Subgroups — C₁₃₇×#28726 #46878112

Order 35072.

870 conjugacy classes of subgroups.

The subgroup lattice has 432 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	2	yes	maximal
2	#2868×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#124×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2072×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#2071×C₁₃₇	C₂	1	2	yes	maximal
6	#1993×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1803×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1802×C₁₃₇	C₂	1	2	yes	maximal
9	#1767×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄⋊Q₈×C₁₃₇	—	2	1	no	—
11	C₂×C₄⋊Q₈×C₁₃₇	—	2	1	no	—
12	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	2	yes	—
13	C₂×#124×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
16	#489×C₁₃₇	—	2	8	no	—
17	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
18	C₂×#103×C₁₃₇	C₂²	1	4	yes	—
19	C₂×#102×C₁₃₇	C₂²	1	4	yes	—
20	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
21	#391×C₁₃₇	C₂²	1	1	yes	characteristic
22	#390×C₁₃₇	C₂²	1	1	yes	characteristic
23	#388×C₁₃₇	—	2	1	no	—
24	#388×C₁₃₇	—	2	1	no	—
25	#384×C₁₃₇	—	2	1	no	—
26	#384×C₁₃₇	—	2	1	no	—
27	#384×C₁₃₇	C₂²	1	2	yes	—
28	#384×C₁₃₇	C₂²	1	2	yes	—
29	#382×C₁₃₇	C₂²	1	1	yes	characteristic
30	C₄×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
31	C₄×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
32	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
33	#340×C₁₃₇	C₂²	1	4	yes	—
34	#340×C₁₃₇	C₂²	1	4	yes	—
35	#336×C₁₃₇	C₂²	1	2	yes	—
36	C₂²×Q₈×C₁₃₇	—	2	2	no	—
37	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
38	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₃₇	—	2	1	no	—
40	C₂²×C₈×C₁₃₇	C₂³	1	4	yes	—
41	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
42	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
43	C₄⋊Q₈×C₁₃₇	—	4	4	no	—
44	C₄⋊Q₈×C₁₃₇	—	4	4	no	—
45	#124×C₁₃₇	—	2	2	no	—
46	#124×C₁₃₇	D₄	1	4	yes	—
47	C₄×Q₈×C₁₃₇	—	2	4	no	—
48	C₄×D₄×C₁₃₇	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
58	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
60	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
63	C₂×C₄²×C₁₃₇	—	2	1	no	—
64	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₁₃₇	—	2	4	no	—
72	#103×C₁₃₇	—	2	8	no	—
73	#102×C₁₃₇	—	2	8	no	—
74	#97×C₁₃₇	—	2	4	no	—
75	#95×C₁₃₇	—	2	1	no	—
76	#95×C₁₃₇	—	2	1	no	—
77	#95×C₁₃₇	—	2	1	no	—
78	#95×C₁₃₇	—	2	1	no	—
79	C₂⁴×C₁₃₇	—	2	1	no	—
80	C₂×Q₈×C₁₃₇	—	2	1	no	—
81	C₂×Q₈×C₁₃₇	—	2	2	no	—
82	C₂×Q₈×C₁₃₇	—	2	2	no	—
83	C₂×Q₈×C₁₃₇	—	4	4	no	—
84	C₂×Q₈×C₁₃₇	—	4	4	no	—
85	C₂×Q₈×C₁₃₇	—	4	4	no	—
86	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
87	C₂×D₄×C₁₃₇	—	2	2	no	—
88	C₂×D₄×C₁₃₇	—	2	1	no	—
89	C₂×D₄×C₁₃₇	—	2	2	no	—
90	C₂×D₄×C₁₃₇	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₃₇	—	2	1	no	—
92	C₂²×C₄×C₁₃₇	—	2	1	no	—
93	C₂²×C₄×C₁₃₇	—	2	1	no	—
94	C₂²×C₄×C₁₃₇	—	2	4	no	—
95	C₂²×C₄×C₁₃₇	—	4	2	no	—
96	C₂²×C₄×C₁₃₇	—	4	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	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
