Subgroups — C₁₃₇×#28758 #46878144

Order 35072.

812 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#489×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#487×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2658×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2331×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2043×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2042×C₁₃₇	C₂	1	2	yes	maximal
7	#1983×C₁₃₇	C₂	1	2	yes	maximal
8	#1981×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1960×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1958×C₁₃₇	C₂	1	1	yes	maximal, characteristic
11	#1768×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×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	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×#124×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×#124×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂×#124×C₁₃₇	C₂²	1	1	yes	characteristic
19	#489×C₁₃₇	—	2	4	no	—
20	#487×C₁₃₇	—	2	4	no	—
21	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
22	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
23	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
24	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
25	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
26	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
27	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
28	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
29	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
30	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
32	#399×C₁₃₇	—	2	2	no	—
33	#399×C₁₃₇	—	2	2	no	—
34	#391×C₁₃₇	—	2	2	no	—
35	#389×C₁₃₇	C₂²	1	2	yes	—
36	#387×C₁₃₇	—	2	2	no	—
37	#382×C₁₃₇	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
39	#376×C₁₃₇	C₂²	1	1	yes	characteristic
40	#336×C₁₃₇	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃₇	—	2	1	no	—
42	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
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	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
51	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
52	C₄⋊Q₈×C₁₃₇	—	4	2	no	—
53	C₄⋊Q₈×C₁₃₇	D₄	1	4	yes	—
54	#124×C₁₃₇	—	2	2	no	—
55	#124×C₁₃₇	—	2	2	no	—
56	#124×C₁₃₇	—	2	4	no	—
57	#124×C₁₃₇	—	4	2	no	—
58	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
70	C₂×C₄²×C₁₃₇	—	2	2	no	—
71	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₁₃₇	—	2	4	no	—
75	#103×C₁₃₇	—	2	4	no	—
76	#103×C₁₃₇	—	2	4	no	—
77	#103×C₁₃₇	—	2	4	no	—
78	#103×C₁₃₇	—	4	2	no	—
79	#103×C₁₃₇	—	4	2	no	—
80	#103×C₁₃₇	—	4	2	no	—
81	#102×C₁₃₇	—	2	4	no	—
82	#102×C₁₃₇	—	4	2	no	—
83	#97×C₁₃₇	—	2	2	no	—
84	C₄×C₈×C₁₃₇	—	2	2	no	—
85	#95×C₁₃₇	—	2	2	no	—
86	#95×C₁₃₇	—	2	1	no	—
87	#95×C₁₃₇	—	2	1	no	—
88	#95×C₁₃₇	—	2	2	no	—
89	#95×C₁₃₇	D₄	1	2	yes	—
90	#95×C₁₃₇	D₄	1	2	yes	—
91	C₂⁴×C₁₃₇	—	2	1	no	—
92	C₂×Q₈×C₁₃₇	—	2	4	no	—
93	C₂×Q₈×C₁₃₇	—	2	1	no	—
94	C₂×Q₈×C₁₃₇	—	2	1	no	—
95	C₂×Q₈×C₁₃₇	—	2	1	no	—
