Subgroups — C₁₃₇×#21413 #46870799

Order 35072.

1070 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#541×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#405×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2314×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1992×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1991×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#1960×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1956×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1894×C₁₃₇	C₂	1	2	yes	maximal
9	#1892×C₁₃₇	C₂	1	2	yes	maximal
10	#1763×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	C₄×#103×C₁₃₇	C₂	1	2	yes	maximal, complemented
12	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
14	#541×C₁₃₇	—	2	4	no	—
15	#541×C₁₃₇	C₄	1	8	yes	complemented
16	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×#126×C₁₃₇	—	2	2	no	—
18	C₂×#125×C₁₃₇	—	2	2	no	—
19	C₂×#125×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₁₃₇	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₃₇	C₂²	1	2	yes	—
22	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
24	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
25	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
26	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
27	#405×C₁₃₇	—	2	4	no	—
28	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
29	C₂×#97×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	#388×C₁₃₇	—	2	2	no	—
33	#387×C₁₃₇	—	2	2	no	—
34	#384×C₁₃₇	C₂²	1	1	yes	characteristic
35	#382×C₁₃₇	C₂²	1	1	yes	characteristic
36	#380×C₁₃₇	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
38	#340×C₁₃₇	C₂²	1	2	yes	—
39	#340×C₁₃₇	C₂²	1	2	yes	—
40	#340×C₁₃₇	C₂²	1	2	yes	—
41	#340×C₁₃₇	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₃₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₁₃₇	—	2	2	no	—
45	C₂×M₁₆×C₁₃₇	—	2	2	no	—
46	C₂×M₁₆×C₁₃₇	—	2	2	no	—
47	C₂²×C₈×C₁₃₇	—	2	2	no	—
48	C₂²×C₈×C₁₃₇	—	2	2	no	—
49	C₂²×C₈×C₁₃₇	—	2	2	no	—
50	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
54	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
55	C₄⋊Q₈×C₁₃₇	C₂×C₄	1	4	yes	—
56	#126×C₁₃₇	—	2	16	no	—
57	#125×C₁₃₇	—	2	16	no	—
58	#125×C₁₃₇	—	2	2	no	—
59	#125×C₁₃₇	C₂×C₄	1	4	yes	—
60	C₂²⋊Q₈×C₁₃₇	—	2	4	no	—
61	C₂²⋊Q₈×C₁₃₇	C₂×C₄	1	8	yes	—
62	C₄×Q₈×C₁₃₇	—	2	4	no	—
63	C₄×Q₈×C₁₃₇	C₂×C₄	1	8	yes	—
64	#117×C₁₃₇	C₂×C₄	1	4	yes	—
65	#117×C₁₃₇	D₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₃₇	D₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₃₇	D₄	1	2	yes	—
78	C₂×C₄²×C₁₃₇	—	2	2	no	—
79	C₂×C₄²×C₁₃₇	—	2	2	no	—
80	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
82	#103×C₁₃₇	—	2	4	no	—
83	#103×C₁₃₇	—	2	4	no	—
84	#103×C₁₃₇	—	2	4	no	—
85	#103×C₁₃₇	—	2	4	no	—
86	#97×C₁₃₇	—	2	2	no	—
87	#97×C₁₃₇	—	2	2	no	—
88	C₄×C₈×C₁₃₇	—	2	2	no	—
89	C₄×C₈×C₁₃₇	—	2	2	no	—
90	#95×C₁₃₇	—	2	2	no	—
91	#95×C₁₃₇	—	2	2	no	—
92	#95×C₁₃₇	—	2	2	no	—
93	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
94	C₂×Q₈×C₁₃₇	—	2	2	no	—
95	C₂×Q₈×C₁₃₇	—	2	2	no	—
96	C₂×Q₈×C₁₃₇	—	2	2	no	—
97	C₂×Q₈×C₁₃₇	—	2	2	no	—
98	C₂×Q₈×C₁₃₇	—	2	2	no	—
99	C₂×Q₈×C₁₃₇	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₁₃₇	—	2	1	no	—
