Subgroups — C₁₃₇×#21817 #46871203

Order 35072.

1282 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3449×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2921×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2298×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#1980×C₁₃₇	C₂	1	4	yes	maximal, complemented
5	#1963×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1962×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1789×C₁₃₇	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₁₃₇	C₂²	1	2	yes	—
9	#537×C₁₃₇	—	2	2	no	—
10	#536×C₁₃₇	C₄	1	4	yes	complemented
11	#535×C₁₃₇	C₄	1	4	yes	complemented
12	#534×C₁₃₇	—	2	2	no	—
13	#532×C₁₃₇	C₂²	1	2	yes	—
14	#532×C₁₃₇	C₂²	1	2	yes	—
15	#525×C₁₃₇	—	2	4	no	—
16	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
17	#433×C₁₃₇	—	2	4	no	—
18	#423×C₁₃₇	C₂²	1	2	yes	complemented
19	C₂×#104×C₁₃₇	C₂²	1	8	yes	complemented
20	C₂×#104×C₁₃₇	C₂²	1	8	yes	complemented
21	#407×C₁₃₇	C₂²	1	2	yes	—
22	C₄×M₁₆×C₁₃₇	C₂²	1	2	yes	complemented
23	#388×C₁₃₇	—	2	2	no	—
24	#387×C₁₃₇	—	2	2	no	—
25	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	complemented
26	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
27	#376×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
28	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×#41×C₁₃₇	—	2	2	no	—
30	C₂×#41×C₁₃₇	—	2	2	no	—
31	C₂×#41×C₁₃₇	—	4	8	no	—
32	C₂×#41×C₁₃₇	C₂×C₄	1	4	yes	—
33	C₂×#41×C₁₃₇	C₂³	1	4	yes	—
34	C₂²×Q₈×C₁₃₇	C₂×C₄	1	2	yes	—
35	C₂²×D₄×C₁₃₇	—	2	2	no	—
36	C₂²×D₄×C₁₃₇	C₂×C₄	1	2	yes	—
37	C₂³×C₄×C₁₃₇	—	2	2	no	—
38	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
39	C₂×M₁₆×C₁₃₇	C₂³	1	4	yes	—
40	C₄⋊Q₈×C₁₃₇	C₂×C₄	1	2	yes	—
41	C₄⋊Q₈×C₁₃₇	C₂×C₄	1	2	yes	—
42	#127×C₁₃₇	C₂×C₄	1	2	yes	—
43	#127×C₁₃₇	C₂×C₄	1	2	yes	—
44	#124×C₁₃₇	C₂×C₄	1	4	yes	—
45	#124×C₁₃₇	C₂×C₄	1	4	yes	—
46	#123×C₁₃₇	—	2	8	no	—
47	C₂²⋊Q₈×C₁₃₇	—	2	8	no	—
48	#121×C₁₃₇	—	2	4	no	—
49	#121×C₁₃₇	—	2	4	no	—
50	#121×C₁₃₇	—	2	8	no	—
51	#120×C₁₃₇	—	2	8	no	—
52	C₄×D₄×C₁₃₇	—	2	4	no	—
53	C₄×D₄×C₁₃₇	—	2	4	no	—
54	#117×C₁₃₇	C₂×C₄	1	4	yes	—
55	#117×C₁₃₇	D₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₃₇	D₄	1	2	yes	—
58	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₁₃₇	D₄	1	2	yes	—
60	C₂×C₄²×C₁₃₇	—	2	2	no	—
61	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
62	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
63	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
65	C₄⋊C₈×C₁₃₇	—	2	4	no	—
66	#104×C₁₃₇	—	4	8	no	—
