Subgroups — C₁₃₇×#11050 #46860436

Order 35072.

1110 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#103×C₁₃₇	C₂	1	2	yes	maximal
2	C₂×#391×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#384×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#340×C₁₃₇	C₂	1	2	yes	maximal
5	C₂×#336×C₁₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₃₇	C₂²	1	2	yes	—
8	C₂²×C₄⋊C₄×C₁₃₇	—	2	2	no	—
9	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
11	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂×#103×C₁₃₇	—	2	4	no	—
13	C₂×#103×C₁₃₇	—	2	4	no	—
14	C₂×#103×C₁₃₇	—	2	4	no	—
15	#391×C₁₃₇	—	2	2	no	—
16	#391×C₁₃₇	C₄	1	4	yes	complemented
17	#384×C₁₃₇	—	2	4	no	—
18	C₂×#95×C₁₃₇	—	2	2	no	—
19	#340×C₁₃₇	—	2	4	no	—
20	#336×C₁₃₇	—	2	2	no	—
21	C₂²×Q₈×C₁₃₇	—	2	1	no	—
22	C₂²×Q₈×C₁₃₇	—	2	1	no	—
23	C₂²×Q₈×C₁₃₇	—	2	1	no	—
24	C₂²×Q₈×C₁₃₇	—	2	2	no	—
25	C₂²×Q₈×C₁₃₇	—	2	2	no	—
26	C₂²×Q₈×C₁₃₇	—	2	2	no	—
27	C₂²×Q₈×C₁₃₇	—	2	2	no	—
28	C₂²×Q₈×C₁₃₇	C₂×C₄	1	2	yes	—
29	C₂²×Q₈×C₁₃₇	D₄	1	2	yes	—
30	C₂²×Q₈×C₁₃₇	Q₈	1	2	yes	—
31	C₂³×C₄×C₁₃₇	—	2	1	no	—
32	C₂³×C₄×C₁₃₇	—	2	1	no	—
33	C₂³×C₄×C₁₃₇	—	2	2	no	—
34	C₂³×C₄×C₁₃₇	D₄	1	2	yes	—
35	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₁₃₇	—	2	2	no	—
37	C₂²×C₈×C₁₃₇	—	2	2	no	—
38	C₂²×C₈×C₁₃₇	—	2	2	no	—
39	C₂²×C₈×C₁₃₇	—	2	2	no	—
40	C₂²×C₈×C₁₃₇	—	2	2	no	—
41	C₂²×C₈×C₁₃₇	—	2	2	no	—
42	C₂²×C₈×C₁₃₇	D₄	1	4	yes	—
43	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
45	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₃₇	—	2	8	no	—
50	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₃₇	—	4	4	no	—
53	C₂×C₄⋊C₄×C₁₃₇	—	4	4	no	—
54	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₃₇	D₄	1	4	yes	—
56	C₂×C₄²×C₁₃₇	—	2	2	no	—
57	C₂×C₄²×C₁₃₇	—	2	2	no	—
58	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₁₃₇	D₄	1	2	yes	—
60	#103×C₁₃₇	—	2	16	no	—
61	#95×C₁₃₇	—	2	8	no	—
62	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
63	C₂×Q₈×C₁₃₇	—	2	2	no	—
64	C₂×Q₈×C₁₃₇	—	2	2	no	—
65	C₂×Q₈×C₁₃₇	—	2	2	no	—
66	C₂×Q₈×C₁₃₇	—	2	4	no	—
67	C₂×Q₈×C₁₃₇	—	2	4	no	—
68	C₂×Q₈×C₁₃₇	—	2	4	no	—
69	C₂×Q₈×C₁₃₇	—	2	4	no	—
70	C₂×Q₈×C₁₃₇	—	2	4	no	—
71	C₂×Q₈×C₁₃₇	—	2	4	no	—
72	C₂×Q₈×C₁₃₇	—	4	2	no	—
73	C₂×Q₈×C₁₃₇	—	4	2	no	—
74	C₂×Q₈×C₁₃₇	—	4	2	no	—
75	C₂×Q₈×C₁₃₇	—	4	2	no	—
