Subgroups — C₁₃₇×#22829 #46872215

Order 35072.

636 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2295×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#1984×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#1984×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1917×C₁₃₇	C₂	1	2	yes	maximal
5	#1916×C₁₃₇	C₂	1	2	yes	maximal
6	#1840×C₁₃₇	C₂	1	2	yes	maximal
7	#1831×C₁₃₇	C₂	1	1	yes	maximal, characteristic
8	#1770×C₁₃₇	C₂	1	1	yes	maximal, characteristic
9	C₈×C₄⋊C₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic
10	C₄×C₄⋊C₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
11	#1746×C₁₃₇	C₂	1	2	yes	maximal
12	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
21	#391×C₁₃₇	C₄	1	1	yes	characteristic
22	#391×C₁₃₇	C₄	1	1	yes	characteristic
23	#389×C₁₃₇	C₄	1	1	yes	characteristic
24	#389×C₁₃₇	C₄	1	1	yes	characteristic
25	#387×C₁₃₇	C₄	1	2	yes	—
26	#387×C₁₃₇	C₄	1	2	yes	—
27	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
29	#376×C₁₃₇	C₂²	1	2	yes	—
30	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
31	#336×C₁₃₇	C₂²	1	1	yes	characteristic
32	#336×C₁₃₇	C₂²	1	1	yes	characteristic
33	#336×C₁₃₇	C₂²	1	2	yes	—
34	#336×C₁₃₇	C₂²	1	2	yes	—
35	#336×C₁₃₇	C₂²	1	2	yes	—
36	#336×C₁₃₇	C₂²	1	2	yes	—
37	#336×C₁₃₇	C₂²	1	2	yes	—
38	#336×C₁₃₇	C₂²	1	2	yes	—
39	#336×C₁₃₇	C₂²	1	2	yes	—
40	#336×C₁₃₇	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
48	C₄×Q₈×C₁₃₇	—	2	2	no	—
49	C₄×Q₈×C₁₃₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
63	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
64	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
65	C₄⋊C₈×C₁₃₇	—	2	2	no	—
66	C₄⋊C₈×C₁₃₇	—	2	2	no	—
67	C₄⋊C₈×C₁₃₇	—	2	2	no	—
68	C₄⋊C₈×C₁₃₇	—	2	2	no	—
69	#97×C₁₃₇	—	2	4	no	—
70	C₄×C₈×C₁₃₇	—	2	4	no	—
71	C₄×C₈×C₁₃₇	—	2	2	no	—
72	C₄×C₈×C₁₃₇	—	2	2	no	—
73	#95×C₁₃₇	C₂×C₄	1	2	yes	—
74	#95×C₁₃₇	C₂×C₄	1	2	yes	—
75	#95×C₁₃₇	C₂×C₄	1	2	yes	—
76	#95×C₁₃₇	C₂×C₄	1	2	yes	—
77	#95×C₁₃₇	C₂×C₄	1	2	yes	—
78	#95×C₁₃₇	C₂×C₄	1	2	yes	—
79	#95×C₁₃₇	C₂×C₄	1	2	yes	—
80	C₂×Q₈×C₁₃₇	—	2	2	no	—
81	C₂×Q₈×C₁₃₇	—	2	2	no	—
82	C₂×Q₈×C₁₃₇	—	2	2	no	—
83	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
94	C₂×C₈×C₁₃₇	—	2	1	no	—
95	C₂×C₈×C₁₃₇	—	2	1	no	—
96	C₂×C₈×C₁₃₇	—	2	1	no	—
97	C₂×C₈×C₁₃₇	—	2	1	no	—
98	C₂×C₈×C₁₃₇	—	2	1	no	—
99	C₂×C₈×C₁₃₇	—	2	1	no	—
100	C₂×C₈×C₁₃₇	—	2	2	no	—
101	C₂×C₈×C₁₃₇	—	2	2	no	—
102	C₂×C₈×C₁₃₇	—	2	1	no	—
103	C₂×C₈×C₁₃₇	—	2	1	no	—
104	C₂×C₈×C₁₃₇	—	2	2	no	—
105	C₂×C₈×C₁₃₇	—	2	2	no	—
106	C₂×C₈×C₁₃₇	—	2	1	no	—
107	C₂×C₈×C₁₃₇	—	2	1	no	—
108	C₂×C₈×C₁₃₇	—	2	2	no	—
109	C₂×C₈×C₁₃₇	—	2	2	no	—
110	C₂×C₈×C₁₃₇	#41	1	2	yes	—
111	C₂×C₈×C₁₃₇	#41	1	2	yes	—
112	C₄⋊C₄×C₁₃₇	—	2	2	no	—
113	C₄⋊C₄×C₁₃₇	—	2	4	no	—
