no	—
13	#508×C₁₃₇	—	2	1	no	—
14	#508×C₁₃₇	—	2	1	no	—
15	#508×C₁₃₇	—	2	1	no	—
16	C₂×Q₃₂×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
17	C₂×SD₃₂×C₁₃₇	C₂²	1	2	yes	complemented
18	C₂×D₁₆×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
19	#504×C₁₃₇	—	2	1	no	—
20	#504×C₁₃₇	—	2	1	no	—
21	#504×C₁₃₇	C₂²	1	2	yes	—
22	#504×C₁₃₇	C₂²	1	2	yes	—
23	C₂×M₃₂×C₁₃₇	—	2	1	no	—
24	C₂×M₃₂×C₁₃₇	C₂²	1	1	yes	characteristic
25	C₂²×C₁₆×C₁₃₇	—	2	1	no	—
26	C₂²×C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
27	#473×C₁₃₇	C₂²	1	4	yes	—
28	#472×C₁₃₇	C₂²	1	4	yes	—
29	#471×C₁₃₇	—	2	4	no	—
30	C₂×#108×C₁₃₇	C₂²	1	2	yes	—
31	#413×C₁₃₇	—	2	2	no	—
32	#368×C₁₃₇	C₂²	1	2	yes	complemented
33	#368×C₁₃₇	C₂²	1	2	yes	complemented
34	#362×C₁₃₇	C₂²	1	4	yes	complemented
35	#361×C₁₃₇	C₂²	1	4	yes	complemented
36	C₂×#41×C₁₃₇	—	2	2	no	—
37	C₂×#41×C₁₃₇	D₄	1	1	yes	characteristic
38	#137×C₁₃₇	—	2	4	no	—
39	#137×C₁₃₇	—	4	2	no	—
40	AGL(1,ℤ/8)×C₁₃₇	—	2	4	no	—
41	AGL(1,ℤ/8)×C₁₃₇	—	4	2	no	—
42	#135×C₁₃₇	—	2	2	no	—
43	#135×C₁₃₇	—	2	2	no	—
44	#135×C₁₃₇	—	2	2	no	—
45	#135×C₁₃₇	—	2	2	no	—
46	#135×C₁₃₇	—	4	4	no	—
47	C₂×Q₁₆×C₁₃₇	C₂³	1	2	yes	—
48	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
49	C₂×D₈×C₁₃₇	C₂³	1	2	yes	—
50	#131×C₁₃₇	—	2	1	no	—
51	#131×C₁₃₇	—	2	1	no	—
52	#131×C₁₃₇	D₄	1	2	yes	—
53	#131×C₁₃₇	C₂³	1	2	yes	—
54	C₂×M₁₆×C₁₃₇	—	2	1	no	—
55	C₂×M₁₆×C₁₃₇	—	2	2	no	—
56	C₂×M₁₆×C₁₃₇	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₃₇	—	2	1	no	—
58	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
59	Q₃₂×C₁₃₇	—	2	1	no	—
60	Q₃₂×C₁₃₇	—	2	1	no	—
61	SD₃₂×C₁₃₇	—	2	2	no	—
62	SD₃₂×C₁₃₇	—	2	2	no	—
63	D₁₆×C₁₃₇	—	2	1	no	—
64	D₁₆×C₁₃₇	—	2	1	no	—
65	M₃₂×C₁₃₇	—	2	1	no	—
66	M₃₂×C₁₃₇	—	2	2	no	—
67	M₃₂×C₁₃₇	—	2	2	no	—
68	M₃₂×C₁₃₇	C₂³	1	2	yes	—
69	C₂×C₁₆×C₁₃₇	—	2	1	no	—
70	C₂×C₁₆×C₁₃₇	—	2	2	no	—
71	C₂×C₁₆×C₁₃₇	—	2	2	no	—
72	C₂×C₁₆×C₁₃₇	D₄	1	1	yes	characteristic
73	C₂×C₁₆×C₁₃₇	D₄	1	1	yes	characteristic
74	C₂×C₁₆×C₁₃₇	D₄	1	1	yes	characteristic
75	C₂×C₁₆×C₁₃₇	D₄	1	1	yes	characteristic
76	C₂×C₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
77	C₂×C₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
78	#108×C₁₃₇	—	2	2	no	—
79	#108×C₁₃₇	C₂³	1	4	yes	—
80	#101×C₁₃₇	—	2	4	no	—
81	#100×C₁₃₇	—	2	4	no	—
82	#41×C₁₃₇	—	2	1	no	—
83	#41×C₁₃₇	—	2	1	no	—
84	#41×C₁₃₇	—	4	2	no	—
85	#41×C₁₃₇	—	4	2	no	—
86	#41×C₁₃₇	—	4	2	no	—
87	#41×C₁₃₇	—	4	2	no	—
88	#41×C₁₃₇	D₈	1	2	yes	—
89	#41×C₁₃₇	C₂×D₄	1	2	yes	—
90	C₂×Q₈×C₁₃₇	—	2	2	no	—
