Subgroups — C₁₃₇×#10881 #46860267

Order 35072.

926 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#97×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#389×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#340×C₁₃₇	C₂	1	2	yes	maximal
4	C₂×#340×C₁₃₇	C₂	1	2	yes	maximal
5	C₄⋊#95×C₁₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₃₇	C₂²	1	2	yes	—
7	C₂²×C₄⋊C₄×C₁₃₇	—	2	1	no	—
8	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂×#97×C₁₃₇	—	2	4	no	—
13	C₂×#97×C₁₃₇	—	2	2	no	—
14	#389×C₁₃₇	—	2	2	no	—
15	#389×C₁₃₇	C₄	1	4	yes	complemented
16	C₂×#95×C₁₃₇	—	2	1	no	—
17	C₂×#95×C₁₃₇	—	2	1	no	—
18	C₂×#95×C₁₃₇	—	2	1	no	—
19	#340×C₁₃₇	—	2	4	no	—
20	#340×C₁₃₇	C₄	1	8	yes	complemented
21	C₂³×C₄×C₁₃₇	—	2	1	no	—
22	C₂³×C₄×C₁₃₇	—	2	2	no	—
23	C₂³×C₄×C₁₃₇	—	2	1	no	—
24	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
27	C₂²×C₈×C₁₃₇	—	2	2	no	—
28	C₂²×C₈×C₁₃₇	—	2	2	no	—
29	C₂²×C₈×C₁₃₇	—	2	2	no	—
30	C₂²×C₈×C₁₃₇	—	2	2	no	—
31	C₂²×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
32	C₂²×C₈×C₁₃₇	D₄	1	4	yes	—
33	C₂²×C₈×C₁₃₇	Q₈	1	4	yes	—
34	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
38	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
39	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
40	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
43	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
45	C₂×C₄⋊C₄×C₁₃₇	—	4	4	no	—
46	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
48	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
50	C₂×C₄²×C₁₃₇	—	2	2	no	—
51	C₂×C₄²×C₁₃₇	—	2	2	no	—
52	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₁₃₇	D₄	1	2	yes	—
54	#97×C₁₃₇	—	2	8	no	—
55	#95×C₁₃₇	—	2	4	no	—
56	#95×C₁₃₇	—	4	2	no	—
57	#95×C₁₃₇	—	4	2	no	—
58	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₃₇	—	2	2	no	—
60	C₂²×C₄×C₁₃₇	—	2	4	no	—
61	C₂²×C₄×C₁₃₇	—	2	2	no	—
62	C₂²×C₄×C₁₃₇	—	2	2	no	—
63	C₂²×C₄×C₁₃₇	—	2	1	no	—
64	C₂²×C₄×C₁₃₇	—	2	1	no	—
65	C₂²×C₄×C₁₃₇	—	2	2	no	—
66	C₂²×C₄×C₁₃₇	—	2	1	no	—
67	C₂²×C₄×C₁₃₇	—	2	1	no	—
68	C₂²×C₄×C₁₃₇	—	2	2	no	—
69	C₂²×C₄×C₁₃₇	—	2	2	no	—
70	C₂²×C₄×C₁₃₇	—	2	4	no	—
71	C₂²×C₄×C₁₃₇	—	4	2	no	—
72	C₂²×C₄×C₁₃₇	—	4	1	no	—
73	C₂²×C₄×C₁₃₇	—	4	1	no	—
74	C₂²×C₄×C₁₃₇	—	4	2	no	—
75	C₂²×C₄×C₁₃₇	—	4	2	no	—
76	C₂²×C₄×C₁₃₇	—	4	2	no	—
77	C₂²×C₄×C₁₃₇	—	4	2	no	—
78	C₂²×C₄×C₁₃₇	—	4	2	no	—
79	C₂²×C₄×C₁₃₇	—	4	2	no	—
80	C₂²×C₄×C₁₃₇	—	4	1	no	—
81	C₂²×C₄×C₁₃₇	—	4	2	no	—
82	C₂²×C₄×C₁₃₇	—	4	1	no	—
83	C₂²×C₄×C₁₃₇	—	4	2	no	—
84	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	2	yes	—
85	C₂²×C₄×C₁₃₇	C₂²⋊C₄	1	2	yes	—
