Subgroups — C₃₇×#28665 #22649918

Order 9472.

774 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#490	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2641	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2330	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2067	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2065	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1992	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1957	C₂	1	1	yes	maximal, characteristic
9	C₃₇×#1926	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1925	C₂	1	2	yes	maximal, complemented
11	C₃₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
15	C₃₇×#499	—	2	4	no	—
16	C₃₇×#490	—	2	4	no	—
17	C₂×#107×C₃₇	C₂²	1	2	yes	—
18	C₂×#106×C₃₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
21	C₂×#102×C₃₇	C₂²	1	2	yes	—
22	C₂×#102×C₃₇	C₂²	1	2	yes	—
23	C₂×#102×C₃₇	C₂²	1	2	yes	—
24	C₂×#102×C₃₇	C₂²	1	2	yes	—
25	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
27	C₃₇×#394	—	2	2	no	—
28	C₃₇×#394	—	2	2	no	—
29	C₃₇×#390	C₂²	1	2	yes	—
30	C₃₇×#390	C₂²	1	2	yes	—
31	C₃₇×#389	—	2	2	no	—
32	C₃₇×#389	C₂²	1	2	yes	—
33	C₃₇×#387	—	2	2	no	—
34	C₃₇×#384	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
36	C₃₇×#376	C₂²	1	1	yes	characteristic
37	C₃₇×#340	C₂²	1	2	yes	—
38	C₃₇×#340	C₂²	1	2	yes	—
39	C₃₇×#336	C₂²	1	1	yes	characteristic
40	C₃₇×#336	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₃₇	—	2	2	no	—
42	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
43	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
47	#127×C₃₇	—	2	2	no	—
48	#127×C₃₇	—	2	2	no	—
49	#125×C₃₇	—	2	2	no	—
50	#125×C₃₇	—	2	2	no	—
51	#125×C₃₇	—	2	2	no	—
52	#125×C₃₇	D₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₃₇	—	2	2	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	#107×C₃₇	—	2	4	no	—
69	#106×C₃₇	—	2	4	no	—
70	C₄⋊C₈×C₃₇	—	2	2	no	—
71	C₄⋊C₈×C₃₇	—	2	2	no	—
72	#102×C₃₇	—	2	4	no	—
73	#102×C₃₇	—	2	4	no	—
74	#102×C₃₇	—	2	4	no	—
75	#102×C₃₇	—	2	4	no	—
76	#97×C₃₇	—	2	2	no	—
77	C₄×C₈×C₃₇	—	2	2	no	—
78	#95×C₃₇	—	2	2	no	—
79	#95×C₃₇	—	2	2	no	—
80	#95×C₃₇	D₄	1	2	yes	—
81	#95×C₃₇	D₄	1	2	yes	—
82	C₂⁴×C₃₇	—	2	2	no	—
83	C₂×D₄×C₃₇	—	2	2	no	—
84	C₂×D₄×C₃₇	—	2	2	no	—
85	C₂×D₄×C₃₇	—	2	2	no	—
86	C₂×D₄×C₃₇	—	2	2	no	—
87	C₂×D₄×C₃₇	—	2	2	no	—
88	C₂×D₄×C₃₇	—	2	2	no	—
89	C₂×D₄×C₃₇	—	4	4	no	—
90	C₂×D₄×C₃₇	—	8	2	no	—
91	C₂×D₄×C₃₇	—	8	2	no	—
92	C₂²×C₄×C₃₇	—	2	2	no	—
93	C₂²×C₄×C₃₇	—	2	2	no	—
94	C₂²×C₄×C₃₇	—	2	2	no	—
95	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
100	C₂×C₈×C₃₇	—	2	1	no	—
101	C₂×C₈×C₃₇	—	2	1	no	—
