Subgroups — C₁₃₇×#21991 #46871377

Order 35072.

762 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#433×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2317×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2314×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1949×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1947×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1854×C₁₃₇	C₂	1	2	yes	maximal
7	#1852×C₁₃₇	C₂	1	2	yes	maximal
8	#1847×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1845×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1836×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#1835×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
15	#433×C₁₃₇	C₄	1	8	yes	complemented
16	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
17	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
18	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
19	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
21	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
22	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
24	#389×C₁₃₇	—	2	2	no	—
25	#388×C₁₃₇	—	2	2	no	—
26	#387×C₁₃₇	—	2	2	no	—
27	#385×C₁₃₇	—	2	2	no	—
28	#384×C₁₃₇	C₂²	1	1	yes	characteristic
29	#384×C₁₃₇	C₂²	1	1	yes	characteristic
30	#384×C₁₃₇	C₂²	1	1	yes	characteristic
31	#382×C₁₃₇	C₂²	1	1	yes	characteristic
32	#382×C₁₃₇	C₂²	1	1	yes	characteristic
33	#382×C₁₃₇	C₂²	1	1	yes	characteristic
34	#380×C₁₃₇	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
36	#340×C₁₃₇	C₂²	1	2	yes	—
37	#340×C₁₃₇	C₂²	1	2	yes	—
38	#340×C₁₃₇	C₂²	1	2	yes	—
39	#340×C₁₃₇	C₂²	1	2	yes	—
40	C₂³×C₄×C₁₃₇	—	2	1	no	—
41	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
44	#117×C₁₃₇	—	4	2	no	—
45	#117×C₁₃₇	C₂×C₄	1	4	yes	—
46	#117×C₁₃₇	Q₈	1	4	yes	—
47	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₃₇	—	4	2	no	—
52	C₂×C₄⋊C₄×C₁₃₇	D₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
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	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
59	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
60	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₃₇	D₄	1	2	yes	—
62	C₂×C₄²×C₁₃₇	—	2	1	no	—
63	C₂×C₄²×C₁₃₇	—	2	2	no	—
64	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
66	#107×C₁₃₇	—	4	2	no	—
67	#107×C₁₃₇	—	4	2	no	—
68	#107×C₁₃₇	—	4	2	no	—
69	#106×C₁₃₇	—	4	2	no	—
70	C₄⋊C₈×C₁₃₇	C₂×C₄	1	8	yes	complemented
71	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	8	yes	—
72	#97×C₁₃₇	C₂×C₄	1	4	yes	complemented
73	C₄×C₈×C₁₃₇	C₂×C₄	1	4	yes	complemented
74	#95×C₁₃₇	—	2	2	no	—
75	#95×C₁₃₇	—	2	2	no	—
76	#95×C₁₃₇	—	2	2	no	—
77	#95×C₁₃₇	—	2	2	no	—
78	#95×C₁₃₇	—	2	2	no	—
79	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃₇	—	2	2	no	—
81	C₂²×C₄×C₁₃₇	—	2	2	no	—
82	C₂²×C₄×C₁₃₇	—	2	1	no	—
83	C₂²×C₄×C₁₃₇	—	2	2	no	—
84	C₂²×C₄×C₁₃₇	—	2	2	no	—
85	C₂²×C₄×C₁₃₇	—	2	1	no	—
86	C₂²×C₄×C₁₃₇	—	2	1	no	—
87	C₂²×C₄×C₁₃₇	—	2	1	no	—
88	C₂²×C₄×C₁₃₇	—	4	2	no	—
89	C₂²×C₄×C₁₃₇	—	8	2	no	—
90	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
