Subgroups — C₁₃₇×#20485 #46869871

Order 35072.

1150 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#436×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#405×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#2293×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#1770×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×C₄⋊C₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1767×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1753×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	C₈×C₂²⋊C₄×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	#1750×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	C₄²×C₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×M₁₆×C₁₃₇	C₂²	1	2	yes	—
13	C₂³×C₈×C₁₃₇	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂×#117×C₁₃₇	C₂²	1	2	yes	—
16	#436×C₁₃₇	C₄	1	8	yes	complemented
17	C₈×D₄×C₁₃₇	C₄	1	8	yes	complemented
18	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
21	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
22	#405×C₁₃₇	—	2	8	no	—
23	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
24	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
32	#390×C₁₃₇	C₄	1	2	yes	—
33	#389×C₁₃₇	C₄	1	2	yes	—
34	#388×C₁₃₇	C₄	1	4	yes	—
35	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
36	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
37	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
38	#336×C₁₃₇	C₂²	1	2	yes	—
39	#336×C₁₃₇	C₂²	1	2	yes	—
40	#336×C₁₃₇	C₂²	1	2	yes	—
41	C₂²×D₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
43	C₂×M₁₆×C₁₃₇	—	2	4	no	—
44	C₂×M₁₆×C₁₃₇	—	2	4	no	—
45	C₂×M₁₆×C₁₃₇	C₂×C₄	1	8	yes	—
46	C₂²×C₈×C₁₃₇	—	2	4	no	—
47	C₂²×C₈×C₁₃₇	—	2	4	no	—
48	C₂²×C₈×C₁₃₇	C₂×C₄	1	8	yes	—
49	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
55	C₄×D₄×C₁₃₇	C₂×C₄	1	4	yes	—
56	C₄×D₄×C₁₃₇	C₂×C₄	1	4	yes	—
57	#117×C₁₃₇	—	2	4	no	—
58	#117×C₁₃₇	—	2	4	no	—
59	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
63	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
64	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₁₃₇	C₂×C₄	1	4	yes	—
72	C₄⋊C₈×C₁₃₇	C₂×C₄	1	4	yes	—
73	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	8	yes	—
74	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	8	yes	—
75	#97×C₁₃₇	—	2	4	no	—
76	#97×C₁₃₇	—	2	4	no	—
77	C₄×C₈×C₁₃₇	—	2	4	no	—
78	C₄×C₈×C₁₃₇	—	2	2	no	—
79	C₄×C₈×C₁₃₇	—	2	2	no	—
80	C₄×C₈×C₁₃₇	—	2	2	no	—
81	C₄×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
82	C₄×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
83	C₄×C₈×C₁₃₇	D₄	1	4	yes	complemented
84	#95×C₁₃₇	C₂×C₄	1	4	yes	—
85	#95×C₁₃₇	C₂×C₄	1	2	yes	—
86	C₂⁴×C₁₃₇	C₂²×C₄	1	2	yes	—
87	C₂×D₄×C₁₃₇	—	2	4	no	—
88	C₂×D₄×C₁₃₇	C₄²	1	4	yes	—
89	C₂²×C₄×C₁₃₇	—	2	2	no	—
90	C₂²×C₄×C₁₃₇	—	2	2	no	—
91	C₂²×C₄×C₁₃₇	—	2	2	no	—
92	C₂²×C₄×C₁₃₇	—	2	2	no	—
93	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
94	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
102	M₁₆×C₁₃₇	—	2	16	no	—
103	C₂×C₈×C₁₃₇	—	2	2	no	—
104	C₂×C₈×C₁₃₇	—	2	2	no	—
105	C₂×C₈×C₁₃₇	—	2	1	no	—
106	C₂×C₈×C₁₃₇	—	2	1	no	—
107	C₂×C₈×C₁₃₇	—	2	1	no	—
108	C₂×C₈×C₁₃₇	—	2	1	no	—
109	C₂×C₈×C₁₃₇	—	2	2	no	—
110	C₂×C₈×C₁₃₇	—	2	2	no	—
111	C₂×C₈×C₁₃₇	—	2	16	no	—
112	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₁₃₇	C₂²×C₄	1	4	yes	—
115	C₂×C₈×C₁₃₇	C₂²×C₄	1	4	yes	—
116	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₁₃₇	#41	1	2	yes	—
121	C₂×C₈×C₁₃₇	#41	1	2	yes	—
122	C₄⋊C₄×C₁₃₇	—	2	8	no	—
123	C₄⋊C₄×C₁₃₇	—	2	4	no	—
124	C₄⋊C₄×C₁₃₇	C₄²	1	4	yes	—
125	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
