Subgroups — C₁₃₇×#28728 #46878114

Order 35072.

838 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#490×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#486×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2660×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#2328×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#2073×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2071×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1993×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1991×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1804×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	#1802×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	#1768×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×#125×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃₇	C₂²	1	2	yes	—
16	#490×C₁₃₇	—	2	4	no	—
17	#486×C₁₃₇	—	2	4	no	—
18	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
19	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
20	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
21	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
22	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
23	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
25	#398×C₁₃₇	—	2	2	no	—
26	#395×C₁₃₇	—	2	2	no	—
27	#390×C₁₃₇	C₂²	1	2	yes	—
28	#386×C₁₃₇	—	2	2	no	—
29	#386×C₁₃₇	—	2	2	no	—
30	#384×C₁₃₇	C₂²	1	1	yes	characteristic
31	#384×C₁₃₇	C₂²	1	1	yes	characteristic
32	#382×C₁₃₇	C₂²	1	1	yes	characteristic
33	#382×C₁₃₇	C₂²	1	1	yes	characteristic
34	#382×C₁₃₇	C₂²	1	1	yes	characteristic
35	#376×C₁₃₇	C₂²	1	1	yes	characteristic
36	#340×C₁₃₇	C₂²	1	2	yes	—
37	#340×C₁₃₇	C₂²	1	2	yes	—
38	#340×C₁₃₇	C₂²	1	2	yes	—
39	#340×C₁₃₇	C₂²	1	2	yes	—
40	#336×C₁₃₇	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃₇	—	2	1	no	—
42	C₂²×D₄×C₁₃₇	—	2	1	no	—
43	C₂²×D₄×C₁₃₇	—	2	1	no	—
44	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃₇	—	2	2	no	—
46	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
48	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
49	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
50	#127×C₁₃₇	—	2	2	no	—
51	#127×C₁₃₇	D₄	1	4	yes	—
52	#125×C₁₃₇	—	2	2	no	—
53	#125×C₁₃₇	—	2	2	no	—
54	C₄×D₄×C₁₃₇	—	2	8	no	—
55	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
68	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₁₃₇	—	2	4	no	—
72	#102×C₁₃₇	—	2	4	no	—
73	#102×C₁₃₇	—	2	4	no	—
74	#102×C₁₃₇	—	2	4	no	—
75	#102×C₁₃₇	—	2	4	no	—
76	#97×C₁₃₇	—	2	2	no	—
77	C₄×C₈×C₁₃₇	—	2	2	no	—
78	#95×C₁₃₇	—	2	1	no	—
79	#95×C₁₃₇	—	2	1	no	—
80	#95×C₁₃₇	—	2	2	no	—
81	#95×C₁₃₇	—	2	2	no	—
82	#95×C₁₃₇	D₄	1	2	yes	—
83	#95×C₁₃₇	D₄	1	2	yes	—
84	C₂⁴×C₁₃₇	—	2	2	no	—
85	C₂×Q₈×C₁₃₇	—	4	2	no	—
86	C₂×Q₈×C₁₃₇	—	8	2	no	—
87	C₂×D₄×C₁₃₇	—	2	4	no	—
88	C₂×D₄×C₁₃₇	—	2	4	no	—
89	C₂×D₄×C₁₃₇	—	2	4	no	—
90	C₂×D₄×C₁₃₇	—	2	2	no	—