96	C₂×C₈×C₁₃₇	—	2	2	no	—
97	C₂×C₈×C₁₃₇	—	2	2	no	—
98	C₂×C₈×C₁₃₇	—	2	2	no	—
99	C₂×C₈×C₁₃₇	—	2	2	no	—
100	C₂×C₈×C₁₃₇	C₂²×C₄	1	4	yes	—
101	C₂×C₈×C₁₃₇	C₂²×C₄	1	4	yes	—
102	C₄⋊C₄×C₁₃₇	—	2	2	no	—
103	C₄⋊C₄×C₁₃₇	—	2	2	no	—
104	C₄⋊C₄×C₁₃₇	—	2	2	no	—
105	C₄⋊C₄×C₁₃₇	—	2	2	no	—
106	C₄⋊C₄×C₁₃₇	—	2	2	no	—
107	C₄⋊C₄×C₁₃₇	—	2	2	no	—
108	C₄⋊C₄×C₁₃₇	—	2	4	no	—
109	C₄⋊C₄×C₁₃₇	—	4	2	no	—
110	C₄⋊C₄×C₁₃₇	—	8	2	no	—
111	C₄⋊C₄×C₁₃₇	—	8	2	no	—
112	C₄⋊C₄×C₁₃₇	—	8	2	no	—
113	C₄⋊C₄×C₁₃₇	C₄⋊C₄	1	8	yes	—
114	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
115	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
116	C₂²⋊C₄×C₁₃₇	C₄⋊C₄	1	8	yes	—
117	C₄²×C₁₃₇	—	4	2	no	—
118	C₄²×C₁₃₇	—	8	2	no	—
119	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
120	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
121	C₄²×C₁₃₇	C₂×Q₈	1	2	yes	—
122	C₄²×C₁₃₇	C₂×Q₈	1	2	yes	—
123	C₂³×C₁₃₇	—	2	1	no	—
124	C₂³×C₁₃₇	—	2	1	no	—
125	C₂³×C₁₃₇	—	2	2	no	—
126	C₂³×C₁₃₇	—	2	2	no	—
127	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
128	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
129	C₂×C₄×C₁₃₇	—	2	1	no	—
130	C₂×C₄×C₁₃₇	—	2	1	no	—
131	C₂×C₄×C₁₃₇	—	2	2	no	—
132	C₂×C₄×C₁₃₇	—	2	2	no	—
133	C₂×C₄×C₁₃₇	—	2	2	no	—
134	C₂×C₄×C₁₃₇	—	2	2	no	—
135	C₂×C₄×C₁₃₇	—	2	4	no	—
136	C₂×C₄×C₁₃₇	—	2	4	no	—
137	C₂×C₄×C₁₃₇	—	4	1	no	—
138	C₂×C₄×C₁₃₇	—	4	1	no	—
139	C₂×C₄×C₁₃₇	—	4	1	no	—
140	C₂×C₄×C₁₃₇	—	4	1	no	—
141	C₂×C₄×C₁₃₇	—	4	2	no	—
142	C₂×C₄×C₁₃₇	—	4	2	no	—
143	C₂×C₄×C₁₃₇	—	4	2	no	—
144	C₂×C₄×C₁₃₇	—	4	2	no	—
145	C₂×C₄×C₁₃₇	—	4	2	no	—
146	C₂×C₄×C₁₃₇	—	4	2	no	—
147	C₂×C₄×C₁₃₇	—	4	2	no	—
148	C₂×C₄×C₁₃₇	—	4	2	no	—
149	C₂×C₄×C₁₃₇	—	4	2	no	—
150	C₂×C₄×C₁₃₇	—	4	2	no	—
151	C₂×C₄×C₁₃₇	—	8	4	no	—
152	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
153	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
154	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
155	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
157	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
158	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
159	C₈×C₁₃₇	—	2	4	no	—
160	C₈×C₁₃₇	—	2	4	no	—
161	C₂²×C₁₃₇	—	2	2	no	—
162	C₂²×C₁₃₇	—	2	4	no	—
163	C₂²×C₁₃₇	—	4	1	no	—
164	C₂²×C₁₃₇	—	4	1	no	—
165	C₂²×C₁₃₇	—	4	2	no	—
166	C₂²×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
167	C₂²×C₁₃₇	#535	1	1	yes	characteristic
168	C₂²×C₁₃₇	#536	1	1	yes	characteristic
169	C₂²×C₁₃₇	#576	1	2	yes	—
170	C₂²×C₁₃₇	#578	1	2	yes	—
171	C₄×C₁₃₇	—	2	2	no	—
172	C₄×C₁₃₇	—	2	4	no	—
173	C₄×C₁₃₇	—	2	4	no	—
174	C₄×C₁₃₇	—	8	1	no	—
175	C₄×C₁₃₇	—	8	2	no	—
176	C₄×C₁₃₇	—	8	1	no	—
177	C₄×C₁₃₇	—	8	1	no	—
178	C₄×C₁₃₇	—	8	1	no	—
179	C₄×C₁₃₇	—	8	2	no	—
180	C₄×C₁₃₇	#520	1	2	yes	—
181	C₄×C₁₃₇	#544	1	2	yes	—
182	C₂×C₁₃₇	—	4	2	no	—
183	C₂×C₁₃₇	#2317	1	1	yes	characteristic
184	C₂×C₁₃₇	#2913	1	2	yes	—
185	C₂×C₁₃₇	#3220	1	1	yes	characteristic
186	C₂×C₁₃₇	#3223	1	1	yes	characteristic
187	C₂×C₁₃₇	#3243	1	2	yes	—
188	#21991	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₁₃₇	#21991	1	1	yes	characteristic, direct product factor, Sylow