105	C₂×C₈×C₁₃₇	—	2	4	no	—
106	C₂×C₈×C₁₃₇	—	2	4	no	—
107	C₂×C₈×C₁₃₇	—	2	4	no	—
108	C₄⋊C₄×C₁₃₇	—	2	4	no	—
109	C₄⋊C₄×C₁₃₇	—	2	2	no	—
110	C₄⋊C₄×C₁₃₇	—	2	2	no	—
111	C₄⋊C₄×C₁₃₇	—	2	4	no	—
112	C₄⋊C₄×C₁₃₇	—	4	4	no	—
113	C₄⋊C₄×C₁₃₇	—	4	4	no	—
114	C₄⋊C₄×C₁₃₇	—	4	4	no	—
115	C₄⋊C₄×C₁₃₇	—	4	2	no	—
116	C₄⋊C₄×C₁₃₇	—	4	4	no	—
117	C₄⋊C₄×C₁₃₇	—	4	4	no	—
118	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
119	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
120	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
121	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
122	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
123	C₄²×C₁₃₇	—	2	2	no	—
124	C₄²×C₁₃₇	—	2	2	no	—
125	C₄²×C₁₃₇	—	2	2	no	—
126	C₄²×C₁₃₇	—	2	2	no	—
127	C₄²×C₁₃₇	—	2	2	no	—
128	C₄²×C₁₃₇	—	4	2	no	—
129	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
130	C₄²×C₁₃₇	#41	1	2	yes	—
131	C₄²×C₁₃₇	#41	1	4	yes	—
132	C₂³×C₁₃₇	—	2	2	no	—
133	C₂³×C₁₃₇	—	4	1	no	—
134	C₂³×C₁₃₇	—	4	1	no	—
135	C₂³×C₁₃₇	—	4	1	no	—
136	C₂³×C₁₃₇	—	4	1	no	—
137	C₂³×C₁₃₇	—	4	1	no	—
138	C₂³×C₁₃₇	—	4	1	no	—
139	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₁₃₇	—	2	4	no	—
141	Q₈×C₁₃₇	—	4	2	no	—
142	Q₈×C₁₃₇	—	8	8	no	—
143	D₄×C₁₃₇	—	2	4	no	—
144	D₄×C₁₃₇	—	4	2	no	—
145	C₂×C₄×C₁₃₇	—	2	1	no	—
146	C₂×C₄×C₁₃₇	—	2	1	no	—
147	C₂×C₄×C₁₃₇	—	2	1	no	—
148	C₂×C₄×C₁₃₇	—	2	1	no	—
149	C₂×C₄×C₁₃₇	—	2	1	no	—
150	C₂×C₄×C₁₃₇	—	2	1	no	—
151	C₂×C₄×C₁₃₇	—	2	1	no	—
152	C₂×C₄×C₁₃₇	—	2	1	no	—
153	C₂×C₄×C₁₃₇	—	2	1	no	—
154	C₂×C₄×C₁₃₇	—	2	1	no	—
155	C₂×C₄×C₁₃₇	—	2	2	no	—
156	C₂×C₄×C₁₃₇	—	4	1	no	—
157	C₂×C₄×C₁₃₇	—	4	1	no	—
158	C₂×C₄×C₁₃₇	—	4	4	no	—
159	C₂×C₄×C₁₃₇	—	4	1	no	—
160	C₂×C₄×C₁₃₇	—	4	1	no	—
161	C₂×C₄×C₁₃₇	—	4	1	no	—
162	C₂×C₄×C₁₃₇	—	4	4	no	—
163	C₂×C₄×C₁₃₇	—	4	4	no	—
164	C₂×C₄×C₁₃₇	—	4	1	no	—
165	C₂×C₄×C₁₃₇	—	4	1	no	—
166	C₂×C₄×C₁₃₇	—	4	1	no	—
167	C₂×C₄×C₁₃₇	—	8	4	no	—
168	C₂×C₄×C₁₃₇	#121	1	2	yes	—
169	C₂×C₄×C₁₃₇	#121	1	2	yes	—
170	C₂×C₄×C₁₃₇	#124	1	2	yes	—
171	C₂×C₄×C₁₃₇	#124	1	2	yes	—
172	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
173	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
174	C₂×C₄×C₁₃₇	#137	1	2	yes	—
175	C₂×C₄×C₁₃₇	#137	1	2	yes	—
176	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
178	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
180	C₈×C₁₃₇	—	4	4	no	—
181	C₂²×C₁₃₇	—	4	2	no	—
182	C₂²×C₁₃₇	—	4	2	no	—
183	C₂²×C₁₃₇	—	4	2	no	—
184	C₂²×C₁₃₇	—	8	1	no	—
185	C₂²×C₁₃₇	—	8	1	no	—
186	C₂²×C₁₃₇	—	8	1	no	—
187	C₂²×C₁₃₇	—	8	1	no	—
188	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
189	C₂²×C₁₃₇	C₂×#124	1	1	yes	characteristic
190	C₂²×C₁₃₇	#536	1	1	yes	characteristic
191	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
192	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
193	C₂²×C₁₃₇	C₂×#137	1	1	yes	characteristic
194	C₂²×C₁₃₇	C₂×#137	1	1	yes	characteristic
195	C₄×C₁₃₇	—	2	2	no	—
196	C₄×C₁₃₇	—	2	2	no	—
197	C₄×C₁₃₇	—	2	2	no	—
198	C₄×C₁₃₇	—	2	2	no	—
199	C₄×C₁₃₇	—	2	2	no	—
200	C₄×C₁₃₇	—	4	2	no	—
201	C₄×C₁₃₇	—	8	1	no	—
202	C₄×C₁₃₇	—	8	1	no	—
203	C₄×C₁₃₇	—	8	4	no	—