102	C₂×C₈×C₃₇	—	2	1	no	—
103	C₂×C₈×C₃₇	—	2	1	no	—
104	C₂×C₈×C₃₇	—	2	1	no	—
105	C₂×C₈×C₃₇	—	2	1	no	—
106	C₂×C₈×C₃₇	—	2	1	no	—
107	C₂×C₈×C₃₇	—	2	1	no	—
108	C₂×C₈×C₃₇	—	2	1	no	—
109	C₂×C₈×C₃₇	—	2	1	no	—
110	C₂×C₈×C₃₇	#41	1	2	yes	—
111	C₂×C₈×C₃₇	#41	1	2	yes	—
112	C₄⋊C₄×C₃₇	—	2	8	no	—
113	C₄⋊C₄×C₃₇	—	2	2	no	—
114	C₄⋊C₄×C₃₇	—	2	2	no	—
115	C₄⋊C₄×C₃₇	—	2	2	no	—
116	C₄⋊C₄×C₃₇	—	2	2	no	—
117	C₄⋊C₄×C₃₇	—	2	2	no	—
118	C₄⋊C₄×C₃₇	—	4	4	no	—
119	C₄⋊C₄×C₃₇	—	8	2	no	—
120	C₄⋊C₄×C₃₇	—	8	2	no	—
121	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
122	C₂²⋊C₄×C₃₇	—	8	2	no	—
123	C₂²⋊C₄×C₃₇	—	8	2	no	—
124	C₂²⋊C₄×C₃₇	—	8	2	no	—
125	C₂²⋊C₄×C₃₇	—	8	2	no	—
126	C₄²×C₃₇	—	2	1	no	—
127	C₄²×C₃₇	—	2	1	no	—
128	C₄²×C₃₇	—	2	1	no	—
129	C₄²×C₃₇	—	2	1	no	—
130	C₄²×C₃₇	—	8	2	no	—
131	C₄²×C₃₇	C₂×D₄	1	2	yes	—
132	C₄²×C₃₇	#41	1	2	yes	—
133	C₂³×C₃₇	—	4	2	no	—
134	C₂³×C₃₇	—	4	2	no	—
135	C₂³×C₃₇	—	4	2	no	—
136	C₂³×C₃₇	—	4	2	no	—
137	C₂³×C₃₇	—	4	2	no	—
138	C₂³×C₃₇	—	4	2	no	—
139	C₂³×C₃₇	—	4	2	no	—
140	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
141	D₄×C₃₇	—	4	2	no	—
142	D₄×C₃₇	—	4	2	no	—
143	D₄×C₃₇	—	4	2	no	—
144	D₄×C₃₇	—	4	2	no	—
145	D₄×C₃₇	—	8	8	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	1	no	—
150	C₂×C₄×C₃₇	—	2	1	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	—	2	2	no	—
156	C₂×C₄×C₃₇	—	4	2	no	—
157	C₂×C₄×C₃₇	—	4	2	no	—
158	C₂×C₄×C₃₇	—	4	2	no	—
159	C₂×C₄×C₃₇	—	4	2	no	—
160	C₂×C₄×C₃₇	—	4	2	no	—
161	C₂×C₄×C₃₇	—	4	2	no	—
162	C₂×C₄×C₃₇	—	4	2	no	—
163	C₂×C₄×C₃₇	—	4	2	no	—
164	C₂×C₄×C₃₇	#121	1	4	yes	—
165	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
170	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
171	C₈×C₃₇	—	2	2	no	—
172	C₈×C₃₇	—	2	2	no	—
173	C₈×C₃₇	—	4	1	no	—
174	C₈×C₃₇	—	4	1	no	—
175	#28665	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	2	no	—
179	C₂²×C₃₇	—	8	2	no	—
180	C₂²×C₃₇	—	8	2	no	—
181	C₂²×C₃₇	—	8	2	no	—
182	C₂²×C₃₇	—	8	2	no	—
183	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
184	C₂²×C₃₇	#532	1	1	yes	characteristic
185	C₂²×C₃₇	#536	1	1	yes	characteristic
186	C₂²×C₃₇	#576	1	2	yes	—
187	C₂²×C₃₇	#577	1	2	yes	—
188	C₄×C₃₇	—	2	4	no	—
189	C₄×C₃₇	—	4	1	no	—
190	C₄×C₃₇	—	4	1	no	—
191	C₄×C₃₇	—	4	2	no	—
192	C₄×C₃₇	—	4	4	no	—
193	C₄×C₃₇	—	8	2	no	—
194	C₄×C₃₇	—	8	2	no	—
195	C₄×C₃₇	#548	1	1	yes	characteristic
196	C₄×C₃₇	#548	1	1	yes	characteristic
197	C₄×C₃₇	#556	1	1	yes	characteristic
198	C₄×C₃₇	#556	1	1	yes	characteristic
199	C₂×#499	C₂×C₃₇	1	1	yes	characteristic, complemented
200	C₂×#490	C₂×C₃₇	1	1	yes	characteristic
201	#2641	C₂×C₃₇	1	1	yes	characteristic
