Subgroups — C₁₃₇×#19189 #46868575

Order 35072.

746 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3245×C₁₃₇	C₂	1	2	yes	maximal, complemented
2	#3147×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2931×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#1689×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1687×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1665×C₁₃₇	C₂	1	4	yes	maximal, complemented
7	C₂×#334×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1547×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	C₂×#135×C₁₃₇	—	2	1	no	—
10	C₂×#135×C₁₃₇	—	2	1	no	—
11	C₂×#131×C₁₃₇	—	2	1	no	—
12	#532×C₁₃₇	C₂²	1	2	yes	—
13	#532×C₁₃₇	C₂²	1	1	yes	characteristic
14	#495×C₁₃₇	—	2	1	no	—
15	#495×C₁₃₇	—	2	1	no	—
16	#494×C₁₃₇	C₂²	1	1	yes	characteristic
17	#493×C₁₃₇	C₂²	1	1	yes	characteristic
18	#492×C₁₃₇	C₂²	1	2	yes	—
19	#474×C₁₃₇	—	2	2	no	—
20	#474×C₁₃₇	C₂²	1	4	yes	—
21	#466×C₁₃₇	—	2	4	no	—
22	#459×C₁₃₇	—	2	2	no	—
23	#459×C₁₃₇	C₂²	1	4	yes	—
24	#436×C₁₃₇	—	2	1	no	—
25	#436×C₁₃₇	C₂²	1	2	yes	—
26	C₈×D₄×C₁₃₇	—	2	1	no	—
27	C₈×D₄×C₁₃₇	C₂²	1	2	yes	—
28	#423×C₁₃₇	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
30	#408×C₁₃₇	—	2	1	no	—
31	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
32	#334×C₁₃₇	C₂²	1	2	yes	—
33	#334×C₁₃₇	C₂²	1	2	yes	—
34	#332×C₁₃₇	C₂²	1	4	yes	—
35	#331×C₁₃₇	C₂²	1	4	yes	—
36	C₂×#41×C₁₃₇	—	2	1	no	—
37	C₂×#41×C₁₃₇	—	2	2	no	—
38	#135×C₁₃₇	—	4	4	no	—
39	#135×C₁₃₇	—	4	4	no	—
40	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
41	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
42	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
43	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
44	C₂×D₈×C₁₃₇	—	2	4	no	—
45	C₂×D₈×C₁₃₇	—	2	1	no	—
46	C₂×D₈×C₁₃₇	—	2	1	no	—
47	#131×C₁₃₇	—	4	4	no	—
48	C₂×M₁₆×C₁₃₇	—	2	1	no	—
49	C₂×M₁₆×C₁₃₇	—	2	2	no	—
50	C₂²×C₈×C₁₃₇	—	2	2	no	—
51	C₂²×C₈×C₁₃₇	—	2	2	no	—
52	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
54	C₄⋊Q₈×C₁₃₇	D₄	1	1	yes	characteristic
55	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
56	#127×C₁₃₇	D₄	1	1	yes	characteristic
57	#127×C₁₃₇	C₂³	1	2	yes	—
58	#124×C₁₃₇	—	2	2	no	—
59	#124×C₁₃₇	—	2	1	no	—
60	#121×C₁₃₇	—	2	1	no	—
61	#121×C₁₃₇	—	2	2	no	—
62	#121×C₁₃₇	—	2	2	no	—
63	#121×C₁₃₇	D₄	1	2	yes	—
64	C₄×D₄×C₁₃₇	—	2	1	no	—
65	C₄×D₄×C₁₃₇	—	2	2	no	—
66	C₄×D₄×C₁₃₇	—	2	2	no	—
67	C₄×D₄×C₁₃₇	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
69	#107×C₁₃₇	—	2	4	no	—
70	C₄⋊C₈×C₁₃₇	—	2	2	no	—
71	C₄⋊C₈×C₁₃₇	—	2	1	no	—
72	C₄⋊C₈×C₁₃₇	C₂³	1	4	yes	—
73	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
74	#102×C₁₃₇	—	2	4	no	—
75	#102×C₁₃₇	—	2	4	no	—
76	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
77	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
78	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
80	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
82	#41×C₁₃₇	—	4	2	no	—
83	#41×C₁₃₇	—	4	2	no	—
84	#41×C₁₃₇	—	4	4	no	—
85	#41×C₁₃₇	—	4	4	no	—
86	C₂×Q₈×C₁₃₇	—	2	1	no	—
87	C₂×Q₈×C₁₃₇	—	2	2	no	—
88	C₂×D₄×C₁₃₇	—	2	2	no	—
