Subgroups — C₁₃₇×#18070 #46867456

Order 35072.

600 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3168×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2969×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	#1590×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#1584×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1581×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	C₈×SD₁₆×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1564×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1482×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	C₈×M₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#529×C₁₃₇	C₂²	1	2	yes	—
11	#499×C₁₃₇	C₄	1	1	yes	characteristic
12	#495×C₁₃₇	C₄	1	1	yes	characteristic
13	#488×C₁₃₇	C₄	1	2	yes	—
14	#467×C₁₃₇	C₄	1	1	yes	characteristic
15	#466×C₁₃₇	C₄	1	1	yes	characteristic
16	#465×C₁₃₇	C₄	1	2	yes	—
17	#446×C₁₃₇	C₂²	1	2	yes	—
18	C₈×Q₈×C₁₃₇	C₂²	1	2	yes	—
19	C₄×Q₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₄×SD₁₆×C₁₃₇	C₂²	1	2	yes	—
21	C₄×D₈×C₁₃₇	C₂²	1	1	yes	characteristic
22	#436×C₁₃₇	—	2	2	no	—
23	#436×C₁₃₇	C₂²	1	2	yes	—
24	#435×C₁₃₇	—	2	2	no	—
25	C₈×D₄×C₁₃₇	C₂²	1	2	yes	—
26	#433×C₁₃₇	—	2	2	no	—
27	#431×C₁₃₇	C₂²	1	2	yes	—
28	#431×C₁₃₇	C₂²	1	1	yes	characteristic
29	#405×C₁₃₇	—	2	2	no	—
30	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
32	#335×C₁₃₇	C₂²	1	2	yes	—
33	#334×C₁₃₇	C₂²	1	1	yes	characteristic
34	#334×C₁₃₇	C₂²	1	1	yes	characteristic
35	Q₈⋊C₈×C₁₃₇	C₂²	1	2	yes	—
36	Q₈⋊C₈×C₁₃₇	C₂²	1	2	yes	—
37	D₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
38	D₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
39	#322×C₁₃₇	C₂²	1	2	yes	—
40	C₈²×C₁₃₇	C₂²	1	2	yes	—
41	C₂×Q₁₆×C₁₃₇	C₂×C₄	1	1	yes	characteristic
42	C₂×SD₁₆×C₁₃₇	C₂×C₄	1	2	yes	—
43	C₂×D₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
44	C₂×M₁₆×C₁₃₇	—	2	2	no	—
45	C₂×M₁₆×C₁₃₇	D₄	1	2	yes	—
46	C₂²×C₈×C₁₃₇	—	2	2	no	—
47	C₂²×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
49	#126×C₁₃₇	—	2	2	no	—
50	#125×C₁₃₇	C₂×C₄	1	2	yes	—
51	#124×C₁₃₇	C₂×C₄	1	2	yes	—
52	#123×C₁₃₇	—	2	2	no	—
53	C₂²⋊Q₈×C₁₃₇	C₂×C₄	1	2	yes	—
54	#121×C₁₃₇	C₂×C₄	1	2	yes	—
55	C₄×Q₈×C₁₃₇	C₂³	1	2	yes	—
56	C₄×D₄×C₁₃₇	—	2	2	no	—
57	C₄×D₄×C₁₃₇	C₂³	1	2	yes	—
58	#117×C₁₃₇	—	2	2	no	—
59	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
60	#107×C₁₃₇	C₂×C₄	1	1	yes	characteristic
61	#107×C₁₃₇	C₂×C₄	1	1	yes	characteristic
62	#106×C₁₃₇	C₂×C₄	1	2	yes	—
63	C₄⋊C₈×C₁₃₇	—	2	2	no	—
64	C₄⋊C₈×C₁₃₇	—	2	2	no	—
65	C₄⋊C₈×C₁₃₇	—	2	1	no	—
66	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
67	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
68	#103×C₁₃₇	C₂×C₄	1	2	yes	—
69	#103×C₁₃₇	C₂×C₄	1	2	yes	—
70	#102×C₁₃₇	C₂×C₄	1	2	yes	—
71	#102×C₁₃₇	C₂×C₄	1	2	yes	—
72	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
73	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
74	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
75	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
76	#97×C₁₃₇	—	2	2	no	—
77	#97×C₁₃₇	D₄	1	1	yes	characteristic
78	#97×C₁₃₇	D₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃₇	—	2	2	no	—
