Subgroups — C₁₃₇×#17924 #46867310

Order 35072.

638 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3101×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2985×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2972×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1585×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1582×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	SD₁₆⋊C₈×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	C₈×SD₁₆×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1572×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1490×C₁₃₇	C₂	1	1	yes	maximal, characteristic
10	#1485×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#1453×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#533×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
14	#483×C₁₃₇	C₄	1	2	yes	—
15	#476×C₁₃₇	C₄	1	2	yes	—
16	#461×C₁₃₇	C₄	1	2	yes	—
17	#450×C₁₃₇	C₄	1	2	yes	—
18	#446×C₁₃₇	—	2	2	no	—
19	#446×C₁₃₇	C₂²	1	2	yes	complemented
20	C₈×Q₈×C₁₃₇	C₂²	1	2	yes	complemented
21	C₄×SD₁₆×C₁₃₇	C₂²	1	2	yes	—
22	C₄×SD₁₆×C₁₃₇	C₂²	1	2	yes	—
23	C₈×D₄×C₁₃₇	—	2	2	no	—
24	C₈×D₄×C₁₃₇	C₂²	1	2	yes	—
25	C₈×D₄×C₁₃₇	C₂²	1	2	yes	—
26	#433×C₁₃₇	—	2	2	no	—
27	#432×C₁₃₇	C₂²	1	1	yes	characteristic
28	#431×C₁₃₇	C₂²	1	1	yes	characteristic
29	#431×C₁₃₇	C₂²	1	1	yes	characteristic
30	#431×C₁₃₇	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₈×C₁₃₇	—	2	2	no	—
32	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
33	#335×C₁₃₇	C₂²	1	2	yes	complemented
34	#334×C₁₃₇	C₂²	1	2	yes	complemented
35	Q₈⋊C₈×C₁₃₇	C₂²	1	2	yes	complemented
36	Q₈⋊C₈×C₁₃₇	C₂²	1	2	yes	complemented
37	D₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
38	D₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
39	#322×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
40	#322×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
41	#322×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
42	C₈²×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
43	C₂²×D₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃₇	—	2	1	no	—
45	C₂×SD₁₆×C₁₃₇	C₂×C₄	1	2	yes	—
46	C₂×SD₁₆×C₁₃₇	C₂×C₄	1	2	yes	—
47	C₂×M₁₆×C₁₃₇	—	2	1	no	—
48	C₂²×C₈×C₁₃₇	—	2	2	no	—
49	C₂²×C₈×C₁₃₇	—	2	2	no	—
50	C₄⋊Q₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
51	C₄⋊Q₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
52	#125×C₁₃₇	—	2	1	no	—
53	C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
54	C₂²⋊Q₈×C₁₃₇	C₂×C₄	1	2	yes	—
55	C₄×Q₈×C₁₃₇	—	2	1	no	—
56	C₄×Q₈×C₁₃₇	C₂³	1	2	yes	—
57	C₄×D₄×C₁₃₇	—	2	1	no	—
58	C₄×D₄×C₁₃₇	—	2	1	no	—
59	C₄×D₄×C₁₃₇	C₂×C₄	1	2	yes	—
60	C₄×D₄×C₁₃₇	C₂³	1	2	yes	—
61	#117×C₁₃₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
64	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
65	#106×C₁₃₇	C₂×C₄	1	2	yes	—
66	#106×C₁₃₇	C₂×C₄	1	2	yes	—
67	C₄⋊C₈×C₁₃₇	—	2	2	no	—
68	C₄⋊C₈×C₁₃₇	—	2	2	no	—
69	C₄⋊C₈×C₁₃₇	C₂×C₄	1	2	yes	—
70	C₄⋊C₈×C₁₃₇	D₄	1	2	yes	—
71	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
72	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
73	#103×C₁₃₇	C₂×C₄	1	2	yes	—
74	#103×C₁₃₇	C₂×C₄	1	2	yes	—
75	#102×C₁₃₇	C₂×C₄	1	2	yes	—
76	#102×C₁₃₇	C₂×C₄	1	2	yes	—
77	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
78	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
79	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
80	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