67	#104×C₁₃₇	—	4	8	no	—
68	C₂²⋊C₈×C₁₃₇	—	2	4	no	—
69	#97×C₁₃₇	—	2	2	no	—
70	C₄×C₈×C₁₃₇	—	2	2	no	—
71	#95×C₁₃₇	—	2	2	no	—
72	#95×C₁₃₇	—	2	2	no	—
73	#95×C₁₃₇	—	2	2	no	—
74	C₂⁴×C₁₃₇	—	2	2	no	—
75	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
76	#41×C₁₃₇	—	2	8	no	—
77	#41×C₁₃₇	—	2	8	no	—
78	#41×C₁₃₇	—	4	8	no	—
79	#41×C₁₃₇	—	4	8	no	—
80	#41×C₁₃₇	—	4	8	no	—
81	C₂×Q₈×C₁₃₇	—	2	2	no	—
82	C₂×Q₈×C₁₃₇	—	4	4	no	—
83	C₂×Q₈×C₁₃₇	C₂²×C₄	1	4	yes	—
84	C₂×D₄×C₁₃₇	—	2	4	no	—
85	C₂×D₄×C₁₃₇	—	2	4	no	—
86	C₂×D₄×C₁₃₇	—	2	2	no	—
87	C₂×D₄×C₁₃₇	—	2	4	no	—
88	C₂×D₄×C₁₃₇	—	2	4	no	—
89	C₂×D₄×C₁₃₇	—	4	4	no	—
90	C₂×D₄×C₁₃₇	—	4	8	no	—
91	C₂×D₄×C₁₃₇	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₁₃₇	—	2	4	no	—
93	C₂²×C₄×C₁₃₇	—	2	2	no	—
94	C₂²×C₄×C₁₃₇	—	2	2	no	—
95	C₂²×C₄×C₁₃₇	—	2	4	no	—
96	C₂²×C₄×C₁₃₇	—	2	4	no	—
97	C₂²×C₄×C₁₃₇	—	2	2	no	—
98	C₂²×C₄×C₁₃₇	—	4	8	no	—
99	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
105	M₁₆×C₁₃₇	—	2	8	no	—
106	C₂×C₈×C₁₃₇	—	2	4	no	—
107	C₄⋊C₄×C₁₃₇	—	2	4	no	—
108	C₄⋊C₄×C₁₃₇	—	2	4	no	—
109	C₄⋊C₄×C₁₃₇	—	4	4	no	—
110	C₄⋊C₄×C₁₃₇	C₂²⋊C₄	1	8	yes	—
111	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
112	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
113	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
114	C₂²⋊C₄×C₁₃₇	C₂²⋊C₄	1	8	yes	—
115	C₄²×C₁₃₇	—	2	4	no	—
116	C₄²×C₁₃₇	—	2	4	no	—
117	C₄²×C₁₃₇	—	4	4	no	—
118	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
119	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
120	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
121	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
122	C₂³×C₁₃₇	—	2	2	no	—
123	C₂³×C₁₃₇	—	2	4	no	—
124	C₂³×C₁₃₇	—	4	2	no	—
125	C₂³×C₁₃₇	—	4	4	no	—
126	C₂³×C₁₃₇	—	8	4	no	—
127	C₂³×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
128	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
129	Q₈×C₁₃₇	—	2	8	no	—
130	Q₈×C₁₃₇	—	4	4	no	—
131	D₄×C₁₃₇	—	2	8	no	—
132	D₄×C₁₃₇	—	4	4	no	—
133	D₄×C₁₃₇	—	4	8	no	—
134	D₄×C₁₃₇	—	4	8	no	—
135	D₄×C₁₃₇	—	8	4	no	—
136	D₄×C₁₃₇	—	8	4	no	—
137	C₂×C₄×C₁₃₇	—	2	2	no	—
138	C₂×C₄×C₁₃₇	—	2	4	no	—
139	C₂×C₄×C₁₃₇	—	2	4	no	—
140	C₂×C₄×C₁₃₇	—	2	4	no	—
141	C₂×C₄×C₁₃₇	—	2	4	no	—
142	C₂×C₄×C₁₃₇	—	4	2	no	—
143	C₂×C₄×C₁₃₇	—	4	2	no	—
144	C₂×C₄×C₁₃₇	—	4	8	no	—
145	C₂×C₄×C₁₃₇	—	4	2	no	—
146	C₂×C₄×C₁₃₇	—	4	4	no	—
147	C₂×C₄×C₁₃₇	—	4	2	no	—
148	C₂×C₄×C₁₃₇	—	4	4	no	—
149	C₂×C₄×C₁₃₇	—	4	4	no	—
150	C₂×C₄×C₁₃₇	—	4	2	no	—
151	C₂×C₄×C₁₃₇	—	4	2	no	—
152	C₂×C₄×C₁₃₇	—	4	2	no	—
