Subgroups — C₁₃₇×#28706 #46878092

Order 35072.

858 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#498×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×D₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2563×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2547×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#2077×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	#1988×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1987×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1807×C₁₃₇	C₂	1	4	yes	maximal, complemented
9	C₄×#106×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×C₈×C₁₃₇	C₂²	1	2	yes	—
11	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×#124×C₁₃₇	—	2	1	no	—
14	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
15	#498×C₁₃₇	—	2	4	no	—
16	C₈×D₄×C₁₃₇	—	2	4	no	—
17	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
18	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
19	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
23	#397×C₁₃₇	—	2	2	no	—
24	#393×C₁₃₇	—	2	2	no	—
25	#391×C₁₃₇	—	2	1	no	—
26	#390×C₁₃₇	—	2	1	no	—
27	#382×C₁₃₇	—	2	1	no	—
28	#380×C₁₃₇	C₂²	1	4	yes	—
29	#380×C₁₃₇	C₂²	1	4	yes	—
30	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
32	#340×C₁₃₇	C₂²	1	2	yes	—
33	#340×C₁₃₇	C₂²	1	4	yes	—
34	#340×C₁₃₇	C₂²	1	4	yes	—
35	C₂²×Q₈×C₁₃₇	—	2	1	no	—
36	C₂²×Q₈×C₁₃₇	—	2	1	no	—
37	C₂²×D₄×C₁₃₇	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
39	C₂²×C₈×C₁₃₇	—	2	4	no	—
40	C₂²×C₈×C₁₃₇	—	2	8	no	—
41	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
44	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
45	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
46	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
47	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
48	#124×C₁₃₇	—	4	4	no	—
49	C₄×D₄×C₁₃₇	—	2	2	no	—
50	C₄×D₄×C₁₃₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
58	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
60	C₂×C₂²⋊C₄×C₁₃₇	D₄	1	2	yes	—
61	C₂×C₄²×C₁₃₇	—	2	1	no	—
62	C₂×C₄²×C₁₃₇	—	2	1	no	—
63	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
64	#106×C₁₃₇	—	2	4	no	—
65	#106×C₁₃₇	—	2	4	no	—
66	#106×C₁₃₇	—	2	4	no	—
67	C₄⋊C₈×C₁₃₇	—	2	2	no	—
68	C₂²⋊C₈×C₁₃₇	—	2	4	no	—
69	C₄×C₈×C₁₃₇	D₄	1	4	yes	—
70	#95×C₁₃₇	—	2	1	no	—
71	#95×C₁₃₇	—	2	1	no	—
72	#95×C₁₃₇	—	2	4	no	—
73	#95×C₁₃₇	—	2	4	no	—
74	C₂⁴×C₁₃₇	C₂×D₄	1	2	yes	—
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	—	4	2	no	—
79	C₂×Q₈×C₁₃₇	—	8	2	no	—
80	C₂×D₄×C₁₃₇	—	2	2	no	—
81	C₂×D₄×C₁₃₇	—	2	2	no	—
82	C₂×D₄×C₁₃₇	SD₁₆	1	4	yes	—
83	C₂²×C₄×C₁₃₇	—	2	2	no	—
84	C₂²×C₄×C₁₃₇	—	2	2	no	—
85	C₂²×C₄×C₁₃₇	—	2	4	no	—
86	C₂²×C₄×C₁₃₇	—	2	4	no	—
87	C₂²×C₄×C₁₃₇	—	2	2	no	—
88	C₂²×C₄×C₁₃₇	—	2	2	no	—
89	C₂²×C₄×C₁₃₇	—	2	2	no	—
90	C₂²×C₄×C₁₃₇	—	2	2	no	—
