Subgroups — C₃₇×#28662 #22649915

Order 9472.

740 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#489	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2640	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2331	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2066	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2065	C₂	1	2	yes	maximal
7	C₃₇×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1958	C₂	1	1	yes	maximal, characteristic
9	C₃₇×#1927	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1926	C₂	1	2	yes	maximal
11	C₃₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
15	C₃₇×#498	—	2	4	no	—
16	C₃₇×#489	—	2	4	no	—
17	C₂×#106×C₃₇	C₂²	1	2	yes	—
18	C₂×#106×C₃₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
20	C₂×#103×C₃₇	C₂²	1	2	yes	—
21	C₂×#103×C₃₇	C₂²	1	2	yes	—
22	C₂×#102×C₃₇	C₂²	1	2	yes	—
23	C₂×#102×C₃₇	C₂²	1	2	yes	—
24	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
26	C₃₇×#397	—	2	2	no	—
27	C₃₇×#393	—	2	2	no	—
28	C₃₇×#391	—	2	2	no	—
29	C₃₇×#391	C₂²	1	1	yes	characteristic
30	C₃₇×#391	C₂²	1	1	yes	characteristic
31	C₃₇×#390	C₂²	1	1	yes	characteristic
32	C₃₇×#390	C₂²	1	1	yes	characteristic
33	C₃₇×#389	C₂²	1	2	yes	—
34	C₃₇×#387	—	2	2	no	—
35	C₃₇×#382	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
37	C₃₇×#376	C₂²	1	1	yes	characteristic
38	C₃₇×#340	C₂²	1	2	yes	—
39	C₃₇×#340	C₂²	1	2	yes	—
40	C₃₇×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₃₇	—	2	1	no	—
42	C₂²×Q₈×C₃₇	—	2	1	no	—
43	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
46	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
47	C₄⋊Q₈×C₃₇	—	2	2	no	—
48	C₄⋊Q₈×C₃₇	—	2	2	no	—
49	C₄⋊Q₈×C₃₇	—	2	2	no	—
50	C₄⋊Q₈×C₃₇	D₄	1	4	yes	—
51	#124×C₃₇	—	2	2	no	—
52	#124×C₃₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
54	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
64	C₂×C₄²×C₃₇	—	2	2	no	—
65	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
68	#106×C₃₇	—	2	4	no	—
69	#106×C₃₇	—	2	4	no	—
70	C₄⋊C₈×C₃₇	—	2	4	no	—
71	#103×C₃₇	—	2	4	no	—
72	#103×C₃₇	—	2	4	no	—
73	#102×C₃₇	—	2	4	no	—
74	#102×C₃₇	—	2	4	no	—
75	#97×C₃₇	—	2	2	no	—
76	C₄×C₈×C₃₇	—	2	2	no	—
77	#95×C₃₇	—	2	2	no	—
78	#95×C₃₇	—	2	1	no	—
79	#95×C₃₇	—	2	1	no	—
80	#95×C₃₇	—	2	2	no	—
81	#95×C₃₇	—	2	2	no	—
82	#95×C₃₇	—	2	2	no	—
83	#95×C₃₇	D₄	1	2	yes	—
84	#95×C₃₇	D₄	1	2	yes	—
85	C₂⁴×C₃₇	—	2	1	no	—
86	C₂×Q₈×C₃₇	—	2	4	no	—
87	C₂×Q₈×C₃₇	—	2	1	no	—
88	C₂×Q₈×C₃₇	—	2	2	no	—
89	C₂×Q₈×C₃₇	—	2	1	no	—
90	C₂×Q₈×C₃₇	—	2	2	no	—
91	C₂×Q₈×C₃₇	—	4	2	no	—
92	C₂×Q₈×C₃₇	—	8	2	no	—
93	C₂×Q₈×C₃₇	—	8	2	no	—
94	C₂×D₄×C₃₇	—	2	1	no	—
