Subgroups — C₁₃₇×#21022 #46870408

Order 35072.

906 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#424×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×M₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2296×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1917×C₁₃₇	C₂	1	4	yes	maximal, complemented
5	#1916×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	#1729×C₁₃₇	C₂	1	1	yes	maximal, characteristic
7	#1729×C₁₃₇	C₂	1	1	yes	maximal, characteristic
8	#1729×C₁₃₇	C₂	1	1	yes	maximal, characteristic
9	C₂×#336×C₁₃₇	C₂	1	1	yes	maximal, characteristic
10	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
17	#424×C₁₃₇	—	2	4	no	—
18	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	4	yes	—
19	C₄×M₁₆×C₁₃₇	—	2	4	no	—
20	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
22	#389×C₁₃₇	C₄	1	2	yes	—
23	#389×C₁₃₇	C₄	1	2	yes	—
24	#385×C₁₃₇	C₄	1	4	yes	—
25	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
26	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
27	#336×C₁₃₇	C₂²	1	2	yes	—
28	#336×C₁₃₇	C₂²	1	4	yes	—
29	#336×C₁₃₇	C₂²	1	4	yes	—
30	#336×C₁₃₇	C₂²	1	4	yes	—
31	#336×C₁₃₇	C₂²	1	2	yes	—
32	C₂³×C₄×C₁₃₇	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
34	C₂×M₁₆×C₁₃₇	—	2	2	no	—
35	C₂×M₁₆×C₁₃₇	—	2	2	no	—
36	C₂×M₁₆×C₁₃₇	—	2	2	no	—
37	C₂×M₁₆×C₁₃₇	—	2	2	no	—
38	C₂×M₁₆×C₁₃₇	D₄	1	4	yes	—
39	C₂×M₁₆×C₁₃₇	Q₈	1	4	yes	—
40	C₂²×C₈×C₁₃₇	—	2	2	no	—
41	C₂²×C₈×C₁₃₇	—	2	2	no	—
42	C₂²×C₈×C₁₃₇	—	2	2	no	—
43	C₂²×C₈×C₁₃₇	—	2	2	no	—
44	C₂²×C₈×C₁₃₇	—	2	2	no	—
45	C₂²×C₈×C₁₃₇	—	2	2	no	—
46	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
50	#117×C₁₃₇	—	2	2	no	—
51	#117×C₁₃₇	—	2	2	no	—
52	#117×C₁₃₇	—	2	2	no	—
53	#117×C₁₃₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
55	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
59	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
61	C₂×C₄²×C₁₃₇	—	2	2	no	—
62	C₂×C₄²×C₁₃₇	—	2	2	no	—
63	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
67	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
68	C₄⋊C₈×C₁₃₇	—	2	8	no	—
69	#97×C₁₃₇	—	2	4	no	—
70	C₄×C₈×C₁₃₇	—	2	4	no	—
71	#95×C₁₃₇	C₂×C₄	1	4	yes	—
72	#95×C₁₃₇	C₂×C₄	1	4	yes	—
73	C₂⁴×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃₇	—	2	4	no	—
75	C₂²×C₄×C₁₃₇	—	2	4	no	—
76	C₂²×C₄×C₁₃₇	—	4	2	no	—
77	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
81	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
85	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
86	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
87	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
88	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
89	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
90	M₁₆×C₁₃₇	—	2	8	no	—
91	M₁₆×C₁₃₇	—	2	8	no	—
92	C₂×C₈×C₁₃₇	—	2	2	no	—
93	C₂×C₈×C₁₃₇	—	2	2	no	—
94	C₂×C₈×C₁₃₇	—	2	2	no	—
95	C₂×C₈×C₁₃₇	—	2	2	no	—
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	—	2	2	no	—
101	C₂×C₈×C₁₃₇	—	2	2	no	—
102	C₂×C₈×C₁₃₇	—	4	4	no	—
103	C₂×C₈×C₁₃₇	—	4	4	no	—
104	C₂×C₈×C₁₃₇	C₂×D₄	1	4	yes	—
105	C₂×C₈×C₁₃₇	C₂×Q₈	1	4	yes	—
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	—	2	8	no	—
110	C₄⋊C₄×C₁₃₇	—	4	4	no	—
111	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
112	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
113	C₄²×C₁₃₇	—	2	4	no	—
114	C₄²×C₁₃₇	—	2	1	no	—
115	C₄²×C₁₃₇	—	2	1	no	—
116	C₄²×C₁₃₇	—	2	2	no	—
117	C₄²×C₁₃₇	—	2	1	no	—
118	C₄²×C₁₃₇	—	2	1	no	—
119	C₄²×C₁₃₇	—	2	2	no	—
120	C₄²×C₁₃₇	—	2	2	no	—
121	C₄²×C₁₃₇	—	2	2	no	—
122	C₂³×C₁₃₇	—	2	2	no	—
123	C₂³×C₁₃₇	—	2	2	no	—
124	C₂³×C₁₃₇	#117	1	2	yes	—
125	C₂³×C₁₃₇	C₄×D₄	1	2	yes	—
126	C₂³×C₁₃₇	C₄×Q₈	1	2	yes	—
127	C₂³×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
128	C₂×C₄×C₁₃₇	—	2	2	no	—
129	C₂×C₄×C₁₃₇	—	2	2	no	—
130	C₂×C₄×C₁₃₇	—	2	2	no	—
131	C₂×C₄×C₁₃₇	—	2	2	no	—
132	C₂×C₄×C₁₃₇	—	2	2	no	—
133	C₂×C₄×C₁₃₇	—	2	4	no	—
134	C₂×C₄×C₁₃₇	—	2	4	no	—
135	C₂×C₄×C₁₃₇	—	2	4	no	—
136	C₂×C₄×C₁₃₇	—	2	2	no	—
137	C₂×C₄×C₁₃₇	—	2	2	no	—