76	C₂×Q₈×C₁₃₇	—	4	2	no	—
77	C₂×Q₈×C₁₃₇	—	4	2	no	—
78	C₂×Q₈×C₁₃₇	C₄⋊C₄	1	4	yes	complemented
79	C₂²×C₄×C₁₃₇	—	2	2	no	—
80	C₂²×C₄×C₁₃₇	—	2	2	no	—
81	C₂²×C₄×C₁₃₇	—	2	2	no	—
82	C₂²×C₄×C₁₃₇	—	2	2	no	—
83	C₂²×C₄×C₁₃₇	—	2	2	no	—
84	C₂²×C₄×C₁₃₇	—	2	2	no	—
85	C₂²×C₄×C₁₃₇	—	2	2	no	—
86	C₂²×C₄×C₁₃₇	—	2	2	no	—
87	C₂²×C₄×C₁₃₇	—	2	4	no	—
88	C₂²×C₄×C₁₃₇	—	4	1	no	—
89	C₂²×C₄×C₁₃₇	—	4	1	no	—
90	C₂²×C₄×C₁₃₇	—	4	1	no	—
91	C₂²×C₄×C₁₃₇	—	4	1	no	—
92	C₂²×C₄×C₁₃₇	—	4	2	no	—
93	C₂²×C₄×C₁₃₇	—	4	1	no	—
94	C₂²×C₄×C₁₃₇	—	4	1	no	—
95	C₂²×C₄×C₁₃₇	—	4	2	no	—
96	C₂²×C₄×C₁₃₇	—	4	4	no	—
97	C₂²×C₄×C₁₃₇	—	4	4	no	—
98	C₂²×C₄×C₁₃₇	—	4	2	no	—
99	C₂²×C₄×C₁₃₇	—	4	2	no	—
100	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	4	yes	—
101	C₂²×C₄×C₁₃₇	SD₁₆	1	4	yes	—
102	C₂²×C₄×C₁₃₇	Q₁₆	1	4	yes	—
103	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
112	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
113	C₂×C₈×C₁₃₇	—	2	4	no	—
114	C₂×C₈×C₁₃₇	—	2	4	no	—
115	C₂×C₈×C₁₃₇	—	2	4	no	—
116	C₂×C₈×C₁₃₇	—	4	2	no	—
117	C₂×C₈×C₁₃₇	—	4	2	no	—
118	C₂×C₈×C₁₃₇	—	4	2	no	—
119	C₂×C₈×C₁₃₇	—	4	2	no	—
120	C₄⋊C₄×C₁₃₇	—	2	4	no	—
121	C₄⋊C₄×C₁₃₇	—	2	4	no	—
122	C₄⋊C₄×C₁₃₇	—	2	4	no	—
123	C₄⋊C₄×C₁₃₇	—	4	16	no	—
124	C₄⋊C₄×C₁₃₇	—	4	2	no	—
125	C₄⋊C₄×C₁₃₇	—	4	2	no	—
126	C₄⋊C₄×C₁₃₇	—	4	2	no	—
127	C₄²×C₁₃₇	—	2	4	no	—
128	C₄²×C₁₃₇	—	2	4	no	—
129	C₂³×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂³×C₁₃₇	#120	1	1	yes	characteristic
131	C₂³×C₁₃₇	#121	1	1	yes	characteristic
132	C₂³×C₁₃₇	C₂²⋊Q₈	1	1	yes	characteristic
133	C₂³×C₁₃₇	#123	1	1	yes	characteristic
134	C₂³×C₁₃₇	#124	1	1	yes	characteristic
135	C₂³×C₁₃₇	#127	1	1	yes	characteristic
136	C₂³×C₁₃₇	C₂×SD₁₆	1	2	yes	—
137	C₂³×C₁₃₇	C₂×Q₁₆	1	2	yes	—
138	C₂³×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
139	C₂³×C₁₃₇	#137	1	2	yes	—
140	Q₈×C₁₃₇	—	2	8	no	—
141	Q₈×C₁₃₇	—	4	4	no	—
142	Q₈×C₁₃₇	—	4	4	no	—
143	Q₈×C₁₃₇	—	4	4	no	—
144	C₂×C₄×C₁₃₇	—	2	4	no	—
145	C₂×C₄×C₁₃₇	—	2	4	no	—
146	C₂×C₄×C₁₃₇	—	2	4	no	—
147	C₂×C₄×C₁₃₇	—	2	4	no	—
148	C₂×C₄×C₁₃₇	—	2	4	no	—
149	C₂×C₄×C₁₃₇	—	2	4	no	—
150	C₂×C₄×C₁₃₇	—	2	4	no	—
151	C₂×C₄×C₁₃₇	—	4	2	no	—
152	C₂×C₄×C₁₃₇	—	4	2	no	—
153	C₂×C₄×C₁₃₇	—	4	2	no	—
154	C₂×C₄×C₁₃₇	—	4	2	no	—
155	C₂×C₄×C₁₃₇	—	4	2	no	—
156	C₂×C₄×C₁₃₇	—	4	2	no	—