81	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	2	yes	—
82	C₂²⋊C₈×C₁₃₇	D₄	1	2	yes	—
83	#97×C₁₃₇	—	2	2	no	—
84	#97×C₁₃₇	—	2	1	no	—
85	#97×C₁₃₇	—	2	1	no	—
86	C₄×C₈×C₁₃₇	—	2	2	no	—
87	C₄×C₈×C₁₃₇	—	2	1	no	—
88	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
94	C₂⁴×C₁₃₇	—	2	1	no	—
95	C₂×Q₈×C₁₃₇	—	2	1	no	—
96	C₂×Q₈×C₁₃₇	C₂²×C₄	1	2	yes	—
97	C₂×D₄×C₁₃₇	—	2	4	no	—
98	C₂×D₄×C₁₃₇	—	2	1	no	—
99	C₂×D₄×C₁₃₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₃₇	—	2	1	no	—
101	C₂²×C₄×C₁₃₇	—	2	2	no	—
102	C₂²×C₄×C₁₃₇	—	2	2	no	—
103	C₂²×C₄×C₁₃₇	—	8	2	no	—
104	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
107	SD₁₆×C₁₃₇	—	2	4	no	—
108	SD₁₆×C₁₃₇	—	2	4	no	—
109	M₁₆×C₁₃₇	—	4	2	no	—
110	C₂×C₈×C₁₃₇	—	2	1	no	—
111	C₂×C₈×C₁₃₇	—	2	2	no	—
112	C₂×C₈×C₁₃₇	—	2	2	no	—
113	C₂×C₈×C₁₃₇	—	2	1	no	—
114	C₂×C₈×C₁₃₇	—	8	2	no	—
115	C₂×C₈×C₁₃₇	—	8	2	no	—
116	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
120	C₄⋊C₄×C₁₃₇	—	2	1	no	—
121	C₄⋊C₄×C₁₃₇	—	2	1	no	—
122	C₄⋊C₄×C₁₃₇	—	2	1	no	—
123	C₄⋊C₄×C₁₃₇	—	2	1	no	—
124	C₄⋊C₄×C₁₃₇	—	2	2	no	—
125	C₄⋊C₄×C₁₃₇	—	2	2	no	—
126	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
127	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
128	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
129	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
130	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
131	C₄²×C₁₃₇	—	2	2	no	—
132	C₄²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₁₃₇	#41	1	1	yes	characteristic
135	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
136	C₂³×C₁₃₇	—	2	4	no	—
137	C₂³×C₁₃₇	—	2	2	no	—
138	C₂³×C₁₃₇	—	8	1	no	—
139	C₂³×C₁₃₇	—	8	1	no	—
140	C₂³×C₁₃₇	C₄×D₄	1	1	yes	characteristic
141	Q₈×C₁₃₇	—	2	2	no	—
142	Q₈×C₁₃₇	—	2	2	no	—
143	Q₈×C₁₃₇	—	8	1	no	—
144	D₄×C₁₃₇	—	2	4	no	—
145	D₄×C₁₃₇	—	2	2	no	—
146	D₄×C₁₃₇	#131	1	4	yes	—
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	—	4	1	no	—
153	C₂×C₄×C₁₃₇	—	4	2	no	—
154	C₂×C₄×C₁₃₇	—	4	2	no	—
155	C₂×C₄×C₁₃₇	—	8	2	no	—
156	C₂×C₄×C₁₃₇	—	8	1	no	—
157	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
163	C₈×C₁₃₇	—	2	2	no	—
164	C₈×C₁₃₇	—	2	2	no	—
165	C₈×C₁₃₇	—	2	2	no	—
166	C₈×C₁₃₇	—	2	2	no	—
167	C₈×C₁₃₇	—	2	2	no	—
168	C₈×C₁₃₇	—	4	1	no	—
169	C₈×C₁₃₇	—	4	2	no	—
170	C₈×C₁₃₇	—	4	2	no	—
171	C₂²×C₁₃₇	—	2	1	no	—
172	C₂²×C₁₃₇	—	2	4	no	—
173	C₂²×C₁₃₇	—	2	1	no	—
174	C₂²×C₁₃₇	—	2	1	no	—
175	C₂²×C₁₃₇	—	4	2	no	—
176	C₂²×C₁₃₇	—	4	2	no	—
177	C₂²×C₁₃₇	—	8	4	no	—
178	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
179	C₄×C₁₃₇	—	2	1	no	—
180	C₄×C₁₃₇	—	2	1	no	—
181	C₄×C₁₃₇	—	2	1	no	—
182	C₄×C₁₃₇	—	2	1	no	—
183	C₄×C₁₃₇	—	4	2	no	—
184	C₄×C₁₃₇	—	4	2	no	—
185	C₄×C₁₃₇	—	4	2	no	—
186	C₄×C₁₃₇	C₂×#131	1	2	yes	—
187	C₄×C₁₃₇	#577	1	2	yes	—
188	C₂×C₁₃₇	—	4	1	no	—
189	C₂×C₁₃₇	—	4	4	no	—
190	C₂×C₁₃₇	#2929	1	1	yes	characteristic
191	C₂×C₁₃₇	#2949	1	1	yes	characteristic
192	C₂×C₁₃₇	#2956	1	1	yes	characteristic
193	#17924	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₁₃₇	#17924	1	1	yes	characteristic, direct product factor, Sylow
195	#3101	C₂×C₁₃₇	1	1	yes	characteristic
196	#2985	C₂×C₁₃₇	1	1	yes	characteristic, complemented
197	#2972	C₂×C₁₃₇	1	1	yes	characteristic
198	#1585	C₂×C₁₃₇	1	2	yes	complemented
199	#1582	C₂×C₁₃₇	1	2	yes	complemented
200	SD₁₆⋊C₈	C₂×C₁₃₇	1	2	yes	complemented
201	C₈×SD₁₆	C₂×C₁₃₇	1	2	yes	complemented
202	#1572	C₂×C₁₃₇	1	1	yes	characteristic, complemented
