Subgroups — C₃₇×#28453 #22649706

Order 9472.

1096 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#497	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#495	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₇×#463	C₂	1	1	yes	maximal, characteristic
6	C₂×C₃₇×#461	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2658	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2326	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#2016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#2015	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#2013	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#2012	C₂	1	1	yes	maximal, characteristic
13	C₃₇×#1959	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#1956	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
22	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
23	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
27	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
28	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
29	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
33	C₃₇×#497	—	2	4	no	—
34	C₃₇×#495	—	2	4	no	—
35	C₃₇×#464	—	2	4	no	—
36	C₃₇×#463	—	2	4	no	—
37	C₃₇×#462	—	2	4	no	—
38	C₃₇×#461	—	2	4	no	—
39	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
41	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
42	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
43	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
44	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
45	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
46	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
47	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
48	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
49	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
51	C₃₇×#399	—	2	2	no	—
52	C₃₇×#399	—	2	2	no	—
53	C₃₇×#391	C₂²	1	1	yes	characteristic
54	C₃₇×#390	C₂²	1	1	yes	characteristic
55	C₃₇×#388	—	2	2	no	—
56	C₃₇×#385	—	2	2	no	—
57	C₃₇×#384	C₂²	1	1	yes	characteristic
58	C₃₇×#376	C₂²	1	1	yes	characteristic
59	C₃₇×#336	C₂²	1	1	yes	characteristic
60	C₃₇×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₃₇	—	2	1	no	—
68	C₂×Q₁₆×C₃₇	—	2	2	no	—
69	C₂×Q₁₆×C₃₇	—	2	2	no	—
70	C₂×Q₁₆×C₃₇	—	2	2	no	—
71	C₂×Q₁₆×C₃₇	—	2	2	no	—
72	C₂×Q₁₆×C₃₇	—	2	2	no	—
73	C₂×Q₁₆×C₃₇	—	2	2	no	—
74	C₂×Q₁₆×C₃₇	—	4	1	no	—
75	C₂×Q₁₆×C₃₇	—	4	1	no	—
76	C₂×Q₁₆×C₃₇	—	4	1	no	—
77	C₂×SD₁₆×C₃₇	—	2	2	no	—
78	C₂×SD₁₆×C₃₇	—	2	2	no	—
79	C₂×SD₁₆×C₃₇	—	2	2	no	—
80	C₂×SD₁₆×C₃₇	—	2	2	no	—
81	C₂×SD₁₆×C₃₇	—	2	2	no	—