157	C₂×C₄×C₁₃₇	—	4	2	no	—
158	C₂×C₄×C₁₃₇	—	4	4	no	—
159	C₂×C₄×C₁₃₇	—	4	4	no	—
160	C₂×C₄×C₁₃₇	—	4	8	no	—
161	C₂×C₄×C₁₃₇	—	8	4	no	—
162	C₂×C₄×C₁₃₇	—	8	2	no	—
163	C₂×C₄×C₁₃₇	—	8	2	no	—
164	C₂×C₄×C₁₃₇	—	8	1	no	—
165	C₂×C₄×C₁₃₇	—	8	2	no	—
166	C₂×C₄×C₁₃₇	—	8	1	no	—
167	C₂×C₄×C₁₃₇	#103	1	8	yes	complemented
168	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃₇	#117	1	1	yes	characteristic
170	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
172	C₂×C₄×C₁₃₇	#120	1	2	yes	—
173	C₂×C₄×C₁₃₇	#121	1	2	yes	—
174	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₃₇	#121	1	2	yes	—
176	C₂×C₄×C₁₃₇	#121	1	2	yes	—
177	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
178	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
179	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃₇	#123	1	2	yes	—
181	C₂×C₄×C₁₃₇	#123	1	2	yes	—
182	C₂×C₄×C₁₃₇	#124	1	2	yes	—
183	C₂×C₄×C₁₃₇	#126	1	2	yes	—
184	C₈×C₁₃₇	—	4	4	no	—
185	C₂²×C₁₃₇	#380	1	1	yes	characteristic
186	C₂²×C₁₃₇	#386	1	1	yes	characteristic
187	C₂²×C₁₃₇	#390	1	1	yes	characteristic
188	C₂²×C₁₃₇	#392	1	1	yes	characteristic
189	C₂²×C₁₃₇	#393	1	1	yes	characteristic
190	C₂²×C₁₃₇	#397	1	1	yes	characteristic
191	C₂²×C₁₃₇	#399	1	1	yes	characteristic
192	C₂²×C₁₃₇	C₂×#103	1	2	yes	—
193	C₂²×C₁₃₇	#417	1	2	yes	—
194	C₂²×C₁₃₇	#450	1	2	yes	—
195	C₂²×C₁₃₇	#451	1	2	yes	—
196	C₂²×C₁₃₇	#460	1	2	yes	—
197	C₂²×C₁₃₇	#462	1	2	yes	—
198	C₂²×C₁₃₇	#475	1	2	yes	—
199	C₂²×C₁₃₇	#477	1	2	yes	—
200	C₂²×C₁₃₇	#483	1	2	yes	—
201	C₂²×C₁₃₇	#484	1	2	yes	—
202	C₂²×C₁₃₇	#487	1	2	yes	—
203	C₂²×C₁₃₇	#489	1	2	yes	—
204	C₂²×C₁₃₇	#492	1	1	yes	characteristic
205	C₂²×C₁₃₇	#494	1	1	yes	characteristic
206	C₂²×C₁₃₇	#496	1	1	yes	characteristic
207	C₂²×C₁₃₇	#497	1	1	yes	characteristic
208	C₄×C₁₃₇	—	2	8	no	—
209	C₄×C₁₃₇	—	4	4	no	—
210	C₄×C₁₃₇	—	8	2	no	—
211	C₄×C₁₃₇	—	8	4	no	—
212	C₄×C₁₃₇	#385	1	2	yes	—
213	C₄×C₁₃₇	#388	1	2	yes	—
214	C₄×C₁₃₇	#394	1	2	yes	—
215	C₄×C₁₃₇	#396	1	2	yes	—
216	C₂×C₁₃₇	#1439	1	1	yes	characteristic
217	C₂×C₁₃₇	#1803	1	2	yes	—
218	C₂×C₁₃₇	#1872	1	2	yes	—
219	C₂×C₁₃₇	#1956	1	1	yes	characteristic
220	C₂×C₁₃₇	#1959	1	1	yes	characteristic
221	C₂×C₁₃₇	#2014	1	1	yes	characteristic
222	C₂×C₁₃₇	#2016	1	1	yes	characteristic
223	C₂×C₁₃₇	#2024	1	2	yes	—