95	C₂×D₄×C₃₇	—	2	2	no	—
96	C₂×D₄×C₃₇	—	2	1	no	—
97	C₂×D₄×C₃₇	—	2	2	no	—
98	C₂²×C₄×C₃₇	—	2	2	no	—
99	C₂²×C₄×C₃₇	—	2	2	no	—
100	C₂²×C₄×C₃₇	—	2	1	no	—
101	C₂²×C₄×C₃₇	—	2	1	no	—
102	C₂²×C₄×C₃₇	—	2	1	no	—
103	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
108	C₂×C₈×C₃₇	—	2	2	no	—
109	C₂×C₈×C₃₇	—	2	2	no	—
110	C₂×C₈×C₃₇	—	2	2	no	—
111	C₂×C₈×C₃₇	—	2	2	no	—
112	C₂×C₈×C₃₇	—	2	2	no	—
113	C₂×C₈×C₃₇	#41	1	4	yes	—
114	C₄⋊C₄×C₃₇	—	2	4	no	—
115	C₄⋊C₄×C₃₇	—	2	2	no	—
116	C₄⋊C₄×C₃₇	—	2	1	no	—
117	C₄⋊C₄×C₃₇	—	2	1	no	—
118	C₄⋊C₄×C₃₇	—	2	2	no	—
119	C₄⋊C₄×C₃₇	—	2	2	no	—
120	C₄⋊C₄×C₃₇	—	2	1	no	—
121	C₄⋊C₄×C₃₇	—	2	1	no	—
122	C₄⋊C₄×C₃₇	—	4	2	no	—
123	C₄⋊C₄×C₃₇	—	8	2	no	—
124	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
125	C₂²⋊C₄×C₃₇	—	4	2	no	—
126	C₂²⋊C₄×C₃₇	—	4	2	no	—
127	C₂²⋊C₄×C₃₇	—	8	2	no	—
128	C₂²⋊C₄×C₃₇	—	8	2	no	—
129	C₄²×C₃₇	—	2	2	no	—
130	C₄²×C₃₇	—	2	2	no	—
131	C₄²×C₃₇	—	8	2	no	—
132	C₄²×C₃₇	C₂×D₄	1	2	yes	—
133	C₄²×C₃₇	#41	1	2	yes	—
134	C₂³×C₃₇	—	4	1	no	—
135	C₂³×C₃₇	—	4	1	no	—
136	C₂³×C₃₇	—	4	1	no	—
137	C₂³×C₃₇	—	4	2	no	—
138	C₂³×C₃₇	—	4	2	no	—
139	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₃₇	—	4	2	no	—
141	Q₈×C₃₇	—	4	2	no	—
142	Q₈×C₃₇	—	8	4	no	—
143	Q₈×C₃₇	—	8	4	no	—
144	D₄×C₃₇	—	4	2	no	—
145	D₄×C₃₇	—	4	2	no	—
146	C₂×C₄×C₃₇	—	2	2	no	—
147	C₂×C₄×C₃₇	—	2	2	no	—
148	C₂×C₄×C₃₇	—	2	4	no	—
149	C₂×C₄×C₃₇	—	2	2	no	—
150	C₂×C₄×C₃₇	—	2	2	no	—
151	C₂×C₄×C₃₇	—	2	2	no	—
152	C₂×C₄×C₃₇	—	2	2	no	—
153	C₂×C₄×C₃₇	—	2	2	no	—
154	C₂×C₄×C₃₇	—	2	2	no	—
155	C₂×C₄×C₃₇	—	4	2	no	—
156	C₂×C₄×C₃₇	—	4	2	no	—
157	C₂×C₄×C₃₇	—	4	1	no	—
158	C₂×C₄×C₃₇	—	4	1	no	—
159	C₂×C₄×C₃₇	—	4	1	no	—
160	C₂×C₄×C₃₇	—	4	2	no	—
161	C₂×C₄×C₃₇	—	4	1	no	—
162	C₂×C₄×C₃₇	—	4	1	no	—
163	C₂×C₄×C₃₇	—	4	2	no	—
164	C₂×C₄×C₃₇	—	4	2	no	—
165	C₂×C₄×C₃₇	—	4	2	no	—
166	C₂×C₄×C₃₇	—	4	2	no	—
167	C₂×C₄×C₃₇	#121	1	2	yes	—
168	C₂×C₄×C₃₇	#121	1	2	yes	—
169	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
171	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₃₇	2₋¹⁺⁴	1	2	yes	—
173	C₈×C₃₇	—	2	4	no	—
174	C₈×C₃₇	—	4	2	no	—
175	#28662	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂²×C₃₇	—	8	2	no	—
177	C₂²×C₃₇	—	8	2	no	—
178	C₂²×C₃₇	—	8	1	no	—
179	C₂²×C₃₇	—	8	1	no	—
180	C₂²×C₃₇	—	8	1	no	—
181	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
182	C₂²×C₃₇	#532	1	1	yes	characteristic
183	C₂²×C₃₇	#536	1	1	yes	characteristic
184	C₂²×C₃₇	#577	1	2	yes	—
185	C₂²×C₃₇	#577	1	2	yes	—
186	C₄×C₃₇	—	2	2	no	—
187	C₄×C₃₇	—	2	2	no	—
188	C₄×C₃₇	—	4	2	no	—
189	C₄×C₃₇	—	4	2	no	—
190	C₄×C₃₇	—	4	4	no	—
191	C₄×C₃₇	—	8	2	no	—
192	C₄×C₃₇	—	8	1	no	—
193	C₄×C₃₇	—	8	1	no	—
