Subgroups — C₁₃₇×#21025 #46870411

Order 35072.

906 conjugacy classes of subgroups.

The subgroup lattice has 396 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×#405×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2285×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	#1728×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	2	yes	—
19	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
20	#405×C₁₃₇	—	2	4	no	—
21	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
23	#384×C₁₃₇	C₄	1	1	yes	characteristic
24	#384×C₁₃₇	C₄	1	1	yes	characteristic
25	#382×C₁₃₇	C₄	1	1	yes	characteristic
26	#382×C₁₃₇	C₄	1	1	yes	characteristic
27	#380×C₁₃₇	C₄	1	4	yes	—
28	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	4	yes	—
29	#336×C₁₃₇	C₂²	1	2	yes	—
30	#336×C₁₃₇	C₂²	1	4	yes	—
31	#336×C₁₃₇	C₂²	1	4	yes	—
32	#336×C₁₃₇	C₂²	1	4	yes	—
33	#336×C₁₃₇	C₂²	1	2	yes	—
34	C₂³×C₄×C₁₃₇	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₁₃₇	—	2	2	no	—
37	C₂×M₁₆×C₁₃₇	—	2	2	no	—
38	C₂×M₁₆×C₁₃₇	—	2	2	no	—
39	C₂×M₁₆×C₁₃₇	—	2	2	no	—
40	C₂×M₁₆×C₁₃₇	—	2	2	no	—
41	C₂×M₁₆×C₁₃₇	Q₈	1	4	yes	—
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	—	2	2	no	—
47	C₂²×C₈×C₁₃₇	D₄	1	4	yes	—
48	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
53	#117×C₁₃₇	—	2	2	no	—
54	#117×C₁₃₇	—	2	2	no	—
55	#117×C₁₃₇	—	2	2	no	—
56	#117×C₁₃₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
63	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₁₃₇	—	2	2	no	—
66	C₂×C₄²×C₁₃₇	—	2	2	no	—
67	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
72	C₄⋊C₈×C₁₃₇	—	2	4	no	—
73	C₄⋊C₈×C₁₃₇	—	2	4	no	—
74	#97×C₁₃₇	—	2	4	no	—
75	C₄×C₈×C₁₃₇	—	2	4	no	—
76	#95×C₁₃₇	C₂×C₄	1	4	yes	—
77	#95×C₁₃₇	C₂×C₄	1	4	yes	—
78	C₂⁴×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃₇	—	2	4	no	—
80	C₂²×C₄×C₁₃₇	—	2	4	no	—
81	C₂²×C₄×C₁₃₇	—	4	2	no	—
82	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
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	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
92	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
93	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
94	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
95	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
96	M₁₆×C₁₃₇	—	2	8	no	—
97	M₁₆×C₁₃₇	—	4	4	no	—
98	C₂×C₈×C₁₃₇	—	2	8	no	—
99	C₂×C₈×C₁₃₇	—	2	2	no	—
100	C₂×C₈×C₁₃₇	—	2	1	no	—
101	C₂×C₈×C₁₃₇	—	2	1	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	2	no	—
107	C₂×C₈×C₁₃₇	—	2	2	no	—
108	C₂×C₈×C₁₃₇	—	2	2	no	—
109	C₂×C₈×C₁₃₇	—	2	2	no	—
110	C₂×C₈×C₁₃₇	—	2	2	no	—
111	C₂×C₈×C₁₃₇	—	4	4	no	—
112	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₁₃₇	C₂×Q₈	1	4	yes	—
115	C₄⋊C₄×C₁₃₇	—	2	2	no	—
116	C₄⋊C₄×C₁₃₇	—	2	2	no	—
117	C₄⋊C₄×C₁₃₇	—	2	2	no	—
118	C₄⋊C₄×C₁₃₇	—	2	2	no	—
119	C₄⋊C₄×C₁₃₇	—	2	8	no	—
120	C₄⋊C₄×C₁₃₇	—	4	4	no	—
121	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
122	C₂²⋊C₄×C₁₃₇	—	2	4	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	—	2	2	no	—
129	C₄²×C₁₃₇	—	2	2	no	—
130	C₄²×C₁₃₇	—	2	2	no	—
131	C₂³×C₁₃₇	—	2	2	no	—
132	C₂³×C₁₃₇	—	2	2	no	—
133	C₂³×C₁₃₇	#117	1	2	yes	—
134	C₂³×C₁₃₇	C₄×D₄	1	2	yes	—
135	C₂³×C₁₃₇	C₄×Q₈	1	2	yes	—
136	C₂³×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₃₇	—	2	2	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	2	no	—
143	C₂×C₄×C₁₃₇	—	2	2	no	—
144	C₂×C₄×C₁₃₇	—	2	4	no	—
145	C₂×C₄×C₁₃₇	—	2	4	no	—
146	C₂×C₄×C₁₃₇	—	2	2	no	—
147	C₂×C₄×C₁₃₇	—	2	4	no	—
148	C₂×C₄×C₁₃₇	—	2	4	no	—
149	C₂×C₄×C₁₃₇	—	2	2	no	—
150	C₂×C₄×C₁₃₇	—	4	8	no	—
151	C₂×C₄×C₁₃₇	#117	1	2	yes	—
152	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₁₃₇	C₄×Q₈	1	2	yes	—