190	C₂×#433	C₂×C₁₃₇	1	1	yes	characteristic
191	#2317	C₂×C₁₃₇	1	1	yes	characteristic
192	#2314	C₂×C₁₃₇	1	1	yes	characteristic
193	#1949	C₂×C₁₃₇	1	2	yes	complemented
194	#1947	C₂×C₁₃₇	1	2	yes	complemented
195	#1854	C₂×C₁₃₇	1	2	yes	—
196	#1852	C₂×C₁₃₇	1	2	yes	—
197	#1847	C₂×C₁₃₇	1	1	yes	characteristic, complemented
198	#1845	C₂×C₁₃₇	1	1	yes	characteristic, complemented
199	#1836	C₂×C₁₃₇	1	1	yes	characteristic, complemented
200	#1835	C₂×C₁₃₇	1	1	yes	characteristic, complemented
201	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
202	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
203	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
204	#433	C₄×C₁₃₇	1	8	yes	complemented
205	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
206	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
207	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
208	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
209	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
210	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
211	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
212	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
213	#389	—	2	2	no	—
214	#388	—	2	2	no	—
215	#387	—	2	2	no	—
216	#385	—	2	2	no	—
217	#384	C₂²×C₁₃₇	1	1	yes	characteristic
218	#384	C₂²×C₁₃₇	1	1	yes	characteristic
219	#384	C₂²×C₁₃₇	1	1	yes	characteristic
220	#382	C₂²×C₁₃₇	1	1	yes	characteristic
221	#382	C₂²×C₁₃₇	1	1	yes	characteristic
222	#382	C₂²×C₁₃₇	1	1	yes	characteristic
223	#380	C₂²×C₁₃₇	1	2	yes	—
224	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
225	#340	C₂²×C₁₃₇	1	2	yes	—
226	#340	C₂²×C₁₃₇	1	2	yes	—
227	#340	C₂²×C₁₃₇	1	2	yes	—
228	#340	C₂²×C₁₃₇	1	2	yes	—
229	C₂³×C₄	—	2	1	no	—
230	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
232	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
233	#117	—	4	2	no	—
234	#117	C₂×C₄×C₁₃₇	1	4	yes	—
235	#117	Q₈×C₁₃₇	1	4	yes	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	4	2	no	—
241	C₂×C₄⋊C₄	D₄×C₁₃₇	1	2	yes	—
242	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
247	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
248	C₂×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	D₄×C₁₃₇	1	2	yes	—
251	C₂×C₄²	—	2	1	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
254	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
255	#107	—	4	2	no	—
256	#107	—	4	2	no	—
257	#107	—	4	2	no	—
258	#106	—	4	2	no	—
259	C₄⋊C₈	C₂×C₄×C₁₃₇	1	8	yes	complemented
260	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	8	yes	—
261	#97	C₂×C₄×C₁₃₇	1	4	yes	complemented
262	C₄×C₈	C₂×C₄×C₁₃₇	1	4	yes	complemented
263	#95	—	2	2	no	—
264	#95	—	2	2	no	—
265	#95	—	2	2	no	—
266	#95	—	2	2	no	—
267	#95	—	2	2	no	—
268	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	8	2	no	—
279	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
280	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
283	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
284	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	C₂²×C₄×C₁₃₇	1	4	yes	—