82	C₂×SD₁₆×C₃₇	—	2	2	no	—
83	C₂×SD₁₆×C₃₇	—	2	2	no	—
84	C₂×SD₁₆×C₃₇	—	2	2	no	—
85	C₂×SD₁₆×C₃₇	—	4	1	no	—
86	C₂×SD₁₆×C₃₇	—	4	1	no	—
87	C₂×SD₁₆×C₃₇	—	4	1	no	—
88	C₂×SD₁₆×C₃₇	—	4	1	no	—
89	C₂×D₈×C₃₇	—	2	2	no	—
90	C₂×D₈×C₃₇	—	2	2	no	—
91	C₂×D₈×C₃₇	—	4	1	no	—
92	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
96	C₄⋊Q₈×C₃₇	—	2	2	no	—
97	C₄⋊Q₈×C₃₇	—	2	2	no	—
98	C₄⋊Q₈×C₃₇	—	2	2	no	—
99	C₄⋊Q₈×C₃₇	—	2	2	no	—
100	C₄⋊Q₈×C₃₇	—	4	1	no	—
101	C₄⋊Q₈×C₃₇	—	4	1	no	—
102	#124×C₃₇	—	2	2	no	—
103	#124×C₃₇	—	2	2	no	—
104	#124×C₃₇	—	2	2	no	—
105	#124×C₃₇	—	2	2	no	—
106	#124×C₃₇	—	2	2	no	—
107	#124×C₃₇	—	4	1	no	—
108	#124×C₃₇	—	4	1	no	—
109	#124×C₃₇	D₄	1	4	yes	—
110	C₄×Q₈×C₃₇	—	2	2	no	—
111	C₄×Q₈×C₃₇	—	2	2	no	—
112	C₄×D₄×C₃₇	—	2	2	no	—
113	C₄×D₄×C₃₇	—	2	2	no	—
114	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
115	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
116	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
117	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
118	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
119	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
120	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
123	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
124	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
125	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
129	C₂×C₄²×C₃₇	—	2	1	no	—
130	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
133	C₄⋊C₈×C₃₇	D₄	1	4	yes	—
134	C₄⋊C₈×C₃₇	D₄	1	4	yes	—
135	#103×C₃₇	—	2	2	no	—
136	#103×C₃₇	—	2	2	no	—
137	#103×C₃₇	—	2	2	no	—
138	#103×C₃₇	—	2	2	no	—
139	#103×C₃₇	—	2	2	no	—
140	#103×C₃₇	—	2	2	no	—
141	#102×C₃₇	—	2	2	no	—
142	#102×C₃₇	—	2	2	no	—
143	#97×C₃₇	—	2	2	no	—
144	C₄×C₈×C₃₇	—	2	2	no	—
145	#95×C₃₇	—	2	2	no	—
146	#95×C₃₇	D₄	1	2	yes	—
147	#95×C₃₇	D₄	1	2	yes	—
148	C₂⁴×C₃₇	—	2	1	no	—
149	C₂⁴×C₃₇	—	2	1	no	—
150	C₂×Q₈×C₃₇	—	2	1	no	—
151	C₂×Q₈×C₃₇	—	2	1	no	—
152	C₂×Q₈×C₃₇	—	2	1	no	—
153	C₂×Q₈×C₃₇	—	2	1	no	—
154	C₂×Q₈×C₃₇	—	2	1	no	—
155	C₂×Q₈×C₃₇	—	2	1	no	—
156	C₂×Q₈×C₃₇	—	2	1	no	—
157	C₂×Q₈×C₃₇	—	2	1	no	—
158	C₂×Q₈×C₃₇	—	2	1	no	—
159	C₂×Q₈×C₃₇	—	2	1	no	—
160	C₂×Q₈×C₃₇	—	2	1	no	—
161	C₂×Q₈×C₃₇	—	2	1	no	—
162	C₂×Q₈×C₃₇	—	2	1	no	—
163	C₂×Q₈×C₃₇	—	2	1	no	—
164	C₂×Q₈×C₃₇	—	2	1	no	—
165	C₂×Q₈×C₃₇	—	2	1	no	—
166	C₂×Q₈×C₃₇	—	2	1	no	—
167	C₂×Q₈×C₃₇	—	2	1	no	—
168	C₂×Q₈×C₃₇	—	2	1	no	—
169	C₂×Q₈×C₃₇	—	2	1	no	—
170	C₂×Q₈×C₃₇	—	2	1	no	—
171	C₂×Q₈×C₃₇	—	2	1	no	—
172	C₂×Q₈×C₃₇	—	2	1	no	—
173	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
174	C₂×D₄×C₃₇	—	2	1	no	—
