Subgroups — C₁₃₇×#21644 #46871030

Order 35072.

890 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#486×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2331×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2328×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1993×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1961×C₁₃₇	C₂	1	1	yes	maximal, characteristic
6	#1936×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1934×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1835×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1762×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	C₄×#102×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	#1726×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃₇	C₂²	1	2	yes	—
15	#486×C₁₃₇	C₄	1	8	yes	complemented
16	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
17	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
18	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
19	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
20	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
26	#391×C₁₃₇	—	2	2	no	—
27	#390×C₁₃₇	C₂²	1	2	yes	—
28	#389×C₁₃₇	C₂²	1	2	yes	—
29	#387×C₁₃₇	—	2	2	no	—
30	#386×C₁₃₇	—	2	2	no	—
31	#386×C₁₃₇	—	2	2	no	—
32	#382×C₁₃₇	C₂²	1	1	yes	characteristic
33	#382×C₁₃₇	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
35	#376×C₁₃₇	C₂²	1	1	yes	characteristic
36	#340×C₁₃₇	C₂²	1	2	yes	—
37	#340×C₁₃₇	C₂²	1	2	yes	—
38	#340×C₁₃₇	C₂²	1	2	yes	—
39	#340×C₁₃₇	C₂²	1	2	yes	—
40	C₂²×Q₈×C₁₃₇	—	2	1	no	—
41	C₂²×D₄×C₁₃₇	—	2	1	no	—
42	C₂²×D₄×C₁₃₇	—	2	1	no	—
43	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₃₇	—	2	2	no	—
45	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
49	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
50	C₄⋊Q₈×C₁₃₇	C₂×C₄	1	4	yes	complemented
51	#127×C₁₃₇	—	2	2	no	—
52	#127×C₁₃₇	C₂×C₄	1	4	yes	—
53	C₄×D₄×C₁₃₇	—	2	4	no	—
54	C₄×D₄×C₁₃₇	—	2	4	no	—
55	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
63	C₂×C₄²×C₁₃₇	—	2	2	no	—
64	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
67	#102×C₁₃₇	—	2	4	no	—
68	#102×C₁₃₇	—	2	4	no	—
69	#102×C₁₃₇	C₂×C₄	1	8	yes	complemented
70	#102×C₁₃₇	C₂×C₄	1	8	yes	complemented
71	#97×C₁₃₇	—	2	2	no	—
72	#97×C₁₃₇	—	2	2	no	—
73	#97×C₁₃₇	—	2	2	no	—
74	C₄×C₈×C₁₃₇	—	2	2	no	—
75	C₄×C₈×C₁₃₇	—	2	2	no	—
76	C₄×C₈×C₁₃₇	C₂×C₄	1	4	yes	complemented
77	#95×C₁₃₇	—	2	2	no	—
78	#95×C₁₃₇	—	2	1	no	—
79	#95×C₁₃₇	—	2	1	no	—
80	#95×C₁₃₇	—	2	1	no	—
81	#95×C₁₃₇	—	2	1	no	—
82	#95×C₁₃₇	—	2	2	no	—
83	#95×C₁₃₇	D₄	1	2	yes	—
84	#95×C₁₃₇	D₄	1	2	yes	—
85	C₂⁴×C₁₃₇	—	2	2	no	—
86	C₂×Q₈×C₁₃₇	—	2	4	no	—
87	C₂×Q₈×C₁₃₇	—	8	2	no	—
88	C₂×D₄×C₁₃₇	—	2	4	no	—
89	C₂×D₄×C₁₃₇	—	2	4	no	—
90	C₂×D₄×C₁₃₇	—	2	2	no	—
91	C₂×D₄×C₁₃₇	—	2	2	no	—
92	C₂×D₄×C₁₃₇	—	2	2	no	—
93	C₂×D₄×C₁₃₇	—	2	2	no	—
94	C₂×D₄×C₁₃₇	—	2	2	no	—
95	C₂×D₄×C₁₃₇	—	8	2	no	—
96	C₂×D₄×C₁₃₇	—	8	2	no	—
97	C₂×D₄×C₁₃₇	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₁₃₇	—	2	2	no	—
99	C₂²×C₄×C₁₃₇	—	2	2	no	—
100	C₂²×C₄×C₁₃₇	—	2	2	no	—
101	C₂²×C₄×C₁₃₇	—	4	4	no	—
102	C₂²×C₄×C₁₃₇	—	8	2	no	—
103	C₂²×C₄×C₁₃₇	—	8	2	no	—
104	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₁₃₇	—	2	1	no	—
110	C₂×C₈×C₁₃₇	—	2	1	no	—