91	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
95	C₂×C₈×C₁₃₇	—	2	2	no	—
96	C₂×C₈×C₁₃₇	—	2	2	no	—
97	C₂×C₈×C₁₃₇	—	2	4	no	—
98	C₂×C₈×C₁₃₇	—	4	8	no	—
99	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
100	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
101	C₂×C₈×C₁₃₇	#41	1	4	yes	—
102	C₄⋊C₄×C₁₃₇	—	2	2	no	—
103	C₄⋊C₄×C₁₃₇	—	2	2	no	—
104	C₄⋊C₄×C₁₃₇	—	2	2	no	—
105	C₄⋊C₄×C₁₃₇	—	2	2	no	—
106	C₄⋊C₄×C₁₃₇	—	2	2	no	—
107	C₄⋊C₄×C₁₃₇	—	2	2	no	—
108	C₄⋊C₄×C₁₃₇	—	2	2	no	—
109	C₄⋊C₄×C₁₃₇	—	2	2	no	—
110	C₄⋊C₄×C₁₃₇	—	2	2	no	—
111	C₄⋊C₄×C₁₃₇	—	4	2	no	—
112	C₄⋊C₄×C₁₃₇	—	4	2	no	—
113	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
114	C₂²⋊C₄×C₁₃₇	—	4	8	no	—
115	C₂²⋊C₄×C₁₃₇	—	8	4	no	—
116	C₄²×C₁₃₇	—	4	2	no	—
117	C₄²×C₁₃₇	—	4	2	no	—
118	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
119	C₄²×C₁₃₇	#41	1	2	yes	—
120	C₂³×C₁₃₇	—	2	2	no	—
121	C₂³×C₁₃₇	—	2	4	no	—
122	C₂³×C₁₃₇	—	2	2	no	—
123	C₂³×C₁₃₇	—	2	4	no	—
124	C₂³×C₁₃₇	C₂×SD₁₆	1	4	yes	—
125	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
126	Q₈×C₁₃₇	—	8	4	no	—
127	Q₈×C₁₃₇	—	8	4	no	—
128	D₄×C₁₃₇	—	2	8	no	—
129	C₂×C₄×C₁₃₇	—	2	2	no	—
130	C₂×C₄×C₁₃₇	—	2	2	no	—
131	C₂×C₄×C₁₃₇	—	2	4	no	—
132	C₂×C₄×C₁₃₇	—	4	2	no	—
133	C₂×C₄×C₁₃₇	—	4	2	no	—
134	C₂×C₄×C₁₃₇	—	4	4	no	—
135	C₂×C₄×C₁₃₇	—	4	2	no	—
136	C₂×C₄×C₁₃₇	—	4	2	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	2	no	—
143	C₂×C₄×C₁₃₇	—	4	2	no	—
144	C₂×C₄×C₁₃₇	—	4	4	no	—
145	C₂×C₄×C₁₃₇	—	4	2	no	—
146	C₂×C₄×C₁₃₇	#121	1	2	yes	—
147	C₂×C₄×C₁₃₇	#121	1	2	yes	—
148	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	2	yes	—
149	C₂×C₄×C₁₃₇	#135	1	2	yes	—
150	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
152	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
154	C₈×C₁₃₇	—	2	2	no	—
155	C₈×C₁₃₇	—	4	2	no	—
156	C₈×C₁₃₇	#124	1	4	yes	complemented
157	C₂²×C₁₃₇	—	2	8	no	—
158	C₂²×C₁₃₇	—	2	4	no	—
159	C₂²×C₁₃₇	—	4	4	no	—
160	C₂²×C₁₃₇	—	4	2	no	—
161	C₂²×C₁₃₇	—	4	2	no	—
162	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
163	C₂²×C₁₃₇	#547	1	2	yes	—
164	C₂²×C₁₃₇	C₂²×SD₁₆	1	1	yes	characteristic
165	C₂²×C₁₃₇	C₂×#135	1	1	yes	characteristic
166	C₂²×C₁₃₇	#577	1	2	yes	—
167	C₄×C₁₃₇	—	2	2	no	—
168	C₄×C₁₃₇	—	4	2	no	—
169	C₄×C₁₃₇	—	8	2	no	—
170	C₄×C₁₃₇	—	8	2	no	—
171	C₄×C₁₃₇	—	8	2	no	—
172	C₄×C₁₃₇	—	8	2	no	—
173	C₄×C₁₃₇	#465	1	4	yes	—
174	C₄×C₁₃₇	C₂×#124	1	1	yes	characteristic
175	C₄×C₁₃₇	#536	1	1	yes	characteristic
176	C₄×C₁₃₇	#556	1	2	yes	—
177	C₂×C₁₃₇	—	4	4	no	—
178	C₂×C₁₃₇	#2547	1	1	yes	characteristic
179	C₂×C₁₃₇	C₂×#465	1	1	yes	characteristic
180	C₂×C₁₃₇	#3057	1	1	yes	characteristic
181	C₂×C₁₃₇	#3335	1	2	yes	—
182	C₂×C₁₃₇	#3340	1	2	yes	—
183	#28706	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₁₃₇	#28706	1	1	yes	characteristic, direct product factor, Sylow
185	C₂×#498	C₂×C₁₃₇	1	1	yes	characteristic, complemented
