Subgroups — C₁₃₇×#19404 #46868790

Order 35072.

676 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	#3226×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#3037×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#462×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#2982×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1682×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	#1674×C₁₃₇	C₂	1	4	yes	maximal, complemented
7	#1571×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1546×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1540×C₁₃₇	C₂	1	1	yes	maximal, characteristic
10	C₂×#137×C₁₃₇	—	2	1	no	—
11	C₂²×Q₁₆×C₁₃₇	—	2	1	no	—
12	#532×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
15	#500×C₁₃₇	C₂²	1	2	yes	—
16	#486×C₁₃₇	C₂²	1	2	yes	—
17	#480×C₁₃₇	—	2	2	no	—
18	#474×C₁₃₇	—	2	2	no	—
19	#464×C₁₃₇	—	2	2	no	—
20	#462×C₁₃₇	—	2	2	no	—
21	#462×C₁₃₇	C₂²	1	2	yes	—
22	#462×C₁₃₇	C₂²	1	4	yes	—
23	#460×C₁₃₇	C₂²	1	2	yes	—
24	C₈×Q₈×C₁₃₇	—	2	2	no	—
25	C₈×Q₈×C₁₃₇	C₂²	1	4	yes	—
26	#431×C₁₃₇	—	2	2	no	—
27	#431×C₁₃₇	C₂²	1	1	yes	characteristic
28	#431×C₁₃₇	C₂²	1	1	yes	characteristic
29	#423×C₁₃₇	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
31	#417×C₁₃₇	—	2	1	no	—
32	C₂×#103×C₁₃₇	—	2	1	no	—
33	#335×C₁₃₇	C₂²	1	4	yes	—
34	#332×C₁₃₇	C₂²	1	2	yes	—
35	#332×C₁₃₇	C₂²	1	4	yes	—
36	#331×C₁₃₇	C₂²	1	2	yes	—
37	C₂×#41×C₁₃₇	—	2	1	no	—
38	C₂²×Q₈×C₁₃₇	—	2	1	no	—
39	C₂²×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
40	#137×C₁₃₇	—	4	4	no	—
41	C₂×Q₁₆×C₁₃₇	—	2	4	no	—
42	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
43	C₂×Q₁₆×C₁₃₇	—	4	4	no	—
44	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
45	C₂×M₁₆×C₁₃₇	—	2	1	no	—
46	C₂²×C₈×C₁₃₇	—	2	1	no	—
47	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
48	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
49	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
50	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
52	#127×C₁₃₇	C₂³	1	1	yes	characteristic
53	#124×C₁₃₇	—	2	1	no	—
54	#121×C₁₃₇	—	2	1	no	—
55	#121×C₁₃₇	—	2	1	no	—
56	C₄×Q₈×C₁₃₇	—	2	1	no	—
57	C₄×Q₈×C₁₃₇	—	2	1	no	—
58	C₄×Q₈×C₁₃₇	D₄	1	2	yes	—
59	C₄×Q₈×C₁₃₇	C₂³	1	2	yes	—
60	C₄×D₄×C₁₃₇	—	2	1	no	—
61	C₄×D₄×C₁₃₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃₇	—	2	1	no	—
67	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
68	#107×C₁₃₇	—	2	4	no	—
69	C₄⋊C₈×C₁₃₇	—	2	4	no	—
70	C₄⋊C₈×C₁₃₇	—	2	1	no	—
71	C₄⋊C₈×C₁₃₇	—	2	1	no	—
72	C₄⋊C₈×C₁₃₇	D₄	1	2	yes	—
73	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
74	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
75	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
76	#103×C₁₃₇	—	2	4	no	—
77	#103×C₁₃₇	—	2	2	no	—
78	#102×C₁₃₇	—	2	4	no	—
79	#102×C₁₃₇	—	2	2	no	—
80	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
81	C₂²⋊C₈×C₁₃₇	D₄	1	2	yes	—
82	C₄×C₈×C₁₃₇	—	2	4	no	—
83	C₄×C₈×C₁₃₇	—	2	1	no	—
84	C₄×C₈×C₁₃₇	C₂³	1	2	yes	—
85	#41×C₁₃₇	—	4	2	no	—