153	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	4	yes	—
154	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	4	yes	—
155	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	4	yes	—
159	C₈×C₁₃₇	—	4	4	no	—
160	C₂²×C₁₃₇	—	2	2	no	—
161	C₂²×C₁₃₇	—	2	2	no	—
162	C₂²×C₁₃₇	—	2	4	no	—
163	C₂²×C₁₃₇	—	4	4	no	—
164	C₂²×C₁₃₇	—	4	8	no	—
165	C₂²×C₁₃₇	—	8	2	no	—
166	C₂²×C₁₃₇	—	8	8	no	—
167	C₂²×C₁₃₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
168	C₂²×C₁₃₇	#535	1	2	yes	—
169	C₄×C₁₃₇	—	2	2	no	—
170	C₄×C₁₃₇	—	2	4	no	—
171	C₄×C₁₃₇	—	2	4	no	—
172	C₄×C₁₃₇	—	4	4	no	—
173	C₄×C₁₃₇	—	4	4	no	—
174	C₄×C₁₃₇	—	8	2	no	—
175	C₄×C₁₃₇	#518	1	2	yes	—
176	C₄×C₁₃₇	#535	1	2	yes	—
177	C₂×C₁₃₇	—	2	2	no	—
178	C₂×C₁₃₇	—	4	2	no	—
179	C₂×C₁₃₇	—	8	4	no	—
180	C₂×C₁₃₇	#2309	1	1	yes	characteristic
181	C₂×C₁₃₇	#2901	1	2	yes	—
182	#21817	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₁₃₇	#21817	1	1	yes	characteristic, direct product factor, Sylow
184	#3449	C₂×C₁₃₇	1	1	yes	characteristic
185	#2921	C₂×C₁₃₇	1	1	yes	characteristic, complemented
186	#2298	C₂×C₁₃₇	1	1	yes	characteristic, complemented
187	#1980	C₂×C₁₃₇	1	4	yes	complemented
188	#1963	C₂×C₁₃₇	1	2	yes	complemented
189	#1962	C₂×C₁₃₇	1	2	yes	complemented
190	#1789	C₂×C₁₃₇	1	4	yes	complemented
191	C₂²×#41	C₂²×C₁₃₇	1	2	yes	—
192	#537	—	2	2	no	—
193	#536	C₄×C₁₃₇	1	4	yes	complemented
194	#535	C₄×C₁₃₇	1	4	yes	complemented
195	#534	—	2	2	no	—
196	#532	C₂²×C₁₃₇	1	2	yes	—
197	#532	C₂²×C₁₃₇	1	2	yes	—
198	#525	—	2	4	no	—
199	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
200	#433	—	2	4	no	—
201	#423	C₂²×C₁₃₇	1	2	yes	complemented
202	C₂×#104	C₂²×C₁₃₇	1	8	yes	complemented
203	C₂×#104	C₂²×C₁₃₇	1	8	yes	complemented
204	#407	C₂²×C₁₃₇	1	2	yes	—
205	C₄×M₁₆	C₂²×C₁₃₇	1	2	yes	complemented
206	#388	—	2	2	no	—
207	#387	—	2	2	no	—
208	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	complemented
209	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
210	#376	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
211	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
212	C₂×#41	—	2	2	no	—
213	C₂×#41	—	2	2	no	—
214	C₂×#41	—	4	8	no	—
215	C₂×#41	C₂×C₄×C₁₃₇	1	4	yes	—
216	C₂×#41	C₂³×C₁₃₇	1	4	yes	—
217	C₂²×Q₈	C₂×C₄×C₁₃₇	1	2	yes	—
218	C₂²×D₄	—	2	2	no	—
219	C₂²×D₄	C₂×C₄×C₁₃₇	1	2	yes	—
220	C₂³×C₄	—	2	2	no	—
221	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
222	C₂×M₁₆	C₂³×C₁₃₇	1	4	yes	—
223	C₄⋊Q₈	C₂×C₄×C₁₃₇	1	2	yes	—
224	C₄⋊Q₈	C₂×C₄×C₁₃₇	1	2	yes	—
