Subgroups — C₃₇×#25039 #22646292

Order 9472.

784 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#470	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#2423	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2421	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2074	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2072	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2036	C₂	1	1	yes	maximal, characteristic
8	C₃₇×#2035	C₂	1	1	yes	maximal, characteristic
9	C₃₇×#1971	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1941	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1865	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#1863	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₇×#1847	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#1809	C₂	1	1	yes	maximal, characteristic
15	C₃₇×#1753	C₂	1	1	yes	maximal, characteristic
16	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
22	C₃₇×#470	—	2	4	no	—
23	C₄×Q₁₆×C₃₇	—	2	4	no	—
24	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
26	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
27	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
28	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
29	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
32	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
33	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
34	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
36	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
38	C₃₇×#400	—	2	1	no	—
39	C₃₇×#399	—	2	1	no	—
40	C₃₇×#398	—	2	1	no	—
41	C₃₇×#397	—	2	1	no	—
42	C₃₇×#391	C₂²	1	1	yes	characteristic
43	C₃₇×#391	C₂²	1	1	yes	characteristic
44	C₃₇×#389	C₂²	1	1	yes	characteristic
45	C₃₇×#389	C₂²	1	1	yes	characteristic
46	C₃₇×#388	—	2	1	no	—
47	C₃₇×#388	—	2	1	no	—
48	C₃₇×#387	—	2	1	no	—
49	C₃₇×#387	—	2	1	no	—
50	C₃₇×#384	C₂²	1	1	yes	characteristic
51	C₃₇×#382	C₂²	1	1	yes	characteristic
52	C₃₇×#380	C₂²	1	1	yes	characteristic
53	C₃₇×#380	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
55	C₃₇×#340	C₂²	1	1	yes	characteristic
56	C₃₇×#340	C₂²	1	1	yes	characteristic
57	C₃₇×#340	C₂²	1	1	yes	characteristic
58	C₃₇×#340	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	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
64	C₂×Q₁₆×C₃₇	—	2	2	no	—
65	C₂×Q₁₆×C₃₇	—	2	2	no	—
66	C₂×Q₁₆×C₃₇	D₄	1	4	yes	—
67	C₂×M₁₆×C₃₇	—	2	2	no	—
68	C₂×M₁₆×C₃₇	—	2	2	no	—
69	C₂×M₁₆×C₃₇	—	2	2	no	—
70	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
74	C₂²⋊Q₈×C₃₇	—	2	2	no	—
75	C₂²⋊Q₈×C₃₇	—	2	2	no	—
76	C₂²⋊Q₈×C₃₇	—	4	1	no	—
77	C₂²⋊Q₈×C₃₇	—	4	1	no	—
78	C₄×Q₈×C₃₇	—	2	2	no	—
79	C₄×Q₈×C₃₇	—	2	2	no	—
80	C₄×Q₈×C₃₇	—	4	1	no	—
81	C₄×Q₈×C₃₇	—	4	1	no	—
82	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
85	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