111	C₂×C₈×C₁₃₇	—	2	1	no	—
112	C₂×C₈×C₁₃₇	—	2	1	no	—
113	C₂×C₈×C₁₃₇	—	2	1	no	—
114	C₂×C₈×C₁₃₇	—	2	1	no	—
115	C₂×C₈×C₁₃₇	—	2	1	no	—
116	C₂×C₈×C₁₃₇	—	2	1	no	—
117	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₁₃₇	#41	1	2	yes	—
120	C₂×C₈×C₁₃₇	#41	1	2	yes	—
121	C₄⋊C₄×C₁₃₇	—	2	4	no	—
122	C₄⋊C₄×C₁₃₇	—	2	2	no	—
123	C₄⋊C₄×C₁₃₇	—	2	2	no	—
124	C₄⋊C₄×C₁₃₇	—	2	2	no	—
125	C₄⋊C₄×C₁₃₇	—	2	2	no	—
126	C₄⋊C₄×C₁₃₇	—	2	2	no	—
127	C₄⋊C₄×C₁₃₇	—	8	2	no	—
128	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
129	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
130	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
131	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
132	C₄²×C₁₃₇	—	2	1	no	—
133	C₄²×C₁₃₇	—	2	1	no	—
134	C₄²×C₁₃₇	—	8	2	no	—
135	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
136	C₄²×C₁₃₇	#41	1	2	yes	—
137	C₄²×C₁₃₇	#41	1	2	yes	—
138	C₄²×C₁₃₇	#41	1	2	yes	—
139	C₂³×C₁₃₇	—	2	4	no	—
140	C₂³×C₁₃₇	—	4	2	no	—
141	C₂³×C₁₃₇	—	4	2	no	—
142	C₂³×C₁₃₇	—	4	2	no	—
143	C₂³×C₁₃₇	—	4	2	no	—
144	C₂³×C₁₃₇	—	4	2	no	—
145	C₂³×C₁₃₇	—	4	2	no	—
146	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₁₃₇	—	8	4	no	—
148	D₄×C₁₃₇	—	2	4	no	—
149	D₄×C₁₃₇	—	2	4	no	—
150	D₄×C₁₃₇	—	4	2	no	—
151	D₄×C₁₃₇	—	4	2	no	—
152	D₄×C₁₃₇	—	8	4	no	—
153	D₄×C₁₃₇	—	8	4	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	4	no	—
159	C₂×C₄×C₁₃₇	—	2	2	no	—
160	C₂×C₄×C₁₃₇	—	2	2	no	—
161	C₂×C₄×C₁₃₇	—	2	2	no	—
162	C₂×C₄×C₁₃₇	—	4	2	no	—
163	C₂×C₄×C₁₃₇	—	4	2	no	—
164	C₂×C₄×C₁₃₇	—	4	2	no	—
165	C₂×C₄×C₁₃₇	—	4	2	no	—
166	C₂×C₄×C₁₃₇	—	4	2	no	—
167	C₂×C₄×C₁₃₇	—	4	2	no	—
168	C₂×C₄×C₁₃₇	—	4	2	no	—
169	C₂×C₄×C₁₃₇	—	4	2	no	—
170	C₂×C₄×C₁₃₇	—	8	8	no	—
171	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
172	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₁₃₇	#124	1	4	yes	—
174	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
180	C₈×C₁₃₇	—	2	2	no	—
181	C₈×C₁₃₇	—	2	2	no	—
182	C₈×C₁₃₇	—	2	2	no	—
183	C₈×C₁₃₇	—	2	2	no	—
184	C₂²×C₁₃₇	—	4	4	no	—
185	C₂²×C₁₃₇	—	4	4	no	—
186	C₂²×C₁₃₇	—	4	4	no	—
187	C₂²×C₁₃₇	—	8	2	no	—
188	C₂²×C₁₃₇	—	8	2	no	—
189	C₂²×C₁₃₇	—	8	2	no	—
190	C₂²×C₁₃₇	—	8	2	no	—
191	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
192	C₂²×C₁₃₇	C₂×#124	1	1	yes	characteristic
193	C₂²×C₁₃₇	#532	1	1	yes	characteristic
194	C₂²×C₁₃₇	#576	1	2	yes	—
195	C₂²×C₁₃₇	#577	1	2	yes	—
196	C₄×C₁₃₇	—	2	4	no	—
197	C₄×C₁₃₇	—	2	2	no	—
198	C₄×C₁₃₇	—	2	2	no	—
199	C₄×C₁₃₇	—	4	2	no	—
200	C₄×C₁₃₇	—	4	4	no	—
201	C₄×C₁₃₇	—	8	2	no	—
202	C₄×C₁₃₇	—	8	2	no	—
203	C₄×C₁₃₇	C₄×#41	1	1	yes	characteristic
204	C₄×C₁₃₇	C₄×#41	1	1	yes	characteristic
205	C₄×C₁₃₇	#529	1	1	yes	characteristic
206	C₄×C₁₃₇	#529	1	1	yes	characteristic
207	C₂×C₁₃₇	—	8	4	no	—
208	C₂×C₁₃₇	C₄×#124	1	1	yes	characteristic
209	C₂×C₁₃₇	#2948	1	1	yes	characteristic
210	C₂×C₁₃₇	#2949	1	1	yes	characteristic
211	C₂×C₁₃₇	#3136	1	2	yes	—
212	C₂×C₁₃₇	#3179	1	2	yes	—
213	#21644	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₁₃₇	#21644	1	1	yes	characteristic, direct product factor, Sylow
215	C₂×#486	C₂×C₁₃₇	1	1	yes	characteristic
216	#2331	C₂×C₁₃₇	1	1	yes	characteristic, complemented
217	#2328	C₂×C₁₃₇	1	1	yes	characteristic
218	#1993	C₂×C₁₃₇	1	1	yes	characteristic, complemented