175	C₂×D₄×C₃₇	—	2	1	no	—
176	C₂×D₄×C₃₇	—	2	1	no	—
177	C₂×D₄×C₃₇	—	2	1	no	—
178	C₂×D₄×C₃₇	—	2	1	no	—
179	C₂×D₄×C₃₇	—	2	1	no	—
180	C₂×D₄×C₃₇	—	2	1	no	—
181	C₂×D₄×C₃₇	—	2	1	no	—
182	C₂×D₄×C₃₇	—	2	1	no	—
183	C₂×D₄×C₃₇	—	2	1	no	—
184	C₂×D₄×C₃₇	—	2	1	no	—
185	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
186	C₂²×C₄×C₃₇	—	2	1	no	—
187	C₂²×C₄×C₃₇	—	2	1	no	—
188	C₂²×C₄×C₃₇	—	2	1	no	—
189	C₂²×C₄×C₃₇	—	2	1	no	—
190	C₂²×C₄×C₃₇	—	2	1	no	—
191	C₂²×C₄×C₃₇	—	2	1	no	—
192	C₂²×C₄×C₃₇	—	4	2	no	—
193	C₂²×C₄×C₃₇	—	8	2	no	—
194	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
195	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
196	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
199	Q₁₆×C₃₇	—	4	4	no	—
200	Q₁₆×C₃₇	—	4	4	no	—
201	Q₁₆×C₃₇	—	4	4	no	—
202	SD₁₆×C₃₇	—	4	4	no	—
203	SD₁₆×C₃₇	—	4	4	no	—
204	SD₁₆×C₃₇	—	4	4	no	—
205	SD₁₆×C₃₇	—	4	4	no	—
206	D₈×C₃₇	—	4	4	no	—
207	C₂×C₈×C₃₇	—	2	1	no	—
208	C₂×C₈×C₃₇	—	2	1	no	—
209	C₂×C₈×C₃₇	—	2	1	no	—
210	C₂×C₈×C₃₇	—	2	1	no	—
211	C₂×C₈×C₃₇	—	2	1	no	—
212	C₂×C₈×C₃₇	—	2	1	no	—
213	C₂×C₈×C₃₇	—	2	1	no	—
214	C₂×C₈×C₃₇	—	2	1	no	—
215	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
216	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
217	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
218	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
219	C₄⋊C₄×C₃₇	—	2	1	no	—
220	C₄⋊C₄×C₃₇	—	2	1	no	—
221	C₄⋊C₄×C₃₇	—	2	1	no	—
222	C₄⋊C₄×C₃₇	—	2	1	no	—
223	C₄⋊C₄×C₃₇	—	4	4	no	—
224	C₄⋊C₄×C₃₇	—	4	4	no	—
225	C₄⋊C₄×C₃₇	—	4	2	no	—
226	C₄⋊C₄×C₃₇	—	4	2	no	—
227	C₄⋊C₄×C₃₇	—	4	2	no	—
228	C₄⋊C₄×C₃₇	—	8	2	no	—
229	C₂²⋊C₄×C₃₇	—	2	8	no	—
230	C₂²⋊C₄×C₃₇	—	4	4	no	—
231	C₂²⋊C₄×C₃₇	—	4	4	no	—
232	C₂²⋊C₄×C₃₇	—	4	2	no	—
233	C₂²⋊C₄×C₃₇	—	4	2	no	—
234	C₂²⋊C₄×C₃₇	—	4	2	no	—
235	C₂²⋊C₄×C₃₇	—	8	2	no	—
236	C₄²×C₃₇	—	2	1	no	—
237	C₄²×C₃₇	—	2	1	no	—
238	C₄²×C₃₇	—	4	2	no	—
239	C₄²×C₃₇	C₂×D₄	1	2	yes	—
240	C₄²×C₃₇	C₂×D₄	1	2	yes	—
241	C₄²×C₃₇	C₂×D₄	1	2	yes	—
242	C₄²×C₃₇	#41	1	2	yes	—
243	C₂³×C₃₇	—	2	2	no	—
244	C₂³×C₃₇	—	4	1	no	—
245	C₂³×C₃₇	—	4	1	no	—
246	C₂³×C₃₇	—	4	2	no	—
247	C₂³×C₃₇	—	4	2	no	—
248	C₂³×C₃₇	—	4	1	no	—
249	C₂³×C₃₇	—	4	1	no	—
250	C₂³×C₃₇	—	4	1	no	—
251	C₂³×C₃₇	—	4	2	no	—
252	C₂³×C₃₇	—	4	2	no	—
253	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
254	Q₈×C₃₇	—	2	2	no	—
255	Q₈×C₃₇	—	2	2	no	—
256	Q₈×C₃₇	—	4	1	no	—
257	Q₈×C₃₇	—	4	1	no	—
258	Q₈×C₃₇	—	4	1	no	—
259	Q₈×C₃₇	—	4	1	no	—
260	Q₈×C₃₇	—	4	1	no	—
261	Q₈×C₃₇	—	4	1	no	—
262	Q₈×C₃₇	—	4	1	no	—
263	Q₈×C₃₇	—	4	1	no	—
264	Q₈×C₃₇	—	4	1	no	—
265	Q₈×C₃₇	—	4	1	no	—