114	C₄⋊C₄×C₁₃₇	—	2	4	no	—
115	C₄⋊C₄×C₁₃₇	—	2	2	no	—
116	C₄⋊C₄×C₁₃₇	—	2	2	no	—
117	C₄⋊C₄×C₁₃₇	—	4	2	no	—
118	C₄²×C₁₃₇	—	2	2	no	—
119	C₄²×C₁₃₇	—	2	2	no	—
120	C₄²×C₁₃₇	—	2	2	no	—
121	C₄²×C₁₃₇	—	2	2	no	—
122	C₄²×C₁₃₇	—	2	2	no	—
123	C₄²×C₁₃₇	—	2	1	no	—
124	C₄²×C₁₃₇	—	2	1	no	—
125	C₄²×C₁₃₇	—	2	2	no	—
126	C₄²×C₁₃₇	—	2	2	no	—
127	C₄²×C₁₃₇	—	2	1	no	—
128	C₄²×C₁₃₇	—	2	1	no	—
129	C₄²×C₁₃₇	—	4	1	no	—
130	C₄²×C₁₃₇	#41	1	2	yes	—
131	C₄²×C₁₃₇	#41	1	2	yes	—
132	C₂³×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
133	Q₈×C₁₃₇	—	4	4	no	—
134	C₂×C₄×C₁₃₇	—	2	1	no	—
135	C₂×C₄×C₁₃₇	—	2	1	no	—
136	C₂×C₄×C₁₃₇	—	2	1	no	—
137	C₂×C₄×C₁₃₇	—	2	1	no	—
138	C₂×C₄×C₁₃₇	—	2	2	no	—
139	C₂×C₄×C₁₃₇	—	2	2	no	—
140	C₂×C₄×C₁₃₇	—	2	2	no	—
141	C₂×C₄×C₁₃₇	—	2	2	no	—
142	C₂×C₄×C₁₃₇	—	2	1	no	—
143	C₂×C₄×C₁₃₇	—	2	1	no	—
144	C₂×C₄×C₁₃₇	—	2	1	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	2	no	—
150	C₂×C₄×C₁₃₇	—	2	2	no	—
151	C₂×C₄×C₁₃₇	—	2	2	no	—
152	C₂×C₄×C₁₃₇	—	2	2	no	—
153	C₂×C₄×C₁₃₇	—	2	2	no	—
154	C₂×C₄×C₁₃₇	—	2	2	no	—
155	C₂×C₄×C₁₃₇	—	2	1	no	—
156	C₂×C₄×C₁₃₇	—	2	1	no	—
157	C₂×C₄×C₁₃₇	—	2	2	no	—
158	C₂×C₄×C₁₃₇	—	2	2	no	—
159	C₂×C₄×C₁₃₇	#117	1	2	yes	—
160	C₂×C₄×C₁₃₇	#117	1	2	yes	—
161	C₂×C₄×C₁₃₇	#131	1	2	yes	—
162	C₂×C₄×C₁₃₇	#131	1	2	yes	—
163	C₂×C₄×C₁₃₇	#131	1	2	yes	—
164	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	1	yes	characteristic
169	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	1	yes	characteristic
170	C₈×C₁₃₇	—	2	2	no	—
171	C₈×C₁₃₇	—	2	2	no	—
172	C₈×C₁₃₇	—	4	1	no	—
173	C₈×C₁₃₇	—	4	1	no	—
174	C₈×C₁₃₇	—	4	2	no	—
175	C₈×C₁₃₇	—	4	2	no	—
176	C₂²×C₁₃₇	C₂×#117	1	1	yes	characteristic
177	C₂²×C₁₃₇	C₄×#41	1	1	yes	characteristic
178	C₂²×C₁₃₇	#519	1	1	yes	characteristic
179	C₂²×C₁₃₇	C₂×#131	1	1	yes	characteristic
180	C₂²×C₁₃₇	C₂×#131	1	1	yes	characteristic
181	C₂²×C₁₃₇	C₂×#131	1	1	yes	characteristic
182	C₂²×C₁₃₇	#568	1	1	yes	characteristic
183	C₄×C₁₃₇	—	2	2	no	—
184	C₄×C₁₃₇	—	2	2	no	—
185	C₄×C₁₃₇	—	4	2	no	—
186	C₄×C₁₃₇	—	4	2	no	—
187	C₄×C₁₃₇	—	4	2	no	—
188	C₄×C₁₃₇	—	4	1	no	—
189	C₄×C₁₃₇	—	4	2	no	—
190	C₄×C₁₃₇	—	4	1	no	—
191	C₄×C₁₃₇	—	4	1	no	—
192	C₄×C₁₃₇	#433	1	4	yes	—
193	C₄×C₁₃₇	#552	1	1	yes	characteristic
194	C₄×C₁₃₇	#552	1	1	yes	characteristic
195	C₄×C₁₃₇	#556	1	1	yes	characteristic
196	C₄×C₁₃₇	#556	1	1	yes	characteristic
197	C₂×C₁₃₇	#2356	1	1	yes	characteristic
198	C₂×C₁₃₇	C₂×#433	1	1	yes	characteristic
199	C₂×C₁₃₇	#2925	1	1	yes	characteristic
200	C₂×C₁₃₇	#2966	1	1	yes	characteristic
201	C₂×C₁₃₇	#2969	1	1	yes	characteristic
202	C₂×C₁₃₇	#2985	1	1	yes	characteristic
203	C₂×C₁₃₇	#2986	1	1	yes	characteristic
204	#22829	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₁₃₇	#22829	1	1	yes	characteristic, direct product factor, Sylow