224	C₂×C₁₃₇	#2072	1	2	yes	—
225	C₂×C₁₃₇	#2095	1	1	yes	characteristic
226	C₂×C₁₃₇	#2096	1	1	yes	characteristic
227	#11050	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₁₃₇	#11050	1	1	yes	characteristic, direct product factor, Sylow
229	C₂²×#103	C₂×C₁₃₇	1	2	yes	—
230	C₂×#391	C₂×C₁₃₇	1	1	yes	characteristic
231	C₂×#384	C₂×C₁₃₇	1	1	yes	characteristic
232	C₂×#340	C₂×C₁₃₇	1	2	yes	—
233	C₂×#336	C₂×C₁₃₇	1	1	yes	characteristic
234	C₂³×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
235	C₂³×C₈	C₂²×C₁₃₇	1	2	yes	—
236	C₂²×C₄⋊C₄	—	2	2	no	—
237	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
238	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
239	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
240	C₂×#103	—	2	4	no	—
241	C₂×#103	—	2	4	no	—
242	C₂×#103	—	2	4	no	—
243	#391	—	2	2	no	—
244	#391	C₄×C₁₃₇	1	4	yes	complemented
245	#384	—	2	4	no	—
246	C₂×#95	—	2	2	no	—
247	#340	—	2	4	no	—
248	#336	—	2	2	no	—
249	C₂²×Q₈	—	2	1	no	—
250	C₂²×Q₈	—	2	1	no	—
251	C₂²×Q₈	—	2	1	no	—
252	C₂²×Q₈	—	2	2	no	—
253	C₂²×Q₈	—	2	2	no	—
254	C₂²×Q₈	—	2	2	no	—
255	C₂²×Q₈	—	2	2	no	—
256	C₂²×Q₈	C₂×C₄×C₁₃₇	1	2	yes	—
257	C₂²×Q₈	D₄×C₁₃₇	1	2	yes	—
258	C₂²×Q₈	Q₈×C₁₃₇	1	2	yes	—
259	C₂³×C₄	—	2	1	no	—
260	C₂³×C₄	—	2	2	no	—
261	C₂³×C₄	—	2	1	no	—
262	C₂³×C₄	D₄×C₁₃₇	1	2	yes	—
263	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
264	C₂²×C₈	—	2	2	no	—
265	C₂²×C₈	—	2	2	no	—
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	D₄×C₁₃₇	1	4	yes	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	8	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	4	4	no	—
281	C₂×C₄⋊C₄	—	4	4	no	—
282	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
283	C₂×C₄⋊C₄	D₄×C₁₃₇	1	4	yes	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
287	C₂×C₄²	D₄×C₁₃₇	1	2	yes	—
288	#103	—	2	16	no	—
289	#95	—	2	8	no	—
290	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	4	no	—
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	—	2	4	no	—
297	C₂×Q₈	—	2	4	no	—
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	—	4	2	no	—
301	C₂×Q₈	—	4	2	no	—
302	C₂×Q₈	—	4	2	no	—
303	C₂×Q₈	—	4	2	no	—
304	C₂×Q₈	—	4	2	no	—
305	C₂×Q₈	—	4	2	no	—
306	C₂×Q₈	C₄⋊C₄×C₁₃₇	1	4	yes	complemented
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	4	4	no	—