86	#41×C₁₃₇	—	4	2	no	—
87	C₂×Q₈×C₁₃₇	—	2	1	no	—
88	C₂×Q₈×C₁₃₇	—	2	2	no	—
89	C₂×Q₈×C₁₃₇	—	2	1	no	—
90	C₂×Q₈×C₁₃₇	—	2	2	no	—
91	C₂×Q₈×C₁₃₇	—	4	1	no	—
92	C₂×Q₈×C₁₃₇	—	4	2	no	—
93	C₂×Q₈×C₁₃₇	—	4	2	no	—
94	C₂×Q₈×C₁₃₇	D₈	1	4	yes	—
95	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
96	C₂×D₄×C₁₃₇	—	2	1	no	—
97	C₂×D₄×C₁₃₇	—	2	1	no	—
98	C₂×D₄×C₁₃₇	—	2	1	no	—
99	C₂×D₄×C₁₃₇	—	4	1	no	—
100	C₂²×C₄×C₁₃₇	—	2	1	no	—
101	C₂²×C₄×C₁₃₇	—	2	1	no	—
102	C₂²×C₄×C₁₃₇	—	4	1	no	—
103	C₂²×C₄×C₁₃₇	—	4	1	no	—
104	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
107	Q₁₆×C₁₃₇	—	4	8	no	—
108	Q₁₆×C₁₃₇	—	4	4	no	—
109	SD₁₆×C₁₃₇	—	4	4	no	—
110	M₁₆×C₁₃₇	—	4	2	no	—
111	C₂×C₈×C₁₃₇	—	2	2	no	—
112	C₂×C₈×C₁₃₇	—	2	2	no	—
113	C₂×C₈×C₁₃₇	—	2	2	no	—
114	C₂×C₈×C₁₃₇	—	4	2	no	—
115	C₂×C₈×C₁₃₇	C₂×D₄	1	4	yes	—
116	C₄⋊C₄×C₁₃₇	—	2	2	no	—
117	C₄⋊C₄×C₁₃₇	—	2	1	no	—
118	C₄⋊C₄×C₁₃₇	—	2	2	no	—
119	C₄⋊C₄×C₁₃₇	—	2	2	no	—
120	C₄⋊C₄×C₁₃₇	—	2	1	no	—
121	C₄⋊C₄×C₁₃₇	—	2	2	no	—
122	C₄⋊C₄×C₁₃₇	—	2	1	no	—
123	C₄⋊C₄×C₁₃₇	—	4	1	no	—
124	C₄⋊C₄×C₁₃₇	—	4	1	no	—
125	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
126	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
127	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
128	C₄²×C₁₃₇	—	2	2	no	—
129	C₄²×C₁₃₇	—	2	2	no	—
130	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₃₇	#41	1	1	yes	characteristic
133	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
134	C₂³×C₁₃₇	—	4	1	no	—
135	C₂³×C₁₃₇	#121	1	1	yes	characteristic
136	Q₈×C₁₃₇	—	2	2	no	—
137	Q₈×C₁₃₇	—	2	4	no	—
138	Q₈×C₁₃₇	—	4	2	no	—
139	Q₈×C₁₃₇	—	4	1	no	—
140	Q₈×C₁₃₇	—	4	2	no	—
141	Q₈×C₁₃₇	—	4	1	no	—
142	Q₈×C₁₃₇	—	8	2	no	—
143	Q₈×C₁₃₇	C₂×D₈	1	4	yes	—
144	D₄×C₁₃₇	—	4	1	no	—
145	D₄×C₁₃₇	—	4	1	no	—
146	D₄×C₁₃₇	—	4	2	no	—
147	D₄×C₁₃₇	—	8	1	no	—
148	D₄×C₁₃₇	—	8	2	no	—
149	C₂×C₄×C₁₃₇	—	2	2	no	—
150	C₂×C₄×C₁₃₇	—	2	4	no	—
151	C₂×C₄×C₁₃₇	—	2	2	no	—
152	C₂×C₄×C₁₃₇	—	2	2	no	—
153	C₂×C₄×C₁₃₇	—	4	1	no	—
154	C₂×C₄×C₁₃₇	—	4	1	no	—
155	C₂×C₄×C₁₃₇	—	4	2	no	—
156	C₂×C₄×C₁₃₇	—	8	1	no	—
157	C₂×C₄×C₁₃₇	—	8	2	no	—
158	C₂×C₄×C₁₃₇	—	8	2	no	—
159	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
160	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
161	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
162	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
163	C₂×C₄×C₁₃₇	#135	1	2	yes	—
164	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
167	C₈×C₁₃₇	—	2	4	no	—
168	C₈×C₁₃₇	—	4	2	no	—
169	C₈×C₁₃₇	—	4	2	no	—
170	C₈×C₁₃₇	—	4	2	no	—
171	C₂²×C₁₃₇	—	2	1	no	—
172	C₂²×C₁₃₇	—	2	1	no	—
173	C₂²×C₁₃₇	—	8	1	no	—
174	C₂²×C₁₃₇	—	8	1	no	—
175	C₂²×C₁₃₇	—	8	1	no	—
176	C₂²×C₁₃₇	#466	1	2	yes	—
177	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
178	C₄×C₁₃₇	—	2	1	no	—
179	C₄×C₁₃₇	—	2	4	no	—
180	C₄×C₁₃₇	—	2	1	no	—
181	C₄×C₁₃₇	—	2	1	no	—
182	C₄×C₁₃₇	—	4	2	no	—
183	C₄×C₁₃₇	—	8	1	no	—
184	C₄×C₁₃₇	—	8	2	no	—
185	C₄×C₁₃₇	#466	1	2	yes	—
186	C₄×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