89	C₂×D₄×C₁₃₇	—	2	1	no	—
90	C₂×D₄×C₁₃₇	—	2	1	no	—
91	C₂×D₄×C₁₃₇	—	2	2	no	—
92	C₂×D₄×C₁₃₇	—	2	2	no	—
93	C₂×D₄×C₁₃₇	—	2	2	no	—
94	C₂×D₄×C₁₃₇	—	4	2	no	—
95	C₂×D₄×C₁₃₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₃₇	—	2	2	no	—
97	C₂²×C₄×C₁₃₇	—	4	2	no	—
98	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
101	Q₁₆×C₁₃₇	—	4	2	no	—
102	Q₁₆×C₁₃₇	—	4	2	no	—
103	SD₁₆×C₁₃₇	—	4	4	no	—
104	SD₁₆×C₁₃₇	—	4	4	no	—
105	D₈×C₁₃₇	—	4	2	no	—
106	D₈×C₁₃₇	—	4	2	no	—
107	D₈×C₁₃₇	—	8	4	no	—
108	M₁₆×C₁₃₇	—	4	2	no	—
109	M₁₆×C₁₃₇	—	4	4	no	—
110	C₂×C₈×C₁₃₇	—	2	2	no	—
111	C₂×C₈×C₁₃₇	—	2	2	no	—
112	C₂×C₈×C₁₃₇	—	2	4	no	—
113	C₂×C₈×C₁₃₇	—	4	4	no	—
114	C₂×C₈×C₁₃₇	—	8	2	no	—
115	C₂×C₈×C₁₃₇	D₈	1	4	yes	complemented
116	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
120	C₄⋊C₄×C₁₃₇	—	2	1	no	—
121	C₄⋊C₄×C₁₃₇	—	2	2	no	—
122	C₄⋊C₄×C₁₃₇	—	2	2	no	—
123	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
124	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
125	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
126	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
127	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
128	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₃₇	#41	1	1	yes	characteristic
131	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
132	C₂³×C₁₃₇	—	2	2	no	—
133	C₂³×C₁₃₇	—	4	2	no	—
134	C₂³×C₁₃₇	#121	1	1	yes	characteristic
135	Q₈×C₁₃₇	—	4	2	no	—
136	Q₈×C₁₃₇	—	4	2	no	—
137	Q₈×C₁₃₇	—	4	2	no	—
138	D₄×C₁₃₇	—	2	4	no	—
139	D₄×C₁₃₇	—	4	2	no	—
140	D₄×C₁₃₇	—	4	4	no	—
141	D₄×C₁₃₇	—	4	2	no	—
142	D₄×C₁₃₇	—	4	2	no	—
143	D₄×C₁₃₇	—	4	2	no	—
144	D₄×C₁₃₇	—	4	2	no	—
145	D₄×C₁₃₇	—	4	2	no	—
146	D₄×C₁₃₇	—	8	2	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	—	4	1	no	—
151	C₂×C₄×C₁₃₇	—	4	2	no	—
152	C₂×C₄×C₁₃₇	—	4	2	no	—
153	C₂×C₄×C₁₃₇	—	4	2	no	—
154	C₂×C₄×C₁₃₇	—	8	4	no	—
155	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
156	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
157	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
158	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
159	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
160	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
163	C₈×C₁₃₇	—	2	1	no	—
164	C₈×C₁₃₇	—	2	1	no	—
165	C₈×C₁₃₇	—	4	2	no	—
166	C₈×C₁₃₇	—	4	4	no	—
167	C₈×C₁₃₇	C₂×D₈	1	2	yes	—
168	C₈×C₁₃₇	C₂×D₈	1	2	yes	—
169	C₂²×C₁₃₇	—	2	1	no	—
170	C₂²×C₁₃₇	—	2	1	no	—
171	C₂²×C₁₃₇	—	4	2	no	—
172	C₂²×C₁₃₇	—	4	2	no	—
173	C₂²×C₁₃₇	—	4	2	no	—
174	C₂²×C₁₃₇	—	8	2	no	—
175	C₂²×C₁₃₇	—	8	2	no	—
176	C₂²×C₁₃₇	—	8	2	no	—
177	C₂²×C₁₃₇	#459	1	2	yes	—
178	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
179	C₄×C₁₃₇	—	2	1	no	—
180	C₄×C₁₃₇	—	2	1	no	—
181	C₄×C₁₃₇	—	2	1	no	—
182	C₄×C₁₃₇	—	4	2	no	—
183	C₄×C₁₃₇	—	8	2	no	—
184	C₄×C₁₃₇	#459	1	2	yes	—
185	C₄×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
186	C₄×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₄×C₁₃₇	#577	1	2	yes	—
188	C₂×C₁₃₇	—	2	2	no	—
189	C₂×C₁₃₇	—	8	2	no	—
190	C₂×C₁₃₇	—	16	2	no	—
191	C₂×C₁₃₇	C₂×#459	1	1	yes	characteristic
192	C₂×C₁₃₇	#3060	1	1	yes	characteristic