91	C₂×D₄×C₁₃₇	—	2	4	no	—
92	C₂×D₄×C₁₃₇	—	8	2	no	—
93	C₂×D₄×C₁₃₇	—	8	2	no	—
94	C₂×D₄×C₁₃₇	C₂×D₄	1	4	yes	—
95	C₂²×C₄×C₁₃₇	—	2	1	no	—
96	C₂²×C₄×C₁₃₇	—	2	2	no	—
97	C₂²×C₄×C₁₃₇	—	2	1	no	—
98	C₂²×C₄×C₁₃₇	—	2	1	no	—
99	C₂²×C₄×C₁₃₇	—	2	1	no	—
100	C₂²×C₄×C₁₃₇	—	4	4	no	—
101	C₂²×C₄×C₁₃₇	—	8	2	no	—
102	C₂²×C₄×C₁₃₇	—	8	2	no	—
103	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
108	C₂×C₈×C₁₃₇	—	2	2	no	—
109	C₂×C₈×C₁₃₇	—	2	2	no	—
110	C₂×C₈×C₁₃₇	—	2	2	no	—
111	C₂×C₈×C₁₃₇	—	2	2	no	—
112	C₂×C₈×C₁₃₇	—	2	2	no	—
113	C₂×C₈×C₁₃₇	—	2	2	no	—
114	C₄⋊C₄×C₁₃₇	—	2	1	no	—
115	C₄⋊C₄×C₁₃₇	—	2	1	no	—
116	C₄⋊C₄×C₁₃₇	—	2	1	no	—
117	C₄⋊C₄×C₁₃₇	—	2	1	no	—
118	C₄⋊C₄×C₁₃₇	—	2	4	no	—
119	C₄⋊C₄×C₁₃₇	—	2	1	no	—
120	C₄⋊C₄×C₁₃₇	—	2	1	no	—
121	C₄⋊C₄×C₁₃₇	—	2	1	no	—
122	C₄⋊C₄×C₁₃₇	—	2	1	no	—
123	C₄⋊C₄×C₁₃₇	—	4	2	no	—
124	C₄⋊C₄×C₁₃₇	—	4	2	no	—
125	C₄⋊C₄×C₁₃₇	—	4	2	no	—
126	C₄⋊C₄×C₁₃₇	—	8	2	no	—
127	C₄⋊C₄×C₁₃₇	—	8	2	no	—
128	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
129	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
130	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
131	C₄²×C₁₃₇	—	2	2	no	—
132	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
133	C₄²×C₁₃₇	#41	1	2	yes	—
134	C₄²×C₁₃₇	#41	1	4	yes	—
135	C₂³×C₁₃₇	—	2	4	no	—
136	C₂³×C₁₃₇	—	4	2	no	—
137	C₂³×C₁₃₇	—	4	2	no	—
138	C₂³×C₁₃₇	—	4	2	no	—
139	C₂³×C₁₃₇	—	4	2	no	—
140	C₂³×C₁₃₇	—	4	2	no	—
141	C₂³×C₁₃₇	—	4	2	no	—
142	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₁₃₇	—	8	4	no	—
144	D₄×C₁₃₇	—	2	8	no	—
145	D₄×C₁₃₇	—	4	4	no	—
146	D₄×C₁₃₇	—	8	4	no	—
147	D₄×C₁₃₇	—	8	4	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	2	no	—
153	C₂×C₄×C₁₃₇	—	2	2	no	—
154	C₂×C₄×C₁₃₇	—	2	2	no	—
155	C₂×C₄×C₁₃₇	—	4	1	no	—
156	C₂×C₄×C₁₃₇	—	4	1	no	—
157	C₂×C₄×C₁₃₇	—	4	1	no	—
158	C₂×C₄×C₁₃₇	—	4	1	no	—
159	C₂×C₄×C₁₃₇	—	4	2	no	—
160	C₂×C₄×C₁₃₇	—	4	2	no	—
161	C₂×C₄×C₁₃₇	—	4	2	no	—
162	C₂×C₄×C₁₃₇	—	4	2	no	—
163	C₂×C₄×C₁₃₇	—	4	2	no	—
164	C₂×C₄×C₁₃₇	—	4	2	no	—
165	C₂×C₄×C₁₃₇	—	4	2	no	—
166	C₂×C₄×C₁₃₇	—	8	8	no	—
167	C₂×C₄×C₁₃₇	#121	1	2	yes	—
168	C₂×C₄×C₁₃₇	#121	1	2	yes	—
169	C₂×C₄×C₁₃₇	#124	1	4	yes	—
170	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
172	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
174	C₈×C₁₃₇	—	4	2	no	—
175	C₈×C₁₃₇	—	4	2	no	—
176	C₂²×C₁₃₇	—	4	4	no	—
177	C₂²×C₁₃₇	—	4	4	no	—
178	C₂²×C₁₃₇	—	4	4	no	—
179	C₂²×C₁₃₇	—	8	2	no	—
180	C₂²×C₁₃₇	—	8	2	no	—
181	C₂²×C₁₃₇	—	8	2	no	—
182	C₂²×C₁₃₇	—	8	2	no	—
183	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
184	C₂²×C₁₃₇	C₂×#124	1	1	yes	characteristic
185	C₂²×C₁₃₇	#536	1	1	yes	characteristic
186	C₂²×C₁₃₇	#576	1	2	yes	—
187	C₂²×C₁₃₇	#577	1	2	yes	—
188	C₄×C₁₃₇	—	2	4	no	—
189	C₄×C₁₃₇	—	2	2	no	—
190	C₄×C₁₃₇	—	2	2	no	—
191	C₄×C₁₃₇	—	4	2	no	—
192	C₄×C₁₃₇	—	8	2	no	—
193	C₄×C₁₃₇	—	8	1	no	—
194	C₄×C₁₃₇	—	8	1	no	—
195	C₄×C₁₃₇	—	8	1	no	—
