Subgroups — C₁₃₇×#28670 #46878056

Order 35072.

698 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3165×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#3138×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#486×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2960×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2063×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	#1997×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1965×C₁₃₇	C₂	1	1	yes	maximal, characteristic
8	#1931×C₁₃₇	C₂	1	4	yes	maximal, complemented
9	C₄×#108×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#533×C₁₃₇	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
13	#501×C₁₃₇	—	2	2	no	—
14	#500×C₁₃₇	—	2	1	no	—
15	#498×C₁₃₇	—	2	1	no	—
16	#490×C₁₃₇	—	2	2	no	—
17	#486×C₁₃₇	—	2	1	no	—
18	#486×C₁₃₇	—	2	1	no	—
19	#486×C₁₃₇	—	2	1	no	—
20	#486×C₁₃₇	—	2	1	no	—
21	#486×C₁₃₇	—	2	1	no	—
22	#486×C₁₃₇	—	2	1	no	—
23	#446×C₁₃₇	—	2	1	no	—
24	#446×C₁₃₇	—	2	1	no	—
25	C₈×Q₈×C₁₃₇	—	2	1	no	—
26	C₈×Q₈×C₁₃₇	—	2	1	no	—
27	C₂×#108×C₁₃₇	C₂²	1	2	yes	—
28	#428×C₁₃₇	C₂²	1	4	yes	—
29	#424×C₁₃₇	C₂²	1	2	yes	—
30	#423×C₁₃₇	C₂²	1	1	yes	characteristic
31	#418×C₁₃₇	C₂²	1	4	yes	—
32	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
33	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
34	C₂×#100×C₁₃₇	C₂²	1	4	yes	—
35	#405×C₁₃₇	C₂²	1	2	yes	—
36	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
37	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
39	#343×C₁₃₇	C₂²	1	4	yes	—
40	#341×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	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
46	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
47	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
50	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
51	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
52	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
53	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
54	C₄⋊Q₈×C₁₃₇	D₄	1	1	yes	characteristic
55	C₄⋊Q₈×C₁₃₇	D₄	1	1	yes	characteristic
56	#127×C₁₃₇	—	2	1	no	—
57	#127×C₁₃₇	—	2	1	no	—
58	#127×C₁₃₇	—	2	1	no	—
59	#127×C₁₃₇	—	2	1	no	—
60	#125×C₁₃₇	D₄	1	2	yes	—
61	C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
62	C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
63	C₄×Q₈×C₁₃₇	—	2	1	no	—
64	C₄×Q₈×C₁₃₇	—	2	1	no	—
65	#117×C₁₃₇	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
69	#108×C₁₃₇	—	2	4	no	—
70	#107×C₁₃₇	—	2	4	no	—
71	#106×C₁₃₇	—	2	4	no	—
72	C₄⋊C₈×C₁₃₇	—	2	2	no	—
73	C₄⋊C₈×C₁₃₇	—	2	2	no	—
74	C₄⋊C₈×C₁₃₇	—	2	1	no	—
75	C₄⋊C₈×C₁₃₇	—	2	1	no	—
76	#102×C₁₃₇	—	2	2	no	—
77	#102×C₁₃₇	—	2	2	no	—
78	#102×C₁₃₇	—	2	2	no	—
79	#102×C₁₃₇	—	2	2	no	—
80	#102×C₁₃₇	—	2	4	no	—
81	#102×C₁₃₇	—	2	4	no	—
82	#100×C₁₃₇	—	2	8	no	—
83	#97×C₁₃₇	—	2	2	no	—
84	#97×C₁₃₇	—	2	1	no	—
85	#97×C₁₃₇	—	2	1	no	—
86	C₄×C₈×C₁₃₇	—	2	2	no	—
87	C₄×C₈×C₁₃₇	—	2	1	no	—
88	C₄×C₈×C₁₃₇	—	2	1	no	—
89	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
90	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
91	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