86	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
92	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
93	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
94	C₂×C₈×C₁₃₇	—	2	4	no	—
95	C₂×C₈×C₁₃₇	—	2	4	no	—
96	C₂×C₈×C₁₃₇	—	2	4	no	—
97	C₂×C₈×C₁₃₇	—	2	4	no	—
98	C₂×C₈×C₁₃₇	—	2	4	no	—
99	C₂×C₈×C₁₃₇	—	2	4	no	—
100	C₂×C₈×C₁₃₇	C₄⋊C₄	1	8	yes	complemented
101	C₄⋊C₄×C₁₃₇	—	2	2	no	—
102	C₄⋊C₄×C₁₃₇	—	2	4	no	—
103	C₄⋊C₄×C₁₃₇	—	2	4	no	—
104	C₄⋊C₄×C₁₃₇	—	2	4	no	—
105	C₄⋊C₄×C₁₃₇	—	2	4	no	—
106	C₄⋊C₄×C₁₃₇	—	4	8	no	—
107	C₄⋊C₄×C₁₃₇	—	4	1	no	—
108	C₄⋊C₄×C₁₃₇	—	4	1	no	—
109	C₄⋊C₄×C₁₃₇	—	4	2	no	—
110	C₄⋊C₄×C₁₃₇	—	4	2	no	—
111	C₄⋊C₄×C₁₃₇	C₄²	1	4	yes	—
112	C₄²×C₁₃₇	—	2	4	no	—
113	C₄²×C₁₃₇	—	2	2	no	—
114	C₄²×C₁₃₇	—	2	2	no	—
115	C₂³×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
116	C₂³×C₁₃₇	C₄×D₄	1	2	yes	—
117	C₂³×C₁₃₇	#121	1	2	yes	—
118	C₂³×C₁₃₇	#124	1	1	yes	characteristic
119	C₂³×C₁₃₇	C₄⋊Q₈	1	1	yes	characteristic
120	C₂³×C₁₃₇	AGL(1,ℤ/8)	1	1	yes	characteristic
121	C₂³×C₁₃₇	AGL(1,ℤ/8)	1	1	yes	characteristic
122	C₂³×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
123	C₂³×C₁₃₇	#137	1	1	yes	characteristic
124	C₂³×C₁₃₇	#137	1	1	yes	characteristic
125	C₂³×C₁₃₇	#137	1	2	yes	—
126	C₂×C₄×C₁₃₇	—	2	4	no	—
127	C₂×C₄×C₁₃₇	—	2	2	no	—
128	C₂×C₄×C₁₃₇	—	2	2	no	—
129	C₂×C₄×C₁₃₇	—	2	2	no	—
130	C₂×C₄×C₁₃₇	—	2	2	no	—
131	C₂×C₄×C₁₃₇	—	2	2	no	—
132	C₂×C₄×C₁₃₇	—	2	2	no	—
133	C₂×C₄×C₁₃₇	—	4	2	no	—
134	C₂×C₄×C₁₃₇	—	4	2	no	—
135	C₂×C₄×C₁₃₇	—	4	4	no	—
136	C₂×C₄×C₁₃₇	—	4	4	no	—
137	C₂×C₄×C₁₃₇	—	4	2	no	—
138	C₂×C₄×C₁₃₇	—	4	2	no	—
139	C₂×C₄×C₁₃₇	—	4	2	no	—
140	C₂×C₄×C₁₃₇	—	4	2	no	—
141	C₂×C₄×C₁₃₇	—	4	2	no	—
142	C₂×C₄×C₁₃₇	—	4	4	no	—
143	C₂×C₄×C₁₃₇	—	4	2	no	—
144	C₂×C₄×C₁₃₇	—	4	2	no	—
145	C₂×C₄×C₁₃₇	—	4	4	no	—
146	C₂×C₄×C₁₃₇	—	4	4	no	—
147	C₂×C₄×C₁₃₇	—	8	2	no	—
148	C₂×C₄×C₁₃₇	—	8	2	no	—
149	C₂×C₄×C₁₃₇	—	8	2	no	—
150	C₂×C₄×C₁₃₇	—	8	2	no	—
151	C₂×C₄×C₁₃₇	—	8	2	no	—
152	C₂×C₄×C₁₃₇	—	8	2	no	—
153	C₂×C₄×C₁₃₇	C₂×C₄²	1	1	yes	characteristic
154	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
155	C₂×C₄×C₁₃₇	#117	1	2	yes	—
156	C₂×C₄×C₁₃₇	#117	1	1	yes	characteristic
157	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
158	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
159	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
160	C₂×C₄×C₁₃₇	C₄×Q₈	1	2	yes	—
161	C₂×C₄×C₁₃₇	C₄×Q₈	1	2	yes	—
162	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
163	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
164	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
165	C₂×C₄×C₁₃₇	#123	1	2	yes	—