96	C₂×Q₈×C₁₃₇	—	2	1	no	—
97	C₂×Q₈×C₁₃₇	—	2	2	no	—
98	C₂×Q₈×C₁₃₇	—	2	1	no	—
99	C₂×Q₈×C₁₃₇	—	2	1	no	—
100	C₂×Q₈×C₁₃₇	—	2	2	no	—
101	C₂×Q₈×C₁₃₇	—	2	2	no	—
102	C₂×Q₈×C₁₃₇	—	2	2	no	—
103	C₂×Q₈×C₁₃₇	—	2	2	no	—
104	C₂×Q₈×C₁₃₇	—	2	2	no	—
105	C₂×Q₈×C₁₃₇	—	8	2	no	—
106	C₂×D₄×C₁₃₇	—	2	1	no	—
107	C₂×D₄×C₁₃₇	—	2	2	no	—
108	C₂×D₄×C₁₃₇	—	2	1	no	—
109	C₂×D₄×C₁₃₇	—	2	2	no	—
110	C₂²×C₄×C₁₃₇	—	2	2	no	—
111	C₂²×C₄×C₁₃₇	—	2	2	no	—
112	C₂²×C₄×C₁₃₇	—	2	1	no	—
113	C₂²×C₄×C₁₃₇	—	2	1	no	—
114	C₂²×C₄×C₁₃₇	—	2	1	no	—
115	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
124	C₂×C₈×C₁₃₇	—	2	2	no	—
125	C₂×C₈×C₁₃₇	—	2	2	no	—
126	C₄⋊C₄×C₁₃₇	—	2	4	no	—
127	C₄⋊C₄×C₁₃₇	—	2	2	no	—
128	C₄⋊C₄×C₁₃₇	—	2	2	no	—
129	C₄⋊C₄×C₁₃₇	—	2	2	no	—
130	C₄⋊C₄×C₁₃₇	—	4	4	no	—
131	C₄⋊C₄×C₁₃₇	—	4	2	no	—
132	C₄⋊C₄×C₁₃₇	—	4	2	no	—
133	C₄⋊C₄×C₁₃₇	—	4	4	no	—
134	C₄⋊C₄×C₁₃₇	—	8	2	no	—
135	C₄⋊C₄×C₁₃₇	C₂×D₄	1	4	yes	—
136	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
137	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
138	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
139	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
140	C₄²×C₁₃₇	—	2	2	no	—
141	C₄²×C₁₃₇	—	8	2	no	—
142	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
143	C₄²×C₁₃₇	#41	1	2	yes	—
144	C₄²×C₁₃₇	#41	1	4	yes	—
145	C₂³×C₁₃₇	—	4	1	no	—
146	C₂³×C₁₃₇	—	4	1	no	—
147	C₂³×C₁₃₇	—	4	1	no	—
148	C₂³×C₁₃₇	—	4	2	no	—
149	C₂³×C₁₃₇	—	4	2	no	—
150	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₁₃₇	—	4	2	no	—
152	Q₈×C₁₃₇	—	4	2	no	—
153	Q₈×C₁₃₇	—	4	2	no	—
154	Q₈×C₁₃₇	—	4	2	no	—
155	Q₈×C₁₃₇	—	4	2	no	—
156	Q₈×C₁₃₇	—	4	2	no	—
157	Q₈×C₁₃₇	—	8	4	no	—
158	D₄×C₁₃₇	—	4	2	no	—
159	D₄×C₁₃₇	—	4	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	—	2	2	no	—
164	C₂×C₄×C₁₃₇	—	2	4	no	—
165	C₂×C₄×C₁₃₇	—	2	2	no	—
166	C₂×C₄×C₁₃₇	—	2	2	no	—
167	C₂×C₄×C₁₃₇	—	2	2	no	—
168	C₂×C₄×C₁₃₇	—	4	2	no	—
169	C₂×C₄×C₁₃₇	—	4	2	no	—
170	C₂×C₄×C₁₃₇	—	4	1	no	—
171	C₂×C₄×C₁₃₇	—	4	1	no	—
172	C₂×C₄×C₁₃₇	—	4	1	no	—
173	C₂×C₄×C₁₃₇	—	4	1	no	—
174	C₂×C₄×C₁₃₇	—	4	1	no	—
175	C₂×C₄×C₁₃₇	—	4	1	no	—
176	C₂×C₄×C₁₃₇	—	4	1	no	—
177	C₂×C₄×C₁₃₇	—	4	2	no	—
178	C₂×C₄×C₁₃₇	—	4	1	no	—
179	C₂×C₄×C₁₃₇	—	4	1	no	—
180	C₂×C₄×C₁₃₇	—	4	2	no	—
181	C₂×C₄×C₁₃₇	—	4	2	no	—
182	C₂×C₄×C₁₃₇	#121	1	2	yes	—
183	C₂×C₄×C₁₃₇	#121	1	2	yes	—
184	C₂×C₄×C₁₃₇	#124	1	4	yes	—
185	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
187	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
189	C₈×C₁₃₇	—	4	2	no	—
190	C₈×C₁₃₇	—	4	2	no	—
191	C₂²×C₁₃₇	—	8	2	no	—
192	C₂²×C₁₃₇	—	8	2	no	—
193	C₂²×C₁₃₇	—	8	1	no	—
194	C₂²×C₁₃₇	—	8	1	no	—
195	C₂²×C₁₃₇	—	8	1	no	—
196	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
197	C₂²×C₁₃₇	C₂×#124	1	1	yes	characteristic
198	C₂²×C₁₃₇	#535	1	1	yes	characteristic
199	C₂²×C₁₃₇	#577	1	2	yes	—
200	C₂²×C₁₃₇	#578	1	2	yes	—
201	C₄×C₁₃₇	—	2	4	no	—
202	C₄×C₁₃₇	—	2	2	no	—
203	C₄×C₁₃₇	—	2	2	no	—
204	C₄×C₁₃₇	—	4	2	no	—
205	C₄×C₁₃₇	—	4	4	no	—
206	C₄×C₁₃₇	—	8	2	no	—
207	C₄×C₁₃₇	—	8	1	no	—