219	#1961	C₂×C₁₃₇	1	1	yes	characteristic
220	#1936	C₂×C₁₃₇	1	2	yes	complemented
221	#1934	C₂×C₁₃₇	1	2	yes	complemented
222	#1835	C₂×C₁₃₇	1	1	yes	characteristic, complemented
223	#1762	C₂×C₁₃₇	1	2	yes	complemented
224	C₄×#102	C₂×C₁₃₇	1	2	yes	complemented
225	#1726	C₂×C₁₃₇	1	1	yes	characteristic, complemented
226	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
227	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
228	C₂×C₄×D₄	C₂²×C₁₃₇	1	2	yes	—
229	#486	C₄×C₁₃₇	1	8	yes	complemented
230	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
231	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
232	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
233	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
234	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
235	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
236	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
237	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
238	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
239	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
240	#391	—	2	2	no	—
241	#390	C₂²×C₁₃₇	1	2	yes	—
242	#389	C₂²×C₁₃₇	1	2	yes	—
243	#387	—	2	2	no	—
244	#386	—	2	2	no	—
245	#386	—	2	2	no	—
246	#382	C₂²×C₁₃₇	1	1	yes	characteristic
247	#382	C₂²×C₁₃₇	1	1	yes	characteristic
248	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
249	#376	C₂²×C₁₃₇	1	1	yes	characteristic
250	#340	C₂²×C₁₃₇	1	2	yes	—
251	#340	C₂²×C₁₃₇	1	2	yes	—
252	#340	C₂²×C₁₃₇	1	2	yes	—
253	#340	C₂²×C₁₃₇	1	2	yes	—
254	C₂²×Q₈	—	2	1	no	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	—	2	1	no	—
257	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
258	C₂³×C₄	—	2	2	no	—
259	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
261	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
263	C₄⋊Q₈	—	2	2	no	—
264	C₄⋊Q₈	C₂×C₄×C₁₃₇	1	4	yes	complemented
265	#127	—	2	2	no	—
266	#127	C₂×C₄×C₁₃₇	1	4	yes	—
267	C₄×D₄	—	2	4	no	—
268	C₄×D₄	—	2	4	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
279	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
280	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
281	#102	—	2	4	no	—
282	#102	—	2	4	no	—
283	#102	C₂×C₄×C₁₃₇	1	8	yes	complemented
284	#102	C₂×C₄×C₁₃₇	1	8	yes	complemented
285	#97	—	2	2	no	—
286	#97	—	2	2	no	—
287	#97	—	2	2	no	—
288	C₄×C₈	—	2	2	no	—
289	C₄×C₈	—	2	2	no	—
290	C₄×C₈	C₂×C₄×C₁₃₇	1	4	yes	complemented
291	#95	—	2	2	no	—
292	#95	—	2	1	no	—
293	#95	—	2	1	no	—
294	#95	—	2	1	no	—
295	#95	—	2	1	no	—
296	#95	—	2	2	no	—
297	#95	D₄×C₁₃₇	1	2	yes	—
298	#95	D₄×C₁₃₇	1	2	yes	—
299	C₂⁴	—	2	2	no	—
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	—	8	2	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	8	2	no	—
310	C₂×D₄	—	8	2	no	—
311	C₂×D₄	C₂²×C₄×C₁₃₇	1	4	yes	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	4	4	no	—
316	C₂²×C₄	—	8	2	no	—
317	C₂²×C₄	—	8	2	no	—
318	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
322	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
332	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
333	C₂×C₈	#41×C₁₃₇	1	2	yes	—
334	C₂×C₈	#41×C₁₃₇	1	2	yes	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	8	2	no	—