206	#2295	C₂×C₁₃₇	1	1	yes	characteristic
207	#1984	C₂×C₁₃₇	1	1	yes	characteristic
208	#1984	C₂×C₁₃₇	1	1	yes	characteristic
209	#1917	C₂×C₁₃₇	1	2	yes	—
210	#1916	C₂×C₁₃₇	1	2	yes	—
211	#1840	C₂×C₁₃₇	1	2	yes	—
212	#1831	C₂×C₁₃₇	1	1	yes	characteristic
213	#1770	C₂×C₁₃₇	1	1	yes	characteristic
214	C₈×C₄⋊C₄	C₂×C₁₃₇	1	1	yes	characteristic
215	C₄×C₄⋊C₈	C₂×C₁₃₇	1	1	yes	characteristic
216	#1746	C₂×C₁₃₇	1	2	yes	—
217	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
218	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
221	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
222	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
223	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
224	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
225	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
226	#391	C₄×C₁₃₇	1	1	yes	characteristic
227	#391	C₄×C₁₃₇	1	1	yes	characteristic
228	#389	C₄×C₁₃₇	1	1	yes	characteristic
229	#389	C₄×C₁₃₇	1	1	yes	characteristic
230	#387	C₄×C₁₃₇	1	2	yes	—
231	#387	C₄×C₁₃₇	1	2	yes	—
232	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
233	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
234	#376	C₂²×C₁₃₇	1	2	yes	—
235	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
236	#336	C₂²×C₁₃₇	1	2	yes	—
237	#336	C₂²×C₁₃₇	1	2	yes	—
238	#336	C₂²×C₁₃₇	1	1	yes	characteristic
239	#336	C₂²×C₁₃₇	1	2	yes	—
240	#336	C₂²×C₁₃₇	1	2	yes	—
241	#336	C₂²×C₁₃₇	1	2	yes	—
242	#336	C₂²×C₁₃₇	1	2	yes	—
243	#336	C₂²×C₁₃₇	1	2	yes	—
244	#336	C₂²×C₁₃₇	1	2	yes	—
245	#336	C₂²×C₁₃₇	1	1	yes	characteristic
246	C₂²×Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
248	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
251	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
256	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
258	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
261	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
262	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
263	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
264	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
266	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
269	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
270	C₄⋊C₈	—	2	2	no	—
271	C₄⋊C₈	—	2	2	no	—
272	C₄⋊C₈	—	2	2	no	—
273	C₄⋊C₈	—	2	2	no	—
274	#97	—	2	4	no	—
275	C₄×C₈	—	2	4	no	—
276	C₄×C₈	—	2	2	no	—
277	C₄×C₈	—	2	2	no	—
278	#95	C₂×C₄×C₁₃₇	1	2	yes	—
279	#95	C₂×C₄×C₁₃₇	1	2	yes	—
280	#95	C₂×C₄×C₁₃₇	1	2	yes	—
281	#95	C₂×C₄×C₁₃₇	1	2	yes	—
282	#95	C₂×C₄×C₁₃₇	1	2	yes	—
283	#95	C₂×C₄×C₁₃₇	1	2	yes	—
284	#95	C₂×C₄×C₁₃₇	1	2	yes	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