92	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
93	C₂⁴×C₁₃₇	—	2	2	no	—
94	C₂×Q₈×C₁₃₇	—	2	1	no	—
95	C₂×Q₈×C₁₃₇	—	2	1	no	—
96	C₂×Q₈×C₁₃₇	—	4	1	no	—
97	C₂×Q₈×C₁₃₇	—	4	1	no	—
98	C₂×Q₈×C₁₃₇	—	8	2	no	—
99	C₂×D₄×C₁₃₇	—	2	2	no	—
100	C₂×D₄×C₁₃₇	—	2	2	no	—
101	C₂×D₄×C₁₃₇	—	2	4	no	—
102	C₂×D₄×C₁₃₇	—	2	4	no	—
103	C₂×D₄×C₁₃₇	—	4	1	no	—
104	C₂×D₄×C₁₃₇	—	4	1	no	—
105	C₂×D₄×C₁₃₇	—	4	1	no	—
106	C₂×D₄×C₁₃₇	—	4	1	no	—
107	C₂×D₄×C₁₃₇	—	8	2	no	—
108	C₂×D₄×C₁₃₇	—	8	2	no	—
109	C₂²×C₄×C₁₃₇	—	2	2	no	—
110	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
112	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
113	M₁₆×C₁₃₇	—	2	2	no	—
114	M₁₆×C₁₃₇	—	2	4	no	—
115	M₁₆×C₁₃₇	—	2	2	no	—
116	M₁₆×C₁₃₇	—	2	2	no	—
117	M₁₆×C₁₃₇	#41	1	4	yes	—
118	C₂×C₈×C₁₃₇	—	2	2	no	—
119	C₂×C₈×C₁₃₇	—	2	2	no	—
120	C₂×C₈×C₁₃₇	—	2	2	no	—
121	C₂×C₈×C₁₃₇	—	2	2	no	—
122	C₂×C₈×C₁₃₇	—	2	2	no	—
123	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₁₃₇	—	2	2	no	—
128	C₄⋊C₄×C₁₃₇	—	2	2	no	—
129	C₄⋊C₄×C₁₃₇	—	2	1	no	—
130	C₄⋊C₄×C₁₃₇	—	2	1	no	—
131	C₄⋊C₄×C₁₃₇	—	2	2	no	—
132	C₄⋊C₄×C₁₃₇	—	2	2	no	—
133	C₄⋊C₄×C₁₃₇	—	4	1	no	—
134	C₄⋊C₄×C₁₃₇	—	4	1	no	—
135	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
137	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
138	C₄²×C₁₃₇	—	2	2	no	—
139	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
143	C₂³×C₁₃₇	—	4	2	no	—
144	C₂³×C₁₃₇	—	4	4	no	—
145	C₂³×C₁₃₇	—	8	2	no	—
146	C₂³×C₁₃₇	—	8	2	no	—
147	C₂³×C₁₃₇	C₂×#41	1	1	yes	characteristic
148	Q₈×C₁₃₇	—	4	2	no	—
149	Q₈×C₁₃₇	—	4	2	no	—
150	Q₈×C₁₃₇	—	8	2	no	—
151	Q₈×C₁₃₇	—	8	2	no	—
152	D₄×C₁₃₇	—	4	2	no	—
153	D₄×C₁₃₇	—	4	2	no	—
154	D₄×C₁₃₇	—	4	4	no	—
155	D₄×C₁₃₇	—	8	2	no	—
156	D₄×C₁₃₇	—	8	2	no	—
157	D₄×C₁₃₇	—	8	2	no	—
158	D₄×C₁₃₇	—	8	2	no	—
159	C₂×C₄×C₁₃₇	—	2	2	no	—
160	C₂×C₄×C₁₃₇	—	2	2	no	—
161	C₂×C₄×C₁₃₇	—	2	2	no	—
162	C₂×C₄×C₁₃₇	—	2	2	no	—
163	C₂×C₄×C₁₃₇	—	4	2	no	—
164	C₂×C₄×C₁₃₇	—	8	2	no	—
165	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
166	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
167	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
168	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
169	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
172	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
173	C₈×C₁₃₇	—	2	1	no	—
174	C₈×C₁₃₇	—	2	1	no	—
175	C₈×C₁₃₇	—	2	1	no	—
176	C₈×C₁₃₇	—	2	1	no	—
177	C₈×C₁₃₇	—	2	4	no	—
178	C₈×C₁₃₇	—	4	2	no	—
179	C₈×C₁₃₇	—	4	2	no	—
180	C₂²×C₁₃₇	—	2	1	no	—
181	C₂²×C₁₃₇	—	2	1	no	—
182	C₂²×C₁₃₇	—	8	2	no	—
183	C₂²×C₁₃₇	—	8	2	no	—
184	C₂²×C₁₃₇	—	8	2	no	—
185	C₂²×C₁₃₇	—	16	4	no	—
186	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
187	C₂²×C₁₃₇	#556	1	2	yes	—
188	C₄×C₁₃₇	—	2	1	no	—
189	C₄×C₁₃₇	—	2	1	no	—
190	C₄×C₁₃₇	—	4	2	no	—
191	C₄×C₁₃₇	—	4	2	no	—
192	C₄×C₁₃₇	—	8	2	no	—
193	C₄×C₁₃₇	#471	1	2	yes	—
194	C₄×C₁₃₇	#472	1	2	yes	—
195	C₄×C₁₃₇	#532	1	1	yes	characteristic
196	C₄×C₁₃₇	#536	1	1	yes	characteristic
197	C₄×C₁₃₇	#548	1	2	yes	—
198	C₂×C₁₃₇	—	2	2	no	—
199	C₂×C₁₃₇	—	16	2	no	—
200	C₂×C₁₃₇	#2545	1	1	yes	characteristic
201	C₂×C₁₃₇	C₂×#471	1	1	yes	characteristic
202	C₂×C₁₃₇	C₂×#472	1	1	yes	characteristic