91	C₂×Q₈×C₁₃₇	D₈	1	1	yes	characteristic
92	C₂×D₄×C₁₃₇	—	2	1	no	—
93	C₂×D₄×C₁₃₇	—	2	2	no	—
94	C₂×D₄×C₁₃₇	—	4	2	no	—
95	C₂×D₄×C₁₃₇	D₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₃₇	—	2	1	no	—
97	C₂²×C₄×C₁₃₇	—	4	2	no	—
98	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
99	Q₁₆×C₁₃₇	—	2	2	no	—
100	Q₁₆×C₁₃₇	—	2	2	no	—
101	Q₁₆×C₁₃₇	—	4	4	no	—
102	SD₁₆×C₁₃₇	—	4	4	no	—
103	SD₁₆×C₁₃₇	—	4	4	no	—
104	SD₁₆×C₁₃₇	—	4	2	no	—
105	SD₁₆×C₁₃₇	—	4	2	no	—
106	D₈×C₁₃₇	—	2	2	no	—
107	D₈×C₁₃₇	—	2	2	no	—
108	D₈×C₁₃₇	—	4	4	no	—
109	M₁₆×C₁₃₇	—	2	1	no	—
110	M₁₆×C₁₃₇	—	2	2	no	—
111	M₁₆×C₁₃₇	—	2	2	no	—
112	M₁₆×C₁₃₇	—	2	4	no	—
113	M₁₆×C₁₃₇	—	4	2	no	—
114	M₁₆×C₁₃₇	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₁₃₇	—	2	1	no	—
116	C₂×C₈×C₁₃₇	—	2	2	no	—
117	C₂×C₈×C₁₃₇	—	2	2	no	—
118	C₂×C₈×C₁₃₇	—	4	2	no	—
119	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃₇	#41	1	1	yes	characteristic
123	C₂×C₈×C₁₃₇	#41	1	1	yes	characteristic
124	C₂×C₈×C₁₃₇	C₂⁴	1	1	yes	characteristic
125	C₁₆×C₁₃₇	—	2	2	no	—
126	C₁₆×C₁₃₇	C₂×D₄	1	1	yes	characteristic
127	C₁₆×C₁₃₇	C₂×D₄	1	1	yes	characteristic
128	C₁₆×C₁₃₇	C₂×D₄	1	1	yes	characteristic
129	C₁₆×C₁₃₇	C₂×D₄	1	1	yes	characteristic
130	C₂³×C₁₃₇	—	2	1	no	—
131	C₂³×C₁₃₇	—	4	2	no	—
132	C₂³×C₁₃₇	#135	1	1	yes	characteristic
133	Q₈×C₁₃₇	—	2	1	no	—
134	Q₈×C₁₃₇	—	4	2	no	—
135	Q₈×C₁₃₇	—	4	2	no	—
136	Q₈×C₁₃₇	C₂×D₈	1	2	yes	—
137	D₄×C₁₃₇	—	2	2	no	—
138	D₄×C₁₃₇	—	2	2	no	—
139	D₄×C₁₃₇	—	2	1	no	—
140	D₄×C₁₃₇	—	4	2	no	—
141	D₄×C₁₃₇	—	4	2	no	—
142	D₄×C₁₃₇	—	8	2	no	—
143	D₄×C₁₃₇	—	8	2	no	—
144	D₄×C₁₃₇	C₂×D₈	1	2	yes	—
145	C₂×C₄×C₁₃₇	—	2	1	no	—
146	C₂×C₄×C₁₃₇	—	2	2	no	—
147	C₂×C₄×C₁₃₇	—	2	2	no	—
148	C₂×C₄×C₁₃₇	—	4	2	no	—
149	C₂×C₄×C₁₃₇	—	8	2	no	—
150	C₂×C₄×C₁₃₇	—	8	2	no	—
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	1	yes	characteristic
154	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₁₃₇	#135	1	1	yes	characteristic
156	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
157	C₈×C₁₃₇	—	2	2	no	—
158	C₈×C₁₃₇	—	4	4	no	—
159	C₈×C₁₃₇	#121	1	1	yes	characteristic
160	C₈×C₁₃₇	#121	1	1	yes	characteristic
161	C₈×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
162	C₈×C₁₃₇	C₂×#41	1	1	yes	characteristic
163	C₂²×C₁₃₇	—	2	2	no	—
164	C₂²×C₁₃₇	—	4	1	no	—
165	C₂²×C₁₃₇	—	4	2	no	—
166	C₂²×C₁₃₇	—	8	2	no	—
167	C₂²×C₁₃₇	—	16	2	no	—
168	C₂²×C₁₃₇	#466	1	1	yes	characteristic
169	C₂²×C₁₃₇	#466	1	1	yes	characteristic
170	C₂²×C₁₃₇	C₂×#135	1	1	yes	characteristic