225	#127	C₂×C₄×C₁₃₇	1	2	yes	—
226	#127	C₂×C₄×C₁₃₇	1	2	yes	—
227	#124	C₂×C₄×C₁₃₇	1	4	yes	—
228	#124	C₂×C₄×C₁₃₇	1	4	yes	—
229	#123	—	2	8	no	—
230	C₂²⋊Q₈	—	2	8	no	—
231	#121	—	2	4	no	—
232	#121	—	2	4	no	—
233	#121	—	2	8	no	—
234	#120	—	2	8	no	—
235	C₄×D₄	—	2	4	no	—
236	C₄×D₄	—	2	4	no	—
237	#117	C₂×C₄×C₁₃₇	1	4	yes	—
238	#117	D₄×C₁₃₇	1	4	yes	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	D₄×C₁₃₇	1	2	yes	—
241	C₂×C₂²⋊C₄	—	2	2	no	—
242	C₂×C₂²⋊C₄	D₄×C₁₃₇	1	2	yes	—
243	C₂×C₄²	—	2	2	no	—
244	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
245	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
246	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
247	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
248	C₄⋊C₈	—	2	4	no	—
249	#104	—	4	8	no	—
250	#104	—	4	8	no	—
251	C₂²⋊C₈	—	2	4	no	—
252	#97	—	2	2	no	—
253	C₄×C₈	—	2	2	no	—
254	#95	—	2	2	no	—
255	#95	—	2	2	no	—
256	#95	—	2	2	no	—
257	C₂⁴	—	2	2	no	—
258	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
259	#41	—	2	8	no	—
260	#41	—	2	8	no	—
261	#41	—	4	8	no	—
262	#41	—	4	8	no	—
263	#41	—	4	8	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	4	4	no	—
266	C₂×Q₈	C₂²×C₄×C₁₃₇	1	4	yes	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	2	4	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	2	4	no	—
271	C₂×D₄	—	2	4	no	—
272	C₂×D₄	—	4	4	no	—
273	C₂×D₄	—	4	8	no	—
274	C₂×D₄	C₂²×C₄×C₁₃₇	1	4	yes	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	4	8	no	—
282	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
285	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
287	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
288	M₁₆	—	2	8	no	—
289	C₂×C₈	—	2	4	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	4	4	no	—
293	C₄⋊C₄	C₂²⋊C₄×C₁₃₇	1	8	yes	—
294	C₂²⋊C₄	—	2	8	no	—
295	C₂²⋊C₄	—	2	8	no	—
296	C₂²⋊C₄	—	4	4	no	—
297	C₂²⋊C₄	C₂²⋊C₄×C₁₃₇	1	8	yes	—
298	C₄²	—	2	4	no	—
299	C₄²	—	2	4	no	—
300	C₄²	—	4	4	no	—
301	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
302	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
303	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
304	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
305	C₂³	—	2	2	no	—
306	C₂³	—	2	4	no	—
307	C₂³	—	4	2	no	—
308	C₂³	—	4	4	no	—
309	C₂³	—	8	4	no	—
310	C₂³	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
311	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
312	Q₈	—	2	8	no	—
313	Q₈	—	4	4	no	—
314	D₄	—	2	8	no	—