86	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
87	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
88	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
89	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
90	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₃₇	D₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₃₇	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₃₇	—	2	1	no	—
103	C₂×C₄²×C₃₇	—	2	1	no	—
104	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
106	#107×C₃₇	—	2	2	no	—
107	#107×C₃₇	—	4	1	no	—
108	#106×C₃₇	—	2	2	no	—
109	#106×C₃₇	—	2	2	no	—
110	#106×C₃₇	—	4	1	no	—
111	#103×C₃₇	—	2	2	no	—
112	#103×C₃₇	—	2	2	no	—
113	#103×C₃₇	—	2	2	no	—
114	#103×C₃₇	—	2	2	no	—
115	#103×C₃₇	—	2	2	no	—
116	#103×C₃₇	—	2	2	no	—
117	C₂²⋊C₈×C₃₇	—	2	2	no	—
118	#97×C₃₇	—	2	2	no	—
119	C₄×C₈×C₃₇	—	2	2	no	—
120	#95×C₃₇	—	2	1	no	—
121	#95×C₃₇	—	2	1	no	—
122	#95×C₃₇	—	2	1	no	—
123	#95×C₃₇	—	2	1	no	—
124	#95×C₃₇	—	2	1	no	—
125	#95×C₃₇	—	2	1	no	—
126	#95×C₃₇	—	2	1	no	—
127	#95×C₃₇	—	2	1	no	—
128	#95×C₃₇	—	2	1	no	—
129	#95×C₃₇	—	2	1	no	—
130	#95×C₃₇	D₄	1	1	yes	characteristic
131	#95×C₃₇	D₄	1	1	yes	characteristic
132	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
133	C₂×Q₈×C₃₇	—	2	1	no	—
134	C₂×Q₈×C₃₇	—	2	1	no	—
135	C₂×Q₈×C₃₇	—	2	1	no	—
136	C₂×Q₈×C₃₇	—	2	1	no	—
137	C₂×Q₈×C₃₇	—	2	1	no	—
138	C₂×Q₈×C₃₇	—	2	1	no	—
139	C₂×Q₈×C₃₇	—	2	1	no	—
140	C₂×Q₈×C₃₇	—	2	1	no	—
141	C₂×Q₈×C₃₇	—	2	1	no	—
142	C₂×Q₈×C₃₇	—	2	1	no	—
143	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
144	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₃₇	—	2	1	no	—
146	C₂²×C₄×C₃₇	—	2	1	no	—
147	C₂²×C₄×C₃₇	—	2	1	no	—
148	C₂²×C₄×C₃₇	—	2	1	no	—
149	C₂²×C₄×C₃₇	—	2	1	no	—
150	C₂²×C₄×C₃₇	—	2	1	no	—
151	C₂²×C₄×C₃₇	—	2	1	no	—
152	C₂²×C₄×C₃₇	—	2	1	no	—
153	C₂²×C₄×C₃₇	—	2	1	no	—
154	C₂²×C₄×C₃₇	—	2	1	no	—
155	C₂²×C₄×C₃₇	—	2	1	no	—
156	C₂²×C₄×C₃₇	—	2	1	no	—
157	C₂²×C₄×C₃₇	—	2	1	no	—
158	C₂²×C₄×C₃₇	—	2	1	no	—
159	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
165	Q₁₆×C₃₇	—	2	8	no	—
166	M₁₆×C₃₇	—	4	4	no	—
167	C₂×C₈×C₃₇	—	2	1	no	—
168	C₂×C₈×C₃₇	—	2	1	no	—
169	C₂×C₈×C₃₇	—	2	1	no	—
170	C₂×C₈×C₃₇	—	2	1	no	—
171	C₂×C₈×C₃₇	—	2	1	no	—
172	C₂×C₈×C₃₇	—	2	1	no	—
173	C₂×C₈×C₃₇	—	2	1	no	—
174	C₂×C₈×C₃₇	—	2	1	no	—
175	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
176	C₂×C₈×C₃₇	#41	1	2	yes	—
177	C₂×C₈×C₃₇	#41	1	2	yes	—
178	C₂×C₈×C₃₇	#41	1	2	yes	—
179	C₄⋊C₄×C₃₇	—	2	1	no	—
180	C₄⋊C₄×C₃₇	—	2	1	no	—
181	C₄⋊C₄×C₃₇	—	2	1	no	—
182	C₄⋊C₄×C₃₇	—	2	1	no	—
183	C₄⋊C₄×C₃₇	—	2	1	no	—
184	C₄⋊C₄×C₃₇	—	2	1	no	—
185	C₄⋊C₄×C₃₇	—	2	1	no	—
186	C₄⋊C₄×C₃₇	—	2	1	no	—
187	C₄⋊C₄×C₃₇	—	2	1	no	—
188	C₄⋊C₄×C₃₇	—	2	1	no	—
189	C₄⋊C₄×C₃₇	—	2	1	no	—
190	C₄⋊C₄×C₃₇	—	2	1	no	—
191	C₄⋊C₄×C₃₇	—	4	2	no	—
192	C₄⋊C₄×C₃₇	—	4	2	no	—
