Subgroups — C₁₃₇×#22628 #46872014

Order 35072.

724 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2285×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#1940×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	#1917×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#1916×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1798×C₁₃₇	C₂	1	2	yes	maximal
6	#1797×C₁₃₇	C₂	1	1	yes	maximal, characteristic
7	#1771×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1750×C₁₃₇	C₂	1	2	yes	maximal
9	#1749×C₁₃₇	C₂	1	1	yes	maximal, characteristic
10	C₂×#117×C₁₃₇	C₂²	1	2	yes	—
11	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
13	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
14	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
15	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
19	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
21	#384×C₁₃₇	C₄	1	1	yes	characteristic
22	#384×C₁₃₇	C₄	1	1	yes	characteristic
23	#382×C₁₃₇	C₄	1	2	yes	—
24	#380×C₁₃₇	C₄	1	2	yes	—
25	#380×C₁₃₇	C₄	1	1	yes	characteristic
26	#380×C₁₃₇	C₄	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
30	#336×C₁₃₇	C₂²	1	2	yes	—
31	#336×C₁₃₇	C₂²	1	2	yes	—
32	#336×C₁₃₇	C₂²	1	1	yes	characteristic
33	#336×C₁₃₇	C₂²	1	1	yes	characteristic
34	#336×C₁₃₇	C₂²	1	2	yes	—
35	#336×C₁₃₇	C₂²	1	2	yes	—
36	#336×C₁₃₇	C₂²	1	2	yes	—
37	C₂³×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
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	—	4	2	no	—
46	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
54	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₁₃₇	—	2	4	no	—
57	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
60	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
61	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₁₃₇	—	2	4	no	—
64	C₄⋊C₈×C₁₃₇	—	4	2	no	—
65	C₄⋊C₈×C₁₃₇	—	4	2	no	—
66	C₂²⋊C₈×C₁₃₇	—	2	4	no	—
67	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
68	C₂²⋊C₈×C₁₃₇	Q₈	1	4	yes	—
69	#97×C₁₃₇	—	2	4	no	—
70	#97×C₁₃₇	—	4	2	no	—
71	C₄×C₈×C₁₃₇	—	4	2	no	—
72	#95×C₁₃₇	C₂×C₄	1	2	yes	—
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	C₂⁴×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃₇	—	2	2	no	—
78	C₂²×C₄×C₁₃₇	—	2	2	no	—
79	C₂²×C₄×C₁₃₇	—	2	2	no	—
80	C₂²×C₄×C₁₃₇	—	2	2	no	—
81	C₂²×C₄×C₁₃₇	—	2	2	no	—
82	C₂²×C₄×C₁₃₇	—	4	1	no	—
83	C₂²×C₄×C₁₃₇	—	4	1	no	—
84	C₂²×C₄×C₁₃₇	—	4	1	no	—
85	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
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	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
96	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
101	C₂×C₈×C₁₃₇	—	2	2	no	—
102	C₂×C₈×C₁₃₇	—	2	2	no	—
103	C₂×C₈×C₁₃₇	—	2	2	no	—
104	C₂×C₈×C₁₃₇	—	2	2	no	—
105	C₂×C₈×C₁₃₇	—	2	2	no	—
106	C₂×C₈×C₁₃₇	—	2	2	no	—
107	C₂×C₈×C₁₃₇	—	2	2	no	—
108	C₂×C₈×C₁₃₇	C₂×Q₈	1	4	yes	—
109	C₄⋊C₄×C₁₃₇	—	2	4	no	—
110	C₄⋊C₄×C₁₃₇	—	4	1	no	—
111	C₄⋊C₄×C₁₃₇	—	4	1	no	—
112	C₄⋊C₄×C₁₃₇	—	4	1	no	—
113	C₄⋊C₄×C₁₃₇	—	4	1	no	—
114	C₄⋊C₄×C₁₃₇	—	4	2	no	—
115	C₄⋊C₄×C₁₃₇	—	4	2	no	—
116	C₄⋊C₄×C₁₃₇	—	4	2	no	—
117	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
118	C₂²⋊C₄×C₁₃₇	—	4	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	2	no	—
124	C₄²×C₁₃₇	—	2	2	no	—
125	C₄²×C₁₃₇	—	2	2	no	—
126	C₄²×C₁₃₇	#41	1	4	yes	—
127	C₂³×C₁₃₇	—	2	1	no	—
128	C₂³×C₁₃₇	—	2	1	no	—
129	C₂³×C₁₃₇	—	2	1	no	—
130	C₂³×C₁₃₇	—	2	1	no	—
131	C₂³×C₁₃₇	—	2	1	no	—
132	C₂³×C₁₃₇	—	2	1	no	—
133	C₂³×C₁₃₇	C₄×Q₈	1	2	yes	—
134	C₂³×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
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	1	no	—
139	C₂×C₄×C₁₃₇	—	2	1	no	—
140	C₂×C₄×C₁₃₇	—	2	1	no	—
141	C₂×C₄×C₁₃₇	—	2	1	no	—
142	C₂×C₄×C₁₃₇	—	2	1	no	—
143	C₂×C₄×C₁₃₇	—	2	4	no	—
144	C₂×C₄×C₁₃₇	—	2	4	no	—
145	C₂×C₄×C₁₃₇	—	2	1	no	—
146	C₂×C₄×C₁₃₇	—	2	2	no	—