266	Q₈×C₃₇	—	4	1	no	—
267	Q₈×C₃₇	—	4	1	no	—
268	Q₈×C₃₇	—	4	1	no	—
269	Q₈×C₃₇	—	4	1	no	—
270	D₄×C₃₇	—	2	2	no	—
271	D₄×C₃₇	—	2	2	no	—
272	D₄×C₃₇	—	4	1	no	—
273	D₄×C₃₇	—	4	1	no	—
274	D₄×C₃₇	—	4	1	no	—
275	D₄×C₃₇	—	4	1	no	—
276	D₄×C₃₇	—	4	1	no	—
277	D₄×C₃₇	—	4	1	no	—
278	C₂×C₄×C₃₇	—	2	2	no	—
279	C₂×C₄×C₃₇	—	2	2	no	—
280	C₂×C₄×C₃₇	—	2	2	no	—
281	C₂×C₄×C₃₇	—	2	2	no	—
282	C₂×C₄×C₃₇	—	2	2	no	—
283	C₂×C₄×C₃₇	—	2	2	no	—
284	C₂×C₄×C₃₇	—	2	2	no	—
285	C₂×C₄×C₃₇	—	2	2	no	—
286	C₂×C₄×C₃₇	—	4	1	no	—
287	C₂×C₄×C₃₇	—	4	1	no	—
288	C₂×C₄×C₃₇	—	4	1	no	—
289	C₂×C₄×C₃₇	—	4	1	no	—
290	C₂×C₄×C₃₇	—	4	1	no	—
291	C₂×C₄×C₃₇	—	4	1	no	—
292	C₂×C₄×C₃₇	—	4	1	no	—
293	C₂×C₄×C₃₇	—	4	1	no	—
294	C₂×C₄×C₃₇	—	4	1	no	—
295	C₂×C₄×C₃₇	—	4	1	no	—
296	C₂×C₄×C₃₇	—	4	1	no	—
297	C₂×C₄×C₃₇	—	4	1	no	—
298	C₂×C₄×C₃₇	—	4	1	no	—
299	C₂×C₄×C₃₇	—	4	2	no	—
300	C₂×C₄×C₃₇	—	4	2	no	—
301	C₂×C₄×C₃₇	—	8	4	no	—
302	C₂×C₄×C₃₇	#121	1	4	yes	—
303	C₂×C₄×C₃₇	#127	1	2	yes	—
304	C₂×C₄×C₃₇	#127	1	2	yes	—
305	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
310	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
311	C₈×C₃₇	—	2	2	no	—
312	C₈×C₃₇	—	2	2	no	—
313	C₈×C₃₇	—	2	2	no	—
314	C₈×C₃₇	—	2	2	no	—
315	#28453	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₂²×C₃₇	—	4	4	no	—
317	C₂²×C₃₇	—	4	2	no	—
318	C₂²×C₃₇	—	8	1	no	—
319	C₂²×C₃₇	—	8	1	no	—
320	C₂²×C₃₇	—	8	2	no	—
321	C₂²×C₃₇	—	8	1	no	—
322	C₂²×C₃₇	—	8	1	no	—
323	C₂²×C₃₇	—	8	2	no	—
324	C₂²×C₃₇	—	8	2	no	—
325	C₂²×C₃₇	—	8	1	no	—
326	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
327	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
328	C₂²×C₃₇	#535	1	1	yes	characteristic
329	C₂²×C₃₇	#577	1	2	yes	—
330	C₂²×C₃₇	#578	1	2	yes	—
331	C₄×C₃₇	—	2	2	no	—
332	C₄×C₃₇	—	2	2	no	—
333	C₄×C₃₇	—	2	4	no	—
334	C₄×C₃₇	—	4	2	no	—
335	C₄×C₃₇	—	4	2	no	—
336	C₄×C₃₇	—	8	1	no	—
337	C₄×C₃₇	—	8	1	no	—
338	C₄×C₃₇	—	8	1	no	—
339	C₄×C₃₇	—	8	1	no	—
340	C₄×C₃₇	—	8	1	no	—
341	C₄×C₃₇	D₄²	1	1	yes	characteristic
342	C₄×C₃₇	D₄²	1	1	yes	characteristic
343	C₄×C₃₇	#550	1	1	yes	characteristic
344	C₄×C₃₇	#550	1	1	yes	characteristic
345	C₂×#497	C₂×C₃₇	1	1	yes	characteristic, complemented
346	C₂×#495	C₂×C₃₇	1	1	yes	characteristic
347	C₂×#464	C₂×C₃₇	1	1	yes	characteristic, complemented
348	C₂×#462	C₂×C₃₇	1	1	yes	characteristic, complemented
349	C₂×#463	C₂×C₃₇	1	1	yes	characteristic
350	C₂×#461	C₂×C₃₇	1	1	yes	characteristic, complemented
351	#2658	C₂×C₃₇	1	1	yes	characteristic, complemented
352	#2326	C₂×C₃₇	1	1	yes	characteristic, complemented
353	#2016	C₂×C₃₇	1	1	yes	characteristic, complemented