196	C₄×C₁₃₇	—	8	1	no	—
197	C₄×C₁₃₇	#547	1	2	yes	—
198	C₄×C₁₃₇	#556	1	2	yes	—
199	C₂×C₁₃₇	—	8	4	no	—
200	C₂×C₁₃₇	#2547	1	1	yes	characteristic
201	C₂×C₁₃₇	#3041	1	1	yes	characteristic
202	C₂×C₁₃₇	#3042	1	1	yes	characteristic
203	C₂×C₁₃₇	#3136	1	2	yes	—
204	C₂×C₁₃₇	#3241	1	2	yes	—
205	#28728	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₁₃₇	#28728	1	1	yes	characteristic, direct product factor, Sylow
207	C₂×#490	C₂×C₁₃₇	1	1	yes	characteristic
208	C₂×#486	C₂×C₁₃₇	1	1	yes	characteristic
209	#2660	C₂×C₁₃₇	1	1	yes	characteristic, complemented
210	#2328	C₂×C₁₃₇	1	1	yes	characteristic
211	#2073	C₂×C₁₃₇	1	2	yes	complemented
212	#2071	C₂×C₁₃₇	1	2	yes	complemented
213	#1993	C₂×C₁₃₇	1	1	yes	characteristic, complemented
214	#1991	C₂×C₁₃₇	1	1	yes	characteristic, complemented
215	#1804	C₂×C₁₃₇	1	2	yes	complemented
216	#1802	C₂×C₁₃₇	1	2	yes	complemented
217	#1768	C₂×C₁₃₇	1	1	yes	characteristic, complemented
218	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
219	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
220	C₂×#125	C₂²×C₁₃₇	1	1	yes	characteristic
221	C₂×C₄×D₄	C₂²×C₁₃₇	1	2	yes	—
222	#490	—	2	4	no	—
223	#486	—	2	4	no	—
224	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
225	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
226	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
227	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
228	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
229	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
230	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
231	#398	—	2	2	no	—
232	#395	—	2	2	no	—
233	#390	C₂²×C₁₃₇	1	2	yes	—
234	#386	—	2	2	no	—
235	#386	—	2	2	no	—
236	#384	C₂²×C₁₃₇	1	1	yes	characteristic
237	#384	C₂²×C₁₃₇	1	1	yes	characteristic
238	#382	C₂²×C₁₃₇	1	1	yes	characteristic
239	#382	C₂²×C₁₃₇	1	1	yes	characteristic
240	#382	C₂²×C₁₃₇	1	1	yes	characteristic
241	#376	C₂²×C₁₃₇	1	1	yes	characteristic
242	#340	C₂²×C₁₃₇	1	2	yes	—
243	#340	C₂²×C₁₃₇	1	2	yes	—
244	#340	C₂²×C₁₃₇	1	2	yes	—
245	#340	C₂²×C₁₃₇	1	2	yes	—
246	#336	C₂²×C₁₃₇	1	2	yes	—
247	C₂²×Q₈	—	2	1	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
251	C₂³×C₄	—	2	2	no	—
252	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
253	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
254	C₄⋊Q₈	—	2	2	no	—
255	C₄⋊Q₈	—	2	2	no	—
256	#127	—	2	2	no	—
257	#127	D₄×C₁₃₇	1	4	yes	—
258	#125	—	2	2	no	—
259	#125	—	2	2	no	—
260	C₄×D₄	—	2	8	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
276	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
277	C₄⋊C₈	—	2	4	no	—
278	#102	—	2	4	no	—
279	#102	—	2	4	no	—
280	#102	—	2	4	no	—
281	#102	—	2	4	no	—
282	#97	—	2	2	no	—
283	C₄×C₈	—	2	2	no	—
284	#95	—	2	1	no	—
285	#95	—	2	1	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	#95	D₄×C₁₃₇	1	2	yes	—