203	#28670	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₁₃₇	#28670	1	1	yes	characteristic, direct product factor, Sylow
205	#3165	C₂×C₁₃₇	1	1	yes	characteristic, complemented
206	#3138	C₂×C₁₃₇	1	1	yes	characteristic
207	C₂×#486	C₂×C₁₃₇	1	1	yes	characteristic
208	#2960	C₂×C₁₃₇	1	1	yes	characteristic, complemented
209	#2063	C₂×C₁₃₇	1	4	yes	complemented
210	#1997	C₂×C₁₃₇	1	1	yes	characteristic, complemented
211	#1965	C₂×C₁₃₇	1	1	yes	characteristic
212	#1931	C₂×C₁₃₇	1	4	yes	complemented
213	C₄×#108	C₂×C₁₃₇	1	1	yes	characteristic, complemented
214	#533	C₂²×C₁₃₇	1	1	yes	characteristic
215	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
216	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
217	#501	—	2	2	no	—
218	#500	—	2	1	no	—
219	#498	—	2	1	no	—
220	#490	—	2	2	no	—
221	#486	—	2	1	no	—
222	#486	—	2	1	no	—
223	#486	—	2	1	no	—
224	#486	—	2	1	no	—
225	#486	—	2	1	no	—
226	#486	—	2	1	no	—
227	#446	—	2	1	no	—
228	#446	—	2	1	no	—
229	C₈×Q₈	—	2	1	no	—
230	C₈×Q₈	—	2	1	no	—
231	C₂×#108	C₂²×C₁₃₇	1	2	yes	—
232	#428	C₂²×C₁₃₇	1	4	yes	—
233	#424	C₂²×C₁₃₇	1	2	yes	—
234	#423	C₂²×C₁₃₇	1	1	yes	characteristic
235	#418	C₂²×C₁₃₇	1	4	yes	—
236	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
237	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
238	C₂×#100	C₂²×C₁₃₇	1	4	yes	—
239	#405	C₂²×C₁₃₇	1	2	yes	—
240	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
241	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
242	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
243	#343	C₂²×C₁₃₇	1	4	yes	—
244	#341	C₂²×C₁₃₇	1	2	yes	—
245	C₂²×Q₈	—	2	1	no	—
246	C₂²×D₄	—	2	1	no	—
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
249	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
250	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
251	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
252	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	—	2	1	no	—
256	C₄⋊Q₈	—	2	1	no	—
257	C₄⋊Q₈	—	2	1	no	—
258	C₄⋊Q₈	D₄×C₁₃₇	1	1	yes	characteristic
259	C₄⋊Q₈	D₄×C₁₃₇	1	1	yes	characteristic
260	#127	—	2	1	no	—
261	#127	—	2	1	no	—
262	#127	—	2	1	no	—
263	#127	—	2	1	no	—
264	#125	D₄×C₁₃₇	1	2	yes	—
265	C₂²⋊Q₈	—	2	1	no	—
266	C₂²⋊Q₈	—	2	1	no	—
267	C₄×Q₈	—	2	1	no	—
268	C₄×Q₈	—	2	1	no	—
269	#117	C₂³×C₁₃₇	1	2	yes	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
272	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
273	#108	—	2	4	no	—
274	#107	—	2	4	no	—
275	#106	—	2	4	no	—
276	C₄⋊C₈	—	2	2	no	—
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	2	1	no	—
280	#102	—	2	2	no	—
281	#102	—	2	2	no	—
282	#102	—	2	2	no	—
283	#102	—	2	2	no	—
284	#102	—	2	4	no	—
285	#102	—	2	4	no	—
286	#100	—	2	8	no	—
287	#97	—	2	2	no	—
288	#97	—	2	1	no	—
289	#97	—	2	1	no	—
290	C₄×C₈	—	2	2	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
294	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
295	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
296	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
297	C₂⁴	—	2	2	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	4	1	no	—
301	C₂×Q₈	—	4	1	no	—
302	C₂×Q₈	—	8	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	8	2	no	—