193	C₂×C₁₃₇	#3067	1	1	yes	characteristic
194	#19189	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₁₃₇	#19189	1	1	yes	characteristic, direct product factor, Sylow
196	#3245	C₂×C₁₃₇	1	2	yes	complemented
197	#3147	C₂×C₁₃₇	1	1	yes	characteristic, complemented
198	#2931	C₂×C₁₃₇	1	1	yes	characteristic, complemented
199	#1689	C₂×C₁₃₇	1	2	yes	complemented
200	#1687	C₂×C₁₃₇	1	2	yes	complemented
201	#1665	C₂×C₁₃₇	1	4	yes	complemented
202	C₂×#334	C₂×C₁₃₇	1	1	yes	characteristic, complemented
203	#1547	C₂×C₁₃₇	1	2	yes	complemented
204	C₂×#135	—	2	1	no	—
205	C₂×#135	—	2	1	no	—
206	C₂×#131	—	2	1	no	—
207	#532	C₂²×C₁₃₇	1	2	yes	—
208	#532	C₂²×C₁₃₇	1	1	yes	characteristic
209	#495	—	2	1	no	—
210	#495	—	2	1	no	—
211	#494	C₂²×C₁₃₇	1	1	yes	characteristic
212	#493	C₂²×C₁₃₇	1	1	yes	characteristic
213	#492	C₂²×C₁₃₇	1	2	yes	—
214	#474	—	2	2	no	—
215	#474	C₂²×C₁₃₇	1	4	yes	—
216	#466	—	2	4	no	—
217	#459	—	2	2	no	—
218	#459	C₂²×C₁₃₇	1	4	yes	—
219	#436	—	2	1	no	—
220	#436	C₂²×C₁₃₇	1	2	yes	—
221	C₈×D₄	—	2	1	no	—
222	C₈×D₄	C₂²×C₁₃₇	1	2	yes	—
223	#423	C₂²×C₁₃₇	1	1	yes	characteristic
224	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
225	#408	—	2	1	no	—
226	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
227	#334	C₂²×C₁₃₇	1	2	yes	—
228	#334	C₂²×C₁₃₇	1	2	yes	—
229	#332	C₂²×C₁₃₇	1	4	yes	—
230	#331	C₂²×C₁₃₇	1	4	yes	—
231	C₂×#41	—	2	1	no	—
232	C₂×#41	—	2	2	no	—
233	#135	—	4	4	no	—
234	#135	—	4	4	no	—
235	C₂×Q₁₆	—	2	1	no	—
236	C₂×Q₁₆	—	2	1	no	—
237	C₂×SD₁₆	—	2	2	no	—
238	C₂×SD₁₆	—	2	2	no	—
239	C₂×D₈	—	2	4	no	—
240	C₂×D₈	—	2	1	no	—
241	C₂×D₈	—	2	1	no	—
242	#131	—	4	4	no	—
243	C₂×M₁₆	—	2	1	no	—
244	C₂×M₁₆	—	2	2	no	—
245	C₂²×C₈	—	2	2	no	—
246	C₂²×C₈	—	2	2	no	—
247	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
248	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
249	C₄⋊Q₈	D₄×C₁₃₇	1	1	yes	characteristic
250	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
251	#127	D₄×C₁₃₇	1	1	yes	characteristic
252	#127	C₂³×C₁₃₇	1	2	yes	—
253	#124	—	2	2	no	—
254	#124	—	2	1	no	—
255	#121	—	2	1	no	—
256	#121	—	2	2	no	—
257	#121	—	2	2	no	—
258	#121	D₄×C₁₃₇	1	2	yes	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	2	2	no	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	C₂³×C₁₃₇	1	2	yes	—
263	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
264	#107	—	2	4	no	—
265	C₄⋊C₈	—	2	2	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
268	C₄⋊C₈	C₂³×C₁₃₇	1	4	yes	—
269	#102	—	2	4	no	—
270	#102	—	2	4	no	—
271	C₂²⋊C₈	—	2	2	no	—
272	C₂²⋊C₈	—	2	2	no	—
273	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
274	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
275	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
276	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
277	#41	—	4	2	no	—
278	#41	—	4	2	no	—
279	#41	—	4	4	no	—
280	#41	—	4	4	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
295	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
296	Q₁₆	—	4	2	no	—
297	Q₁₆	—	4	2	no	—
298	SD₁₆	—	4	4	no	—
299	SD₁₆	—	4	4	no	—
300	D₈	—	4	2	no	—