354	#2015	C₂×C₃₇	1	1	yes	characteristic, complemented
355	#2013	C₂×C₃₇	1	1	yes	characteristic, complemented
356	#2012	C₂×C₃₇	1	1	yes	characteristic
357	#1959	C₂×C₃₇	1	1	yes	characteristic, complemented
358	#1956	C₂×C₃₇	1	1	yes	characteristic, complemented
359	#1768	C₂×C₃₇	1	1	yes	characteristic, complemented
360	C₂×C₃₇	—	8	2	no	—
361	C₂×C₃₇	—	16	1	no	—
362	C₂×C₃₇	#2541	1	1	yes	characteristic
363	C₂×C₃₇	#3046	1	2	yes	—
364	C₂×C₃₇	#3154	1	1	yes	characteristic
365	C₂×C₃₇	#3156	1	1	yes	characteristic
366	C₂×C₃₇	#3225	1	2	yes	—
367	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
368	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
369	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
370	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
371	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
372	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
373	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
374	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
375	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
376	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
377	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
378	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
379	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
380	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
381	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
382	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
383	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
384	#497	—	2	4	no	—
385	#495	—	2	4	no	—
386	#464	—	2	4	no	—
387	#463	—	2	4	no	—
388	#462	—	2	4	no	—
389	#461	—	2	4	no	—
390	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
391	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
392	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
393	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
394	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
395	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
396	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
397	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
398	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
399	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
400	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
401	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
402	#399	—	2	2	no	—
403	#399	—	2	2	no	—
404	#391	C₂²×C₃₇	1	1	yes	characteristic
405	#390	C₂²×C₃₇	1	1	yes	characteristic
406	#388	—	2	2	no	—
407	#385	—	2	2	no	—