202	#2330	C₂×C₃₇	1	1	yes	characteristic, complemented
203	#2067	C₂×C₃₇	1	2	yes	complemented
204	#2065	C₂×C₃₇	1	2	yes	complemented
205	#1992	C₂×C₃₇	1	1	yes	characteristic, complemented
206	#1957	C₂×C₃₇	1	1	yes	characteristic
207	#1926	C₂×C₃₇	1	2	yes	complemented
208	#1925	C₂×C₃₇	1	2	yes	complemented
209	#1768	C₂×C₃₇	1	1	yes	characteristic, complemented
210	C₂×C₃₇	—	16	2	no	—
211	C₂×C₃₇	#2545	1	1	yes	characteristic
212	C₂×C₃₇	#3045	1	2	yes	—
213	C₂×C₃₇	#3174	1	1	yes	characteristic
214	C₂×C₃₇	#3176	1	1	yes	characteristic
215	C₂×C₃₇	#3241	1	2	yes	—
216	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
217	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
218	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
219	#499	—	2	4	no	—
220	#490	—	2	4	no	—
221	C₂×#107	C₂²×C₃₇	1	2	yes	—
222	C₂×#106	C₂²×C₃₇	1	2	yes	—
223	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
224	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
225	C₂×#102	C₂²×C₃₇	1	2	yes	—
226	C₂×#102	C₂²×C₃₇	1	2	yes	—
227	C₂×#102	C₂²×C₃₇	1	2	yes	—
228	C₂×#102	C₂²×C₃₇	1	2	yes	—
229	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
230	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
231	#394	—	2	2	no	—
232	#394	—	2	2	no	—
233	#390	C₂²×C₃₇	1	2	yes	—
234	#390	C₂²×C₃₇	1	2	yes	—
235	#389	—	2	2	no	—
236	#389	C₂²×C₃₇	1	2	yes	—
237	#387	—	2	2	no	—
238	#384	C₂²×C₃₇	1	1	yes	characteristic
239	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
240	#376	C₂²×C₃₇	1	1	yes	characteristic
241	#340	C₂²×C₃₇	1	2	yes	—
242	#340	C₂²×C₃₇	1	2	yes	—
243	#336	C₂²×C₃₇	1	1	yes	characteristic
244	#336	C₂²×C₃₇	1	1	yes	characteristic
245	C₃₇	#28665	1	1	yes	characteristic, direct product factor, Sylow
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
248	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
252	#127	—	2	2	no	—
253	#127	—	2	2	no	—
254	#125	—	2	2	no	—
255	#125	—	2	2	no	—
256	#125	—	2	2	no	—
257	#125	D₄×C₃₇	1	4	yes	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
273	#107	—	2	4	no	—
274	#106	—	2	4	no	—
275	C₄⋊C₈	—	2	2	no	—
276	C₄⋊C₈	—	2	2	no	—
277	#102	—	2	4	no	—
278	#102	—	2	4	no	—
279	#102	—	2	4	no	—
280	#102	—	2	4	no	—
281	#97	—	2	2	no	—
282	C₄×C₈	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	#95	D₄×C₃₇	1	2	yes	—
286	#95	D₄×C₃₇	1	2	yes	—
287	C₂⁴	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	4	4	no	—
295	C₂×D₄	—	8	2	no	—
296	C₂×D₄	—	8	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
304	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	#41×C₃₇	1	2	yes	—