193	C₄⋊C₄×C₃₇	—	4	2	no	—
194	C₄⋊C₄×C₃₇	—	4	2	no	—
195	C₄⋊C₄×C₃₇	—	4	2	no	—
196	C₄⋊C₄×C₃₇	—	4	2	no	—
197	C₄⋊C₄×C₃₇	—	8	1	no	—
198	C₄⋊C₄×C₃₇	—	8	1	no	—
199	C₂²⋊C₄×C₃₇	—	2	2	no	—
200	C₂²⋊C₄×C₃₇	—	4	1	no	—
201	C₂²⋊C₄×C₃₇	—	4	2	no	—
202	C₂²⋊C₄×C₃₇	—	4	2	no	—
203	C₂²⋊C₄×C₃₇	—	4	2	no	—
204	C₂²⋊C₄×C₃₇	—	8	1	no	—
205	C₄²×C₃₇	—	2	1	no	—
206	C₄²×C₃₇	—	2	1	no	—
207	C₄²×C₃₇	—	2	1	no	—
208	C₄²×C₃₇	—	2	1	no	—
209	C₄²×C₃₇	—	4	2	no	—
210	C₄²×C₃₇	—	4	2	no	—
211	C₂³×C₃₇	—	2	1	no	—
212	C₂³×C₃₇	—	2	1	no	—
213	C₂³×C₃₇	—	2	1	no	—
214	C₂³×C₃₇	—	2	1	no	—
215	C₂³×C₃₇	—	2	1	no	—
216	C₂³×C₃₇	—	2	1	no	—
217	C₂³×C₃₇	—	2	1	no	—
218	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
219	Q₈×C₃₇	—	2	2	no	—
220	Q₈×C₃₇	—	2	2	no	—
221	Q₈×C₃₇	—	2	2	no	—
222	Q₈×C₃₇	—	2	2	no	—
223	Q₈×C₃₇	—	4	1	no	—
224	Q₈×C₃₇	—	4	1	no	—
225	Q₈×C₃₇	—	4	1	no	—
226	Q₈×C₃₇	—	4	1	no	—
227	C₂×C₄×C₃₇	—	2	1	no	—
228	C₂×C₄×C₃₇	—	2	1	no	—
229	C₂×C₄×C₃₇	—	2	1	no	—
230	C₂×C₄×C₃₇	—	2	1	no	—
231	C₂×C₄×C₃₇	—	2	2	no	—
232	C₂×C₄×C₃₇	—	2	2	no	—
233	C₂×C₄×C₃₇	—	2	1	no	—
234	C₂×C₄×C₃₇	—	2	1	no	—
235	C₂×C₄×C₃₇	—	2	1	no	—
236	C₂×C₄×C₃₇	—	2	1	no	—
237	C₂×C₄×C₃₇	—	2	1	no	—
238	C₂×C₄×C₃₇	—	2	1	no	—
239	C₂×C₄×C₃₇	—	2	1	no	—
240	C₂×C₄×C₃₇	—	2	1	no	—
241	C₂×C₄×C₃₇	—	2	1	no	—
242	C₂×C₄×C₃₇	—	2	1	no	—
243	C₂×C₄×C₃₇	—	4	1	no	—
244	C₂×C₄×C₃₇	—	4	1	no	—
245	C₂×C₄×C₃₇	—	4	1	no	—
246	C₂×C₄×C₃₇	—	4	1	no	—
247	C₂×C₄×C₃₇	—	4	1	no	—
248	C₂×C₄×C₃₇	—	4	1	no	—
249	C₂×C₄×C₃₇	—	4	1	no	—
250	C₂×C₄×C₃₇	—	4	1	no	—
251	C₂×C₄×C₃₇	—	4	1	no	—
252	C₂×C₄×C₃₇	—	4	1	no	—
253	C₂×C₄×C₃₇	—	4	1	no	—
254	C₂×C₄×C₃₇	—	4	1	no	—
255	C₂×C₄×C₃₇	—	4	1	no	—
256	C₂×C₄×C₃₇	—	4	1	no	—
257	C₂×C₄×C₃₇	—	4	1	no	—
258	C₂×C₄×C₃₇	—	4	1	no	—
259	C₂×C₄×C₃₇	—	4	1	no	—
260	C₂×C₄×C₃₇	—	4	1	no	—
261	C₂×C₄×C₃₇	—	4	1	no	—
262	C₂×C₄×C₃₇	—	4	1	no	—
263	C₂×C₄×C₃₇	—	4	1	no	—
264	C₂×C₄×C₃₇	—	4	1	no	—
265	C₂×C₄×C₃₇	—	4	1	no	—
266	C₂×C₄×C₃₇	—	4	1	no	—
267	C₂×C₄×C₃₇	—	4	1	no	—
268	C₂×C₄×C₃₇	—	4	1	no	—
269	C₂×C₄×C₃₇	#137	1	2	yes	—
270	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
273	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
274	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
275	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
276	C₈×C₃₇	—	2	2	no	—
277	C₈×C₃₇	—	4	1	no	—
278	C₈×C₃₇	—	4	1	no	—
279	C₈×C₃₇	#123	1	4	yes	—
280	#25039	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₂²×C₃₇	—	4	1	no	—
282	C₂²×C₃₇	—	4	1	no	—
283	C₂²×C₃₇	—	4	1	no	—
284	C₂²×C₃₇	—	4	1	no	—
285	C₂²×C₃₇	—	4	1	no	—
286	C₂²×C₃₇	—	4	1	no	—
287	C₂²×C₃₇	—	4	1	no	—
288	C₂²×C₃₇	#532	1	1	yes	characteristic
289	C₂²×C₃₇	D₄²	1	1	yes	characteristic
290	C₂²×C₃₇	#547	1	1	yes	characteristic
291	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
292	C₂²×C₃₇	#575	1	1	yes	characteristic
293	C₂²×C₃₇	#577	1	1	yes	characteristic
294	C₂²×C₃₇	#578	1	1	yes	characteristic