408	#384	C₂²×C₃₇	1	1	yes	characteristic
409	#376	C₂²×C₃₇	1	1	yes	characteristic
410	#336	C₂²×C₃₇	1	1	yes	characteristic
411	#336	C₂²×C₃₇	1	1	yes	characteristic
412	C₃₇	#28453	1	1	yes	characteristic, direct product factor, Sylow
413	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
414	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
415	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
416	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
417	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
418	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
419	C₂³×C₄	—	2	1	no	—
420	C₂×Q₁₆	—	2	2	no	—
421	C₂×Q₁₆	—	2	2	no	—
422	C₂×Q₁₆	—	2	2	no	—
423	C₂×Q₁₆	—	2	2	no	—
424	C₂×Q₁₆	—	2	2	no	—
425	C₂×Q₁₆	—	2	2	no	—
426	C₂×Q₁₆	—	4	1	no	—
427	C₂×Q₁₆	—	4	1	no	—
428	C₂×Q₁₆	—	4	1	no	—
429	C₂×SD₁₆	—	2	2	no	—
430	C₂×SD₁₆	—	2	2	no	—
431	C₂×SD₁₆	—	2	2	no	—
432	C₂×SD₁₆	—	2	2	no	—
433	C₂×SD₁₆	—	2	2	no	—
434	C₂×SD₁₆	—	2	2	no	—
435	C₂×SD₁₆	—	2	2	no	—
436	C₂×SD₁₆	—	2	2	no	—
437	C₂×SD₁₆	—	4	1	no	—
438	C₂×SD₁₆	—	4	1	no	—
439	C₂×SD₁₆	—	4	1	no	—
440	C₂×SD₁₆	—	4	1	no	—
441	C₂×D₈	—	2	2	no	—
442	C₂×D₈	—	2	2	no	—
443	C₂×D₈	—	4	1	no	—
444	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
445	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
446	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
447	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
448	C₄⋊Q₈	—	2	2	no	—
449	C₄⋊Q₈	—	2	2	no	—
450	C₄⋊Q₈	—	2	2	no	—
451	C₄⋊Q₈	—	2	2	no	—
452	C₄⋊Q₈	—	4	1	no	—
453	C₄⋊Q₈	—	4	1	no	—
454	#124	—	2	2	no	—
455	#124	—	2	2	no	—
456	#124	—	2	2	no	—
457	#124	—	2	2	no	—
458	#124	—	2	2	no	—
459	#124	—	4	1	no	—
460	#124	—	4	1	no	—
461	#124	D₄×C₃₇	1	4	yes	—
462	C₄×Q₈	—	2	2	no	—
463	C₄×Q₈	—	2	2	no	—
464	C₄×D₄	—	2	2	no	—
465	C₄×D₄	—	2	2	no	—
466	C₂×C₄⋊C₄	—	2	1	no	—
467	C₂×C₄⋊C₄	—	2	2	no	—
468	C₂×C₄⋊C₄	—	2	2	no	—
469	C₂×C₄⋊C₄	—	2	1	no	—
470	C₂×C₄⋊C₄	—	2	1	no	—
471	C₂×C₄⋊C₄	—	2	2	no	—
472	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
474	C₂×C₂²⋊C₄	—	2	2	no	—
475	C₂×C₂²⋊C₄	—	2	1	no	—
476	C₂×C₂²⋊C₄	—	2	2	no	—
477	C₂×C₂²⋊C₄	—	2	2	no	—
478	C₂×C₂²⋊C₄	—	2	1	no	—
479	C₂×C₂²⋊C₄	—	2	1	no	—
480	C₂×C₂²⋊C₄	—	2	2	no	—
481	C₂×C₄²	—	2	1	no	—
482	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
483	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
484	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
485	C₄⋊C₈	D₄×C₃₇	1	4	yes	—
486	C₄⋊C₈	D₄×C₃₇	1	4	yes	—
487	#103	—	2	2	no	—
488	#103	—	2	2	no	—
489	#103	—	2	2	no	—
490	#103	—	2	2	no	—
491	#103	—	2	2	no	—
492	#103	—	2	2	no	—