208	C₄×C₁₃₇	—	8	1	no	—
209	C₄×C₁₃₇	—	8	1	no	—
210	C₄×C₁₃₇	#550	1	2	yes	—
211	C₄×C₁₃₇	#559	1	2	yes	—
212	C₂×C₁₃₇	—	16	1	no	—
213	C₂×C₁₃₇	#2548	1	1	yes	characteristic
214	C₂×C₁₃₇	#3042	1	1	yes	characteristic
215	C₂×C₁₃₇	#3044	1	1	yes	characteristic
216	C₂×C₁₃₇	#3137	1	2	yes	—
217	C₂×C₁₃₇	#3225	1	2	yes	—
218	#28758	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₁₃₇	#28758	1	1	yes	characteristic, direct product factor, Sylow
220	C₂×#489	C₂×C₁₃₇	1	1	yes	characteristic
221	C₂×#487	C₂×C₁₃₇	1	1	yes	characteristic, complemented
222	#2658	C₂×C₁₃₇	1	1	yes	characteristic
223	#2331	C₂×C₁₃₇	1	1	yes	characteristic, complemented
224	#2043	C₂×C₁₃₇	1	2	yes	complemented
225	#2042	C₂×C₁₃₇	1	2	yes	—
226	#1983	C₂×C₁₃₇	1	2	yes	—
227	#1981	C₂×C₁₃₇	1	2	yes	complemented
228	#1960	C₂×C₁₃₇	1	1	yes	characteristic, complemented
229	#1958	C₂×C₁₃₇	1	1	yes	characteristic
230	#1768	C₂×C₁₃₇	1	1	yes	characteristic, complemented
231	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
232	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
233	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
234	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
235	C₂×#124	C₂²×C₁₃₇	1	1	yes	characteristic
236	C₂×#124	C₂²×C₁₃₇	1	1	yes	characteristic
237	C₂×#124	C₂²×C₁₃₇	1	1	yes	characteristic
238	#489	—	2	4	no	—
239	#487	—	2	4	no	—
240	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
241	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
242	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
243	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
244	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
245	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
246	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
247	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
248	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
249	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
250	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
251	#399	—	2	2	no	—
252	#399	—	2	2	no	—
253	#391	—	2	2	no	—
254	#389	C₂²×C₁₃₇	1	2	yes	—
255	#387	—	2	2	no	—
256	#382	C₂²×C₁₃₇	1	1	yes	characteristic
257	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
258	#376	C₂²×C₁₃₇	1	1	yes	characteristic
259	#336	C₂²×C₁₃₇	1	2	yes	—
260	C₂²×Q₈	—	2	1	no	—
261	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
262	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
263	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
264	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
266	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
267	C₄⋊Q₈	—	2	2	no	—
268	C₄⋊Q₈	—	2	2	no	—
269	C₄⋊Q₈	—	2	2	no	—
270	C₄⋊Q₈	—	2	4	no	—
271	C₄⋊Q₈	—	4	2	no	—
272	C₄⋊Q₈	D₄×C₁₃₇	1	4	yes	—
273	#124	—	2	2	no	—
274	#124	—	2	2	no	—
275	#124	—	2	4	no	—
276	#124	—	4	2	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
293	C₄⋊C₈	—	2	4	no	—
294	#103	—	2	4	no	—
295	#103	—	2	4	no	—
296	#103	—	2	4	no	—
297	#103	—	4	2	no	—
