Subgroups — C₃₇×#28534 #22649787

Order 9472.

902 conjugacy classes of subgroups.

The subgroup lattice has 390 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×#478	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×D₈×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2566	C₂	1	2	yes	maximal, complemented
5	C₃₇×#2094	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2092	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1970	C₂	1	1	yes	maximal, characteristic
8	C₃₇×#1970	C₂	1	1	yes	maximal, characteristic
9	C₃₇×#1846	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1845	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₄⋊C₄×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×#125×C₃₇	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₃₇	C₂²	1	2	yes	—
15	C₃₇×#499	—	2	4	no	—
16	C₃₇×#478	—	2	8	no	—
17	C₄×D₈×C₃₇	—	2	4	no	—
18	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
20	C₂×#107×C₃₇	C₂²	1	2	yes	—
21	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×#106×C₃₇	C₂²	1	2	yes	—
23	C₂×#106×C₃₇	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×#102×C₃₇	C₂²	1	2	yes	—
26	C₂×#102×C₃₇	C₂²	1	2	yes	—
27	C₂×#102×C₃₇	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
31	C₃₇×#396	—	2	4	no	—
32	C₃₇×#390	C₂²	1	2	yes	—
33	C₃₇×#390	C₂²	1	2	yes	—
34	C₃₇×#385	—	2	4	no	—
35	C₃₇×#384	C₂²	1	2	yes	—
36	C₃₇×#382	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
38	C₃₇×#336	C₂²	1	1	yes	characteristic
39	C₃₇×#336	C₂²	1	1	yes	characteristic
40	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
41	C₂³×C₄×C₃₇	—	2	2	no	—
42	C₂×D₈×C₃₇	—	2	2	no	—
43	C₂×D₈×C₃₇	—	2	2	no	—
44	C₂×D₈×C₃₇	Q₈	1	4	yes	—
45	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
49	#125×C₃₇	—	2	4	no	—
50	#125×C₃₇	—	2	4	no	—
51	C₄×D₄×C₃₇	—	2	4	no	—
52	C₄×D₄×C₃₇	—	2	4	no	—
53	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₃₇	—	2	4	no	—
56	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
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	4	no	—
61	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
63	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
66	#107×C₃₇	—	2	2	no	—
67	#107×C₃₇	—	2	4	no	—
68	#107×C₃₇	—	2	2	no	—
69	#107×C₃₇	—	2	2	no	—
70	#106×C₃₇	—	2	4	no	—
71	#106×C₃₇	—	2	4	no	—
72	C₄⋊C₈×C₃₇	D₄	1	4	yes	—
73	#102×C₃₇	—	2	4	no	—
74	#102×C₃₇	—	2	4	no	—
75	#102×C₃₇	—	2	4	no	—
76	C₄×C₈×C₃₇	—	2	2	no	—
77	C₄×C₈×C₃₇	—	2	2	no	—
78	C₄×C₈×C₃₇	D₄	1	4	yes	—
79	#95×C₃₇	—	2	4	no	—
80	#95×C₃₇	D₄	1	2	yes	—
81	C₂⁴×C₃₇	—	2	2	no	—
82	C₂×D₄×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	C₂×Q₈	1	4	yes	—
88	C₂²×C₄×C₃₇	—	2	2	no	—
89	C₂²×C₄×C₃₇	—	2	2	no	—
90	C₂²×C₄×C₃₇	—	2	2	no	—
91	C₂²×C₄×C₃₇	—	4	4	no	—
92	C₂²×C₄×C₃₇	—	8	4	no	—
93	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
98	D₈×C₃₇	—	2	8	no	—
99	C₂×C₈×C₃₇	—	2	1	no	—