171	C₄×C₁₃₇	—	2	2	no	—
172	C₄×C₁₃₇	—	8	2	no	—
173	C₄×C₁₃₇	#466	1	1	yes	characteristic
174	C₄×C₁₃₇	#466	1	1	yes	characteristic
175	C₄×C₁₃₇	C₂×#121	1	1	yes	characteristic
176	C₄×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
177	C₂×C₁₃₇	—	2	1	no	—
178	C₂×C₁₃₇	—	2	1	no	—
179	C₂×C₁₃₇	—	2	1	no	—
180	C₂×C₁₃₇	—	4	2	no	—
181	C₂×C₁₃₇	—	16	2	no	—
182	C₂×C₁₃₇	C₂×#466	1	1	yes	characteristic
183	#33617	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₁₃₇	#33617	1	1	yes	characteristic, direct product factor, Sylow
185	C₂×#508	C₂×C₁₃₇	1	1	yes	characteristic, complemented
186	C₂×#504	C₂×C₁₃₇	1	1	yes	characteristic, complemented
187	#3067	C₂×C₁₃₇	1	2	yes	complemented
188	#2223	C₂×C₁₃₇	1	4	yes	complemented
189	#2222	C₂×C₁₃₇	1	2	yes	complemented
190	#2221	C₂×C₁₃₇	1	2	yes	complemented
191	C₂×#368	C₂×C₁₃₇	1	1	yes	characteristic, complemented
192	#2148	C₂×C₁₃₇	1	2	yes	complemented
193	#575	—	2	2	no	—
194	C₂×#135	C₂²×C₁₃₇	1	2	yes	—
195	C₂×#131	C₂²×C₁₃₇	1	1	yes	characteristic
196	#508	—	2	1	no	—
197	#508	—	2	1	no	—
198	#508	—	2	1	no	—
199	#508	—	2	1	no	—
200	C₂×Q₃₂	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
201	C₂×SD₃₂	C₂²×C₁₃₇	1	2	yes	complemented
202	C₂×D₁₆	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
203	#504	—	2	1	no	—
204	#504	—	2	1	no	—
205	#504	C₂²×C₁₃₇	1	2	yes	—
206	#504	C₂²×C₁₃₇	1	2	yes	—
207	C₂×M₃₂	—	2	1	no	—
208	C₂×M₃₂	C₂²×C₁₃₇	1	1	yes	characteristic
209	C₂²×C₁₆	—	2	1	no	—
210	C₂²×C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
211	#473	C₂²×C₁₃₇	1	4	yes	—
212	#472	C₂²×C₁₃₇	1	4	yes	—
213	#471	—	2	4	no	—
214	C₂×#108	C₂²×C₁₃₇	1	2	yes	—
215	#413	—	2	2	no	—
216	#368	C₂²×C₁₃₇	1	2	yes	complemented
217	#368	C₂²×C₁₃₇	1	2	yes	complemented
218	#362	C₂²×C₁₃₇	1	4	yes	complemented
219	#361	C₂²×C₁₃₇	1	4	yes	complemented
220	C₂×#41	—	2	2	no	—
221	C₂×#41	D₄×C₁₃₇	1	1	yes	characteristic
222	#137	—	2	4	no	—
223	#137	—	4	2	no	—
224	AGL(1,ℤ/8)	—	2	4	no	—
225	AGL(1,ℤ/8)	—	4	2	no	—
226	#135	—	2	2	no	—
227	#135	—	2	2	no	—
228	#135	—	2	2	no	—
229	#135	—	2	2	no	—
230	#135	—	4	4	no	—
231	C₂×Q₁₆	C₂³×C₁₃₇	1	2	yes	—
232	C₂×SD₁₆	—	2	2	no	—
233	C₂×D₈	C₂³×C₁₃₇	1	2	yes	—
234	#131	—	2	1	no	—
235	#131	—	2	1	no	—
236	#131	D₄×C₁₃₇	1	2	yes	—
237	#131	C₂³×C₁₃₇	1	2	yes	—
238	C₂×M₁₆	—	2	1	no	—
239	C₂×M₁₆	—	2	2	no	—
240	C₂×M₁₆	D₄×C₁₃₇	1	1	yes	characteristic
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
243	Q₃₂	—	2	1	no	—
244	Q₃₂	—	2	1	no	—
245	SD₃₂	—	2	2	no	—
246	SD₃₂	—	2	2	no	—