203	#1490	C₂×C₁₃₇	1	1	yes	characteristic
204	#1485	C₂×C₁₃₇	1	1	yes	characteristic, complemented
205	#1453	C₂×C₁₃₇	1	1	yes	characteristic, complemented
206	#533	C₂²×C₁₃₇	1	1	yes	characteristic
207	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
208	#483	C₄×C₁₃₇	1	2	yes	—
209	#476	C₄×C₁₃₇	1	2	yes	—
210	#461	C₄×C₁₃₇	1	2	yes	—
211	#450	C₄×C₁₃₇	1	2	yes	—
212	#446	—	2	2	no	—
213	#446	C₂²×C₁₃₇	1	2	yes	complemented
214	C₈×Q₈	C₂²×C₁₃₇	1	2	yes	complemented
215	C₄×SD₁₆	C₂²×C₁₃₇	1	2	yes	—
216	C₄×SD₁₆	C₂²×C₁₃₇	1	2	yes	—
217	C₈×D₄	—	2	2	no	—
218	C₈×D₄	C₂²×C₁₃₇	1	2	yes	—
219	C₈×D₄	C₂²×C₁₃₇	1	2	yes	—
220	#433	—	2	2	no	—
221	#432	C₂²×C₁₃₇	1	1	yes	characteristic
222	#431	C₂²×C₁₃₇	1	1	yes	characteristic
223	#431	C₂²×C₁₃₇	1	1	yes	characteristic
224	#431	C₂²×C₁₃₇	1	1	yes	characteristic
225	C₂×C₂²⋊C₈	—	2	2	no	—
226	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
227	#335	C₂²×C₁₃₇	1	2	yes	complemented
228	#334	C₂²×C₁₃₇	1	2	yes	complemented
229	Q₈⋊C₈	C₂²×C₁₃₇	1	2	yes	complemented
230	Q₈⋊C₈	C₂²×C₁₃₇	1	2	yes	complemented
231	D₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
232	D₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
233	#322	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
234	#322	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
235	#322	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
236	C₈²	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
237	C₂²×D₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
238	C₂³×C₄	—	2	1	no	—
239	C₂×SD₁₆	C₂×C₄×C₁₃₇	1	2	yes	—
240	C₂×SD₁₆	C₂×C₄×C₁₃₇	1	2	yes	—
241	C₂×M₁₆	—	2	1	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₄⋊Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
245	C₄⋊Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
246	#125	—	2	1	no	—
247	C₂²⋊Q₈	—	2	1	no	—
248	C₂²⋊Q₈	C₂×C₄×C₁₃₇	1	2	yes	—
249	C₄×Q₈	—	2	1	no	—
250	C₄×Q₈	C₂³×C₁₃₇	1	2	yes	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	C₂×C₄×C₁₃₇	1	2	yes	—
254	C₄×D₄	C₂³×C₁₃₇	1	2	yes	—
255	#117	—	2	1	no	—
256	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	—	2	1	no	—
258	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
259	#106	C₂×C₄×C₁₃₇	1	2	yes	—
260	#106	C₂×C₄×C₁₃₇	1	2	yes	—
261	C₄⋊C₈	—	2	2	no	—
262	C₄⋊C₈	—	2	2	no	—
263	C₄⋊C₈	C₂×C₄×C₁₃₇	1	2	yes	—
264	C₄⋊C₈	D₄×C₁₃₇	1	2	yes	—
265	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
266	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
267	#103	C₂×C₄×C₁₃₇	1	2	yes	—
268	#103	C₂×C₄×C₁₃₇	1	2	yes	—
269	#102	C₂×C₄×C₁₃₇	1	2	yes	—
270	#102	C₂×C₄×C₁₃₇	1	2	yes	—
271	C₂²⋊C₈	—	2	1	no	—
272	C₂²⋊C₈	—	2	1	no	—
273	C₂²⋊C₈	—	2	2	no	—
274	C₂²⋊C₈	—	2	2	no	—
275	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	2	yes	—
276	C₂²⋊C₈	D₄×C₁₃₇	1	2	yes	—
277	#97	—	2	2	no	—
278	#97	—	2	1	no	—
279	#97	—	2	1	no	—
280	C₄×C₈	—	2	2	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
283	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
286	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
287	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
288	C₂⁴	—	2	1	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	C₂²×C₄×C₁₃₇	1	2	yes	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	C₂²×C₄×C₁₃₇	1	2	yes	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	8	2	no	—
298	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
300	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
301	SD₁₆	—	2	4	no	—