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	C₂×D₄	1	2	yes	—
106	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
108	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₃₇	C₂×Q₈	1	2	yes	—
110	C₂×C₈×C₃₇	#41	1	2	yes	—
111	C₄⋊C₄×C₃₇	—	2	4	no	—
112	C₄⋊C₄×C₃₇	—	2	2	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	—	4	4	no	—
120	C₄⋊C₄×C₃₇	—	8	4	no	—
121	C₂²⋊C₄×C₃₇	—	4	4	no	—
122	C₂²⋊C₄×C₃₇	—	4	8	no	—
123	C₂²⋊C₄×C₃₇	—	8	4	no	—
124	C₄²×C₃₇	—	2	1	no	—
125	C₄²×C₃₇	—	2	1	no	—
126	C₄²×C₃₇	—	2	1	no	—
127	C₄²×C₃₇	—	2	1	no	—
128	C₄²×C₃₇	C₂×D₄	1	2	yes	—
129	C₄²×C₃₇	C₂×D₄	1	2	yes	—
130	C₂³×C₃₇	—	2	4	no	—
131	C₂³×C₃₇	—	4	2	no	—
132	C₂³×C₃₇	—	4	2	no	—
133	C₂³×C₃₇	—	4	4	no	—
134	C₂³×C₃₇	—	4	4	no	—
135	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
136	D₄×C₃₇	—	2	4	no	—
137	D₄×C₃₇	—	2	4	no	—
138	D₄×C₃₇	—	4	2	no	—
139	D₄×C₃₇	—	4	2	no	—
140	C₂×C₄×C₃₇	—	2	2	no	—
141	C₂×C₄×C₃₇	—	2	2	no	—
142	C₂×C₄×C₃₇	—	2	2	no	—
143	C₂×C₄×C₃₇	—	2	2	no	—
144	C₂×C₄×C₃₇	—	2	2	no	—
145	C₂×C₄×C₃₇	—	2	2	no	—
146	C₂×C₄×C₃₇	—	2	2	no	—
147	C₂×C₄×C₃₇	—	4	2	no	—
148	C₂×C₄×C₃₇	—	4	2	no	—
149	C₂×C₄×C₃₇	—	4	2	no	—
150	C₂×C₄×C₃₇	—	4	4	no	—
151	C₂×C₄×C₃₇	—	4	4	no	—
152	C₂×C₄×C₃₇	—	4	4	no	—
153	C₂×C₄×C₃₇	—	8	8	no	—
154	C₂×C₄×C₃₇	#127	1	2	yes	—
155	C₂×C₄×C₃₇	#127	1	2	yes	—
156	C₂×C₄×C₃₇	#135	1	4	yes	—
157	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
160	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
162	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
163	C₈×C₃₇	—	2	2	no	—
164	C₈×C₃₇	—	2	2	no	—
165	C₈×C₃₇	—	2	2	no	—
166	C₈×C₃₇	C₂²⋊Q₈	1	4	yes	—
167	#28534	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂²×C₃₇	—	4	8	no	—
169	C₂²×C₃₇	—	4	4	no	—
170	C₂²×C₃₇	—	8	4	no	—
171	C₂²×C₃₇	—	8	2	no	—
172	C₂²×C₃₇	—	8	2	no	—
173	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
174	C₂²×C₃₇	#547	1	1	yes	characteristic
175	C₂²×C₃₇	D₄×Q₈	1	1	yes	characteristic
176	C₂²×C₃₇	C₂×#135	1	2	yes	—
177	C₂²×C₃₇	#576	1	2	yes	—
178	C₄×C₃₇	—	2	4	no	—
179	C₄×C₃₇	—	2	2	no	—
180	C₄×C₃₇	—	2	2	no	—
181	C₄×C₃₇	—	4	2	no	—
182	C₄×C₃₇	—	8	2	no	—
183	C₄×C₃₇	—	8	2	no	—
184	C₄×C₃₇	—	8	2	no	—
185	C₄×C₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
186	C₄×C₃₇	#536	1	1	yes	characteristic
187	C₄×C₃₇	#547	1	1	yes	characteristic
188	C₄×C₃₇	D₄×Q₈	1	1	yes	characteristic
189	C₂×#499	C₂×C₃₇	1	1	yes	characteristic, complemented
190	C₂×#478	C₂×C₃₇	1	2	yes	complemented
191	C₂×C₄×D₈	C₂×C₃₇	1	1	yes	characteristic
192	#2566	C₂×C₃₇	1	2	yes	complemented
193	#2094	C₂×C₃₇	1	2	yes	complemented
194	#2092	C₂×C₃₇	1	2	yes	complemented
195	#1970	C₂×C₃₇	1	1	yes	characteristic
196	#1970	C₂×C₃₇	1	1	yes	characteristic
197	#1846	C₂×C₃₇	1	1	yes	characteristic, complemented
198	#1845	C₂×C₃₇	1	1	yes	characteristic, complemented
199	C₈×C₄⋊C₄	C₂×C₃₇	1	1	yes	characteristic, complemented
200	C₂×C₃₇	—	8	4	no	—
201	C₂×C₃₇	#2542	1	1	yes	characteristic