247	D₁₆	—	2	1	no	—
248	D₁₆	—	2	1	no	—
249	M₃₂	—	2	1	no	—
250	M₃₂	—	2	2	no	—
251	M₃₂	—	2	2	no	—
252	M₃₂	C₂³×C₁₃₇	1	2	yes	—
253	C₂×C₁₆	—	2	1	no	—
254	C₂×C₁₆	—	2	2	no	—
255	C₂×C₁₆	—	2	2	no	—
256	C₂×C₁₆	D₄×C₁₃₇	1	1	yes	characteristic
257	C₂×C₁₆	D₄×C₁₃₇	1	1	yes	characteristic
258	C₂×C₁₆	D₄×C₁₃₇	1	1	yes	characteristic
259	C₂×C₁₆	D₄×C₁₃₇	1	1	yes	characteristic
260	C₂×C₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
261	C₂×C₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
262	#108	—	2	2	no	—
263	#108	C₂³×C₁₃₇	1	4	yes	—
264	#101	—	2	4	no	—
265	#100	—	2	4	no	—
266	#41	—	2	1	no	—
267	#41	—	2	1	no	—
268	#41	—	4	2	no	—
269	#41	—	4	2	no	—
270	#41	—	4	2	no	—
271	#41	—	4	2	no	—
272	#41	D₈×C₁₃₇	1	2	yes	—
273	#41	C₂×D₄×C₁₃₇	1	2	yes	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	D₈×C₁₃₇	1	1	yes	characteristic
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	D₈×C₁₃₇	1	1	yes	characteristic
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
283	Q₁₆	—	2	2	no	—
284	Q₁₆	—	2	2	no	—
285	Q₁₆	—	4	4	no	—
286	SD₁₆	—	4	4	no	—
287	SD₁₆	—	4	4	no	—
288	SD₁₆	—	4	2	no	—
289	SD₁₆	—	4	2	no	—
290	D₈	—	2	2	no	—
291	D₈	—	2	2	no	—
292	D₈	—	4	4	no	—
293	M₁₆	—	2	1	no	—
294	M₁₆	—	2	2	no	—
295	M₁₆	—	2	2	no	—
296	M₁₆	—	2	4	no	—
297	M₁₆	—	4	2	no	—
298	M₁₆	C₂×D₄×C₁₃₇	1	2	yes	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	4	2	no	—
303	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
304	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
305	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
306	C₂×C₈	#41×C₁₃₇	1	1	yes	characteristic
307	C₂×C₈	#41×C₁₃₇	1	1	yes	characteristic
308	C₂×C₈	C₂⁴×C₁₃₇	1	1	yes	characteristic
309	C₁₆	—	2	2	no	—
310	C₁₆	C₂×D₄×C₁₃₇	1	1	yes	characteristic
311	C₁₆	C₂×D₄×C₁₃₇	1	1	yes	characteristic
312	C₁₆	C₂×D₄×C₁₃₇	1	1	yes	characteristic
313	C₁₆	C₂×D₄×C₁₃₇	1	1	yes	characteristic
314	C₂³	—	2	1	no	—
315	C₂³	—	4	2	no	—
316	C₂³	#135×C₁₃₇	1	1	yes	characteristic
317	Q₈	—	2	1	no	—
318	Q₈	—	4	2	no	—
319	Q₈	—	4	2	no	—
320	Q₈	C₂×D₈×C₁₃₇	1	2	yes	—
321	D₄	—	2	2	no	—
322	D₄	—	2	2	no	—
323	D₄	—	2	1	no	—
324	D₄	—	4	2	no	—
325	D₄	—	4	2	no	—
326	D₄	—	8	2	no	—
327	D₄	—	8	2	no	—
328	D₄	C₂×D₈×C₁₃₇	1	2	yes	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	8	2	no	—
334	C₂×C₄	—	8	2	no	—
335	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
336	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
337	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