493	#102	—	2	2	no	—
494	#102	—	2	2	no	—
495	#97	—	2	2	no	—
496	C₄×C₈	—	2	2	no	—
497	#95	—	2	2	no	—
498	#95	D₄×C₃₇	1	2	yes	—
499	#95	D₄×C₃₇	1	2	yes	—
500	C₂⁴	—	2	1	no	—
501	C₂⁴	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
526	C₂×D₄	—	2	1	no	—
527	C₂×D₄	—	2	1	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	2	1	no	—
532	C₂×D₄	—	2	1	no	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	4	2	no	—
545	C₂²×C₄	—	8	2	no	—
546	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
547	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
548	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
549	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
551	Q₁₆	—	4	4	no	—
552	Q₁₆	—	4	4	no	—
553	Q₁₆	—	4	4	no	—
554	SD₁₆	—	4	4	no	—
555	SD₁₆	—	4	4	no	—
556	SD₁₆	—	4	4	no	—
557	SD₁₆	—	4	4	no	—
558	D₈	—	4	4	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
568	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
569	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
570	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	4	4	no	—
576	C₄⋊C₄	—	4	4	no	—
577	C₄⋊C₄	—	4	2	no	—
578	C₄⋊C₄	—	4	2	no	—
579	C₄⋊C₄	—	4	2	no	—
580	C₄⋊C₄	—	8	2	no	—
581	C₂²⋊C₄	—	2	8	no	—
582	C₂²⋊C₄	—	4	4	no	—
583	C₂²⋊C₄	—	4	4	no	—
584	C₂²⋊C₄	—	4	2	no	—
585	C₂²⋊C₄	—	4	2	no	—
586	C₂²⋊C₄	—	4	2	no	—
587	C₂²⋊C₄	—	8	2	no	—
588	C₄²	—	2	1	no	—
589	C₄²	—	2	1	no	—
590	C₄²	—	4	2	no	—
591	C₄²	C₂×D₄×C₃₇	1	2	yes	—
592	C₄²	C₂×D₄×C₃₇	1	2	yes	—
593	C₄²	C₂×D₄×C₃₇	1	2	yes	—
594	C₄²	#41×C₃₇	1	2	yes	—
595	C₂³	—	2	2	no	—
596	C₂³	—	4	1	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	2	no	—
599	C₂³	—	4	2	no	—
600	C₂³	—	4	1	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	2	no	—
604	C₂³	—	4	2	no	—
605	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
606	Q₈	—	2	2	no	—
607	Q₈	—	2	2	no	—
608	Q₈	—	4	1	no	—
609	Q₈	—	4	1	no	—
610	Q₈	—	4	1	no	—
611	Q₈	—	4	1	no	—
612	Q₈	—	4	1	no	—
613	Q₈	—	4	1	no	—
614	Q₈	—	4	1	no	—
615	Q₈	—	4	1	no	—
616	Q₈	—	4	1	no	—
617	Q₈	—	4	1	no	—
618	Q₈	—	4	1	no	—
619	Q₈	—	4	1	no	—
620	Q₈	—	4	1	no	—
621	Q₈	—	4	1	no	—
622	D₄	—	2	2	no	—
623	D₄	—	2	2	no	—
624	D₄	—	4	1	no	—
625	D₄	—	4	1	no	—
626	D₄	—	4	1	no	—
627	D₄	—	4	1	no	—
628	D₄	—	4	1	no	—
629	D₄	—	4	1	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	2	no	—
652	C₂×C₄	—	4	2	no	—
653	C₂×C₄	—	8	4	no	—
654	C₂×C₄	#121×C₃₇	1	4	yes	—
655	C₂×C₄	#127×C₃₇	1	2	yes	—
656	C₂×C₄	#127×C₃₇	1	2	yes	—
657	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
658	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