186	C₂×C₈×D₄	C₂×C₁₃₇	1	1	yes	characteristic
187	#2563	C₂×C₁₃₇	1	1	yes	characteristic
188	#2547	C₂×C₁₃₇	1	1	yes	characteristic
189	#2077	C₂×C₁₃₇	1	4	yes	complemented
190	#1988	C₂×C₁₃₇	1	1	yes	characteristic, complemented
191	#1987	C₂×C₁₃₇	1	1	yes	characteristic, complemented
192	#1807	C₂×C₁₃₇	1	4	yes	complemented
193	C₄×#106	C₂×C₁₃₇	1	1	yes	characteristic, complemented
194	C₂³×C₈	C₂²×C₁₃₇	1	2	yes	—
195	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
196	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
197	C₂×#124	—	2	1	no	—
198	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
199	#498	—	2	4	no	—
200	C₈×D₄	—	2	4	no	—
201	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
202	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
203	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
204	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
205	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
206	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
207	#397	—	2	2	no	—
208	#393	—	2	2	no	—
209	#391	—	2	1	no	—
210	#390	—	2	1	no	—
211	#382	—	2	1	no	—
212	#380	C₂²×C₁₃₇	1	4	yes	—
213	#380	C₂²×C₁₃₇	1	4	yes	—
214	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
215	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
216	#340	C₂²×C₁₃₇	1	4	yes	—
217	#340	C₂²×C₁₃₇	1	4	yes	—
218	#340	C₂²×C₁₃₇	1	2	yes	—
219	C₂²×Q₈	—	2	1	no	—
220	C₂²×Q₈	—	2	1	no	—
221	C₂²×D₄	D₄×C₁₃₇	1	1	yes	characteristic
222	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
223	C₂²×C₈	—	2	4	no	—
224	C₂²×C₈	—	2	8	no	—
225	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
226	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
227	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
228	C₄⋊Q₈	—	2	2	no	—
229	C₄⋊Q₈	—	2	2	no	—
230	C₄⋊Q₈	—	2	2	no	—
231	C₄⋊Q₈	—	2	2	no	—
232	#124	—	4	4	no	—
233	C₄×D₄	—	2	2	no	—
234	C₄×D₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
239	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
240	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
241	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
242	C₂×C₂²⋊C₄	—	2	4	no	—
243	C₂×C₂²⋊C₄	—	2	4	no	—
244	C₂×C₂²⋊C₄	D₄×C₁₃₇	1	2	yes	—
245	C₂×C₄²	—	2	1	no	—
246	C₂×C₄²	—	2	1	no	—
247	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
248	#106	—	2	4	no	—
249	#106	—	2	4	no	—
250	#106	—	2	4	no	—
251	C₄⋊C₈	—	2	2	no	—
252	C₂²⋊C₈	—	2	4	no	—
253	C₄×C₈	D₄×C₁₃₇	1	4	yes	—
254	#95	—	2	1	no	—
255	#95	—	2	1	no	—
256	#95	—	2	4	no	—
257	#95	—	2	4	no	—
258	C₂⁴	C₂×D₄×C₁₃₇	1	2	yes	—
259	C₂×Q₈	—	4	2	no	—
260	C₂×Q₈	—	4	2	no	—
261	C₂×Q₈	—	4	2	no	—
262	C₂×Q₈	—	4	2	no	—
263	C₂×Q₈	—	8	2	no	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	SD₁₆×C₁₃₇	1	4	yes	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