187	C₄×C₁₃₇	C₂×#135	1	1	yes	characteristic
188	C₄×C₁₃₇	#578	1	2	yes	—
189	C₂×C₁₃₇	—	2	2	no	—
190	C₂×C₁₃₇	—	16	1	no	—
191	C₂×C₁₃₇	#3044	1	1	yes	characteristic
192	C₂×C₁₃₇	C₂×#466	1	1	yes	characteristic
193	C₂×C₁₃₇	#3069	1	1	yes	characteristic
194	#19404	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₁₃₇	#19404	1	1	yes	characteristic, direct product factor, Sylow
196	#3226	C₂×C₁₃₇	1	1	yes	characteristic
197	#3037	C₂×C₁₃₇	1	1	yes	characteristic
198	C₂×#462	C₂×C₁₃₇	1	1	yes	characteristic, complemented
199	#2982	C₂×C₁₃₇	1	1	yes	characteristic, complemented
200	#1682	C₂×C₁₃₇	1	4	yes	complemented
201	#1674	C₂×C₁₃₇	1	4	yes	complemented
202	#1571	C₂×C₁₃₇	1	1	yes	characteristic, complemented
203	#1546	C₂×C₁₃₇	1	1	yes	characteristic, complemented
204	#1540	C₂×C₁₃₇	1	1	yes	characteristic
205	C₂×#137	—	2	1	no	—
206	C₂²×Q₁₆	—	2	1	no	—
207	#532	C₂²×C₁₃₇	1	1	yes	characteristic
208	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
209	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
210	#500	C₂²×C₁₃₇	1	2	yes	—
211	#486	C₂²×C₁₃₇	1	2	yes	—
212	#480	—	2	2	no	—
213	#474	—	2	2	no	—
214	#464	—	2	2	no	—
215	#462	—	2	2	no	—
216	#462	C₂²×C₁₃₇	1	2	yes	—
217	#462	C₂²×C₁₃₇	1	4	yes	—
218	#460	C₂²×C₁₃₇	1	2	yes	—
219	C₈×Q₈	—	2	2	no	—
220	C₈×Q₈	C₂²×C₁₃₇	1	4	yes	—
221	#431	—	2	2	no	—
222	#431	C₂²×C₁₃₇	1	1	yes	characteristic
223	#431	C₂²×C₁₃₇	1	1	yes	characteristic
224	#423	C₂²×C₁₃₇	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
226	#417	—	2	1	no	—
227	C₂×#103	—	2	1	no	—
228	#335	C₂²×C₁₃₇	1	4	yes	—
229	#332	C₂²×C₁₃₇	1	2	yes	—
230	#332	C₂²×C₁₃₇	1	4	yes	—
231	#331	C₂²×C₁₃₇	1	2	yes	—
232	C₂×#41	—	2	1	no	—
233	C₂²×Q₈	—	2	1	no	—
234	C₂²×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
235	#137	—	4	4	no	—
236	C₂×Q₁₆	—	2	4	no	—
237	C₂×Q₁₆	—	2	2	no	—
238	C₂×Q₁₆	—	4	4	no	—
239	C₂×SD₁₆	—	2	2	no	—
240	C₂×M₁₆	—	2	1	no	—
241	C₂²×C₈	—	2	1	no	—
242	C₄⋊Q₈	—	2	1	no	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
246	C₄⋊Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
247	#127	C₂³×C₁₃₇	1	1	yes	characteristic
248	#124	—	2	1	no	—
249	#121	—	2	1	no	—
250	#121	—	2	1	no	—
251	C₄×Q₈	—	2	1	no	—
252	C₄×Q₈	—	2	1	no	—
253	C₄×Q₈	D₄×C₁₃₇	1	2	yes	—
254	C₄×Q₈	C₂³×C₁₃₇	1	2	yes	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
263	#107	—	2	4	no	—
264	C₄⋊C₈	—	2	4	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	D₄×C₁₃₇	1	2	yes	—
268	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
269	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
270	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
271	#103	—	2	4	no	—
272	#103	—	2	2	no	—
273	#102	—	2	4	no	—
274	#102	—	2	2	no	—
275	C₂²⋊C₈	—	2	1	no	—
276	C₂²⋊C₈	D₄×C₁₃₇	1	2	yes	—
277	C₄×C₈	—	2	4	no	—
278	C₄×C₈	—	2	1	no	—
279	C₄×C₈	C₂³×C₁₃₇	1	2	yes	—
280	#41	—	4	2	no	—
281	#41	—	4	2	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	—	4	2	no	—
288	C₂×Q₈	—	4	2	no	—