202	C₂×C₃₇	#3147	1	1	yes	characteristic
203	C₂×C₃₇	#3155	1	1	yes	characteristic
204	C₂×C₃₇	#3339	1	2	yes	—
205	C₂×C₃₇	#3380	1	2	yes	—
206	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
207	C₂×#125	C₂²×C₃₇	1	2	yes	—
208	C₂×C₄×D₄	C₂²×C₃₇	1	2	yes	—
209	#499	—	2	4	no	—
210	#478	—	2	8	no	—
211	C₄×D₈	—	2	4	no	—
212	C₂×#107	C₂²×C₃₇	1	2	yes	—
213	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
214	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
215	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
216	C₂×#106	C₂²×C₃₇	1	2	yes	—
217	C₂×#106	C₂²×C₃₇	1	2	yes	—
218	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
219	C₂×#102	C₂²×C₃₇	1	2	yes	—
220	C₂×#102	C₂²×C₃₇	1	2	yes	—
221	C₂×#102	C₂²×C₃₇	1	2	yes	—
222	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
223	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
224	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
225	#396	—	2	4	no	—
226	#390	C₂²×C₃₇	1	2	yes	—
227	#390	C₂²×C₃₇	1	2	yes	—
228	#385	—	2	4	no	—
229	#384	C₂²×C₃₇	1	2	yes	—
230	#382	C₂²×C₃₇	1	2	yes	—
231	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
232	#336	C₂²×C₃₇	1	1	yes	characteristic
233	#336	C₂²×C₃₇	1	1	yes	characteristic
234	C₃₇	#28534	1	1	yes	characteristic, direct product factor, Sylow
235	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
236	C₂³×C₄	—	2	2	no	—
237	C₂×D₈	—	2	2	no	—
238	C₂×D₈	—	2	2	no	—
239	C₂×D₈	Q₈×C₃₇	1	4	yes	—
240	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
244	#125	—	2	4	no	—
245	#125	—	2	4	no	—
246	C₄×D₄	—	2	4	no	—
247	C₄×D₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	4	no	—
251	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
252	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
253	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	4	no	—
257	C₂×C₂²⋊C₄	—	2	4	no	—
258	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
261	#107	—	2	2	no	—
262	#107	—	2	4	no	—
263	#107	—	2	2	no	—
264	#107	—	2	2	no	—
265	#106	—	2	4	no	—
266	#106	—	2	4	no	—
267	C₄⋊C₈	D₄×C₃₇	1	4	yes	—
268	#102	—	2	4	no	—
269	#102	—	2	4	no	—
270	#102	—	2	4	no	—
271	C₄×C₈	—	2	2	no	—
272	C₄×C₈	—	2	2	no	—
273	C₄×C₈	D₄×C₃₇	1	4	yes	—
274	#95	—	2	4	no	—
275	#95	D₄×C₃₇	1	2	yes	—
276	C₂⁴	—	2	2	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	C₂×Q₈×C₃₇	1	4	yes	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	4	4	no	—
287	C₂²×C₄	—	8	4	no	—
288	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
289	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
292	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
293	D₈	—	2	8	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
301	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
302	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
303	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
304	C₂×C₈	C₂×Q₈×C₃₇	1	2	yes	—