101	C₂²×C₄×C₁₃₇	—	2	1	no	—
102	C₂²×C₄×C₁₃₇	—	2	1	no	—
103	C₂²×C₄×C₁₃₇	—	2	1	no	—
104	C₂²×C₄×C₁₃₇	—	2	2	no	—
105	C₂²×C₄×C₁₃₇	—	2	2	no	—
106	C₂²×C₄×C₁₃₇	—	2	2	no	—
107	C₂²×C₄×C₁₃₇	—	2	2	no	—
108	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
114	M₁₆×C₁₃₇	—	2	8	no	—
115	C₂×C₈×C₁₃₇	—	2	8	no	—
116	C₂×C₈×C₁₃₇	—	2	1	no	—
117	C₂×C₈×C₁₃₇	—	2	1	no	—
118	C₂×C₈×C₁₃₇	—	2	1	no	—
119	C₂×C₈×C₁₃₇	—	2	1	no	—
120	C₂×C₈×C₁₃₇	—	2	1	no	—
121	C₂×C₈×C₁₃₇	—	2	1	no	—
122	C₂×C₈×C₁₃₇	—	2	1	no	—
123	C₂×C₈×C₁₃₇	—	2	1	no	—
124	C₂×C₈×C₁₃₇	#41	1	2	yes	—
125	C₂×C₈×C₁₃₇	#41	1	2	yes	—
126	C₂×C₈×C₁₃₇	#41	1	2	yes	—
127	C₂×C₈×C₁₃₇	#41	1	2	yes	—
128	C₄⋊C₄×C₁₃₇	—	2	8	no	—
129	C₄⋊C₄×C₁₃₇	—	2	8	no	—
130	C₄⋊C₄×C₁₃₇	—	2	8	no	—
131	C₄⋊C₄×C₁₃₇	—	2	8	no	—
132	C₄⋊C₄×C₁₃₇	—	2	2	no	—
133	C₄⋊C₄×C₁₃₇	—	2	2	no	—
134	C₄⋊C₄×C₁₃₇	—	2	2	no	—
135	C₄⋊C₄×C₁₃₇	—	2	2	no	—
136	C₄⋊C₄×C₁₃₇	—	2	2	no	—
137	C₄⋊C₄×C₁₃₇	—	8	2	no	—
138	C₄⋊C₄×C₁₃₇	C₂²⋊C₄	1	8	yes	—
139	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
140	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
141	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
142	C₂²⋊C₄×C₁₃₇	C₂²⋊C₄	1	8	yes	—
143	C₄²×C₁₃₇	—	2	8	no	—
144	C₄²×C₁₃₇	—	8	2	no	—
145	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
146	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
147	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
148	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
149	C₂³×C₁₃₇	—	2	1	no	—
150	C₂³×C₁₃₇	—	2	1	no	—
151	C₂³×C₁₃₇	—	2	2	no	—
152	C₂³×C₁₃₇	—	2	2	no	—
153	C₂³×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₁₃₇	—	2	4	no	—
156	Q₈×C₁₃₇	—	2	4	no	—
157	Q₈×C₁₃₇	—	4	2	no	—
158	Q₈×C₁₃₇	—	4	2	no	—
159	C₂×C₄×C₁₃₇	—	2	1	no	—
160	C₂×C₄×C₁₃₇	—	2	1	no	—
161	C₂×C₄×C₁₃₇	—	2	2	no	—
162	C₂×C₄×C₁₃₇	—	2	2	no	—
163	C₂×C₄×C₁₃₇	—	2	2	no	—
164	C₂×C₄×C₁₃₇	—	2	2	no	—
165	C₂×C₄×C₁₃₇	—	2	2	no	—
166	C₂×C₄×C₁₃₇	—	2	2	no	—
167	C₂×C₄×C₁₃₇	—	2	2	no	—
168	C₂×C₄×C₁₃₇	—	2	2	no	—
169	C₂×C₄×C₁₃₇	—	2	4	no	—
170	C₂×C₄×C₁₃₇	—	2	4	no	—
171	C₂×C₄×C₁₃₇	—	4	2	no	—
172	C₂×C₄×C₁₃₇	—	4	2	no	—
173	C₂×C₄×C₁₃₇	—	4	2	no	—
174	C₂×C₄×C₁₃₇	—	4	2	no	—
175	C₂×C₄×C₁₃₇	—	4	2	no	—
176	C₂×C₄×C₁₃₇	—	4	2	no	—
177	C₂×C₄×C₁₃₇	—	4	2	no	—
178	C₂×C₄×C₁₃₇	—	4	2	no	—
179	C₂×C₄×C₁₃₇	—	4	2	no	—
180	C₂×C₄×C₁₃₇	—	4	2	no	—
181	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	4	yes	—
182	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	4	yes	—
183	C₂×C₄×C₁₃₇	C₂×C₂²⋊C₄	1	2	yes	—
184	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
190	C₈×C₁₃₇	—	2	2	no	—
191	C₈×C₁₃₇	—	2	2	no	—
192	C₈×C₁₃₇	—	2	2	no	—
193	C₈×C₁₃₇	—	2	2	no	—
194	C₂²×C₁₃₇	—	2	4	no	—
195	C₂²×C₁₃₇	—	2	2	no	—
196	C₂²×C₁₃₇	—	4	1	no	—
197	C₂²×C₁₃₇	—	4	1	no	—
198	C₂²×C₁₃₇	—	4	2	no	—
199	C₂²×C₁₃₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
200	C₂²×C₁₃₇	#532	1	1	yes	characteristic
201	C₂²×C₁₃₇	#532	1	1	yes	characteristic
202	C₂²×C₁₃₇	#577	1	2	yes	—
203	C₂²×C₁₃₇	#578	1	2	yes	—
204	C₄×C₁₃₇	—	2	4	no	—
205	C₄×C₁₃₇	—	2	4	no	—
206	C₄×C₁₃₇	—	2	2	no	—
207	C₄×C₁₃₇	—	4	4	no	—
208	C₄×C₁₃₇	—	4	4	no	—
209	C₄×C₁₃₇	—	8	2	no	—
210	C₄×C₁₃₇	—	8	2	no	—
211	C₄×C₁₃₇	C₄×#41	1	1	yes	characteristic
212	C₄×C₁₃₇	C₄×#41	1	1	yes	characteristic