325	C₂²×C₄	—	4	4	no	—
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	4	yes	—
329	C₂²×C₄	SD₁₆×C₁₃₇	1	4	yes	—
330	C₂²×C₄	Q₁₆×C₁₃₇	1	4	yes	—
331	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
336	C₂²×C₄	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
337	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
338	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
339	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
340	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
341	C₂×C₈	—	2	4	no	—
342	C₂×C₈	—	2	4	no	—
343	C₂×C₈	—	2	4	no	—
344	C₂×C₈	—	4	2	no	—
345	C₂×C₈	—	4	2	no	—
346	C₂×C₈	—	4	2	no	—
347	C₂×C₈	—	4	2	no	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	2	4	no	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	4	16	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₄²	—	2	4	no	—
356	C₄²	—	2	4	no	—
357	C₂³	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
358	C₂³	#120×C₁₃₇	1	1	yes	characteristic
359	C₂³	#121×C₁₃₇	1	1	yes	characteristic
360	C₂³	C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
361	C₂³	#123×C₁₃₇	1	1	yes	characteristic
362	C₂³	#124×C₁₃₇	1	1	yes	characteristic
363	C₂³	#127×C₁₃₇	1	1	yes	characteristic
364	C₂³	C₂×SD₁₆×C₁₃₇	1	2	yes	—
365	C₂³	C₂×Q₁₆×C₁₃₇	1	2	yes	—
366	C₂³	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
367	C₂³	#137×C₁₃₇	1	2	yes	—
368	Q₈	—	2	8	no	—
369	Q₈	—	4	4	no	—
370	Q₈	—	4	4	no	—
371	Q₈	—	4	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	8	no	—
389	C₂×C₄	—	8	4	no	—
390	C₂×C₄	—	8	2	no	—
391	C₂×C₄	—	8	2	no	—
392	C₂×C₄	—	8	2	no	—
393	C₂×C₄	—	8	1	no	—
394	C₂×C₄	—	8	1	no	—
395	C₂×C₄	#103×C₁₃₇	1	8	yes	complemented
396	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
397	C₂×C₄	#117×C₁₃₇	1	1	yes	characteristic
398	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
399	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
400	C₂×C₄	#120×C₁₃₇	1	2	yes	—
401	C₂×C₄	#121×C₁₃₇	1	2	yes	—
402	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
403	C₂×C₄	#121×C₁₃₇	1	2	yes	—
404	C₂×C₄	#121×C₁₃₇	1	2	yes	—
405	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
406	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
407	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