289	#95	D₄×C₁₃₇	1	2	yes	—
290	C₂⁴	—	2	2	no	—
291	C₂×Q₈	—	4	2	no	—
292	C₂×Q₈	—	8	2	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	8	2	no	—
299	C₂×D₄	—	8	2	no	—
300	C₂×D₄	C₂×D₄×C₁₃₇	1	4	yes	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	8	2	no	—
308	C₂²×C₄	—	8	2	no	—
309	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
313	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	8	2	no	—
333	C₄⋊C₄	—	8	2	no	—
334	C₂²⋊C₄	—	4	4	no	—
335	C₂²⋊C₄	—	8	2	no	—
336	C₂²⋊C₄	—	8	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
339	C₄²	#41×C₁₃₇	1	2	yes	—
340	C₄²	#41×C₁₃₇	1	4	yes	—
341	C₂³	—	2	4	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
349	Q₈	—	8	4	no	—
350	D₄	—	2	8	no	—
351	D₄	—	4	4	no	—
352	D₄	—	8	4	no	—
353	D₄	—	8	4	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	8	8	no	—
373	C₂×C₄	#121×C₁₃₇	1	2	yes	—
374	C₂×C₄	#121×C₁₃₇	1	2	yes	—
375	C₂×C₄	#124×C₁₃₇	1	4	yes	—
376	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
377	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
378	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
379	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
380	C₈	—	4	2	no	—
381	C₈	—	4	2	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
390	C₂²	C₂×#124×C₁₃₇	1	1	yes	characteristic
391	C₂²	#536×C₁₃₇	1	1	yes	characteristic
392	C₂²	#576×C₁₃₇	1	2	yes	—
393	C₂²	#577×C₁₃₇	1	2	yes	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	4	no	—
397	C₄	—	4	2	no	—
398	C₄	—	8	1	no	—
399	C₄	—	8	1	no	—
400	C₄	—	8	1	no	—
401	C₄	—	8	1	no	—
402	C₄	—	8	2	no	—
403	C₄	#547×C₁₃₇	1	2	yes	—
404	C₄	#556×C₁₃₇	1	2	yes	—
405	C₂	—	8	4	no	—
406	C₂	#2547×C₁₃₇	1	1	yes	characteristic
407	C₂	#3041×C₁₃₇	1	1	yes	characteristic
408	C₂	#3042×C₁₃₇	1	1	yes	characteristic
409	C₂	#3136×C₁₃₇	1	2	yes	—
410	C₂	#3241×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂×#127×C₁₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ #376×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. #2660×C₁₃₇	C₂	semidirect
5. #2073×C₁₃₇	C₂	semidirect
6. #2071×C₁₃₇	C₂	semidirect
7. #1993×C₁₃₇	C₂	semidirect
8. #1991×C₁₃₇	C₂	semidirect
9. #1804×C₁₃₇	C₂	semidirect
10. #1802×C₁₃₇	C₂	semidirect
11. #1768×C₁₃₇	C₂	semidirect
205. #28728	C₁₃₇	direct (N × H)
206. C₁₃₇	#28728	direct (N × H)
209. #2660	C₂×C₁₃₇	semidirect
211. #2073	C₂×C₁₃₇	semidirect
212. #2071	C₂×C₁₃₇	semidirect
213. #1993	C₂×C₁₃₇	semidirect
214. #1991	C₂×C₁₃₇	semidirect
215. #1804	C₂×C₁₃₇	semidirect
216. #1802	C₂×C₁₃₇	semidirect
217. #1768	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#490×C₁₃₇	2
C₂×#486×C₁₃₇	2
#2660×C₁₃₇	2
#2328×C₁₃₇	2
#2073×C₁₃₇	2
#2071×C₁₃₇	2
#1993×C₁₃₇	2
#1991×C₁₃₇	2
#1804×C₁₃₇	2
#1802×C₁₃₇	2
#1768×C₁₃₇	2
#28728	137

Subgroups — C137×#28728 #46878114

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28728 #46878114