316	C₂×C₈	#41×C₃₇	1	2	yes	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	4	4	no	—
324	C₄⋊C₄	—	8	2	no	—
325	C₄⋊C₄	—	8	2	no	—
326	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
327	C₂²⋊C₄	—	8	2	no	—
328	C₂²⋊C₄	—	8	2	no	—
329	C₂²⋊C₄	—	8	2	no	—
330	C₂²⋊C₄	—	8	2	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	8	2	no	—
336	C₄²	C₂×D₄×C₃₇	1	2	yes	—
337	C₄²	#41×C₃₇	1	2	yes	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
346	D₄	—	4	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	8	8	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	#121×C₃₇	1	4	yes	—
370	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
372	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
373	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
374	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
375	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
376	C₈	—	2	2	no	—
377	C₈	—	2	2	no	—
378	C₈	—	4	1	no	—
379	C₈	—	4	1	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	8	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
388	C₂²	C₃₇×#532	1	1	yes	characteristic
389	C₂²	C₃₇×#536	1	1	yes	characteristic
390	C₂²	C₃₇×#576	1	2	yes	—
391	C₂²	C₃₇×#577	1	2	yes	—
392	C₄	—	2	4	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	4	no	—
397	C₄	—	8	2	no	—
398	C₄	—	8	2	no	—
399	C₄	C₃₇×#548	1	1	yes	characteristic
400	C₄	C₃₇×#548	1	1	yes	characteristic
401	C₄	C₃₇×#556	1	1	yes	characteristic
402	C₄	C₃₇×#556	1	1	yes	characteristic
403	C₂	—	16	2	no	—
404	C₂	C₃₇×#2545	1	1	yes	characteristic
405	C₂	C₃₇×#3045	1	2	yes	—
406	C₂	C₃₇×#3174	1	1	yes	characteristic
407	C₂	C₃₇×#3176	1	1	yes	characteristic
408	C₂	C₃₇×#3241	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×#127×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×#499	C₂	semidirect
4. C₃₇×#2330	C₂	semidirect
5. C₃₇×#2067	C₂	semidirect
6. C₃₇×#2065	C₂	semidirect
7. C₃₇×#1992	C₂	semidirect
9. C₃₇×#1926	C₂	semidirect
10. C₃₇×#1925	C₂	semidirect
11. C₃₇×#1768	C₂	semidirect
175. #28665	C₃₇	direct (N × H)
199. C₂×#499	C₂×C₃₇	semidirect
202. #2330	C₂×C₃₇	semidirect
203. #2067	C₂×C₃₇	semidirect
204. #2065	C₂×C₃₇	semidirect
205. #1992	C₂×C₃₇	semidirect
207. #1926	C₂×C₃₇	semidirect
208. #1925	C₂×C₃₇	semidirect
209. #1768	C₂×C₃₇	semidirect
245. C₃₇	#28665	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×#499	2
C₂×C₃₇×#490	2
C₃₇×#2641	2
C₃₇×#2330	2
C₃₇×#2067	2
C₃₇×#2065	2
C₃₇×#1992	2
C₃₇×#1957	2
C₃₇×#1926	2
C₃₇×#1925	2
C₃₇×#1768	2
#28665	37

Subgroups — C37×#28665 #22649918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28665 #22649918