204	C₄×C₁₃₇	#489	1	4	yes	complemented
205	C₄×C₁₃₇	#547	1	2	yes	—
206	C₄×C₁₃₇	#556	1	2	yes	—
207	C₂×C₁₃₇	—	8	2	no	—
208	C₂×C₁₃₇	#2547	1	1	yes	characteristic
209	C₂×C₁₃₇	#3038	1	1	yes	characteristic
210	C₂×C₁₃₇	#3039	1	1	yes	characteristic
211	C₂×C₁₃₇	C₂×#489	1	1	yes	characteristic
212	C₂×C₁₃₇	#3141	1	1	yes	characteristic
213	C₂×C₁₃₇	#3238	1	1	yes	characteristic
214	C₂×C₁₃₇	#3239	1	1	yes	characteristic
215	#28726	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₁₃₇	#28726	1	1	yes	characteristic, direct product factor, Sylow
217	C₂×#489	C₂×C₁₃₇	1	2	yes	—
218	#2868	C₂×C₁₃₇	1	1	yes	characteristic, complemented
219	C₄×#124	C₂×C₁₃₇	1	1	yes	characteristic
220	#2072	C₂×C₁₃₇	1	2	yes	complemented
221	#2071	C₂×C₁₃₇	1	2	yes	—
222	#1993	C₂×C₁₃₇	1	2	yes	complemented
223	#1803	C₂×C₁₃₇	1	2	yes	complemented
224	#1802	C₂×C₁₃₇	1	2	yes	—
225	#1767	C₂×C₁₃₇	1	1	yes	characteristic, complemented
226	C₂×C₄⋊Q₈	—	2	1	no	—
227	C₂×C₄⋊Q₈	—	2	1	no	—
228	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	2	yes	—
229	C₂×#124	C₂²×C₁₃₇	1	1	yes	characteristic
230	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
231	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
232	#489	—	2	8	no	—
233	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
234	C₂×#103	C₂²×C₁₃₇	1	4	yes	—
235	C₂×#102	C₂²×C₁₃₇	1	4	yes	—
236	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
237	#391	C₂²×C₁₃₇	1	1	yes	characteristic
238	#390	C₂²×C₁₃₇	1	1	yes	characteristic
239	#388	—	2	1	no	—
240	#388	—	2	1	no	—
241	#384	—	2	1	no	—
242	#384	—	2	1	no	—
243	#384	C₂²×C₁₃₇	1	2	yes	—
244	#384	C₂²×C₁₃₇	1	2	yes	—
245	#382	C₂²×C₁₃₇	1	1	yes	characteristic
246	C₄×C₂²⋊C₄	—	2	1	no	—
247	C₄×C₂²⋊C₄	—	2	1	no	—
248	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
249	#340	C₂²×C₁₃₇	1	4	yes	—
250	#340	C₂²×C₁₃₇	1	4	yes	—
251	#336	C₂²×C₁₃₇	1	2	yes	—
252	C₂²×Q₈	—	2	2	no	—
253	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
254	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
255	C₂³×C₄	—	2	1	no	—
256	C₂²×C₈	C₂³×C₁₃₇	1	4	yes	—
257	C₄⋊Q₈	—	2	4	no	—
258	C₄⋊Q₈	—	2	4	no	—
259	C₄⋊Q₈	—	4	4	no	—
260	C₄⋊Q₈	—	4	4	no	—
261	#124	—	2	2	no	—
262	#124	D₄×C₁₃₇	1	4	yes	—
263	C₄×Q₈	—	2	4	no	—
264	C₄×D₄	—	2	4	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
274	C₂×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
281	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
282	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
283	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
284	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
287	C₄⋊C₈	—	2	4	no	—
288	#103	—	2	8	no	—
289	#102	—	2	8	no	—
290	#97	—	2	4	no	—
291	#95	—	2	1	no	—
292	#95	—	2	1	no	—
293	#95	—	2	1	no	—
294	#95	—	2	1	no	—
295	C₂⁴	—	2	1	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	4	4	no	—
300	C₂×Q₈	—	4	4	no	—
301	C₂×Q₈	—	4	4	no	—
302	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	—	4	2	no	—
313	C₂²×C₄	—	4	2	no	—
314	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