138	C₂×C₄×C₁₃₇	—	2	4	no	—
139	C₂×C₄×C₁₃₇	—	2	4	no	—
140	C₂×C₄×C₁₃₇	—	4	8	no	—
141	C₂×C₄×C₁₃₇	#117	1	2	yes	—
142	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
143	C₂×C₄×C₁₃₇	C₄×Q₈	1	2	yes	—
144	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	4	yes	—
145	C₂×C₄×C₁₃₇	#123	1	4	yes	—
146	C₂×C₄×C₁₃₇	#125	1	4	yes	—
147	C₂×C₄×C₁₃₇	#126	1	4	yes	—
148	C₂×C₄×C₁₃₇	#131	1	4	yes	—
149	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
151	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
155	C₈×C₁₃₇	—	2	4	no	—
156	C₈×C₁₃₇	—	2	4	no	—
157	C₈×C₁₃₇	—	4	2	no	—
158	C₈×C₁₃₇	—	4	2	no	—
159	C₂²×C₁₃₇	—	2	2	no	—
160	C₂²×C₁₃₇	—	2	2	no	—
161	C₂²×C₁₃₇	—	2	4	no	—
162	C₂²×C₁₃₇	—	2	4	no	—
163	C₂²×C₁₃₇	#387	1	4	yes	—
164	C₂²×C₁₃₇	C₂×#117	1	1	yes	characteristic
165	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
166	C₂²×C₁₃₇	C₂×C₄×Q₈	1	1	yes	characteristic
167	C₂²×C₁₃₇	C₂×#131	1	2	yes	—
168	C₂²×C₁₃₇	#568	1	2	yes	—
169	C₄×C₁₃₇	—	2	4	no	—
170	C₄×C₁₃₇	—	4	2	no	—
171	C₄×C₁₃₇	—	4	2	no	—
172	C₄×C₁₃₇	—	4	4	no	—
173	C₄×C₁₃₇	—	4	2	no	—
174	C₄×C₁₃₇	#387	1	4	yes	—
175	C₄×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
176	C₄×C₁₃₇	C₂×#123	1	1	yes	characteristic
177	C₄×C₁₃₇	C₂×#125	1	1	yes	characteristic
178	C₄×C₁₃₇	C₂×#126	1	1	yes	characteristic
179	C₂×C₁₃₇	—	2	4	no	—
180	C₂×C₁₃₇	C₂×#387	1	1	yes	characteristic
181	C₂×C₁₃₇	#2922	1	1	yes	characteristic
182	C₂×C₁₃₇	#2923	1	1	yes	characteristic
183	C₂×C₁₃₇	#2933	1	2	yes	—
184	C₂×C₁₃₇	#2962	1	2	yes	—
185	#21022	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₁₃₇	#21022	1	1	yes	characteristic, direct product factor, Sylow
187	C₂×#424	C₂×C₁₃₇	1	1	yes	characteristic
188	C₂×C₄×M₁₆	C₂×C₁₃₇	1	1	yes	characteristic
189	#2296	C₂×C₁₃₇	1	1	yes	characteristic
190	#1917	C₂×C₁₃₇	1	4	yes	complemented
191	#1916	C₂×C₁₃₇	1	4	yes	complemented
192	#1729	C₂×C₁₃₇	1	1	yes	characteristic
193	#1729	C₂×C₁₃₇	1	1	yes	characteristic
194	#1729	C₂×C₁₃₇	1	1	yes	characteristic
195	C₂×#336	C₂×C₁₃₇	1	1	yes	characteristic
196	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
197	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
198	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
199	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
200	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
201	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
202	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
203	#424	—	2	4	no	—
204	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	4	yes	—
205	C₄×M₁₆	—	2	4	no	—
206	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
207	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
208	#389	C₄×C₁₃₇	1	2	yes	—
209	#389	C₄×C₁₃₇	1	2	yes	—
210	#385	C₄×C₁₃₇	1	4	yes	—
211	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
212	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
213	#336	C₂²×C₁₃₇	1	2	yes	—
214	#336	C₂²×C₁₃₇	1	4	yes	—
215	#336	C₂²×C₁₃₇	1	4	yes	—
216	#336	C₂²×C₁₃₇	1	4	yes	—
217	#336	C₂²×C₁₃₇	1	2	yes	—
218	C₂³×C₄	C₂×C₄×C₁₃₇	1	2	yes	—
219	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
220	C₂×M₁₆	—	2	2	no	—
221	C₂×M₁₆	—	2	2	no	—
222	C₂×M₁₆	—	2	2	no	—
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	D₄×C₁₃₇	1	4	yes	—
225	C₂×M₁₆	Q₈×C₁₃₇	1	4	yes	—
226	C₂²×C₈	—	2	2	no	—
227	C₂²×C₈	—	2	2	no	—
228	C₂²×C₈	—	2	2	no	—
229	C₂²×C₈	—	2	2	no	—
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
233	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
234	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
235	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
236	#117	—	2	2	no	—
237	#117	—	2	2	no	—
238	#117	—	2	2	no	—
239	#117	—	2	2	no	—
240	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
243	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
244	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
245	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
246	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	—	2	2	no	—
