Subgroups — C₁₃₇×#33899 #46883285

Order 35072.

590 conjugacy classes of subgroups.

The subgroup lattice has 374 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	#3287×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2240×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#2233×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#2225×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#2218×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#2206×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#2186×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	C₄×SD₃₂×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	#550×C₁₃₇	—	2	1	no	—
14	#547×C₁₃₇	—	2	1	no	—
15	C₂×SD₃₂×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×D₁₆×C₁₃₇	C₂²	1	2	yes	—
17	C₂×M₃₂×C₁₃₇	C₂²	1	2	yes	—
18	#500×C₁₃₇	C₂²	1	1	yes	characteristic
19	#493×C₁₃₇	C₂²	1	1	yes	characteristic
20	#480×C₁₃₇	—	2	2	no	—
21	#474×C₁₃₇	—	2	1	no	—
22	#466×C₁₃₇	C₂²	1	2	yes	—
23	#466×C₁₃₇	C₂²	1	2	yes	—
24	#460×C₁₃₇	—	2	1	no	—
25	#449×C₁₃₇	—	2	2	no	—
26	C₄×Q₁₆×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	#367×C₁₃₇	C₂²	1	1	yes	characteristic
31	#367×C₁₃₇	C₂²	1	2	yes	—
32	C₄⋊C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
33	#358×C₁₃₇	C₂²	1	1	yes	characteristic
34	#358×C₁₃₇	C₂²	1	2	yes	—
35	#357×C₁₃₇	C₂²	1	2	yes	—
36	#357×C₁₃₇	C₂²	1	2	yes	—
37	#357×C₁₃₇	C₂²	1	1	yes	characteristic
38	#357×C₁₃₇	C₂²	1	2	yes	—
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	C₂³	1	1	yes	characteristic
46	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
47	C₂×D₈×C₁₃₇	—	2	1	no	—
48	C₂×D₈×C₁₃₇	C₂³	1	1	yes	characteristic
49	C₂×D₈×C₁₃₇	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
52	#127×C₁₃₇	—	2	1	no	—
53	#127×C₁₃₇	—	4	1	no	—
54	#123×C₁₃₇	—	4	2	no	—
55	C₂²⋊Q₈×C₁₃₇	—	4	1	no	—
56	#121×C₁₃₇	—	2	2	no	—
57	#121×C₁₃₇	—	2	2	no	—
58	#121×C₁₃₇	—	4	2	no	—
59	C₄×Q₈×C₁₃₇	—	2	1	no	—
60	C₄×D₄×C₁₃₇	—	2	1	no	—
61	C₄×D₄×C₁₃₇	—	4	1	no	—
62	C₄×D₄×C₁₃₇	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
64	SD₃₂×C₁₃₇	—	2	2	no	—
65	D₁₆×C₁₃₇	—	4	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	1	no	—
77	#102×C₁₃₇	—	2	1	no	—
78	#102×C₁₃₇	—	2	2	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	1	no	—
86	C₂×Q₈×C₁₃₇	—	4	1	no	—
87	C₂×D₄×C₁₃₇	—	2	1	no	—
88	C₂×D₄×C₁₃₇	—	2	2	no	—
89	C₂×D₄×C₁₃₇	—	4	2	no	—
90	C₂×D₄×C₁₃₇	—	4	2	no	—
91	C₂×D₄×C₁₃₇	—	4	2	no	—
92	C₂×D₄×C₁₃₇	—	4	1	no	—
93	C₂×D₄×C₁₃₇	—	4	1	no	—
94	C₂×D₄×C₁₃₇	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₃₇	—	4	2	no	—
96	C₂²×C₄×C₁₃₇	—	4	1	no	—
97	C₂²×C₄×C₁₃₇	—	4	2	no	—
98	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
99	Q₁₆×C₁₃₇	—	2	1	no	—
100	Q₁₆×C₁₃₇	#41	1	2	yes	complemented
101	SD₁₆×C₁₃₇	—	4	4	no	—
102	D₈×C₁₃₇	—	2	1	no	—
103	D₈×C₁₃₇	—	2	2	no	—
104	D₈×C₁₃₇	—	2	1	no	—