408	C₂×C₄	#123×C₁₃₇	1	2	yes	—
409	C₂×C₄	#123×C₁₃₇	1	2	yes	—
410	C₂×C₄	#124×C₁₃₇	1	2	yes	—
411	C₂×C₄	#126×C₁₃₇	1	2	yes	—
412	C₈	—	4	4	no	—
413	C₂²	#380×C₁₃₇	1	1	yes	characteristic
414	C₂²	#386×C₁₃₇	1	1	yes	characteristic
415	C₂²	#390×C₁₃₇	1	1	yes	characteristic
416	C₂²	#392×C₁₃₇	1	1	yes	characteristic
417	C₂²	#393×C₁₃₇	1	1	yes	characteristic
418	C₂²	#397×C₁₃₇	1	1	yes	characteristic
419	C₂²	#399×C₁₃₇	1	1	yes	characteristic
420	C₂²	C₂×#103×C₁₃₇	1	2	yes	—
421	C₂²	#417×C₁₃₇	1	2	yes	—
422	C₂²	#450×C₁₃₇	1	2	yes	—
423	C₂²	#451×C₁₃₇	1	2	yes	—
424	C₂²	#460×C₁₃₇	1	2	yes	—
425	C₂²	#462×C₁₃₇	1	2	yes	—
426	C₂²	#475×C₁₃₇	1	2	yes	—
427	C₂²	#477×C₁₃₇	1	2	yes	—
428	C₂²	#483×C₁₃₇	1	2	yes	—
429	C₂²	#484×C₁₃₇	1	2	yes	—
430	C₂²	#487×C₁₃₇	1	2	yes	—
431	C₂²	#489×C₁₃₇	1	2	yes	—
432	C₂²	#492×C₁₃₇	1	1	yes	characteristic
433	C₂²	#494×C₁₃₇	1	1	yes	characteristic
434	C₂²	#496×C₁₃₇	1	1	yes	characteristic
435	C₂²	#497×C₁₃₇	1	1	yes	characteristic
436	C₄	—	2	8	no	—
437	C₄	—	4	4	no	—
438	C₄	—	8	4	no	—
439	C₄	—	8	2	no	—
440	C₄	#385×C₁₃₇	1	2	yes	—
441	C₄	#388×C₁₃₇	1	2	yes	—
442	C₄	#394×C₁₃₇	1	2	yes	—
443	C₄	#396×C₁₃₇	1	2	yes	—
444	C₂	#1439×C₁₃₇	1	1	yes	characteristic
445	C₂	#1803×C₁₃₇	1	2	yes	—
446	C₂	#1872×C₁₃₇	1	2	yes	—
447	C₂	#1956×C₁₃₇	1	1	yes	characteristic
448	C₂	#1959×C₁₃₇	1	1	yes	characteristic
449	C₂	#2014×C₁₃₇	1	1	yes	characteristic
450	C₂	#2016×C₁₃₇	1	1	yes	characteristic
451	C₂	#2024×C₁₃₇	1	2	yes	—
452	C₂	#2072×C₁₃₇	1	2	yes	—
453	C₂	#2095×C₁₃₇	1	1	yes	characteristic
454	C₂	#2096×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃₇	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₃₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₇ ◁ C₂²×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
16. #391×C₁₃₇	C₄	semidirect
78. C₂×Q₈×C₁₃₇	C₄⋊C₄	semidirect
167. C₂×C₄×C₁₃₇	#103	semidirect
227. #11050	C₁₃₇	direct (N × H)
228. C₁₃₇	#11050	direct (N × H)
244. #391	C₄×C₁₃₇	semidirect
306. C₂×Q₈	C₄⋊C₄×C₁₃₇	semidirect
395. C₂×C₄	#103×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#103×C₁₃₇	2
C₂×#391×C₁₃₇	2
C₂×#384×C₁₃₇	2
C₂×#340×C₁₃₇	2
C₂×#336×C₁₃₇	2
#11050	137

Subgroups — C137×#11050 #46860436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#11050 #46860436