249	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
250	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
251	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
252	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
253	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
254	C₄⋊C₈	—	2	8	no	—
255	#97	—	2	4	no	—
256	C₄×C₈	—	2	4	no	—
257	#95	C₂×C₄×C₁₃₇	1	4	yes	—
258	#95	C₂×C₄×C₁₃₇	1	4	yes	—
259	C₂⁴	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
264	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
265	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
266	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
267	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
268	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
270	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
271	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
272	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
273	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
274	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
275	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
276	M₁₆	—	2	8	no	—
277	M₁₆	—	2	8	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	4	4	no	—
289	C₂×C₈	—	4	4	no	—
290	C₂×C₈	C₂×D₄×C₁₃₇	1	4	yes	—
291	C₂×C₈	C₂×Q₈×C₁₃₇	1	4	yes	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	2	8	no	—
296	C₄⋊C₄	—	4	4	no	—
297	C₂²⋊C₄	—	2	4	no	—
298	C₂²⋊C₄	—	2	4	no	—
299	C₄²	—	2	4	no	—
300	C₄²	—	2	1	no	—
301	C₄²	—	2	1	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	1	no	—
304	C₄²	—	2	1	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	—	2	2	no	—
310	C₂³	#117×C₁₃₇	1	2	yes	—
311	C₂³	C₄×D₄×C₁₃₇	1	2	yes	—
312	C₂³	C₄×Q₈×C₁₃₇	1	2	yes	—
313	C₂³	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	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	8	no	—
327	C₂×C₄	#117×C₁₃₇	1	2	yes	—
328	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
329	C₂×C₄	C₄×Q₈×C₁₃₇	1	2	yes	—
330	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	4	yes	—
331	C₂×C₄	#123×C₁₃₇	1	4	yes	—
332	C₂×C₄	#125×C₁₃₇	1	4	yes	—
333	C₂×C₄	#126×C₁₃₇	1	4	yes	—
334	C₂×C₄	#131×C₁₃₇	1	4	yes	—
335	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
336	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
337	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
338	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
339	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
340	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
341	C₈	—	2	4	no	—
342	C₈	—	2	4	no	—
343	C₈	—	4	2	no	—
344	C₈	—	4	2	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	4	no	—
348	C₂²	—	2	4	no	—
349	C₂²	#387×C₁₃₇	1	4	yes	—
350	C₂²	C₂×#117×C₁₃₇	1	1	yes	characteristic
351	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
352	C₂²	C₂×C₄×Q₈×C₁₃₇	1	1	yes	characteristic
353	C₂²	C₂×#131×C₁₃₇	1	2	yes	—
354	C₂²	#568×C₁₃₇	1	2	yes	—
355	C₄	—	2	4	no	—
356	C₄	—	4	2	no	—
357	C₄	—	4	2	no	—
358	C₄	—	4	2	no	—
359	C₄	—	4	4	no	—
360	C₄	#387×C₁₃₇	1	4	yes	—
361	C₄	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
362	C₄	C₂×#123×C₁₃₇	1	1	yes	characteristic
363	C₄	C₂×#125×C₁₃₇	1	1	yes	characteristic
364	C₄	C₂×#126×C₁₃₇	1	1	yes	characteristic
365	C₂	—	2	4	no	—
366	C₂	C₂×#387×C₁₃₇	1	1	yes	characteristic
367	C₂	#2922×C₁₃₇	1	1	yes	characteristic
368	C₂	#2923×C₁₃₇	1	1	yes	characteristic
369	C₂	#2933×C₁₃₇	1	2	yes	—
370	C₂	#2962×C₁₃₇	1	2	yes	—

	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
4. #1917×C₁₃₇	C₂	semidirect
5. #1916×C₁₃₇	C₂	semidirect
185. #21022	C₁₃₇	direct (N × H)
186. C₁₃₇	#21022	direct (N × H)
190. #1917	C₂×C₁₃₇	semidirect
191. #1916	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×#424×C₁₃₇	2
C₂×C₄×M₁₆×C₁₃₇	2
#2296×C₁₃₇	2
#1917×C₁₃₇	2
#1916×C₁₃₇	2
#1729×C₁₃₇	2
C₂×#336×C₁₃₇	2
#21022	137

Subgroups — C137×#21022 #46870408

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#21022 #46870408