166	C₂×C₄×C₁₃₇	#123	1	1	yes	characteristic
167	C₂×C₄×C₁₃₇	#125	1	2	yes	—
168	C₂×C₄×C₁₃₇	#126	1	2	yes	—
169	C₈×C₁₃₇	—	2	8	no	—
170	C₂²×C₁₃₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×C₁₃₇	#386	1	1	yes	characteristic
172	C₂²×C₁₃₇	#388	1	2	yes	—
173	C₂²×C₁₃₇	#389	1	2	yes	—
174	C₂²×C₁₃₇	#391	1	1	yes	characteristic
175	C₂²×C₁₃₇	#417	1	1	yes	characteristic
176	C₂²×C₁₃₇	#417	1	1	yes	characteristic
177	C₂²×C₁₃₇	#418	1	1	yes	characteristic
178	C₂²×C₁₃₇	#419	1	1	yes	characteristic
179	C₂²×C₁₃₇	#440	1	2	yes	—
180	C₂²×C₁₃₇	#440	1	2	yes	—
181	C₂²×C₁₃₇	#441	1	2	yes	—
182	C₂²×C₁₃₇	#442	1	2	yes	—
183	C₂²×C₁₃₇	#468	1	2	yes	—
184	C₂²×C₁₃₇	#468	1	2	yes	—
185	C₂²×C₁₃₇	#469	1	2	yes	—
186	C₂²×C₁₃₇	#470	1	2	yes	—
187	C₂²×C₁₃₇	#489	1	2	yes	—
188	C₂²×C₁₃₇	#490	1	1	yes	characteristic
189	C₂²×C₁₃₇	#491	1	1	yes	characteristic
190	C₂²×C₁₃₇	#501	1	1	yes	characteristic
191	C₂²×C₁₃₇	#501	1	2	yes	—
192	C₂²×C₁₃₇	#501	1	1	yes	characteristic
193	C₄×C₁₃₇	—	4	2	no	—
194	C₄×C₁₃₇	—	4	2	no	—
195	C₄×C₁₃₇	—	4	4	no	—
196	C₄×C₁₃₇	—	8	2	no	—
197	C₄×C₁₃₇	—	8	4	no	—
198	C₄×C₁₃₇	C₄×C₄⋊C₄	1	2	yes	—
199	C₄×C₁₃₇	#385	1	2	yes	—
200	C₄×C₁₃₇	#387	1	2	yes	—
201	C₄×C₁₃₇	#387	1	2	yes	—
202	C₂×C₁₃₇	#1436	1	1	yes	characteristic
203	C₂×C₁₃₇	#1762	1	1	yes	characteristic
204	C₂×C₁₃₇	#1763	1	1	yes	characteristic
205	C₂×C₁₃₇	#1894	1	1	yes	characteristic
206	C₂×C₁₃₇	#1895	1	1	yes	characteristic
207	C₂×C₁₃₇	#1935	1	2	yes	—
208	C₂×C₁₃₇	#1936	1	2	yes	—
209	C₂×C₁₃₇	#1943	1	2	yes	—
210	C₂×C₁₃₇	#1944	1	2	yes	—
211	C₂×C₁₃₇	#1992	1	1	yes	characteristic
212	C₂×C₁₃₇	#1993	1	1	yes	characteristic
213	#10881	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₁₃₇	#10881	1	1	yes	characteristic, direct product factor, Sylow
215	C₂²×#97	C₂×C₁₃₇	1	1	yes	characteristic
216	C₂×#389	C₂×C₁₃₇	1	1	yes	characteristic
217	C₂×#340	C₂×C₁₃₇	1	2	yes	—
218	C₂×#340	C₂×C₁₃₇	1	2	yes	—
219	C₄⋊#95	C₂×C₁₃₇	1	1	yes	characteristic
220	C₂³×C₈	C₂²×C₁₃₇	1	2	yes	—
221	C₂²×C₄⋊C₄	—	2	1	no	—
222	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
223	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
224	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
225	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
226	C₂×#97	—	2	4	no	—
227	C₂×#97	—	2	2	no	—
228	#389	—	2	2	no	—
229	#389	C₄×C₁₃₇	1	4	yes	complemented
230	C₂×#95	—	2	1	no	—
231	C₂×#95	—	2	1	no	—
232	C₂×#95	—	2	1	no	—
233	#340	—	2	4	no	—
234	#340	C₄×C₁₃₇	1	8	yes	complemented
235	C₂³×C₄	—	2	1	no	—
236	C₂³×C₄	—	2	1	no	—
237	C₂³×C₄	—	2	2	no	—
238	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