295	C₄×C₃₇	—	2	2	no	—
296	C₄×C₃₇	—	4	1	no	—
297	C₄×C₃₇	—	4	1	no	—
298	C₄×C₃₇	—	4	1	no	—
299	C₄×C₃₇	—	4	2	no	—
300	C₄×C₃₇	—	4	2	no	—
301	C₄×C₃₇	—	4	1	no	—
302	C₄×C₃₇	—	8	1	no	—
303	C₄×C₃₇	—	8	1	no	—
304	C₄×C₃₇	—	8	1	no	—
305	C₄×C₃₇	—	8	1	no	—
306	C₄×C₃₇	—	8	1	no	—
307	C₄×C₃₇	—	8	1	no	—
308	C₄×C₃₇	C₂×#123	1	1	yes	characteristic
309	C₄×C₃₇	#542	1	1	yes	characteristic
310	C₄×C₃₇	#547	1	1	yes	characteristic
311	C₄×C₃₇	#553	1	1	yes	characteristic
312	C₂×#470	C₂×C₃₇	1	1	yes	characteristic
313	C₂×C₄×Q₁₆	C₂×C₃₇	1	1	yes	characteristic, complemented
314	#2423	C₂×C₃₇	1	1	yes	characteristic
315	#2421	C₂×C₃₇	1	1	yes	characteristic
316	#2074	C₂×C₃₇	1	1	yes	characteristic, complemented
317	#2072	C₂×C₃₇	1	1	yes	characteristic, complemented
318	#2036	C₂×C₃₇	1	1	yes	characteristic
319	#2035	C₂×C₃₇	1	1	yes	characteristic
320	#1971	C₂×C₃₇	1	1	yes	characteristic, complemented
321	#1941	C₂×C₃₇	1	1	yes	characteristic, complemented
322	#1865	C₂×C₃₇	1	1	yes	characteristic, complemented
323	#1863	C₂×C₃₇	1	1	yes	characteristic, complemented
324	#1847	C₂×C₃₇	1	1	yes	characteristic, complemented
325	#1809	C₂×C₃₇	1	1	yes	characteristic
326	#1753	C₂×C₃₇	1	1	yes	characteristic
327	C₂×C₃₇	—	8	1	no	—
328	C₂×C₃₇	#2422	1	1	yes	characteristic
329	C₂×C₃₇	#3172	1	1	yes	characteristic
330	C₂×C₃₇	#3178	1	1	yes	characteristic
331	C₂×C₃₇	#3270	1	1	yes	characteristic
332	C₂×C₃₇	#3271	1	1	yes	characteristic
333	C₂×C₃₇	#3352	1	1	yes	characteristic
334	C₂×C₃₇	#3356	1	1	yes	characteristic
335	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
336	C₂²×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
337	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
338	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
339	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
340	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
341	#470	—	2	4	no	—
342	C₄×Q₁₆	—	2	4	no	—
343	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
344	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
345	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
346	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
347	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
348	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
349	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
350	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
351	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
352	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
353	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
354	C₂×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
355	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
356	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
357	#400	—	2	1	no	—
358	#399	—	2	1	no	—
359	#398	—	2	1	no	—
360	#397	—	2	1	no	—