213	C₄×C₁₃₇	#525	1	1	yes	characteristic
214	C₄×C₁₃₇	#525	1	1	yes	characteristic
215	C₂×C₁₃₇	—	4	2	no	—
216	C₂×C₁₃₇	#2297	1	1	yes	characteristic
217	C₂×C₁₃₇	#2898	1	2	yes	—
218	C₂×C₁₃₇	#3174	1	1	yes	characteristic
219	C₂×C₁₃₇	#3177	1	1	yes	characteristic
220	C₂×C₁₃₇	#3178	1	2	yes	—
221	#21413	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₁₃₇	#21413	1	1	yes	characteristic, direct product factor, Sylow
223	C₂×#541	C₂×C₁₃₇	1	1	yes	characteristic
224	C₂×#405	C₂×C₁₃₇	1	1	yes	characteristic
225	#2314	C₂×C₁₃₇	1	1	yes	characteristic
226	#1992	C₂×C₁₃₇	1	1	yes	characteristic, complemented
227	#1991	C₂×C₁₃₇	1	1	yes	characteristic, complemented
228	#1960	C₂×C₁₃₇	1	1	yes	characteristic, complemented
229	#1956	C₂×C₁₃₇	1	1	yes	characteristic, complemented
230	#1894	C₂×C₁₃₇	1	2	yes	—
231	#1892	C₂×C₁₃₇	1	2	yes	—
232	#1763	C₂×C₁₃₇	1	2	yes	complemented
233	C₄×#103	C₂×C₁₃₇	1	2	yes	complemented
234	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
235	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
236	#541	—	2	4	no	—
237	#541	C₄×C₁₃₇	1	8	yes	complemented
238	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
239	C₂×#126	—	2	2	no	—
240	C₂×#125	—	2	2	no	—
241	C₂×#125	C₂²×C₁₃₇	1	1	yes	characteristic
242	C₂×C₂²⋊Q₈	C₂²×C₁₃₇	1	2	yes	—
243	C₂×C₄×Q₈	C₂²×C₁₃₇	1	2	yes	—
244	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
245	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
246	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
247	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
248	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
249	#405	—	2	4	no	—
250	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
251	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
252	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
253	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
254	#388	—	2	2	no	—
255	#387	—	2	2	no	—
256	#384	C₂²×C₁₃₇	1	1	yes	characteristic
257	#382	C₂²×C₁₃₇	1	1	yes	characteristic
258	#380	C₂²×C₁₃₇	1	2	yes	—
259	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
260	#340	C₂²×C₁₃₇	1	2	yes	—
261	#340	C₂²×C₁₃₇	1	2	yes	—
262	#340	C₂²×C₁₃₇	1	2	yes	—
263	#340	C₂²×C₁₃₇	1	2	yes	—
264	C₂²×Q₈	C₂³×C₁₃₇	1	2	yes	—
265	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
266	C₂×M₁₆	—	2	2	no	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	C₂×C₄×C₁₃₇	1	4	yes	—
278	#126	—	2	16	no	—
279	#125	—	2	16	no	—
280	#125	—	2	2	no	—
281	#125	C₂×C₄×C₁₃₇	1	4	yes	—
282	C₂²⋊Q₈	—	2	4	no	—
283	C₂²⋊Q₈	C₂×C₄×C₁₃₇	1	8	yes	—
284	C₄×Q₈	—	2	4	no	—
285	C₄×Q₈	C₂×C₄×C₁₃₇	1	8	yes	—
286	#117	C₂×C₄×C₁₃₇	1	4	yes	—
287	#117	D₄×C₁₃₇	1	4	yes	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	D₄×C₁₃₇	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
296	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	D₄×C₁₃₇	1	2	yes	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
304	#103	—	2	4	no	—
305	#103	—	2	4	no	—
306	#103	—	2	4	no	—
307	#103	—	2	4	no	—
308	#97	—	2	2	no	—
309	#97	—	2	2	no	—
310	C₄×C₈	—	2	2	no	—
311	C₄×C₈	—	2	2	no	—
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	#95	—	2	2	no	—