239	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
240	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	2	2	no	—
245	C₂²×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
246	C₂²×C₈	D₄×C₁₃₇	1	4	yes	—
247	C₂²×C₈	Q₈×C₁₃₇	1	4	yes	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	4	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	4	4	no	—
260	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
261	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
262	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
263	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
267	C₂×C₄²	D₄×C₁₃₇	1	2	yes	—
268	#97	—	2	8	no	—
269	#95	—	2	4	no	—
270	#95	—	4	2	no	—
271	#95	—	4	2	no	—
272	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	2	yes	—
299	C₂²×C₄	C₂²⋊C₄×C₁₃₇	1	2	yes	—
300	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
301	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
304	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
305	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
306	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
307	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	2	4	no	—
311	C₂×C₈	—	2	4	no	—
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	C₄⋊C₄×C₁₃₇	1	8	yes	complemented
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	4	8	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	C₄²×C₁₃₇	1	4	yes	—
326	C₄²	—	2	4	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₂³	C₂×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
330	C₂³	C₄×D₄×C₁₃₇	1	2	yes	—
331	C₂³	#121×C₁₃₇	1	2	yes	—
332	C₂³	#124×C₁₃₇	1	1	yes	characteristic
333	C₂³	C₄⋊Q₈×C₁₃₇	1	1	yes	characteristic
334	C₂³	AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
335	C₂³	AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
336	C₂³	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
337	C₂³	#137×C₁₃₇	1	1	yes	characteristic
338	C₂³	#137×C₁₃₇	1	1	yes	characteristic
339	C₂³	#137×C₁₃₇	1	2	yes	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	8	2	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	—	8	2	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	—	8	2	no	—
366	C₂×C₄	—	8	2	no	—
367	C₂×C₄	C₂×C₄²×C₁₃₇	1	1	yes	characteristic
368	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
369	C₂×C₄	#117×C₁₃₇	1	2	yes	—
370	C₂×C₄	#117×C₁₃₇	1	1	yes	characteristic
371	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
372	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