361	#391	C₂²×C₃₇	1	1	yes	characteristic
362	#391	C₂²×C₃₇	1	1	yes	characteristic
363	#389	C₂²×C₃₇	1	1	yes	characteristic
364	#389	C₂²×C₃₇	1	1	yes	characteristic
365	#388	—	2	1	no	—
366	#388	—	2	1	no	—
367	#387	—	2	1	no	—
368	#387	—	2	1	no	—
369	#384	C₂²×C₃₇	1	1	yes	characteristic
370	#382	C₂²×C₃₇	1	1	yes	characteristic
371	#380	C₂²×C₃₇	1	1	yes	characteristic
372	#380	C₂²×C₃₇	1	1	yes	characteristic
373	C₄×C₂²⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
374	#340	C₂²×C₃₇	1	1	yes	characteristic
375	#340	C₂²×C₃₇	1	1	yes	characteristic
376	#340	C₂²×C₃₇	1	1	yes	characteristic
377	#340	C₂²×C₃₇	1	1	yes	characteristic
378	#336	C₂²×C₃₇	1	1	yes	characteristic
379	#336	C₂²×C₃₇	1	1	yes	characteristic
380	C₃₇	#25039	1	1	yes	characteristic, direct product factor, Sylow
381	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
382	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
383	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
384	C₂×Q₁₆	—	2	2	no	—
385	C₂×Q₁₆	—	2	2	no	—
386	C₂×Q₁₆	D₄×C₃₇	1	4	yes	—
387	C₂×M₁₆	—	2	2	no	—
388	C₂×M₁₆	—	2	2	no	—
389	C₂×M₁₆	—	2	2	no	—
390	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
391	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
392	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
394	C₂²⋊Q₈	—	2	2	no	—
395	C₂²⋊Q₈	—	2	2	no	—
396	C₂²⋊Q₈	—	4	1	no	—
397	C₂²⋊Q₈	—	4	1	no	—
398	C₄×Q₈	—	2	2	no	—
399	C₄×Q₈	—	2	2	no	—
400	C₄×Q₈	—	4	1	no	—
401	C₄×Q₈	—	4	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	D₄×C₃₇	1	1	yes	characteristic
421	C₂×C₂²⋊C₄	D₄×C₃₇	1	1	yes	characteristic
422	C₂×C₄²	—	2	1	no	—
423	C₂×C₄²	—	2	1	no	—
424	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
426	#107	—	2	2	no	—
427	#107	—	4	1	no	—
428	#106	—	2	2	no	—
429	#106	—	2	2	no	—
430	#106	—	4	1	no	—
431	#103	—	2	2	no	—
432	#103	—	2	2	no	—
433	#103	—	2	2	no	—
434	#103	—	2	2	no	—
435	#103	—	2	2	no	—
436	#103	—	2	2	no	—
437	C₂²⋊C₈	—	2	2	no	—
438	#97	—	2	2	no	—
439	C₄×C₈	—	2	2	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	#95	D₄×C₃₇	1	1	yes	characteristic
451	#95	D₄×C₃₇	1	1	yes	characteristic
452	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
464	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
484	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
485	Q₁₆	—	2	8	no	—
486	M₁₆	—	4	4	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
496	C₂×C₈	#41×C₃₇	1	2	yes	—
497	C₂×C₈	#41×C₃₇	1	2	yes	—
498	C₂×C₈	#41×C₃₇	1	2	yes	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	4	2	no	—
512	C₄⋊C₄	—	4	2	no	—
513	C₄⋊C₄	—	4	2	no	—
514	C₄⋊C₄	—	4	2	no	—
515	C₄⋊C₄	—	4	2	no	—
516	C₄⋊C₄	—	4	2	no	—
517	C₄⋊C₄	—	8	1	no	—
518	C₄⋊C₄	—	8	1	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	4	1	no	—
521	C₂²⋊C₄	—	4	2	no	—
522	C₂²⋊C₄	—	4	2	no	—
523	C₂²⋊C₄	—	4	2	no	—