290	C₂×C₈	C₂²×C₄×C₁₃₇	1	4	yes	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	4	2	no	—
299	C₄⋊C₄	—	8	2	no	—
300	C₄⋊C₄	—	8	2	no	—
301	C₄⋊C₄	—	8	2	no	—
302	C₄⋊C₄	C₄⋊C₄×C₁₃₇	1	8	yes	—
303	C₂²⋊C₄	—	4	2	no	—
304	C₂²⋊C₄	—	8	2	no	—
305	C₂²⋊C₄	C₄⋊C₄×C₁₃₇	1	8	yes	—
306	C₄²	—	4	2	no	—
307	C₄²	—	8	2	no	—
308	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
309	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
310	C₄²	C₂×Q₈×C₁₃₇	1	2	yes	—
311	C₄²	C₂×Q₈×C₁₃₇	1	2	yes	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	2	2	no	—
315	C₂³	—	2	2	no	—
316	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
317	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	8	4	no	—
341	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
342	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
343	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
344	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
345	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
346	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
347	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
348	C₈	—	2	4	no	—
349	C₈	—	2	4	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	4	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	2	no	—
355	C₂²	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
356	C₂²	#535×C₁₃₇	1	1	yes	characteristic
357	C₂²	#536×C₁₃₇	1	1	yes	characteristic
358	C₂²	#576×C₁₃₇	1	2	yes	—
359	C₂²	#578×C₁₃₇	1	2	yes	—
360	C₄	—	2	2	no	—
361	C₄	—	2	4	no	—
362	C₄	—	2	4	no	—
363	C₄	—	8	1	no	—
364	C₄	—	8	1	no	—
365	C₄	—	8	1	no	—
366	C₄	—	8	2	no	—
367	C₄	—	8	1	no	—
368	C₄	—	8	2	no	—
369	C₄	#520×C₁₃₇	1	2	yes	—
370	C₄	#544×C₁₃₇	1	2	yes	—
371	C₂	—	4	2	no	—
372	C₂	#2317×C₁₃₇	1	1	yes	characteristic
373	C₂	#2913×C₁₃₇	1	2	yes	—
374	C₂	#3220×C₁₃₇	1	1	yes	characteristic
375	C₂	#3223×C₁₃₇	1	1	yes	characteristic
376	C₂	#3243×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂⁴×C₁₃₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂×#117×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1949×C₁₃₇	C₂	semidirect
5. #1947×C₁₃₇	C₂	semidirect
8. #1847×C₁₃₇	C₂	semidirect
9. #1845×C₁₃₇	C₂	semidirect
10. #1836×C₁₃₇	C₂	semidirect
11. #1835×C₁₃₇	C₂	semidirect
15. #433×C₁₃₇	C₄	semidirect
70. C₄⋊C₈×C₁₃₇	C₂×C₄	semidirect
72. #97×C₁₃₇	C₂×C₄	semidirect
73. C₄×C₈×C₁₃₇	C₂×C₄	semidirect
188. #21991	C₁₃₇	direct (N × H)
189. C₁₃₇	#21991	direct (N × H)
193. #1949	C₂×C₁₃₇	semidirect
194. #1947	C₂×C₁₃₇	semidirect
197. #1847	C₂×C₁₃₇	semidirect
198. #1845	C₂×C₁₃₇	semidirect
199. #1836	C₂×C₁₃₇	semidirect
200. #1835	C₂×C₁₃₇	semidirect
204. #433	C₄×C₁₃₇	semidirect
259. C₄⋊C₈	C₂×C₄×C₁₃₇	semidirect
261. #97	C₂×C₄×C₁₃₇	semidirect
262. C₄×C₈	C₂×C₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#433×C₁₃₇	2
#2317×C₁₃₇	2
#2314×C₁₃₇	2
#1949×C₁₃₇	2
#1947×C₁₃₇	2
#1854×C₁₃₇	2
#1852×C₁₃₇	2
#1847×C₁₃₇	2
#1845×C₁₃₇	2
#1836×C₁₃₇	2
#1835×C₁₃₇	2
#21991	137

Subgroups — C137×#21991 #46871377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#21991 #46871377