105	D₈×C₁₃₇	—	2	2	no	—
106	D₈×C₁₃₇	—	8	1	no	—
107	C₂×C₈×C₁₃₇	—	2	2	no	—
108	C₂×C₈×C₁₃₇	—	2	2	no	—
109	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₁₃₇	C₂⁴	1	1	yes	characteristic
112	C₄⋊C₄×C₁₃₇	—	2	1	no	—
113	C₄⋊C₄×C₁₃₇	—	2	1	no	—
114	C₄⋊C₄×C₁₃₇	—	2	2	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	1	no	—
120	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
121	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
122	C₂²⋊C₄×C₁₃₇	D₈	1	2	yes	—
123	C₄²×C₁₃₇	—	4	1	no	—
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	2	no	—
130	C₂³×C₁₃₇	C₂×D₈	1	2	yes	—
131	Q₈×C₁₃₇	—	2	2	no	—
132	Q₈×C₁₃₇	—	4	1	no	—
133	Q₈×C₁₃₇	—	8	2	no	—
134	D₄×C₁₃₇	—	2	2	no	—
135	D₄×C₁₃₇	—	4	2	no	—
136	D₄×C₁₃₇	—	4	1	no	—
137	D₄×C₁₃₇	—	4	2	no	—
138	D₄×C₁₃₇	—	4	1	no	—
139	D₄×C₁₃₇	—	8	4	no	—
140	D₄×C₁₃₇	—	8	4	no	—
141	D₄×C₁₃₇	—	8	2	no	—
142	D₄×C₁₃₇	—	16	1	no	—
143	D₄×C₁₃₇	—	16	2	no	—
144	C₂×C₄×C₁₃₇	—	2	2	no	—
145	C₂×C₄×C₁₃₇	—	2	2	no	—
146	C₂×C₄×C₁₃₇	—	4	1	no	—
147	C₂×C₄×C₁₃₇	—	4	1	no	—
148	C₂×C₄×C₁₃₇	—	4	1	no	—
149	C₂×C₄×C₁₃₇	—	4	2	no	—
150	C₂×C₄×C₁₃₇	—	8	4	no	—
151	C₂×C₄×C₁₃₇	—	8	4	no	—
152	C₂×C₄×C₁₃₇	—	8	2	no	—
153	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
154	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
155	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
157	C₈×C₁₃₇	—	2	2	no	—
158	C₈×C₁₃₇	—	2	1	no	—
159	C₈×C₁₃₇	C₂×#41	1	1	yes	characteristic
160	C₈×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×C₁₃₇	—	2	2	no	—
162	C₂²×C₁₃₇	—	2	2	no	—
163	C₂²×C₁₃₇	—	2	2	no	—
164	C₂²×C₁₃₇	—	8	1	no	—
165	C₂²×C₁₃₇	—	8	2	no	—
166	C₂²×C₁₃₇	—	8	2	no	—
167	C₂²×C₁₃₇	—	8	1	no	—
168	C₂²×C₁₃₇	—	8	2	no	—
169	C₂²×C₁₃₇	—	8	1	no	—
170	C₂²×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
171	C₄×C₁₃₇	—	2	1	no	—
172	C₄×C₁₃₇	—	2	2	no	—
173	C₄×C₁₃₇	—	4	2	no	—
174	C₄×C₁₃₇	—	8	1	no	—
175	C₄×C₁₃₇	—	8	2	no	—
176	C₄×C₁₃₇	—	8	1	no	—
177	C₄×C₁₃₇	#509	1	2	yes	—
178	C₄×C₁₃₇	#546	1	1	yes	characteristic
179	C₄×C₁₃₇	#577	1	1	yes	characteristic
180	C₂×C₁₃₇	—	4	2	no	—
181	C₂×C₁₃₇	—	16	1	no	—
182	C₂×C₁₃₇	—	16	2	no	—
183	C₂×C₁₃₇	#3294	1	1	yes	characteristic
184	C₂×C₁₃₇	C₂×#509	1	1	yes	characteristic
185	C₂×C₁₃₇	#3416	1	1	yes	characteristic
186	#33899	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₁₃₇	#33899	1	1	yes	characteristic, direct product factor, Sylow
188	#3334	C₂×C₁₃₇	1	1	yes	characteristic, complemented
189	#3287	C₂×C₁₃₇	1	1	yes	characteristic, complemented
190	#2240	C₂×C₁₃₇	1	1	yes	characteristic, complemented
191	#2233	C₂×C₁₃₇	1	2	yes	complemented
192	#2225	C₂×C₁₃₇	1	1	yes	characteristic, complemented
193	#2218	C₂×C₁₃₇	1	2	yes	complemented
194	#2206	C₂×C₁₃₇	1	1	yes	characteristic, complemented
195	#2186	C₂×C₁₃₇	1	2	yes	complemented
196	C₄×SD₃₂	C₂×C₁₃₇	1	1	yes	characteristic, complemented
197	#2169	C₂×C₁₃₇	1	1	yes	characteristic, complemented