338	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
339	C₂×C₄	#135×C₁₃₇	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
341	C₈	—	2	2	no	—
342	C₈	—	4	4	no	—
343	C₈	#121×C₁₃₇	1	1	yes	characteristic
344	C₈	#121×C₁₃₇	1	1	yes	characteristic
345	C₈	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
346	C₈	C₂×#41×C₁₃₇	1	1	yes	characteristic
347	C₂²	—	2	2	no	—
348	C₂²	—	4	1	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	8	2	no	—
351	C₂²	—	16	2	no	—
352	C₂²	#466×C₁₃₇	1	1	yes	characteristic
353	C₂²	#466×C₁₃₇	1	1	yes	characteristic
354	C₂²	C₂×#135×C₁₃₇	1	1	yes	characteristic
355	C₄	—	2	2	no	—
356	C₄	—	8	2	no	—
357	C₄	#466×C₁₃₇	1	1	yes	characteristic
358	C₄	#466×C₁₃₇	1	1	yes	characteristic
359	C₄	C₂×#121×C₁₃₇	1	1	yes	characteristic
360	C₄	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
361	C₂	—	2	1	no	—
362	C₂	—	2	1	no	—
363	C₂	—	2	1	no	—
364	C₂	—	4	2	no	—
365	C₂	—	16	2	no	—
366	C₂	C₂×#466×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃₇	#466
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₇
socle	C₂×C₁₃₇	C₂×#466
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃₇ ◁ C₂²×C₄×C₁₃₇ ◁ C₂×#131×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#508×C₁₃₇	C₂	semidirect
2. C₂×#504×C₁₃₇	C₂	semidirect
3. #3067×C₁₃₇	C₂	semidirect
4. #2223×C₁₃₇	C₂	semidirect
5. #2222×C₁₃₇	C₂	semidirect
6. #2221×C₁₃₇	C₂	semidirect
7. C₂×#368×C₁₃₇	C₂	semidirect
8. #2148×C₁₃₇	C₂	semidirect
16. C₂×Q₃₂×C₁₃₇	C₂²	semidirect
17. C₂×SD₃₂×C₁₃₇	C₂²	semidirect
18. C₂×D₁₆×C₁₃₇	C₂²	semidirect
32. #368×C₁₃₇	C₂²	semidirect
33. #368×C₁₃₇	C₂²	semidirect
34. #362×C₁₃₇	C₂²	semidirect
35. #361×C₁₃₇	C₂²	semidirect
183. #33617	C₁₃₇	direct (N × H)
184. C₁₃₇	#33617	direct (N × H)
185. C₂×#508	C₂×C₁₃₇	semidirect
186. C₂×#504	C₂×C₁₃₇	semidirect
187. #3067	C₂×C₁₃₇	semidirect
188. #2223	C₂×C₁₃₇	semidirect
189. #2222	C₂×C₁₃₇	semidirect
190. #2221	C₂×C₁₃₇	semidirect
191. C₂×#368	C₂×C₁₃₇	semidirect
192. #2148	C₂×C₁₃₇	semidirect
200. C₂×Q₃₂	C₂²×C₁₃₇	semidirect
201. C₂×SD₃₂	C₂²×C₁₃₇	semidirect
202. C₂×D₁₆	C₂²×C₁₃₇	semidirect
216. #368	C₂²×C₁₃₇	semidirect
217. #368	C₂²×C₁₃₇	semidirect
218. #362	C₂²×C₁₃₇	semidirect
219. #361	C₂²×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#508×C₁₃₇	2
C₂×#504×C₁₃₇	2
#3067×C₁₃₇	2
#2223×C₁₃₇	2
#2222×C₁₃₇	2
#2221×C₁₃₇	2
C₂×#368×C₁₃₇	2
#2148×C₁₃₇	2
#33617	137

Subgroups — C137×#33617 #46883003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#33617 #46883003