147	C₂×C₄×C₁₃₇	—	2	2	no	—
148	C₂×C₄×C₁₃₇	—	2	2	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	2	no	—
156	C₂×C₄×C₁₃₇	—	2	2	no	—
157	C₂×C₄×C₁₃₇	—	2	2	no	—
158	C₂×C₄×C₁₃₇	—	2	1	no	—
159	C₂×C₄×C₁₃₇	—	2	1	no	—
160	C₂×C₄×C₁₃₇	—	4	4	no	—
161	C₂×C₄×C₁₃₇	—	4	4	no	—
162	C₂×C₄×C₁₃₇	#117	1	2	yes	—
163	C₂×C₄×C₁₃₇	#117	1	2	yes	—
164	C₂×C₄×C₁₃₇	C₄×Q₈	1	2	yes	—
165	C₂×C₄×C₁₃₇	#131	1	2	yes	—
166	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
167	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
169	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
170	C₈×C₁₃₇	—	2	4	no	—
171	C₈×C₁₃₇	—	4	2	no	—
172	C₈×C₁₃₇	—	4	2	no	—
173	C₈×C₁₃₇	—	4	2	no	—
174	C₂²×C₁₃₇	—	2	2	no	—
175	C₂²×C₁₃₇	—	2	2	no	—
176	C₂²×C₁₃₇	—	2	2	no	—
177	C₂²×C₁₃₇	—	4	1	no	—
178	C₂²×C₁₃₇	—	4	1	no	—
179	C₂²×C₁₃₇	—	4	1	no	—
180	C₂²×C₁₃₇	—	4	1	no	—
181	C₂²×C₁₃₇	C₂×#117	1	1	yes	characteristic
182	C₂²×C₁₃₇	C₂×C₄×Q₈	1	1	yes	characteristic
183	C₂²×C₁₃₇	#518	1	1	yes	characteristic
184	C₂²×C₁₃₇	C₂×#131	1	1	yes	characteristic
185	C₂²×C₁₃₇	#568	1	1	yes	characteristic
186	C₂²×C₁₃₇	#568	1	1	yes	characteristic
187	C₂²×C₁₃₇	#568	1	1	yes	characteristic
188	C₄×C₁₃₇	—	2	2	no	—
189	C₄×C₁₃₇	—	2	2	no	—
190	C₄×C₁₃₇	—	2	2	no	—
191	C₄×C₁₃₇	—	2	2	no	—
192	C₄×C₁₃₇	—	4	1	no	—
193	C₄×C₁₃₇	—	4	2	no	—
194	C₄×C₁₃₇	—	4	2	no	—
195	C₄×C₁₃₇	—	4	2	no	—
196	C₄×C₁₃₇	—	4	2	no	—
197	C₄×C₁₃₇	#553	1	2	yes	—
198	C₄×C₁₃₇	#554	1	2	yes	—
199	C₂×C₁₃₇	—	4	2	no	—
200	C₂×C₁₃₇	#2345	1	1	yes	characteristic
201	C₂×C₁₃₇	#2921	1	1	yes	characteristic
202	C₂×C₁₃₇	#2924	1	1	yes	characteristic
203	C₂×C₁₃₇	#2961	1	1	yes	characteristic
204	C₂×C₁₃₇	#2962	1	1	yes	characteristic
205	C₂×C₁₃₇	#2980	1	1	yes	characteristic
206	C₂×C₁₃₇	#2981	1	1	yes	characteristic
207	#22628	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₁₃₇	#22628	1	1	yes	characteristic, direct product factor, Sylow
209	#2285	C₂×C₁₃₇	1	1	yes	characteristic
210	#1940	C₂×C₁₃₇	1	2	yes	complemented
211	#1917	C₂×C₁₃₇	1	2	yes	complemented
212	#1916	C₂×C₁₃₇	1	2	yes	complemented
213	#1798	C₂×C₁₃₇	1	2	yes	—
214	#1797	C₂×C₁₃₇	1	1	yes	characteristic
215	#1771	C₂×C₁₃₇	1	2	yes	complemented
216	#1750	C₂×C₁₃₇	1	2	yes	—
217	#1749	C₂×C₁₃₇	1	1	yes	characteristic
218	C₂×#117	C₂²×C₁₃₇	1	2	yes	—
219	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
221	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
222	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
223	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
224	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
225	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
226	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
227	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
228	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
229	#384	C₄×C₁₃₇	1	1	yes	characteristic
230	#384	C₄×C₁₃₇	1	1	yes	characteristic
231	#382	C₄×C₁₃₇	1	2	yes	—
232	#380	C₄×C₁₃₇	1	2	yes	—
233	#380	C₄×C₁₃₇	1	1	yes	characteristic
234	#380	C₄×C₁₃₇	1	1	yes	characteristic
235	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
236	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
237	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
238	#336	C₂²×C₁₃₇	1	1	yes	characteristic
239	#336	C₂²×C₁₃₇	1	1	yes	characteristic
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	C₂³×C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
246	C₂³×C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
247	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
249	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
250	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
251	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
252	#117	—	4	2	no	—
253	#117	—	4	2	no	—
254	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
255	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