198	#2139	C₂×C₁₃₇	1	2	yes	complemented
199	C₂×#135	C₂²×C₁₃₇	1	2	yes	—
200	#550	—	2	1	no	—
201	#547	—	2	1	no	—
202	C₂×SD₃₂	C₂²×C₁₃₇	1	1	yes	characteristic
203	C₂×D₁₆	C₂²×C₁₃₇	1	2	yes	—
204	C₂×M₃₂	C₂²×C₁₃₇	1	2	yes	—
205	#500	C₂²×C₁₃₇	1	1	yes	characteristic
206	#493	C₂²×C₁₃₇	1	1	yes	characteristic
207	#480	—	2	2	no	—
208	#474	—	2	1	no	—
209	#466	C₂²×C₁₃₇	1	2	yes	—
210	#466	C₂²×C₁₃₇	1	2	yes	—
211	#460	—	2	1	no	—
212	#449	—	2	2	no	—
213	C₄×Q₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
214	C₄×D₈	C₂²×C₁₃₇	1	1	yes	characteristic
215	C₈×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
216	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
217	#367	C₂²×C₁₃₇	1	1	yes	characteristic
218	#367	C₂²×C₁₃₇	1	2	yes	—
219	C₄⋊C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
220	#358	C₂²×C₁₃₇	1	1	yes	characteristic
221	#358	C₂²×C₁₃₇	1	2	yes	—
222	#357	C₂²×C₁₃₇	1	2	yes	—
223	#357	C₂²×C₁₃₇	1	2	yes	—
224	#357	C₂²×C₁₃₇	1	1	yes	characteristic
225	#357	C₂²×C₁₃₇	1	2	yes	—
226	C₂²⋊C₁₆	C₂²×C₁₃₇	1	2	yes	—
227	C₄×C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
228	C₂×#41	—	2	2	no	—
229	C₂×#41	—	4	1	no	—
230	#135	—	2	4	no	—
231	#135	—	4	2	no	—
232	C₂×Q₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
233	C₂×SD₁₆	—	2	2	no	—
234	C₂×D₈	—	2	1	no	—
235	C₂×D₈	C₂³×C₁₃₇	1	2	yes	—
236	C₂×D₈	C₂³×C₁₃₇	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
238	C₄⋊Q₈	—	2	1	no	—
239	#127	—	2	1	no	—
240	#127	—	4	1	no	—
241	#123	—	4	2	no	—
242	C₂²⋊Q₈	—	4	1	no	—
243	#121	—	2	2	no	—
244	#121	—	2	2	no	—
245	#121	—	4	2	no	—
246	C₄×Q₈	—	2	1	no	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	4	1	no	—
249	C₄×D₄	D₄×C₁₃₇	1	1	yes	characteristic
250	C₂×C₄⋊C₄	—	2	2	no	—
251	SD₃₂	—	2	2	no	—
252	D₁₆	—	4	2	no	—
253	M₃₂	—	4	2	no	—
254	C₂×C₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
255	C₂×C₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
256	C₂×C₁₆	C₂³×C₁₃₇	1	2	yes	—
257	#107	—	2	2	no	—
258	#107	—	2	1	no	—
259	#107	C₂³×C₁₃₇	1	1	yes	characteristic
260	#107	C₂³×C₁₃₇	1	2	yes	—
261	#107	C₂³×C₁₃₇	1	1	yes	characteristic
262	C₄⋊C₈	D₄×C₁₃₇	1	1	yes	characteristic
263	#103	—	2	1	no	—
264	#102	—	2	1	no	—
265	#102	—	2	2	no	—
266	#102	—	2	2	no	—
267	C₂²⋊C₈	D₄×C₁₃₇	1	2	yes	—
268	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
269	#41	—	4	4	no	—
270	#41	—	8	2	no	—
271	#41	—	8	4	no	—
272	C₂×Q₈	—	2	1	no	—
273	C₂×Q₈	—	4	1	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂×D₄	D₈×C₁₃₇	1	1	yes	characteristic
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
286	Q₁₆	—	2	1	no	—
287	Q₁₆	#41×C₁₃₇	1	2	yes	complemented
288	SD₁₆	—	4	4	no	—
289	D₈	—	2	1	no	—
290	D₈	—	2	2	no	—
291	D₈	—	2	1	no	—
292	D₈	—	2	2	no	—
293	D₈	—	8	1	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
297	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