80	C₄×C₈×C₁₃₇	—	2	2	no	—
81	C₄×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₁₃₇	C₂³	1	2	yes	—
84	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₁₃₇	C₂³	1	2	yes	—
87	C₂×Q₈×C₁₃₇	C₂²×C₄	1	2	yes	—
88	C₂×D₄×C₁₃₇	—	2	2	no	—
89	C₂×D₄×C₁₃₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₃₇	—	2	2	no	—
91	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
94	Q₁₆×C₁₃₇	—	4	1	no	—
95	SD₁₆×C₁₃₇	—	2	4	no	—
96	D₈×C₁₃₇	—	4	1	no	—
97	M₁₆×C₁₃₇	—	2	4	no	—
98	M₁₆×C₁₃₇	—	4	4	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	—	4	1	no	—
104	C₂×C₈×C₁₃₇	—	4	4	no	—
105	C₂×C₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
110	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
111	C₄⋊C₄×C₁₃₇	—	2	2	no	—
112	C₄⋊C₄×C₁₃₇	—	2	2	no	—
113	C₄⋊C₄×C₁₃₇	—	2	2	no	—
114	C₄⋊C₄×C₁₃₇	—	2	2	no	—
115	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
116	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
117	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
118	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
119	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
120	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
121	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
122	C₄²×C₁₃₇	—	2	2	no	—
123	C₄²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₃₇	#41	1	1	yes	characteristic
126	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
127	C₂³×C₁₃₇	—	2	2	no	—
128	C₂³×C₁₃₇	C₄×D₄	1	1	yes	characteristic
129	Q₈×C₁₃₇	—	2	2	no	—
130	Q₈×C₁₃₇	—	2	2	no	—
131	D₄×C₁₃₇	—	2	2	no	—
132	D₄×C₁₃₇	—	2	2	no	—
133	D₄×C₁₃₇	—	8	2	no	—
134	C₂×C₄×C₁₃₇	—	2	1	no	—
135	C₂×C₄×C₁₃₇	—	2	1	no	—
136	C₂×C₄×C₁₃₇	—	2	2	no	—
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	—	4	1	no	—
141	C₂×C₄×C₁₃₇	—	4	2	no	—
142	C₂×C₄×C₁₃₇	—	4	2	no	—
143	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
149	C₈×C₁₃₇	—	2	1	no	—
150	C₈×C₁₃₇	—	2	1	no	—
151	C₈×C₁₃₇	—	2	1	no	—
152	C₈×C₁₃₇	—	2	2	no	—
153	C₈×C₁₃₇	—	4	2	no	—
154	C₈×C₁₃₇	—	4	2	no	—
155	C₈×C₁₃₇	—	4	2	no	—
156	C₈×C₁₃₇	#131	1	2	yes	—
157	C₈×C₁₃₇	#135	1	4	yes	—
158	C₂²×C₁₃₇	—	2	1	no	—
159	C₂²×C₁₃₇	—	2	1	no	—
160	C₂²×C₁₃₇	—	2	1	no	—
161	C₂²×C₁₃₇	—	4	2	no	—
162	C₂²×C₁₃₇	—	4	2	no	—
163	C₂²×C₁₃₇	—	4	2	no	—
164	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
165	C₄×C₁₃₇	—	2	1	no	—
166	C₄×C₁₃₇	—	2	1	no	—
167	C₄×C₁₃₇	—	2	1	no	—
168	C₄×C₁₃₇	—	2	1	no	—
169	C₄×C₁₃₇	—	4	2	no	—
170	C₄×C₁₃₇	—	4	2	no	—
171	C₄×C₁₃₇	—	4	2	no	—
172	C₄×C₁₃₇	C₂×#131	1	1	yes	characteristic
173	C₄×C₁₃₇	#568	1	1	yes	characteristic
174	C₄×C₁₃₇	C₂×#135	1	2	yes	—
175	C₂×C₁₃₇	—	4	1	no	—
176	C₂×C₁₃₇	—	8	2	no	—
177	C₂×C₁₃₇	#2935	1	1	yes	characteristic
178	C₂×C₁₃₇	C₄×#135	1	1	yes	characteristic
179	C₂×C₁₃₇	#2957	1	1	yes	characteristic
180	#18070	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₁₃₇	#18070	1	1	yes	characteristic, direct product factor, Sylow
182	#3168	C₂×C₁₃₇	1	1	yes	characteristic
183	#2969	C₂×C₁₃₇	1	2	yes	complemented
184	#1590	C₂×C₁₃₇	1	2	yes	complemented
185	#1584	C₂×C₁₃₇	1	2	yes	complemented
186	#1581	C₂×C₁₃₇	1	2	yes	complemented
187	C₈×SD₁₆	C₂×C₁₃₇	1	2	yes	complemented