659	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
660	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
661	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
662	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
663	C₈	—	2	2	no	—
664	C₈	—	2	2	no	—
665	C₈	—	2	2	no	—
666	C₈	—	2	2	no	—
667	C₂²	—	4	4	no	—
668	C₂²	—	4	2	no	—
669	C₂²	—	8	1	no	—
670	C₂²	—	8	1	no	—
671	C₂²	—	8	2	no	—
672	C₂²	—	8	1	no	—
673	C₂²	—	8	1	no	—
674	C₂²	—	8	2	no	—
675	C₂²	—	8	2	no	—
676	C₂²	—	8	1	no	—
677	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
678	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
679	C₂²	C₃₇×#535	1	1	yes	characteristic
680	C₂²	C₃₇×#577	1	2	yes	—
681	C₂²	C₃₇×#578	1	2	yes	—
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	4	no	—
685	C₄	—	4	2	no	—
686	C₄	—	4	2	no	—
687	C₄	—	8	1	no	—
688	C₄	—	8	1	no	—
689	C₄	—	8	1	no	—
690	C₄	—	8	1	no	—
691	C₄	—	8	1	no	—
692	C₄	D₄²×C₃₇	1	1	yes	characteristic
693	C₄	D₄²×C₃₇	1	1	yes	characteristic
694	C₄	C₃₇×#550	1	1	yes	characteristic
695	C₄	C₃₇×#550	1	1	yes	characteristic
696	C₂	—	8	2	no	—
697	C₂	—	16	1	no	—
698	C₂	C₃₇×#2541	1	1	yes	characteristic
699	C₂	C₃₇×#3046	1	2	yes	—
700	C₂	C₃₇×#3154	1	1	yes	characteristic
701	C₂	C₃₇×#3156	1	1	yes	characteristic
702	C₂	C₃₇×#3225	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂²×D₈×C₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₃₇×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#497	C₂	semidirect
3. C₂×C₃₇×#464	C₂	semidirect
4. C₂×C₃₇×#462	C₂	semidirect
6. C₂×C₃₇×#461	C₂	semidirect
7. C₃₇×#2658	C₂	semidirect
8. C₃₇×#2326	C₂	semidirect
9. C₃₇×#2016	C₂	semidirect
10. C₃₇×#2015	C₂	semidirect
11. C₃₇×#2013	C₂	semidirect
13. C₃₇×#1959	C₂	semidirect
14. C₃₇×#1956	C₂	semidirect
15. C₃₇×#1768	C₂	semidirect
315. #28453	C₃₇	direct (N × H)
345. C₂×#497	C₂×C₃₇	semidirect
347. C₂×#464	C₂×C₃₇	semidirect
348. C₂×#462	C₂×C₃₇	semidirect
350. C₂×#461	C₂×C₃₇	semidirect
351. #2658	C₂×C₃₇	semidirect
352. #2326	C₂×C₃₇	semidirect
353. #2016	C₂×C₃₇	semidirect
354. #2015	C₂×C₃₇	semidirect
355. #2013	C₂×C₃₇	semidirect
357. #1959	C₂×C₃₇	semidirect
358. #1956	C₂×C₃₇	semidirect
359. #1768	C₂×C₃₇	semidirect
412. C₃₇	#28453	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#497	2
C₂×C₃₇×#495	2
C₂×C₃₇×#464	2
C₂×C₃₇×#462	2
C₂×C₃₇×#463	2
C₂×C₃₇×#461	2
C₃₇×#2658	2
C₃₇×#2326	2
C₃₇×#2016	2
C₃₇×#2015	2
C₃₇×#2013	2
C₃₇×#2012	2
C₃₇×#1959	2
C₃₇×#1956	2
C₃₇×#1768	2
#28453	37

Subgroups — C37×#28453 #22649706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28453 #22649706