126	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
127	C₂²⋊C₄×C₁₃₇	C₄²	1	8	yes	—
128	C₄²×C₁₃₇	—	2	4	no	—
129	C₄²×C₁₃₇	—	2	4	no	—
130	C₄²×C₁₃₇	—	2	2	no	—
131	C₄²×C₁₃₇	—	2	1	no	—
132	C₄²×C₁₃₇	—	2	1	no	—
133	C₄²×C₁₃₇	—	2	2	no	—
134	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
135	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
136	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
137	C₄²×C₁₃₇	#41	1	2	yes	—
138	C₂³×C₁₃₇	—	2	2	no	—
139	C₂³×C₁₃₇	—	2	2	no	—
140	C₂³×C₁₃₇	—	2	4	no	—
141	C₂³×C₁₃₇	—	2	4	no	—
142	C₂³×C₁₃₇	C₂×C₄²	1	4	yes	—
143	C₂³×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
144	D₄×C₁₃₇	—	2	8	no	—
145	C₂×C₄×C₁₃₇	—	2	2	no	—
146	C₂×C₄×C₁₃₇	—	2	2	no	—
147	C₂×C₄×C₁₃₇	—	2	2	no	—
148	C₂×C₄×C₁₃₇	—	2	2	no	—
149	C₂×C₄×C₁₃₇	—	2	2	no	—
150	C₂×C₄×C₁₃₇	—	2	2	no	—
151	C₂×C₄×C₁₃₇	—	2	2	no	—
152	C₂×C₄×C₁₃₇	—	2	4	no	—
153	C₂×C₄×C₁₃₇	—	2	4	no	—
154	C₂×C₄×C₁₃₇	—	2	4	no	—
155	C₂×C₄×C₁₃₇	—	2	4	no	—
156	C₂×C₄×C₁₃₇	—	2	4	no	—
157	C₂×C₄×C₁₃₇	—	2	4	no	—
158	C₂×C₄×C₁₃₇	—	2	4	no	—
159	C₂×C₄×C₁₃₇	C₂×C₄²	1	2	yes	—
160	C₂×C₄×C₁₃₇	C₂×C₄²	1	4	yes	—
161	C₂×C₄×C₁₃₇	C₂×C₄²	1	2	yes	—
162	C₂×C₄×C₁₃₇	C₄×D₄	1	4	yes	—
163	C₂×C₄×C₁₃₇	#131	1	4	yes	—
164	C₂×C₄×C₁₃₇	#131	1	4	yes	—
165	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
171	C₈×C₁₃₇	—	2	4	no	—
172	C₈×C₁₃₇	—	2	4	no	—
173	C₈×C₁₃₇	—	2	2	no	—
174	C₈×C₁₃₇	—	2	2	no	—
175	C₈×C₁₃₇	C₄×D₄	1	4	yes	—
176	C₈×C₁₃₇	C₄×D₄	1	4	yes	—
177	C₂²×C₁₃₇	—	2	4	no	—
178	C₂²×C₁₃₇	—	2	4	no	—
179	C₂²×C₁₃₇	—	2	4	no	—
180	C₂²×C₁₃₇	—	4	4	no	—
181	C₂²×C₁₃₇	—	4	4	no	—
182	C₂²×C₁₃₇	C₂²×C₄²	1	1	yes	characteristic
183	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
184	C₂²×C₁₃₇	C₄×#41	1	1	yes	characteristic
185	C₂²×C₁₃₇	C₂×#131	1	2	yes	—
186	C₂²×C₁₃₇	C₂×#131	1	2	yes	—
187	C₄×C₁₃₇	—	2	2	no	—
188	C₄×C₁₃₇	—	2	4	no	—
189	C₄×C₁₃₇	—	2	4	no	—
190	C₄×C₁₃₇	—	2	4	no	—
191	C₄×C₁₃₇	—	4	4	no	—
192	C₄×C₁₃₇	#405	1	4	yes	complemented
193	C₄×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
194	C₄×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
195	C₄×C₁₃₇	C₄×#41	1	1	yes	characteristic
196	C₄×C₁₃₇	C₄×#41	1	1	yes	characteristic
197	C₂×C₁₃₇	—	4	4	no	—
198	C₂×C₁₃₇	C₄²×D₄	1	1	yes	characteristic
199	C₂×C₁₃₇	C₂×#405	1	1	yes	characteristic
200	C₂×C₁₃₇	C₄×#131	1	1	yes	characteristic
201	C₂×C₁₃₇	#2931	1	2	yes	—
202	C₂×C₁₃₇	#2966	1	2	yes	—
203	#20485	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₁₃₇	#20485	1	1	yes	characteristic, direct product factor, Sylow
205	C₂×#436	C₂×C₁₃₇	1	1	yes	characteristic
206	C₂×C₈×D₄	C₂×C₁₃₇	1	1	yes	characteristic
207	C₂×#405	C₂×C₁₃₇	1	2	yes	complemented
208	#2293	C₂×C₁₃₇	1	1	yes	characteristic
209	#1770	C₂×C₁₃₇	1	1	yes	characteristic, complemented
210	C₈×C₄⋊C₄	C₂×C₁₃₇	1	1	yes	characteristic, complemented
211	#1767	C₂×C₁₃₇	1	1	yes	characteristic, complemented
212	#1753	C₂×C₁₃₇	1	2	yes	complemented
213	C₈×C₂²⋊C₄	C₂×C₁₃₇	1	2	yes	complemented
214	#1750	C₂×C₁₃₇	1	2	yes	complemented
215	C₄²×C₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
216	C₂²×M₁₆	C₂²×C₁₃₇	1	2	yes	—
217	C₂³×C₈	C₂²×C₁₃₇	1	2	yes	—
218	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
219	C₂×#117	C₂²×C₁₃₇	1	2	yes	—
220	#436	C₄×C₁₃₇	1	8	yes	complemented
221	C₈×D₄	C₄×C₁₃₇	1	8	yes	complemented
222	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
223	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
224	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
225	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
226	#405	—	2	8	no	—
227	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