188	#1564	C₂×C₁₃₇	1	1	yes	characteristic, complemented
189	#1482	C₂×C₁₃₇	1	2	yes	complemented
190	C₈×M₁₆	C₂×C₁₃₇	1	1	yes	characteristic, complemented
191	#529	C₂²×C₁₃₇	1	2	yes	—
192	#499	C₄×C₁₃₇	1	1	yes	characteristic
193	#495	C₄×C₁₃₇	1	1	yes	characteristic
194	#488	C₄×C₁₃₇	1	2	yes	—
195	#467	C₄×C₁₃₇	1	1	yes	characteristic
196	#466	C₄×C₁₃₇	1	1	yes	characteristic
197	#465	C₄×C₁₃₇	1	2	yes	—
198	#446	C₂²×C₁₃₇	1	2	yes	—
199	C₈×Q₈	C₂²×C₁₃₇	1	2	yes	—
200	C₄×Q₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
201	C₄×SD₁₆	C₂²×C₁₃₇	1	2	yes	—
202	C₄×D₈	C₂²×C₁₃₇	1	1	yes	characteristic
203	#436	—	2	2	no	—
204	#436	C₂²×C₁₃₇	1	2	yes	—
205	#435	—	2	2	no	—
206	C₈×D₄	C₂²×C₁₃₇	1	2	yes	—
207	#433	—	2	2	no	—
208	#431	C₂²×C₁₃₇	1	2	yes	—
209	#431	C₂²×C₁₃₇	1	1	yes	characteristic
210	#405	—	2	2	no	—
211	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
212	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
213	#335	C₂²×C₁₃₇	1	2	yes	—
214	#334	C₂²×C₁₃₇	1	1	yes	characteristic
215	#334	C₂²×C₁₃₇	1	1	yes	characteristic
216	Q₈⋊C₈	C₂²×C₁₃₇	1	2	yes	—
217	Q₈⋊C₈	C₂²×C₁₃₇	1	2	yes	—
218	D₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
219	D₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
220	#322	C₂²×C₁₃₇	1	2	yes	—
221	C₈²	C₂²×C₁₃₇	1	2	yes	—
222	C₂×Q₁₆	C₂×C₄×C₁₃₇	1	1	yes	characteristic
223	C₂×SD₁₆	C₂×C₄×C₁₃₇	1	2	yes	—
224	C₂×D₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
225	C₂×M₁₆	—	2	2	no	—
226	C₂×M₁₆	D₄×C₁₃₇	1	2	yes	—
227	C₂²×C₈	—	2	2	no	—
228	C₂²×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
229	C₂²×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
230	#126	—	2	2	no	—
231	#125	C₂×C₄×C₁₃₇	1	2	yes	—
232	#124	C₂×C₄×C₁₃₇	1	2	yes	—
233	#123	—	2	2	no	—
234	C₂²⋊Q₈	C₂×C₄×C₁₃₇	1	2	yes	—
235	#121	C₂×C₄×C₁₃₇	1	2	yes	—
236	C₄×Q₈	C₂³×C₁₃₇	1	2	yes	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	C₂³×C₁₃₇	1	2	yes	—
239	#117	—	2	2	no	—
240	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
241	#107	C₂×C₄×C₁₃₇	1	1	yes	characteristic
242	#107	C₂×C₄×C₁₃₇	1	1	yes	characteristic
243	#106	C₂×C₄×C₁₃₇	1	2	yes	—
244	C₄⋊C₈	—	2	2	no	—
245	C₄⋊C₈	—	2	2	no	—
246	C₄⋊C₈	—	2	1	no	—
247	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
248	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
249	#103	C₂×C₄×C₁₃₇	1	2	yes	—
250	#103	C₂×C₄×C₁₃₇	1	2	yes	—
251	#102	C₂×C₄×C₁₃₇	1	2	yes	—
252	#102	C₂×C₄×C₁₃₇	1	2	yes	—
253	C₂²⋊C₈	—	2	2	no	—
254	C₂²⋊C₈	—	2	1	no	—
255	C₂²⋊C₈	—	2	2	no	—
256	C₂²⋊C₈	—	2	2	no	—
257	#97	—	2	2	no	—
258	#97	D₄×C₁₃₇	1	1	yes	characteristic
259	#97	D₄×C₁₃₇	1	1	yes	characteristic
260	C₄×C₈	—	2	2	no	—
261	C₄×C₈	—	2	2	no	—
262	C₄×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
263	C₄×C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
264	C₄×C₈	C₂³×C₁₃₇	1	2	yes	—
265	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
266	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
267	C₄×C₈	C₂³×C₁₃₇	1	2	yes	—
268	C₂×Q₈	C₂²×C₄×C₁₃₇	1	2	yes	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	C₂²×C₄×C₁₃₇	1	2	yes	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
274	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