154	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	4	yes	—
155	C₂×C₄×C₁₃₇	#123	1	4	yes	—
156	C₂×C₄×C₁₃₇	#125	1	4	yes	—
157	C₂×C₄×C₁₃₇	#126	1	4	yes	—
158	C₂×C₄×C₁₃₇	#131	1	4	yes	—
159	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
165	C₈×C₁₃₇	—	2	4	no	—
166	C₈×C₁₃₇	—	2	2	no	—
167	C₈×C₁₃₇	—	2	2	no	—
168	C₈×C₁₃₇	—	4	2	no	—
169	C₈×C₁₃₇	—	4	2	no	—
170	C₂²×C₁₃₇	—	2	4	no	—
171	C₂²×C₁₃₇	—	2	2	no	—
172	C₂²×C₁₃₇	—	2	2	no	—
173	C₂²×C₁₃₇	—	2	4	no	—
174	C₂²×C₁₃₇	#387	1	4	yes	—
175	C₂²×C₁₃₇	C₂×#117	1	1	yes	characteristic
176	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
177	C₂²×C₁₃₇	C₂×C₄×Q₈	1	1	yes	characteristic
178	C₂²×C₁₃₇	C₂×#131	1	2	yes	—
179	C₂²×C₁₃₇	#568	1	2	yes	—
180	C₄×C₁₃₇	—	2	4	no	—
181	C₄×C₁₃₇	—	4	2	no	—
182	C₄×C₁₃₇	—	4	2	no	—
183	C₄×C₁₃₇	—	4	2	no	—
184	C₄×C₁₃₇	—	4	2	no	—
185	C₄×C₁₃₇	—	4	2	no	—
186	C₄×C₁₃₇	#387	1	4	yes	—
187	C₄×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
188	C₄×C₁₃₇	C₂×#123	1	1	yes	characteristic
189	C₄×C₁₃₇	C₂×#125	1	1	yes	characteristic
190	C₄×C₁₃₇	C₂×#126	1	1	yes	characteristic
191	C₂×C₁₃₇	—	2	4	no	—
192	C₂×C₁₃₇	C₂×#387	1	1	yes	characteristic
193	C₂×C₁₃₇	#2924	1	2	yes	—
194	C₂×C₁₃₇	#2931	1	1	yes	characteristic
195	C₂×C₁₃₇	#2932	1	1	yes	characteristic
196	C₂×C₁₃₇	#2962	1	2	yes	—
197	#21025	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₁₃₇	#21025	1	1	yes	characteristic, direct product factor, Sylow
199	C₂×#424	C₂×C₁₃₇	1	1	yes	characteristic
200	C₂×#405	C₂×C₁₃₇	1	1	yes	characteristic
201	#2285	C₂×C₁₃₇	1	1	yes	characteristic
202	#1917	C₂×C₁₃₇	1	4	yes	complemented
203	#1916	C₂×C₁₃₇	1	4	yes	complemented
204	#1729	C₂×C₁₃₇	1	1	yes	characteristic
205	#1729	C₂×C₁₃₇	1	1	yes	characteristic
206	#1728	C₂×C₁₃₇	1	1	yes	characteristic
207	C₂×#336	C₂×C₁₃₇	1	1	yes	characteristic
208	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
209	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
210	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
211	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
212	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
213	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
214	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
215	#424	—	2	4	no	—
216	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
217	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
218	#405	—	2	4	no	—
219	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
220	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
221	#384	C₄×C₁₃₇	1	1	yes	characteristic
222	#384	C₄×C₁₃₇	1	1	yes	characteristic
223	#382	C₄×C₁₃₇	1	1	yes	characteristic
224	#382	C₄×C₁₃₇	1	1	yes	characteristic
225	#380	C₄×C₁₃₇	1	4	yes	—
226	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	4	yes	—
227	#336	C₂²×C₁₃₇	1	2	yes	—
228	#336	C₂²×C₁₃₇	1	4	yes	—
229	#336	C₂²×C₁₃₇	1	4	yes	—
230	#336	C₂²×C₁₃₇	1	4	yes	—
231	#336	C₂²×C₁₃₇	1	2	yes	—
232	C₂³×C₄	C₂×C₄×C₁₃₇	1	2	yes	—
233	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂×M₁₆	—	2	2	no	—
239	C₂×M₁₆	Q₈×C₁₃₇	1	4	yes	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	2	2	no	—
245	C₂²×C₈	D₄×C₁₃₇	1	4	yes	—
246	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
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	#117	—	2	2	no	—
252	#117	—	2	2	no	—
253	#117	—	2	2	no	—
254	#117	—	2	2	no	—
255	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
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	4	yes	—
260	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
261	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	—	2	2	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	2	yes	—
270	C₄⋊C₈	—	2	4	no	—
271	C₄⋊C₈	—	2	4	no	—
272	#97	—	2	4	no	—