298	#103	—	4	2	no	—
299	#103	—	4	2	no	—
300	#102	—	2	4	no	—
301	#102	—	4	2	no	—
302	#97	—	2	2	no	—
303	C₄×C₈	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	—	2	1	no	—
306	#95	—	2	1	no	—
307	#95	—	2	2	no	—
308	#95	D₄×C₁₃₇	1	2	yes	—
309	#95	D₄×C₁₃₇	1	2	yes	—
310	C₂⁴	—	2	1	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	8	2	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
338	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	4	4	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	4	no	—
353	C₄⋊C₄	—	8	2	no	—
354	C₄⋊C₄	C₂×D₄×C₁₃₇	1	4	yes	—
355	C₂²⋊C₄	—	4	4	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₂²⋊C₄	—	4	2	no	—
358	C₂²⋊C₄	—	4	4	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	8	2	no	—
361	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
362	C₄²	#41×C₁₃₇	1	2	yes	—
363	C₄²	#41×C₁₃₇	1	4	yes	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	2	no	—
369	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	4	2	no	—
373	Q₈	—	4	2	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	4	2	no	—
376	Q₈	—	8	4	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	#121×C₁₃₇	1	2	yes	—
402	C₂×C₄	#121×C₁₃₇	1	2	yes	—
403	C₂×C₄	#124×C₁₃₇	1	4	yes	—
404	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
405	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
406	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
407	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
408	C₈	—	4	2	no	—
409	C₈	—	4	2	no	—
410	C₂²	—	8	1	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
416	C₂²	C₂×#124×C₁₃₇	1	1	yes	characteristic
417	C₂²	#535×C₁₃₇	1	1	yes	characteristic
418	C₂²	#577×C₁₃₇	1	2	yes	—
419	C₂²	#578×C₁₃₇	1	2	yes	—
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	4	no	—
423	C₄	—	4	4	no	—
424	C₄	—	4	2	no	—
425	C₄	—	8	1	no	—
426	C₄	—	8	1	no	—
427	C₄	—	8	1	no	—
428	C₄	—	8	2	no	—
429	C₄	#550×C₁₃₇	1	2	yes	—
430	C₄	#559×C₁₃₇	1	2	yes	—
431	C₂	—	16	1	no	—
432	C₂	#2548×C₁₃₇	1	1	yes	characteristic
433	C₂	#3042×C₁₃₇	1	1	yes	characteristic
434	C₂	#3044×C₁₃₇	1	1	yes	characteristic
435	C₂	#3137×C₁₃₇	1	2	yes	—
436	C₂	#3225×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	C₂³
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
2. C₂×#487×C₁₃₇	C₂	semidirect
4. #2331×C₁₃₇	C₂	semidirect
5. #2043×C₁₃₇	C₂	semidirect
8. #1981×C₁₃₇	C₂	semidirect
9. #1960×C₁₃₇	C₂	semidirect
11. #1768×C₁₃₇	C₂	semidirect
218. #28758	C₁₃₇	direct (N × H)
219. C₁₃₇	#28758	direct (N × H)
221. C₂×#487	C₂×C₁₃₇	semidirect
223. #2331	C₂×C₁₃₇	semidirect
224. #2043	C₂×C₁₃₇	semidirect
227. #1981	C₂×C₁₃₇	semidirect
228. #1960	C₂×C₁₃₇	semidirect
230. #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×#489×C₁₃₇	2
C₂×#487×C₁₃₇	2
#2658×C₁₃₇	2
#2331×C₁₃₇	2
#2043×C₁₃₇	2
#2042×C₁₃₇	2
#1983×C₁₃₇	2
#1981×C₁₃₇	2
#1960×C₁₃₇	2
#1958×C₁₃₇	2
#1768×C₁₃₇	2
#28758	137

Subgroups — C137×#28758 #46878144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28758 #46878144