289	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
290	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
291	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
292	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
293	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
295	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
296	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
297	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
298	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	#41×C₁₃₇	1	2	yes	—
316	C₂×C₈	#41×C₁₃₇	1	2	yes	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	1	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	4	1	no	—
335	C₄²	#41×C₁₃₇	1	2	yes	—
336	C₄²	#41×C₁₃₇	1	2	yes	—
337	C₂³	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
338	Q₈	—	4	4	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	#117×C₁₃₇	1	2	yes	—
365	C₂×C₄	#117×C₁₃₇	1	2	yes	—
366	C₂×C₄	#131×C₁₃₇	1	2	yes	—
367	C₂×C₄	#131×C₁₃₇	1	2	yes	—
368	C₂×C₄	#131×C₁₃₇	1	2	yes	—
369	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
370	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
372	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
373	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
374	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	2	2	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	1	no	—
379	C₈	—	4	2	no	—
380	C₈	—	4	2	no	—
381	C₂²	C₂×#117×C₁₃₇	1	1	yes	characteristic
382	C₂²	C₄×#41×C₁₃₇	1	1	yes	characteristic
383	C₂²	#519×C₁₃₇	1	1	yes	characteristic
384	C₂²	C₂×#131×C₁₃₇	1	1	yes	characteristic
385	C₂²	C₂×#131×C₁₃₇	1	1	yes	characteristic
386	C₂²	C₂×#131×C₁₃₇	1	1	yes	characteristic
387	C₂²	#568×C₁₃₇	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	1	no	—
396	C₄	—	4	1	no	—
397	C₄	#433×C₁₃₇	1	4	yes	—
398	C₄	#552×C₁₃₇	1	1	yes	characteristic
399	C₄	#552×C₁₃₇	1	1	yes	characteristic
400	C₄	#556×C₁₃₇	1	1	yes	characteristic
401	C₄	#556×C₁₃₇	1	1	yes	characteristic
402	C₂	#2356×C₁₃₇	1	1	yes	characteristic
403	C₂	C₂×#433×C₁₃₇	1	1	yes	characteristic
404	C₂	#2925×C₁₃₇	1	1	yes	characteristic
405	C₂	#2966×C₁₃₇	1	1	yes	characteristic
406	C₂	#2969×C₁₃₇	1	1	yes	characteristic
407	C₂	#2985×C₁₃₇	1	1	yes	characteristic
408	C₂	#2986×C₁₃₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
204. #22829	C₁₃₇	direct (N × H)
205. C₁₃₇	#22829	direct (N × H)

Maximal subgroups

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

subgroup	index
#2295×C₁₃₇	2
#1984×C₁₃₇	2
#1917×C₁₃₇	2
#1916×C₁₃₇	2
#1840×C₁₃₇	2
#1831×C₁₃₇	2
#1770×C₁₃₇	2
C₈×C₄⋊C₄×C₁₃₇	2
C₄×C₄⋊C₈×C₁₃₇	2
#1746×C₁₃₇	2
#22829	137

Subgroups — C137×#22829 #46872215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#22829 #46872215