273	C₄×C₈	—	2	4	no	—
274	#95	C₂×C₄×C₁₃₇	1	4	yes	—
275	#95	C₂×C₄×C₁₃₇	1	4	yes	—
276	C₂⁴	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
281	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
282	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
283	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
284	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
285	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
286	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
288	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
289	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
290	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
291	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
292	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
293	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
294	M₁₆	—	2	8	no	—
295	M₁₆	—	4	4	no	—
296	C₂×C₈	—	2	8	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
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	—	4	4	no	—
310	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
311	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
312	C₂×C₈	C₂×Q₈×C₁₃₇	1	4	yes	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄⋊C₄	—	4	4	no	—
319	C₂²⋊C₄	—	2	4	no	—
320	C₂²⋊C₄	—	2	4	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	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	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	2	no	—
331	C₂³	#117×C₁₃₇	1	2	yes	—
332	C₂³	C₄×D₄×C₁₃₇	1	2	yes	—
333	C₂³	C₄×Q₈×C₁₃₇	1	2	yes	—
334	C₂³	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	8	no	—
349	C₂×C₄	#117×C₁₃₇	1	2	yes	—
350	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
351	C₂×C₄	C₄×Q₈×C₁₃₇	1	2	yes	—
352	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	4	yes	—
353	C₂×C₄	#123×C₁₃₇	1	4	yes	—
354	C₂×C₄	#125×C₁₃₇	1	4	yes	—
355	C₂×C₄	#126×C₁₃₇	1	4	yes	—
356	C₂×C₄	#131×C₁₃₇	1	4	yes	—
357	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
358	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
359	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
360	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
361	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
362	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
363	C₈	—	2	4	no	—
364	C₈	—	2	2	no	—
365	C₈	—	2	2	no	—
366	C₈	—	4	2	no	—
367	C₈	—	4	2	no	—
368	C₂²	—	2	4	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	4	no	—
372	C₂²	#387×C₁₃₇	1	4	yes	—
373	C₂²	C₂×#117×C₁₃₇	1	1	yes	characteristic
374	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
375	C₂²	C₂×C₄×Q₈×C₁₃₇	1	1	yes	characteristic
376	C₂²	C₂×#131×C₁₃₇	1	2	yes	—
377	C₂²	#568×C₁₃₇	1	2	yes	—
378	C₄	—	2	4	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	2	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	#387×C₁₃₇	1	4	yes	—
385	C₄	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
386	C₄	C₂×#123×C₁₃₇	1	1	yes	characteristic
387	C₄	C₂×#125×C₁₃₇	1	1	yes	characteristic
388	C₄	C₂×#126×C₁₃₇	1	1	yes	characteristic
389	C₂	—	2	4	no	—
390	C₂	C₂×#387×C₁₃₇	1	1	yes	characteristic
391	C₂	#2924×C₁₃₇	1	2	yes	—
392	C₂	#2931×C₁₃₇	1	1	yes	characteristic
393	C₂	#2932×C₁₃₇	1	1	yes	characteristic
394	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
197. #21025	C₁₃₇	direct (N × H)
198. C₁₃₇	#21025	direct (N × H)
202. #1917	C₂×C₁₃₇	semidirect
203. #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×#405×C₁₃₇	2
#2285×C₁₃₇	2
#1917×C₁₃₇	2
#1916×C₁₃₇	2
#1729×C₁₃₇	2
#1728×C₁₃₇	2
C₂×#336×C₁₃₇	2
#21025	137

Subgroups — C137×#21025 #46870411

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#21025 #46870411