312	C₂×D₄	—	8	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
315	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
316	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	4	no	—
319	M₁₆	—	2	2	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	#41×C₁₃₇	1	4	yes	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
328	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
329	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
330	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
340	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
344	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
345	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
346	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
347	C₂³	—	4	2	no	—
348	C₂³	—	4	4	no	—
349	C₂³	—	8	2	no	—
350	C₂³	—	8	2	no	—
351	C₂³	C₂×#41×C₁₃₇	1	1	yes	characteristic
352	Q₈	—	4	2	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	8	2	no	—
355	Q₈	—	8	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	4	no	—
359	D₄	—	8	2	no	—
360	D₄	—	8	2	no	—
361	D₄	—	8	2	no	—
362	D₄	—	8	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	2	no	—
369	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
370	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
371	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
372	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
373	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
375	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
376	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
377	C₈	—	2	1	no	—
378	C₈	—	2	1	no	—
379	C₈	—	2	1	no	—
380	C₈	—	2	1	no	—
381	C₈	—	2	4	no	—
382	C₈	—	4	2	no	—
383	C₈	—	4	2	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	16	4	no	—
390	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
391	C₂²	#556×C₁₃₇	1	2	yes	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	8	2	no	—
397	C₄	#471×C₁₃₇	1	2	yes	—
398	C₄	#472×C₁₃₇	1	2	yes	—
399	C₄	#532×C₁₃₇	1	1	yes	characteristic
400	C₄	#536×C₁₃₇	1	1	yes	characteristic
401	C₄	#548×C₁₃₇	1	2	yes	—
402	C₂	—	2	2	no	—
403	C₂	—	16	2	no	—
404	C₂	#2545×C₁₃₇	1	1	yes	characteristic
405	C₂	C₂×#471×C₁₃₇	1	1	yes	characteristic
406	C₂	C₂×#472×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂×#127×C₁₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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. #3165×C₁₃₇	C₂	semidirect
4. #2960×C₁₃₇	C₂	semidirect
5. #2063×C₁₃₇	C₂	semidirect
6. #1997×C₁₃₇	C₂	semidirect
8. #1931×C₁₃₇	C₂	semidirect
9. C₄×#108×C₁₃₇	C₂	semidirect
203. #28670	C₁₃₇	direct (N × H)
204. C₁₃₇	#28670	direct (N × H)
205. #3165	C₂×C₁₃₇	semidirect
208. #2960	C₂×C₁₃₇	semidirect
209. #2063	C₂×C₁₃₇	semidirect
210. #1997	C₂×C₁₃₇	semidirect
212. #1931	C₂×C₁₃₇	semidirect
213. C₄×#108	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3165×C₁₃₇	2
#3138×C₁₃₇	2
C₂×#486×C₁₃₇	2
#2960×C₁₃₇	2
#2063×C₁₃₇	2
#1997×C₁₃₇	2
#1965×C₁₃₇	2
#1931×C₁₃₇	2
C₄×#108×C₁₃₇	2
#28670	137

Subgroups — C137×#28670 #46878056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28670 #46878056