275	Q₁₆	—	4	1	no	—
276	SD₁₆	—	2	4	no	—
277	D₈	—	4	1	no	—
278	M₁₆	—	2	4	no	—
279	M₁₆	—	4	4	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	—	4	1	no	—
285	C₂×C₈	—	4	4	no	—
286	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
287	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
288	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
289	C₂×C₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
290	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
291	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
297	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
298	C₂²⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	2	2	no	—
300	C₂²⋊C₄	—	2	2	no	—
301	C₂²⋊C₄	—	2	2	no	—
302	C₂²⋊C₄	—	2	2	no	—
303	C₄²	—	2	2	no	—
304	C₄²	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
305	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
306	C₄²	#41×C₁₃₇	1	1	yes	characteristic
307	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
308	C₂³	—	2	2	no	—
309	C₂³	C₄×D₄×C₁₃₇	1	1	yes	characteristic
310	Q₈	—	2	2	no	—
311	Q₈	—	2	2	no	—
312	D₄	—	2	2	no	—
313	D₄	—	2	2	no	—
314	D₄	—	8	2	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
325	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
326	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
327	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
328	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
329	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
330	C₈	—	2	1	no	—
331	C₈	—	2	1	no	—
332	C₈	—	2	1	no	—
333	C₈	—	2	2	no	—
334	C₈	—	4	2	no	—
335	C₈	—	4	2	no	—
336	C₈	—	4	2	no	—
337	C₈	#131×C₁₃₇	1	2	yes	—
338	C₈	#135×C₁₃₇	1	4	yes	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
346	C₄	—	2	1	no	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	4	2	no	—
351	C₄	—	4	2	no	—
352	C₄	—	4	2	no	—
353	C₄	C₂×#131×C₁₃₇	1	1	yes	characteristic
354	C₄	#568×C₁₃₇	1	1	yes	characteristic
355	C₄	C₂×#135×C₁₃₇	1	2	yes	—
356	C₂	—	4	1	no	—
357	C₂	—	8	2	no	—
358	C₂	#2935×C₁₃₇	1	1	yes	characteristic
359	C₂	C₄×#135×C₁₃₇	1	1	yes	characteristic
360	C₂	#2957×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	#466×C₁₃₇	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₇ ◁ C₄×M₁₆×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2969×C₁₃₇	C₂	semidirect
3. #1590×C₁₃₇	C₂	semidirect
4. #1584×C₁₃₇	C₂	semidirect
5. #1581×C₁₃₇	C₂	semidirect
6. C₈×SD₁₆×C₁₃₇	C₂	semidirect
7. #1564×C₁₃₇	C₂	semidirect
8. #1482×C₁₃₇	C₂	semidirect
9. C₈×M₁₆×C₁₃₇	C₂	semidirect
180. #18070	C₁₃₇	direct (N × H)
181. C₁₃₇	#18070	direct (N × H)
183. #2969	C₂×C₁₃₇	semidirect
184. #1590	C₂×C₁₃₇	semidirect
185. #1584	C₂×C₁₃₇	semidirect
186. #1581	C₂×C₁₃₇	semidirect
187. C₈×SD₁₆	C₂×C₁₃₇	semidirect
188. #1564	C₂×C₁₃₇	semidirect
189. #1482	C₂×C₁₃₇	semidirect
190. C₈×M₁₆	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3168×C₁₃₇	2
#2969×C₁₃₇	2
#1590×C₁₃₇	2
#1584×C₁₃₇	2
#1581×C₁₃₇	2
C₈×SD₁₆×C₁₃₇	2
#1564×C₁₃₇	2
#1482×C₁₃₇	2
C₈×M₁₆×C₁₃₇	2
#18070	137

Subgroups — C137×#18070 #46867456

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#18070 #46867456