320	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	—	2	4	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	4	4	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₄⋊C₄	—	4	4	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	4	no	—
333	C₄⋊C₄	—	4	4	no	—
334	C₂²⋊C₄	—	2	4	no	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	4	2	no	—
345	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
346	C₄²	#41×C₁₃₇	1	2	yes	—
347	C₄²	#41×C₁₃₇	1	4	yes	—
348	C₂³	—	2	2	no	—
349	C₂³	—	4	1	no	—
350	C₂³	—	4	1	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	4	1	no	—
353	C₂³	—	4	1	no	—
354	C₂³	—	4	1	no	—
355	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
356	Q₈	—	2	4	no	—
357	Q₈	—	4	2	no	—
358	Q₈	—	8	8	no	—
359	D₄	—	2	4	no	—
360	D₄	—	4	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	8	4	no	—
384	C₂×C₄	#121×C₁₃₇	1	2	yes	—
385	C₂×C₄	#121×C₁₃₇	1	2	yes	—
386	C₂×C₄	#124×C₁₃₇	1	2	yes	—
387	C₂×C₄	#124×C₁₃₇	1	2	yes	—
388	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
389	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
390	C₂×C₄	#137×C₁₃₇	1	2	yes	—
391	C₂×C₄	#137×C₁₃₇	1	2	yes	—
392	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
393	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
394	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
395	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
396	C₈	—	4	4	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	8	1	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
405	C₂²	C₂×#124×C₁₃₇	1	1	yes	characteristic
406	C₂²	#536×C₁₃₇	1	1	yes	characteristic
407	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
408	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
409	C₂²	C₂×#137×C₁₃₇	1	1	yes	characteristic
410	C₂²	C₂×#137×C₁₃₇	1	1	yes	characteristic
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	8	4	no	—
418	C₄	—	8	1	no	—
419	C₄	—	8	1	no	—
420	C₄	#489×C₁₃₇	1	4	yes	complemented
421	C₄	#547×C₁₃₇	1	2	yes	—
422	C₄	#556×C₁₃₇	1	2	yes	—
423	C₂	—	8	2	no	—
424	C₂	#2547×C₁₃₇	1	1	yes	characteristic
425	C₂	#3038×C₁₃₇	1	1	yes	characteristic
426	C₂	#3039×C₁₃₇	1	1	yes	characteristic
427	C₂	C₂×#489×C₁₃₇	1	1	yes	characteristic
428	C₂	#3141×C₁₃₇	1	1	yes	characteristic
429	C₂	#3238×C₁₃₇	1	1	yes	characteristic
430	C₂	#3239×C₁₃₇	1	1	yes	characteristic

	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 ◁ C₄³×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2868×C₁₃₇	C₂	semidirect
4. #2072×C₁₃₇	C₂	semidirect
6. #1993×C₁₃₇	C₂	semidirect
7. #1803×C₁₃₇	C₂	semidirect
9. #1767×C₁₃₇	C₂	semidirect
204. C₄×C₁₃₇	#489	semidirect
215. #28726	C₁₃₇	direct (N × H)
216. C₁₃₇	#28726	direct (N × H)
218. #2868	C₂×C₁₃₇	semidirect
220. #2072	C₂×C₁₃₇	semidirect
222. #1993	C₂×C₁₃₇	semidirect
223. #1803	C₂×C₁₃₇	semidirect
225. #1767	C₂×C₁₃₇	semidirect
420. C₄	#489×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
#2868×C₁₃₇	2
C₄×#124×C₁₃₇	2
#2072×C₁₃₇	2
#2071×C₁₃₇	2
#1993×C₁₃₇	2
#1803×C₁₃₇	2
#1802×C₁₃₇	2
#1767×C₁₃₇	2
#28726	137

Subgroups — C137×#28726 #46878112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28726 #46878112