194	C₄×C₃₇	—	8	1	no	—
195	C₄×C₃₇	#548	1	2	yes	—
196	C₄×C₃₇	#556	1	2	yes	—
197	C₂×#498	C₂×C₃₇	1	1	yes	characteristic, complemented
198	C₂×#489	C₂×C₃₇	1	1	yes	characteristic
199	#2640	C₂×C₃₇	1	1	yes	characteristic
200	#2331	C₂×C₃₇	1	1	yes	characteristic, complemented
201	#2066	C₂×C₃₇	1	2	yes	complemented
202	#2065	C₂×C₃₇	1	2	yes	—
203	#1993	C₂×C₃₇	1	1	yes	characteristic, complemented
204	#1958	C₂×C₃₇	1	1	yes	characteristic
205	#1927	C₂×C₃₇	1	2	yes	complemented
206	#1926	C₂×C₃₇	1	2	yes	—
207	#1768	C₂×C₃₇	1	1	yes	characteristic, complemented
208	C₂×C₃₇	—	16	1	no	—
209	C₂×C₃₇	#2545	1	1	yes	characteristic
210	C₂×C₃₇	#3042	1	1	yes	characteristic
211	C₂×C₃₇	#3043	1	1	yes	characteristic
212	C₂×C₃₇	#3173	1	2	yes	—
213	C₂×C₃₇	#3244	1	2	yes	—
214	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
215	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
216	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
217	#498	—	2	4	no	—
218	#489	—	2	4	no	—
219	C₂×#106	C₂²×C₃₇	1	2	yes	—
220	C₂×#106	C₂²×C₃₇	1	2	yes	—
221	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
222	C₂×#103	C₂²×C₃₇	1	2	yes	—
223	C₂×#103	C₂²×C₃₇	1	2	yes	—
224	C₂×#102	C₂²×C₃₇	1	2	yes	—
225	C₂×#102	C₂²×C₃₇	1	2	yes	—
226	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
227	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
228	#397	—	2	2	no	—
229	#393	—	2	2	no	—
230	#391	—	2	2	no	—
231	#391	C₂²×C₃₇	1	1	yes	characteristic
232	#391	C₂²×C₃₇	1	1	yes	characteristic
233	#390	C₂²×C₃₇	1	1	yes	characteristic
234	#390	C₂²×C₃₇	1	1	yes	characteristic
235	#389	C₂²×C₃₇	1	2	yes	—
236	#387	—	2	2	no	—
237	#382	C₂²×C₃₇	1	1	yes	characteristic
238	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
239	#376	C₂²×C₃₇	1	1	yes	characteristic
240	#340	C₂²×C₃₇	1	2	yes	—
241	#340	C₂²×C₃₇	1	2	yes	—
242	#336	C₂²×C₃₇	1	2	yes	—
243	C₃₇	#28662	1	1	yes	characteristic, direct product factor, Sylow
244	C₂²×Q₈	—	2	1	no	—
245	C₂²×Q₈	—	2	1	no	—
246	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
247	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
249	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
250	C₄⋊Q₈	—	2	2	no	—
251	C₄⋊Q₈	—	2	2	no	—
252	C₄⋊Q₈	—	2	2	no	—
253	C₄⋊Q₈	D₄×C₃₇	1	4	yes	—
254	#124	—	2	2	no	—
255	#124	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
271	#106	—	2	4	no	—
272	#106	—	2	4	no	—
273	C₄⋊C₈	—	2	4	no	—
274	#103	—	2	4	no	—
275	#103	—	2	4	no	—
276	#102	—	2	4	no	—
277	#102	—	2	4	no	—
278	#97	—	2	2	no	—
279	C₄×C₈	—	2	2	no	—
280	#95	—	2	2	no	—
281	#95	—	2	1	no	—
282	#95	—	2	1	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	D₄×C₃₇	1	2	yes	—