228	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
229	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
230	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
231	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
232	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
233	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
234	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
235	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
236	#390	C₄×C₁₃₇	1	2	yes	—
237	#389	C₄×C₁₃₇	1	2	yes	—
238	#388	C₄×C₁₃₇	1	4	yes	—
239	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
240	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
241	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
242	#336	C₂²×C₁₃₇	1	2	yes	—
243	#336	C₂²×C₁₃₇	1	2	yes	—
244	#336	C₂²×C₁₃₇	1	2	yes	—
245	C₂²×D₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
246	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
247	C₂×M₁₆	—	2	4	no	—
248	C₂×M₁₆	—	2	4	no	—
249	C₂×M₁₆	C₂×C₄×C₁₃₇	1	8	yes	—
250	C₂²×C₈	—	2	4	no	—
251	C₂²×C₈	—	2	4	no	—
252	C₂²×C₈	C₂×C₄×C₁₃₇	1	8	yes	—
253	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
254	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
255	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
259	C₄×D₄	C₂×C₄×C₁₃₇	1	4	yes	—
260	C₄×D₄	C₂×C₄×C₁₃₇	1	4	yes	—
261	#117	—	2	4	no	—
262	#117	—	2	4	no	—
263	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
264	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
265	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
267	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
268	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
269	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
270	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
271	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
272	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
275	C₄⋊C₈	C₂×C₄×C₁₃₇	1	4	yes	—
276	C₄⋊C₈	C₂×C₄×C₁₃₇	1	4	yes	—
277	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	8	yes	—
278	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	8	yes	—
279	#97	—	2	4	no	—
280	#97	—	2	4	no	—
281	C₄×C₈	—	2	4	no	—
282	C₄×C₈	—	2	2	no	—
283	C₄×C₈	—	2	2	no	—
284	C₄×C₈	—	2	2	no	—
285	C₄×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
286	C₄×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
287	C₄×C₈	D₄×C₁₃₇	1	4	yes	complemented
288	#95	C₂×C₄×C₁₃₇	1	4	yes	—
289	#95	C₂×C₄×C₁₃₇	1	2	yes	—
290	C₂⁴	C₂²×C₄×C₁₃₇	1	2	yes	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	C₄²×C₁₃₇	1	4	yes	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
298	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
300	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
301	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
302	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
303	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
304	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
305	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
306	M₁₆	—	2	16	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	16	no	—
316	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
317	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
318	C₂×C₈	C₂²×C₄×C₁₃₇	1	4	yes	—
319	C₂×C₈	C₂²×C₄×C₁₃₇	1	4	yes	—
320	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
321	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
322	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
323	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
324	C₂×C₈	#41×C₁₃₇	1	2	yes	—