301	D₈	—	4	2	no	—
302	D₈	—	8	4	no	—
303	M₁₆	—	4	2	no	—
304	M₁₆	—	4	4	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	4	no	—
308	C₂×C₈	—	4	4	no	—
309	C₂×C₈	—	8	2	no	—
310	C₂×C₈	D₈×C₁₃₇	1	4	yes	complemented
311	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
312	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
313	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
314	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
319	C₂²⋊C₄	—	2	2	no	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
324	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
325	C₄²	#41×C₁₃₇	1	1	yes	characteristic
326	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
327	C₂³	—	2	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	#121×C₁₃₇	1	1	yes	characteristic
330	Q₈	—	4	2	no	—
331	Q₈	—	4	2	no	—
332	Q₈	—	4	2	no	—
333	D₄	—	2	4	no	—
334	D₄	—	4	2	no	—
335	D₄	—	4	4	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	8	2	no	—
342	D₄	—	8	4	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	4	no	—
350	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
351	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
352	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
353	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
354	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
355	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
356	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
357	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	4	2	no	—
361	C₈	—	4	4	no	—
362	C₈	C₂×D₈×C₁₃₇	1	2	yes	—
363	C₈	C₂×D₈×C₁₃₇	1	2	yes	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	#459×C₁₃₇	1	2	yes	—
373	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	8	2	no	—
379	C₄	#459×C₁₃₇	1	2	yes	—
380	C₄	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
381	C₄	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
382	C₄	#577×C₁₃₇	1	2	yes	—
383	C₂	—	2	2	no	—
384	C₂	—	8	2	no	—
385	C₂	—	16	2	no	—
386	C₂	C₂×#459×C₁₃₇	1	1	yes	characteristic
387	C₂	#3060×C₁₃₇	1	1	yes	characteristic
388	C₂	#3067×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₂×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3245×C₁₃₇	C₂	semidirect
2. #3147×C₁₃₇	C₂	semidirect
3. #2931×C₁₃₇	C₂	semidirect
4. #1689×C₁₃₇	C₂	semidirect
5. #1687×C₁₃₇	C₂	semidirect
6. #1665×C₁₃₇	C₂	semidirect
7. C₂×#334×C₁₃₇	C₂	semidirect
8. #1547×C₁₃₇	C₂	semidirect
115. C₂×C₈×C₁₃₇	D₈	semidirect
194. #19189	C₁₃₇	direct (N × H)
195. C₁₃₇	#19189	direct (N × H)
196. #3245	C₂×C₁₃₇	semidirect
197. #3147	C₂×C₁₃₇	semidirect
198. #2931	C₂×C₁₃₇	semidirect
199. #1689	C₂×C₁₃₇	semidirect
200. #1687	C₂×C₁₃₇	semidirect
201. #1665	C₂×C₁₃₇	semidirect
202. C₂×#334	C₂×C₁₃₇	semidirect
203. #1547	C₂×C₁₃₇	semidirect
310. C₂×C₈	D₈×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3245×C₁₃₇	2
#3147×C₁₃₇	2
#2931×C₁₃₇	2
#1689×C₁₃₇	2
#1687×C₁₃₇	2
#1665×C₁₃₇	2
C₂×#334×C₁₃₇	2
#1547×C₁₃₇	2
#19189	137

Subgroups — C137×#19189 #46868575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#19189 #46868575