287	#95	D₄×C₃₇	1	2	yes	—
288	C₂⁴	—	2	1	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	—	8	2	no	—
296	C₂×Q₈	—	8	2	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
310	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	#41×C₃₇	1	4	yes	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	8	2	no	—
327	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	8	2	no	—
331	C₂²⋊C₄	—	8	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	8	2	no	—
335	C₄²	C₂×D₄×C₃₇	1	2	yes	—
336	C₄²	#41×C₃₇	1	2	yes	—
337	C₂³	—	4	1	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	4	1	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
343	Q₈	—	4	2	no	—
344	Q₈	—	4	2	no	—
345	Q₈	—	8	4	no	—
346	Q₈	—	8	4	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	#121×C₃₇	1	2	yes	—
371	C₂×C₄	#121×C₃₇	1	2	yes	—
372	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
373	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
374	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
375	C₂×C₄	2₋¹⁺⁴×C₃₇	1	2	yes	—
376	C₈	—	2	4	no	—
377	C₈	—	4	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	1	no	—
381	C₂²	—	8	1	no	—
382	C₂²	—	8	1	no	—
383	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
384	C₂²	C₃₇×#532	1	1	yes	characteristic
385	C₂²	C₃₇×#536	1	1	yes	characteristic
386	C₂²	C₃₇×#577	1	2	yes	—
387	C₂²	C₃₇×#577	1	2	yes	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	4	no	—
393	C₄	—	8	2	no	—
394	C₄	—	8	1	no	—
395	C₄	—	8	1	no	—
396	C₄	—	8	1	no	—
397	C₄	C₃₇×#548	1	2	yes	—
398	C₄	C₃₇×#556	1	2	yes	—
399	C₂	—	16	1	no	—
400	C₂	C₃₇×#2545	1	1	yes	characteristic
401	C₂	C₃₇×#3042	1	1	yes	characteristic
402	C₂	C₃₇×#3043	1	1	yes	characteristic
403	C₂	C₃₇×#3173	1	2	yes	—
404	C₂	C₃₇×#3244	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂²×D₄×C₃₇	C₂³
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×#498	C₂	semidirect
4. C₃₇×#2331	C₂	semidirect
5. C₃₇×#2066	C₂	semidirect
7. C₃₇×#1993	C₂	semidirect
9. C₃₇×#1927	C₂	semidirect
11. C₃₇×#1768	C₂	semidirect
175. #28662	C₃₇	direct (N × H)
197. C₂×#498	C₂×C₃₇	semidirect
200. #2331	C₂×C₃₇	semidirect
201. #2066	C₂×C₃₇	semidirect
203. #1993	C₂×C₃₇	semidirect
205. #1927	C₂×C₃₇	semidirect
207. #1768	C₂×C₃₇	semidirect
243. C₃₇	#28662	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×#498	2
C₂×C₃₇×#489	2
C₃₇×#2640	2
C₃₇×#2331	2
C₃₇×#2066	2
C₃₇×#2065	2
C₃₇×#1993	2
C₃₇×#1958	2
C₃₇×#1927	2
C₃₇×#1926	2
C₃₇×#1768	2
#28662	37

Subgroups — C37×#28662 #22649915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28662 #22649915