256	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
257	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
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	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
263	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
264	C₂×C₄²	—	2	4	no	—
265	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
266	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
268	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
269	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
271	C₄⋊C₈	—	2	4	no	—
272	C₄⋊C₈	—	4	2	no	—
273	C₄⋊C₈	—	4	2	no	—
274	C₂²⋊C₈	—	2	4	no	—
275	C₂²⋊C₈	—	2	2	no	—
276	C₂²⋊C₈	Q₈×C₁₃₇	1	4	yes	—
277	#97	—	2	4	no	—
278	#97	—	4	2	no	—
279	C₄×C₈	—	4	2	no	—
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	C₂⁴	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	1	no	—
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	2	yes	—
296	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
297	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
298	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
300	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
301	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
302	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
303	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
304	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	C₂×Q₈×C₁₃₇	1	4	yes	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	#41×C₁₃₇	1	4	yes	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	C₄×Q₈×C₁₃₇	1	2	yes	—
342	C₂³	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	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	4	no	—
352	C₂×C₄	—	2	4	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	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	#117×C₁₃₇	1	2	yes	—
371	C₂×C₄	#117×C₁₃₇	1	2	yes	—
372	C₂×C₄	C₄×Q₈×C₁₃₇	1	2	yes	—
373	C₂×C₄	#131×C₁₃₇	1	2	yes	—
374	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
375	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
376	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
377	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
378	C₈	—	2	4	no	—
379	C₈	—	4	2	no	—
380	C₈	—	4	2	no	—
381	C₈	—	4	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	C₂×#117×C₁₃₇	1	1	yes	characteristic
390	C₂²	C₂×C₄×Q₈×C₁₃₇	1	1	yes	characteristic
391	C₂²	#518×C₁₃₇	1	1	yes	characteristic
392	C₂²	C₂×#131×C₁₃₇	1	1	yes	characteristic
393	C₂²	#568×C₁₃₇	1	1	yes	characteristic
394	C₂²	#568×C₁₃₇	1	1	yes	characteristic
395	C₂²	#568×C₁₃₇	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	4	1	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	2	no	—
405	C₄	#553×C₁₃₇	1	2	yes	—
406	C₄	#554×C₁₃₇	1	2	yes	—
407	C₂	—	4	2	no	—
408	C₂	#2345×C₁₃₇	1	1	yes	characteristic
409	C₂	#2921×C₁₃₇	1	1	yes	characteristic
410	C₂	#2924×C₁₃₇	1	1	yes	characteristic
411	C₂	#2961×C₁₃₇	1	1	yes	characteristic
412	C₂	#2962×C₁₃₇	1	1	yes	characteristic
413	C₂	#2980×C₁₃₇	1	1	yes	characteristic
414	C₂	#2981×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	C₂³×C₁₃₇	C₂³×C₄
prime radical	C₂⁴×C₁₃₇	C₂²×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
2. #1940×C₁₃₇	C₂	semidirect
3. #1917×C₁₃₇	C₂	semidirect
4. #1916×C₁₃₇	C₂	semidirect
7. #1771×C₁₃₇	C₂	semidirect
207. #22628	C₁₃₇	direct (N × H)
208. C₁₃₇	#22628	direct (N × H)
210. #1940	C₂×C₁₃₇	semidirect
211. #1917	C₂×C₁₃₇	semidirect
212. #1916	C₂×C₁₃₇	semidirect
215. #1771	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#2285×C₁₃₇	2
#1940×C₁₃₇	2
#1917×C₁₃₇	2
#1916×C₁₃₇	2
#1798×C₁₃₇	2
#1797×C₁₃₇	2
#1771×C₁₃₇	2
#1750×C₁₃₇	2
#1749×C₁₃₇	2
#22628	137

Subgroups — C137×#22628 #46872014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#22628 #46872014