305	C₂×C₈	#41×C₃₇	1	2	yes	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	4	4	no	—
314	C₄⋊C₄	—	4	4	no	—
315	C₄⋊C₄	—	8	4	no	—
316	C₂²⋊C₄	—	4	4	no	—
317	C₂²⋊C₄	—	4	8	no	—
318	C₂²⋊C₄	—	8	4	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	1	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	1	no	—
323	C₄²	C₂×D₄×C₃₇	1	2	yes	—
324	C₄²	C₂×D₄×C₃₇	1	2	yes	—
325	C₂³	—	2	4	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	4	no	—
329	C₂³	—	4	4	no	—
330	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
331	D₄	—	2	4	no	—
332	D₄	—	2	4	no	—
333	D₄	—	4	2	no	—
334	D₄	—	4	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	8	8	no	—
349	C₂×C₄	#127×C₃₇	1	2	yes	—
350	C₂×C₄	#127×C₃₇	1	2	yes	—
351	C₂×C₄	#135×C₃₇	1	4	yes	—
352	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
353	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
354	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
355	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
356	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
357	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
358	C₈	—	2	2	no	—
359	C₈	—	2	2	no	—
360	C₈	—	2	2	no	—
361	C₈	C₂²⋊Q₈×C₃₇	1	4	yes	—
362	C₂²	—	4	8	no	—
363	C₂²	—	4	4	no	—
364	C₂²	—	8	2	no	—
365	C₂²	—	8	2	no	—
366	C₂²	—	8	4	no	—
367	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
368	C₂²	C₃₇×#547	1	1	yes	characteristic
369	C₂²	D₄×Q₈×C₃₇	1	1	yes	characteristic
370	C₂²	C₂×#135×C₃₇	1	2	yes	—
371	C₂²	C₃₇×#576	1	2	yes	—
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	4	no	—
375	C₄	—	4	2	no	—
376	C₄	—	8	2	no	—
377	C₄	—	8	2	no	—
378	C₄	—	8	2	no	—
379	C₄	C₂×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
380	C₄	C₃₇×#536	1	1	yes	characteristic
381	C₄	C₃₇×#547	1	1	yes	characteristic
382	C₄	D₄×Q₈×C₃₇	1	1	yes	characteristic
383	C₂	—	8	4	no	—
384	C₂	C₃₇×#2542	1	1	yes	characteristic
385	C₂	C₃₇×#3147	1	1	yes	characteristic
386	C₂	C₃₇×#3155	1	1	yes	characteristic
387	C₂	C₃₇×#3339	1	2	yes	—
388	C₂	C₃₇×#3380	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 ◁ C₄×C₄⋊C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#499	C₂	semidirect
2. C₂×C₃₇×#478	C₂	semidirect
4. C₃₇×#2566	C₂	semidirect
5. C₃₇×#2094	C₂	semidirect
6. C₃₇×#2092	C₂	semidirect
9. C₃₇×#1846	C₂	semidirect
10. C₃₇×#1845	C₂	semidirect
11. C₈×C₄⋊C₄×C₃₇	C₂	semidirect
167. #28534	C₃₇	direct (N × H)
189. C₂×#499	C₂×C₃₇	semidirect
190. C₂×#478	C₂×C₃₇	semidirect
192. #2566	C₂×C₃₇	semidirect
193. #2094	C₂×C₃₇	semidirect
194. #2092	C₂×C₃₇	semidirect
197. #1846	C₂×C₃₇	semidirect
198. #1845	C₂×C₃₇	semidirect
199. C₈×C₄⋊C₄	C₂×C₃₇	semidirect
234. C₃₇	#28534	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×#478	2
C₂×C₄×D₈×C₃₇	2
C₃₇×#2566	2
C₃₇×#2094	2
C₃₇×#2092	2
C₃₇×#1970	2
C₃₇×#1846	2
C₃₇×#1845	2
C₈×C₄⋊C₄×C₃₇	2
#28534	37

Subgroups — C37×#28534 #22649787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28534 #22649787