289	C₂×Q₈	D₈×C₁₃₇	1	4	yes	—
290	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
301	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
302	Q₁₆	—	4	8	no	—
303	Q₁₆	—	4	4	no	—
304	SD₁₆	—	4	4	no	—
305	M₁₆	—	4	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	4	2	no	—
310	C₂×C₈	C₂×D₄×C₁₃₇	1	4	yes	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
321	C₂²⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	4	1	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
326	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
327	C₄²	#41×C₁₃₇	1	1	yes	characteristic
328	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
329	C₂³	—	4	1	no	—
330	C₂³	#121×C₁₃₇	1	1	yes	characteristic
331	Q₈	—	2	4	no	—
332	Q₈	—	2	2	no	—
333	Q₈	—	4	2	no	—
334	Q₈	—	4	1	no	—
335	Q₈	—	4	2	no	—
336	Q₈	—	4	1	no	—
337	Q₈	—	8	2	no	—
338	Q₈	C₂×D₈×C₁₃₇	1	4	yes	—
339	D₄	—	4	1	no	—
340	D₄	—	4	1	no	—
341	D₄	—	4	2	no	—
342	D₄	—	8	1	no	—
343	D₄	—	8	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	8	1	no	—
352	C₂×C₄	—	8	2	no	—
353	C₂×C₄	—	8	2	no	—
354	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
355	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
356	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
357	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
358	C₂×C₄	#135×C₁₃₇	1	2	yes	—
359	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
361	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
362	C₈	—	2	4	no	—
363	C₈	—	4	2	no	—
364	C₈	—	4	2	no	—
365	C₈	—	4	2	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	—	8	1	no	—
370	C₂²	—	8	1	no	—
371	C₂²	#466×C₁₃₇	1	2	yes	—
372	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
373	C₄	—	2	1	no	—
374	C₄	—	2	4	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	8	1	no	—
379	C₄	—	8	2	no	—
380	C₄	#466×C₁₃₇	1	2	yes	—
381	C₄	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
382	C₄	C₂×#135×C₁₃₇	1	1	yes	characteristic
383	C₄	#578×C₁₃₇	1	2	yes	—
384	C₂	—	2	2	no	—
385	C₂	—	16	1	no	—
386	C₂	#3044×C₁₃₇	1	1	yes	characteristic
387	C₂	C₂×#466×C₁₃₇	1	1	yes	characteristic
388	C₂	#3069×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
prime radical	#532×C₁₃₇	C₂²
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
3. C₂×#462×C₁₃₇	C₂	semidirect
4. #2982×C₁₃₇	C₂	semidirect
5. #1682×C₁₃₇	C₂	semidirect
6. #1674×C₁₃₇	C₂	semidirect
7. #1571×C₁₃₇	C₂	semidirect
8. #1546×C₁₃₇	C₂	semidirect
194. #19404	C₁₃₇	direct (N × H)
195. C₁₃₇	#19404	direct (N × H)
198. C₂×#462	C₂×C₁₃₇	semidirect
199. #2982	C₂×C₁₃₇	semidirect
200. #1682	C₂×C₁₃₇	semidirect
201. #1674	C₂×C₁₃₇	semidirect
202. #1571	C₂×C₁₃₇	semidirect
203. #1546	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3226×C₁₃₇	2
#3037×C₁₃₇	2
C₂×#462×C₁₃₇	2
#2982×C₁₃₇	2
#1682×C₁₃₇	2
#1674×C₁₃₇	2
#1571×C₁₃₇	2
#1546×C₁₃₇	2
#1540×C₁₃₇	2
#19404	137

Subgroups — C137×#19404 #46868790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#19404 #46868790