278	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	4	8	no	—
283	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
284	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
285	C₂×C₈	#41×C₁₃₇	1	4	yes	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	4	2	no	—
296	C₄⋊C₄	—	4	2	no	—
297	C₂²⋊C₄	—	2	4	no	—
298	C₂²⋊C₄	—	4	8	no	—
299	C₂²⋊C₄	—	8	4	no	—
300	C₄²	—	4	2	no	—
301	C₄²	—	4	2	no	—
302	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
303	C₄²	#41×C₁₃₇	1	2	yes	—
304	C₂³	—	2	2	no	—
305	C₂³	—	2	4	no	—
306	C₂³	—	2	2	no	—
307	C₂³	—	2	4	no	—
308	C₂³	C₂×SD₁₆×C₁₃₇	1	4	yes	—
309	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
310	Q₈	—	8	4	no	—
311	Q₈	—	8	4	no	—
312	D₄	—	2	8	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	#121×C₁₃₇	1	2	yes	—
331	C₂×C₄	#121×C₁₃₇	1	2	yes	—
332	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	2	yes	—
333	C₂×C₄	#135×C₁₃₇	1	2	yes	—
334	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
335	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
336	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
337	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
338	C₈	—	2	2	no	—
339	C₈	—	4	2	no	—
340	C₈	#124×C₁₃₇	1	4	yes	complemented
341	C₂²	—	2	4	no	—
342	C₂²	—	2	8	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	4	no	—
346	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
347	C₂²	#547×C₁₃₇	1	2	yes	—
348	C₂²	C₂²×SD₁₆×C₁₃₇	1	1	yes	characteristic
349	C₂²	C₂×#135×C₁₃₇	1	1	yes	characteristic
350	C₂²	#577×C₁₃₇	1	2	yes	—
351	C₄	—	2	2	no	—
352	C₄	—	4	2	no	—
353	C₄	—	8	2	no	—
354	C₄	—	8	2	no	—
355	C₄	—	8	2	no	—
356	C₄	—	8	2	no	—
357	C₄	#465×C₁₃₇	1	4	yes	—
358	C₄	C₂×#124×C₁₃₇	1	1	yes	characteristic
359	C₄	#536×C₁₃₇	1	1	yes	characteristic
360	C₄	#556×C₁₃₇	1	2	yes	—
361	C₂	—	4	4	no	—
362	C₂	#2547×C₁₃₇	1	1	yes	characteristic
363	C₂	C₂×#465×C₁₃₇	1	1	yes	characteristic
364	C₂	#3057×C₁₃₇	1	1	yes	characteristic
365	C₂	#3335×C₁₃₇	1	2	yes	—
366	C₂	#3340×C₁₃₇	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×#498×C₁₃₇	C₂	semidirect
5. #2077×C₁₃₇	C₂	semidirect
6. #1988×C₁₃₇	C₂	semidirect
7. #1987×C₁₃₇	C₂	semidirect
8. #1807×C₁₃₇	C₂	semidirect
9. C₄×#106×C₁₃₇	C₂	semidirect
156. C₈×C₁₃₇	#124	semidirect
183. #28706	C₁₃₇	direct (N × H)
184. C₁₃₇	#28706	direct (N × H)
185. C₂×#498	C₂×C₁₃₇	semidirect
189. #2077	C₂×C₁₃₇	semidirect
190. #1988	C₂×C₁₃₇	semidirect
191. #1987	C₂×C₁₃₇	semidirect
192. #1807	C₂×C₁₃₇	semidirect
193. C₄×#106	C₂×C₁₃₇	semidirect
340. C₈	#124×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#498×C₁₃₇	2
C₂×C₈×D₄×C₁₃₇	2
#2563×C₁₃₇	2
#2547×C₁₃₇	2
#2077×C₁₃₇	2
#1988×C₁₃₇	2
#1987×C₁₃₇	2
#1807×C₁₃₇	2
C₄×#106×C₁₃₇	2
#28706	137

Subgroups — C137×#28706 #46878092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28706 #46878092