315	D₄	—	4	4	no	—
316	D₄	—	4	8	no	—
317	D₄	—	4	8	no	—
318	D₄	—	8	4	no	—
319	D₄	—	8	4	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	8	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	4	yes	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	4	yes	—
338	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
339	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
341	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	4	yes	—
342	C₈	—	4	4	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	2	2	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	4	4	no	—
347	C₂²	—	4	8	no	—
348	C₂²	—	8	2	no	—
349	C₂²	—	8	8	no	—
350	C₂²	C₂²×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
351	C₂²	#535×C₁₃₇	1	2	yes	—
352	C₄	—	2	2	no	—
353	C₄	—	2	4	no	—
354	C₄	—	2	4	no	—
355	C₄	—	4	4	no	—
356	C₄	—	4	4	no	—
357	C₄	—	8	2	no	—
358	C₄	#518×C₁₃₇	1	2	yes	—
359	C₄	#535×C₁₃₇	1	2	yes	—
360	C₂	—	2	2	no	—
361	C₂	—	4	2	no	—
362	C₂	—	8	4	no	—
363	C₂	#2309×C₁₃₇	1	1	yes	characteristic
364	C₂	#2901×C₁₃₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
socle	C₂²×C₁₃₇	C₂²×C₂²⋊C₄
prime radical	#3449×C₁₃₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₇ ◁ C₂×#117×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2921×C₁₃₇	C₂	semidirect
3. #2298×C₁₃₇	C₂	semidirect
4. #1980×C₁₃₇	C₂	semidirect
5. #1963×C₁₃₇	C₂	semidirect
6. #1962×C₁₃₇	C₂	semidirect
7. #1789×C₁₃₇	C₂	semidirect
10. #536×C₁₃₇	C₄	semidirect
11. #535×C₁₃₇	C₄	semidirect
18. #423×C₁₃₇	C₂²	semidirect
19. C₂×#104×C₁₃₇	C₂²	semidirect
20. C₂×#104×C₁₃₇	C₂²	semidirect
22. C₄×M₁₆×C₁₃₇	C₂²	semidirect
25. C₄×C₄⋊C₄×C₁₃₇	C₂²	semidirect
27. #376×C₁₃₇	C₂²	semidirect
28. C₄³×C₁₃₇	C₂²	semidirect
182. #21817	C₁₃₇	direct (N × H)
183. C₁₃₇	#21817	direct (N × H)
185. #2921	C₂×C₁₃₇	semidirect
186. #2298	C₂×C₁₃₇	semidirect
187. #1980	C₂×C₁₃₇	semidirect
188. #1963	C₂×C₁₃₇	semidirect
189. #1962	C₂×C₁₃₇	semidirect
190. #1789	C₂×C₁₃₇	semidirect
193. #536	C₄×C₁₃₇	semidirect
194. #535	C₄×C₁₃₇	semidirect
201. #423	C₂²×C₁₃₇	semidirect
202. C₂×#104	C₂²×C₁₃₇	semidirect
203. C₂×#104	C₂²×C₁₃₇	semidirect
205. C₄×M₁₆	C₂²×C₁₃₇	semidirect
208. C₄×C₄⋊C₄	C₂²×C₁₃₇	semidirect
210. #376	C₂²×C₁₃₇	semidirect
211. C₄³	C₂²×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3449×C₁₃₇	2
#2921×C₁₃₇	2
#2298×C₁₃₇	2
#1980×C₁₃₇	2
#1963×C₁₃₇	2
#1962×C₁₃₇	2
#1789×C₁₃₇	2
#21817	137

Subgroups — C137×#21817 #46871203

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#21817 #46871203