524	C₂²⋊C₄	—	8	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	4	2	no	—
530	C₄²	—	4	2	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
539	Q₈	—	2	2	no	—
540	Q₈	—	2	2	no	—
541	Q₈	—	2	2	no	—
542	Q₈	—	2	2	no	—
543	Q₈	—	4	1	no	—
544	Q₈	—	4	1	no	—
545	Q₈	—	4	1	no	—
546	Q₈	—	4	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	#137×C₃₇	1	2	yes	—
590	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
591	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
592	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
593	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
594	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
595	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
596	C₈	—	2	2	no	—
597	C₈	—	4	1	no	—
598	C₈	—	4	1	no	—
599	C₈	#123×C₃₇	1	4	yes	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	C₃₇×#532	1	1	yes	characteristic
608	C₂²	D₄²×C₃₇	1	1	yes	characteristic
609	C₂²	C₃₇×#547	1	1	yes	characteristic
610	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
611	C₂²	C₃₇×#575	1	1	yes	characteristic
612	C₂²	C₃₇×#577	1	1	yes	characteristic
613	C₂²	C₃₇×#578	1	1	yes	characteristic
614	C₄	—	2	2	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	2	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	1	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	1	no	—
621	C₄	—	8	1	no	—
622	C₄	—	8	1	no	—
623	C₄	—	8	1	no	—
624	C₄	—	8	1	no	—
625	C₄	—	8	1	no	—
626	C₄	—	8	1	no	—
627	C₄	C₂×#123×C₃₇	1	1	yes	characteristic
628	C₄	C₃₇×#542	1	1	yes	characteristic
629	C₄	C₃₇×#547	1	1	yes	characteristic
630	C₄	C₃₇×#553	1	1	yes	characteristic
631	C₂	—	8	1	no	—
632	C₂	C₃₇×#2422	1	1	yes	characteristic
633	C₂	C₃₇×#3172	1	1	yes	characteristic
634	C₂	C₃₇×#3178	1	1	yes	characteristic
635	C₂	C₃₇×#3270	1	1	yes	characteristic
636	C₂	C₃₇×#3271	1	1	yes	characteristic
637	C₂	C₃₇×#3352	1	1	yes	characteristic
638	C₂	C₃₇×#3356	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₁₆×C₃₇	C₂	semidirect
5. C₃₇×#2074	C₂	semidirect
6. C₃₇×#2072	C₂	semidirect
9. C₃₇×#1971	C₂	semidirect
10. C₃₇×#1941	C₂	semidirect
11. C₃₇×#1865	C₂	semidirect
12. C₃₇×#1863	C₂	semidirect
13. C₃₇×#1847	C₂	semidirect
280. #25039	C₃₇	direct (N × H)
313. C₂×C₄×Q₁₆	C₂×C₃₇	semidirect
316. #2074	C₂×C₃₇	semidirect
317. #2072	C₂×C₃₇	semidirect
320. #1971	C₂×C₃₇	semidirect
321. #1941	C₂×C₃₇	semidirect
322. #1865	C₂×C₃₇	semidirect
323. #1863	C₂×C₃₇	semidirect
324. #1847	C₂×C₃₇	semidirect
380. C₃₇	#25039	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×#470	2
C₂×C₄×Q₁₆×C₃₇	2
C₃₇×#2423	2
C₃₇×#2421	2
C₃₇×#2074	2
C₃₇×#2072	2
C₃₇×#2036	2
C₃₇×#2035	2
C₃₇×#1971	2
C₃₇×#1941	2
C₃₇×#1865	2
C₃₇×#1863	2
C₃₇×#1847	2
C₃₇×#1809	2
C₃₇×#1753	2
#25039	37

Subgroups — C37×#25039 #22646292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#25039 #22646292