325	C₂×C₈	#41×C₁₃₇	1	2	yes	—
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	C₄²×C₁₃₇	1	4	yes	—
329	C₂²⋊C₄	—	2	8	no	—
330	C₂²⋊C₄	—	2	8	no	—
331	C₂²⋊C₄	C₄²×C₁₃₇	1	8	yes	—
332	C₄²	—	2	4	no	—
333	C₄²	—	2	4	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	2	no	—
338	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
339	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
340	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
341	C₄²	#41×C₁₃₇	1	2	yes	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	2	4	no	—
346	C₂³	C₂×C₄²×C₁₃₇	1	4	yes	—
347	C₂³	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
348	D₄	—	2	8	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	C₂×C₄²×C₁₃₇	1	2	yes	—
364	C₂×C₄	C₂×C₄²×C₁₃₇	1	4	yes	—
365	C₂×C₄	C₂×C₄²×C₁₃₇	1	2	yes	—
366	C₂×C₄	C₄×D₄×C₁₃₇	1	4	yes	—
367	C₂×C₄	#131×C₁₃₇	1	4	yes	—
368	C₂×C₄	#131×C₁₃₇	1	4	yes	—
369	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
370	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
371	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
372	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
373	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
374	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
375	C₈	—	2	4	no	—
376	C₈	—	2	4	no	—
377	C₈	—	2	2	no	—
378	C₈	—	2	2	no	—
379	C₈	C₄×D₄×C₁₃₇	1	4	yes	—
380	C₈	C₄×D₄×C₁₃₇	1	4	yes	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	4	no	—
386	C₂²	C₂²×C₄²×C₁₃₇	1	1	yes	characteristic
387	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
388	C₂²	C₄×#41×C₁₃₇	1	1	yes	characteristic
389	C₂²	C₂×#131×C₁₃₇	1	2	yes	—
390	C₂²	C₂×#131×C₁₃₇	1	2	yes	—
391	C₄	—	2	4	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	4	no	—
394	C₄	—	2	4	no	—
395	C₄	—	4	4	no	—
396	C₄	#405×C₁₃₇	1	4	yes	complemented
397	C₄	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
398	C₄	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
399	C₄	C₄×#41×C₁₃₇	1	1	yes	characteristic
400	C₄	C₄×#41×C₁₃₇	1	1	yes	characteristic
401	C₂	—	4	4	no	—
402	C₂	C₄²×D₄×C₁₃₇	1	1	yes	characteristic
403	C₂	C₂×#405×C₁₃₇	1	1	yes	characteristic
404	C₂	C₄×#131×C₁₃₇	1	1	yes	characteristic
405	C₂	#2931×C₁₃₇	1	2	yes	—
406	C₂	#2966×C₁₃₇	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈×C₁₃₇	C₂³
commutator	C₂²	C₂²×C₄²×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
socle	C₂³×C₁₃₇	C₂³×C₄
prime radical	C₂²×D₄×C₁₃₇	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×#405×C₁₃₇	C₂	semidirect
5. #1770×C₁₃₇	C₂	semidirect
6. C₈×C₄⋊C₄×C₁₃₇	C₂	semidirect
7. #1767×C₁₃₇	C₂	semidirect
8. #1753×C₁₃₇	C₂	semidirect
9. C₈×C₂²⋊C₄×C₁₃₇	C₂	semidirect
10. #1750×C₁₃₇	C₂	semidirect
11. C₄²×C₈×C₁₃₇	C₂	semidirect
16. #436×C₁₃₇	C₄	semidirect
17. C₈×D₄×C₁₃₇	C₄	semidirect
83. C₄×C₈×C₁₃₇	D₄	semidirect
192. C₄×C₁₃₇	#405	semidirect
203. #20485	C₁₃₇	direct (N × H)
204. C₁₃₇	#20485	direct (N × H)
207. C₂×#405	C₂×C₁₃₇	semidirect
209. #1770	C₂×C₁₃₇	semidirect
210. C₈×C₄⋊C₄	C₂×C₁₃₇	semidirect
211. #1767	C₂×C₁₃₇	semidirect
212. #1753	C₂×C₁₃₇	semidirect
213. C₈×C₂²⋊C₄	C₂×C₁₃₇	semidirect
214. #1750	C₂×C₁₃₇	semidirect
215. C₄²×C₈	C₂×C₁₃₇	semidirect
220. #436	C₄×C₁₃₇	semidirect
221. C₈×D₄	C₄×C₁₃₇	semidirect
287. C₄×C₈	D₄×C₁₃₇	semidirect
396. C₄	#405×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#436×C₁₃₇	2
C₂×C₈×D₄×C₁₃₇	2
C₂×#405×C₁₃₇	2
#2293×C₁₃₇	2
#1770×C₁₃₇	2
C₈×C₄⋊C₄×C₁₃₇	2
#1767×C₁₃₇	2
#1753×C₁₃₇	2
C₈×C₂²⋊C₄×C₁₃₇	2
#1750×C₁₃₇	2
C₄²×C₈×C₁₃₇	2
#20485	137

Subgroups — C137×#20485 #46869871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#20485 #46869871