373	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
374	C₂×C₄	C₄×Q₈×C₁₃₇	1	2	yes	—
375	C₂×C₄	C₄×Q₈×C₁₃₇	1	2	yes	—
376	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
377	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
378	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
379	C₂×C₄	#123×C₁₃₇	1	2	yes	—
380	C₂×C₄	#123×C₁₃₇	1	1	yes	characteristic
381	C₂×C₄	#125×C₁₃₇	1	2	yes	—
382	C₂×C₄	#126×C₁₃₇	1	2	yes	—
383	C₈	—	2	8	no	—
384	C₂²	C₄×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
385	C₂²	#386×C₁₃₇	1	1	yes	characteristic
386	C₂²	#388×C₁₃₇	1	2	yes	—
387	C₂²	#389×C₁₃₇	1	2	yes	—
388	C₂²	#391×C₁₃₇	1	1	yes	characteristic
389	C₂²	#417×C₁₃₇	1	1	yes	characteristic
390	C₂²	#417×C₁₃₇	1	1	yes	characteristic
391	C₂²	#418×C₁₃₇	1	1	yes	characteristic
392	C₂²	#419×C₁₃₇	1	1	yes	characteristic
393	C₂²	#440×C₁₃₇	1	2	yes	—
394	C₂²	#440×C₁₃₇	1	2	yes	—
395	C₂²	#441×C₁₃₇	1	2	yes	—
396	C₂²	#442×C₁₃₇	1	2	yes	—
397	C₂²	#468×C₁₃₇	1	2	yes	—
398	C₂²	#468×C₁₃₇	1	2	yes	—
399	C₂²	#469×C₁₃₇	1	2	yes	—
400	C₂²	#470×C₁₃₇	1	2	yes	—
401	C₂²	#489×C₁₃₇	1	2	yes	—
402	C₂²	#490×C₁₃₇	1	1	yes	characteristic
403	C₂²	#491×C₁₃₇	1	1	yes	characteristic
404	C₂²	#501×C₁₃₇	1	1	yes	characteristic
405	C₂²	#501×C₁₃₇	1	2	yes	—
406	C₂²	#501×C₁₃₇	1	1	yes	characteristic
407	C₄	—	4	4	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	8	2	no	—
411	C₄	—	8	4	no	—
412	C₄	C₄×C₄⋊C₄×C₁₃₇	1	2	yes	—
413	C₄	#385×C₁₃₇	1	2	yes	—
414	C₄	#387×C₁₃₇	1	2	yes	—
415	C₄	#387×C₁₃₇	1	2	yes	—
416	C₂	#1436×C₁₃₇	1	1	yes	characteristic
417	C₂	#1762×C₁₃₇	1	1	yes	characteristic
418	C₂	#1763×C₁₃₇	1	1	yes	characteristic
419	C₂	#1894×C₁₃₇	1	1	yes	characteristic
420	C₂	#1895×C₁₃₇	1	1	yes	characteristic
421	C₂	#1935×C₁₃₇	1	2	yes	—
422	C₂	#1936×C₁₃₇	1	2	yes	—
423	C₂	#1943×C₁₃₇	1	2	yes	—
424	C₂	#1944×C₁₃₇	1	2	yes	—
425	C₂	#1992×C₁₃₇	1	1	yes	characteristic
426	C₂	#1993×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃₇	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₃₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₇
LCS	G ▷ C₂×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
15. #389×C₁₃₇	C₄	semidirect
20. #340×C₁₃₇	C₄	semidirect
100. C₂×C₈×C₁₃₇	C₄⋊C₄	semidirect
213. #10881	C₁₃₇	direct (N × H)
214. C₁₃₇	#10881	direct (N × H)
229. #389	C₄×C₁₃₇	semidirect
234. #340	C₄×C₁₃₇	semidirect
314. C₂×C₈	C₄⋊C₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#97×C₁₃₇	2
C₂×#389×C₁₃₇	2
C₂×#340×C₁₃₇	2
C₄⋊#95×C₁₃₇	2
#10881	137

Subgroups — C137×#10881 #46860267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#10881 #46860267