302	SD₁₆	—	2	4	no	—
303	M₁₆	—	4	2	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	—	8	2	no	—
309	C₂×C₈	—	8	2	no	—
310	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
311	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
312	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
313	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
321	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
327	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
328	C₄²	#41×C₁₃₇	1	1	yes	characteristic
329	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
330	C₂³	—	2	4	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	8	1	no	—
333	C₂³	—	8	1	no	—
334	C₂³	C₄×D₄×C₁₃₇	1	1	yes	characteristic
335	Q₈	—	2	2	no	—
336	Q₈	—	2	2	no	—
337	Q₈	—	8	1	no	—
338	D₄	—	2	4	no	—
339	D₄	—	2	2	no	—
340	D₄	#131×C₁₃₇	1	4	yes	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	8	1	no	—
351	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
352	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
353	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
354	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
356	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
357	C₈	—	2	2	no	—
358	C₈	—	2	2	no	—
359	C₈	—	2	2	no	—
360	C₈	—	2	2	no	—
361	C₈	—	2	2	no	—
362	C₈	—	4	1	no	—
363	C₈	—	4	2	no	—
364	C₈	—	4	2	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	4	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	8	4	no	—
372	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₄	C₂×#131×C₁₃₇	1	2	yes	—
381	C₄	#577×C₁₃₇	1	2	yes	—
382	C₂	—	4	1	no	—
383	C₂	—	4	4	no	—
384	C₂	#2929×C₁₃₇	1	1	yes	characteristic
385	C₂	#2949×C₁₃₇	1	1	yes	characteristic
386	C₂	#2956×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
socle	C₂²×C₁₃₇	C₂×C₄×D₄
prime radical	C₂²×D₄×C₁₃₇	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₇ ◁ #431×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2985×C₁₃₇	C₂	semidirect
4. #1585×C₁₃₇	C₂	semidirect
5. #1582×C₁₃₇	C₂	semidirect
6. SD₁₆⋊C₈×C₁₃₇	C₂	semidirect
7. C₈×SD₁₆×C₁₃₇	C₂	semidirect
8. #1572×C₁₃₇	C₂	semidirect
10. #1485×C₁₃₇	C₂	semidirect
11. #1453×C₁₃₇	C₂	semidirect
19. #446×C₁₃₇	C₂²	semidirect
20. C₈×Q₈×C₁₃₇	C₂²	semidirect
33. #335×C₁₃₇	C₂²	semidirect
34. #334×C₁₃₇	C₂²	semidirect
35. Q₈⋊C₈×C₁₃₇	C₂²	semidirect
36. Q₈⋊C₈×C₁₃₇	C₂²	semidirect
39. #322×C₁₃₇	C₂²	semidirect
40. #322×C₁₃₇	C₂²	semidirect
41. #322×C₁₃₇	C₂²	semidirect
42. C₈²×C₁₃₇	C₂²	semidirect
193. #17924	C₁₃₇	direct (N × H)
194. C₁₃₇	#17924	direct (N × H)
196. #2985	C₂×C₁₃₇	semidirect
198. #1585	C₂×C₁₃₇	semidirect
199. #1582	C₂×C₁₃₇	semidirect
200. SD₁₆⋊C₈	C₂×C₁₃₇	semidirect
201. C₈×SD₁₆	C₂×C₁₃₇	semidirect
202. #1572	C₂×C₁₃₇	semidirect
204. #1485	C₂×C₁₃₇	semidirect
205. #1453	C₂×C₁₃₇	semidirect
213. #446	C₂²×C₁₃₇	semidirect
214. C₈×Q₈	C₂²×C₁₃₇	semidirect
227. #335	C₂²×C₁₃₇	semidirect
228. #334	C₂²×C₁₃₇	semidirect
229. Q₈⋊C₈	C₂²×C₁₃₇	semidirect
230. Q₈⋊C₈	C₂²×C₁₃₇	semidirect
233. #322	C₂²×C₁₃₇	semidirect
234. #322	C₂²×C₁₃₇	semidirect
235. #322	C₂²×C₁₃₇	semidirect
236. C₈²	C₂²×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3101×C₁₃₇	2
#2985×C₁₃₇	2
#2972×C₁₃₇	2
#1585×C₁₃₇	2
#1582×C₁₃₇	2
SD₁₆⋊C₈×C₁₃₇	2
C₈×SD₁₆×C₁₃₇	2
#1572×C₁₃₇	2
#1490×C₁₃₇	2
#1485×C₁₃₇	2
#1453×C₁₃₇	2
#17924	137

Subgroups — C137×#17924 #46867310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#17924 #46867310