298	C₂×C₈	C₂⁴×C₁₃₇	1	1	yes	characteristic
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	D₈×C₁₃₇	1	1	yes	characteristic
306	C₂²⋊C₄	—	4	1	no	—
307	C₂²⋊C₄	—	4	2	no	—
308	C₂²⋊C₄	—	4	2	no	—
309	C₂²⋊C₄	D₈×C₁₃₇	1	2	yes	—
310	C₄²	—	4	1	no	—
311	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
312	C₁₆	—	2	1	no	—
313	C₁₆	—	2	1	no	—
314	C₁₆	—	2	2	no	—
315	C₂³	—	4	1	no	—
316	C₂³	—	4	2	no	—
317	C₂³	C₂×D₈×C₁₃₇	1	2	yes	—
318	Q₈	—	2	2	no	—
319	Q₈	—	4	1	no	—
320	Q₈	—	8	2	no	—
321	D₄	—	2	2	no	—
322	D₄	—	4	2	no	—
323	D₄	—	4	1	no	—
324	D₄	—	4	2	no	—
325	D₄	—	4	1	no	—
326	D₄	—	8	4	no	—
327	D₄	—	8	4	no	—
328	D₄	—	8	2	no	—
329	D₄	—	16	1	no	—
330	D₄	—	16	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	8	4	no	—
338	C₂×C₄	—	8	4	no	—
339	C₂×C₄	—	8	2	no	—
340	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
341	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
342	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
343	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
344	C₈	—	2	2	no	—
345	C₈	—	2	1	no	—
346	C₈	C₂×#41×C₁₃₇	1	1	yes	characteristic
347	C₈	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	8	1	no	—
353	C₂²	—	8	1	no	—
354	C₂²	—	8	2	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	8	1	no	—
357	C₂²	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
358	C₄	—	2	2	no	—
359	C₄	—	2	1	no	—
360	C₄	—	4	2	no	—
361	C₄	—	8	1	no	—
362	C₄	—	8	2	no	—
363	C₄	—	8	1	no	—
364	C₄	#509×C₁₃₇	1	2	yes	—
365	C₄	#546×C₁₃₇	1	1	yes	characteristic
366	C₄	#577×C₁₃₇	1	1	yes	characteristic
367	C₂	—	4	2	no	—
368	C₂	—	16	2	no	—
369	C₂	—	16	1	no	—
370	C₂	#3294×C₁₃₇	1	1	yes	characteristic
371	C₂	C₂×#509×C₁₃₇	1	1	yes	characteristic
372	C₂	#3416×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. #3287×C₁₃₇	C₂	semidirect
3. #2240×C₁₃₇	C₂	semidirect
4. #2233×C₁₃₇	C₂	semidirect
5. #2225×C₁₃₇	C₂	semidirect
6. #2218×C₁₃₇	C₂	semidirect
7. #2206×C₁₃₇	C₂	semidirect
8. #2186×C₁₃₇	C₂	semidirect
9. C₄×SD₃₂×C₁₃₇	C₂	semidirect
10. #2169×C₁₃₇	C₂	semidirect
11. #2139×C₁₃₇	C₂	semidirect
100. Q₁₆×C₁₃₇	#41	semidirect
186. #33899	C₁₃₇	direct (N × H)
187. C₁₃₇	#33899	direct (N × H)
188. #3334	C₂×C₁₃₇	semidirect
189. #3287	C₂×C₁₃₇	semidirect
190. #2240	C₂×C₁₃₇	semidirect
191. #2233	C₂×C₁₃₇	semidirect
192. #2225	C₂×C₁₃₇	semidirect
193. #2218	C₂×C₁₃₇	semidirect
194. #2206	C₂×C₁₃₇	semidirect
195. #2186	C₂×C₁₃₇	semidirect
196. C₄×SD₃₂	C₂×C₁₃₇	semidirect
197. #2169	C₂×C₁₃₇	semidirect
198. #2139	C₂×C₁₃₇	semidirect
287. Q₁₆	#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
#3287×C₁₃₇	2
#2240×C₁₃₇	2
#2233×C₁₃₇	2
#2225×C₁₃₇	2
#2218×C₁₃₇	2
#2206×C₁₃₇	2
#2186×C₁₃₇	2
C₄×SD₃₂×C₁₃₇	2
#2169×C₁₃₇	2
#2139×C₁₃₇	2
#33899	137

Subgroups — C137×#33899 #46883285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#33899 #46883285