342	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
343	C₂²⋊C₄	—	4	4	no	—
344	C₂²⋊C₄	—	8	2	no	—
345	C₂²⋊C₄	—	8	2	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	8	2	no	—
349	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
350	C₄²	#41×C₁₃₇	1	2	yes	—
351	C₄²	#41×C₁₃₇	1	2	yes	—
352	C₄²	#41×C₁₃₇	1	2	yes	—
353	C₂³	—	2	4	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
361	Q₈	—	8	4	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	4	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	8	4	no	—
367	D₄	—	8	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	8	8	no	—
385	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
386	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
387	C₂×C₄	#124×C₁₃₇	1	4	yes	—
388	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
389	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
390	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
391	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
392	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
393	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	2	2	no	—
398	C₂²	—	4	4	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
406	C₂²	C₂×#124×C₁₃₇	1	1	yes	characteristic
407	C₂²	#532×C₁₃₇	1	1	yes	characteristic
408	C₂²	#576×C₁₃₇	1	2	yes	—
409	C₂²	#577×C₁₃₇	1	2	yes	—
410	C₄	—	2	4	no	—
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	4	no	—
415	C₄	—	8	2	no	—
416	C₄	—	8	2	no	—
417	C₄	C₄×#41×C₁₃₇	1	1	yes	characteristic
418	C₄	C₄×#41×C₁₃₇	1	1	yes	characteristic
419	C₄	#529×C₁₃₇	1	1	yes	characteristic
420	C₄	#529×C₁₃₇	1	1	yes	characteristic
421	C₂	—	8	4	no	—
422	C₂	C₄×#124×C₁₃₇	1	1	yes	characteristic
423	C₂	#2948×C₁₃₇	1	1	yes	characteristic
424	C₂	#2949×C₁₃₇	1	1	yes	characteristic
425	C₂	#3136×C₁₃₇	1	2	yes	—
426	C₂	#3179×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂×#127×C₁₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ #376×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2331×C₁₃₇	C₂	semidirect
4. #1993×C₁₃₇	C₂	semidirect
6. #1936×C₁₃₇	C₂	semidirect
7. #1934×C₁₃₇	C₂	semidirect
8. #1835×C₁₃₇	C₂	semidirect
9. #1762×C₁₃₇	C₂	semidirect
10. C₄×#102×C₁₃₇	C₂	semidirect
11. #1726×C₁₃₇	C₂	semidirect
15. #486×C₁₃₇	C₄	semidirect
50. C₄⋊Q₈×C₁₃₇	C₂×C₄	semidirect
69. #102×C₁₃₇	C₂×C₄	semidirect
70. #102×C₁₃₇	C₂×C₄	semidirect
76. C₄×C₈×C₁₃₇	C₂×C₄	semidirect
213. #21644	C₁₃₇	direct (N × H)
214. C₁₃₇	#21644	direct (N × H)
216. #2331	C₂×C₁₃₇	semidirect
218. #1993	C₂×C₁₃₇	semidirect
220. #1936	C₂×C₁₃₇	semidirect
221. #1934	C₂×C₁₃₇	semidirect
222. #1835	C₂×C₁₃₇	semidirect
223. #1762	C₂×C₁₃₇	semidirect
224. C₄×#102	C₂×C₁₃₇	semidirect
225. #1726	C₂×C₁₃₇	semidirect
229. #486	C₄×C₁₃₇	semidirect
264. C₄⋊Q₈	C₂×C₄×C₁₃₇	semidirect
283. #102	C₂×C₄×C₁₃₇	semidirect
284. #102	C₂×C₄×C₁₃₇	semidirect
290. C₄×C₈	C₂×C₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#486×C₁₃₇	2
#2331×C₁₃₇	2
#2328×C₁₃₇	2
#1993×C₁₃₇	2
#1961×C₁₃₇	2
#1936×C₁₃₇	2
#1934×C₁₃₇	2
#1835×C₁₃₇	2
#1762×C₁₃₇	2
C₄×#102×C₁₃₇	2
#1726×C₁₃₇	2
#21644	137

Subgroups — C137×#21644 #46871030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#21644 #46871030