315	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	C₂²×C₄×C₁₃₇	1	4	yes	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
335	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
336	M₁₆	—	2	8	no	—
337	C₂×C₈	—	2	8	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	#41×C₁₃₇	1	2	yes	—
347	C₂×C₈	#41×C₁₃₇	1	2	yes	—
348	C₂×C₈	#41×C₁₃₇	1	2	yes	—
349	C₂×C₈	#41×C₁₃₇	1	2	yes	—
350	C₄⋊C₄	—	2	8	no	—
351	C₄⋊C₄	—	2	8	no	—
352	C₄⋊C₄	—	2	8	no	—
353	C₄⋊C₄	—	2	8	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	8	2	no	—
360	C₄⋊C₄	C₂²⋊C₄×C₁₃₇	1	8	yes	—
361	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₂²⋊C₄	—	8	2	no	—
364	C₂²⋊C₄	C₂²⋊C₄×C₁₃₇	1	8	yes	—
365	C₄²	—	2	8	no	—
366	C₄²	—	8	2	no	—
367	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
368	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
369	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
370	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
376	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
377	Q₈	—	2	4	no	—
378	Q₈	—	2	4	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	4	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	4	yes	—
404	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	4	yes	—
405	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₇	1	2	yes	—
406	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
408	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
409	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
411	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
412	C₈	—	2	2	no	—
413	C₈	—	2	2	no	—
414	C₈	—	2	2	no	—
415	C₈	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	4	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	2	no	—
421	C₂²	C₂²×C₂²⋊C₄×C₁₃₇	1	1	yes	characteristic
422	C₂²	#532×C₁₃₇	1	1	yes	characteristic
423	C₂²	#532×C₁₃₇	1	1	yes	characteristic
424	C₂²	#577×C₁₃₇	1	2	yes	—
425	C₂²	#578×C₁₃₇	1	2	yes	—
426	C₄	—	2	2	no	—
427	C₄	—	2	4	no	—
428	C₄	—	2	4	no	—
429	C₄	—	4	4	no	—
430	C₄	—	4	4	no	—
431	C₄	—	8	2	no	—
432	C₄	—	8	2	no	—
433	C₄	C₄×#41×C₁₃₇	1	1	yes	characteristic
434	C₄	C₄×#41×C₁₃₇	1	1	yes	characteristic
435	C₄	#525×C₁₃₇	1	1	yes	characteristic
436	C₄	#525×C₁₃₇	1	1	yes	characteristic
437	C₂	—	4	2	no	—
438	C₂	#2297×C₁₃₇	1	1	yes	characteristic
439	C₂	#2898×C₁₃₇	1	2	yes	—
440	C₂	#3174×C₁₃₇	1	1	yes	characteristic
441	C₂	#3177×C₁₃₇	1	1	yes	characteristic
442	C₂	#3178×C₁₃₇	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. #1992×C₁₃₇	C₂	semidirect
5. #1991×C₁₃₇	C₂	semidirect
6. #1960×C₁₃₇	C₂	semidirect
7. #1956×C₁₃₇	C₂	semidirect
10. #1763×C₁₃₇	C₂	semidirect
11. C₄×#103×C₁₃₇	C₂	semidirect
15. #541×C₁₃₇	C₄	semidirect
221. #21413	C₁₃₇	direct (N × H)
222. C₁₃₇	#21413	direct (N × H)
226. #1992	C₂×C₁₃₇	semidirect
227. #1991	C₂×C₁₃₇	semidirect
228. #1960	C₂×C₁₃₇	semidirect
229. #1956	C₂×C₁₃₇	semidirect
232. #1763	C₂×C₁₃₇	semidirect
233. C₄×#103	C₂×C₁₃₇	semidirect
237. #541	C₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#541×C₁₃₇	2
C₂×#405×C₁₃₇	2
#2314×C₁₃₇	2
#1992×C₁₃₇	2
#1991×C₁₃₇	2
#1960×C₁₃₇	2
#1956×C₁₃₇	2
#1894×C₁₃₇	2
#1892×C₁₃₇	2
#1763×C₁₃₇	2
C₄×#103×C₁₃₇	2
#21413	137

Subgroups — C137×#21413 #46870799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#21413 #46870799