Subgroups — C₃₇×#28513 #22649766

Order 9472.

866 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#479	C₂	1	2	yes	maximal, complemented
2	C₂×C₃₇×#478	C₂	1	2	yes	maximal
3	C₃₇×#2859	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#124×C₃₇	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2096	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2095	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2094	C₂	1	1	yes	maximal, characteristic
8	C₃₇×#2093	C₂	1	1	yes	maximal, characteristic
9	C₃₇×#1958	C₂	1	2	yes	maximal
10	C₃₇×#1846	C₂	1	2	yes	maximal, complemented
11	C₄×C₄⋊C₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#125×C₃₇	C₂²	1	2	yes	—
13	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
16	C₃₇×#479	—	2	8	no	—
17	C₃₇×#478	—	2	8	no	—
18	C₂×#107×C₃₇	C₂²	1	2	yes	—
19	C₂×#107×C₃₇	C₂²	1	2	yes	—
20	C₂×#106×C₃₇	C₂²	1	2	yes	—
21	C₂×#106×C₃₇	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
23	C₂×#103×C₃₇	C₂²	1	2	yes	—
24	C₂×#103×C₃₇	C₂²	1	2	yes	—
25	C₂×#102×C₃₇	C₂²	1	2	yes	—
26	C₂×#102×C₃₇	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₃₇	C₂²	1	2	yes	—
28	C₃₇×#391	C₂²	1	1	yes	characteristic
29	C₃₇×#390	C₂²	1	1	yes	characteristic
30	C₃₇×#389	—	2	2	no	—
31	C₃₇×#389	—	2	2	no	—
32	C₃₇×#388	—	2	2	no	—
33	C₃₇×#384	C₂²	1	1	yes	characteristic
34	C₃₇×#384	C₂²	1	1	yes	characteristic
35	C₃₇×#382	C₂²	1	1	yes	characteristic
36	C₃₇×#382	C₂²	1	2	yes	—
37	C₄×C₂²⋊C₄×C₃₇	—	2	2	no	—
38	C₄³×C₃₇	C₂²	1	1	yes	characteristic
39	C₃₇×#336	C₂²	1	1	yes	characteristic
40	C₃₇×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₃₇	—	2	1	no	—
44	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
45	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
46	#125×C₃₇	—	2	4	no	—
47	#125×C₃₇	—	2	4	no	—
48	#124×C₃₇	—	2	2	no	—
49	#124×C₃₇	Q₈	1	4	yes	—
50	C₄×Q₈×C₃₇	—	2	4	no	—
51	C₄×D₄×C₃₇	—	2	4	no	—
52	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
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	1	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	1	yes	characteristic
60	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
61	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
64	C₂×C₄²×C₃₇	—	2	1	no	—
65	C₂×C₄²×C₃₇	D₄	1	2	yes	—
66	C₂×C₄²×C₃₇	D₄	1	2	yes	—
67	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
70	#107×C₃₇	—	2	4	no	—
71	#107×C₃₇	—	2	4	no	—
72	#106×C₃₇	—	2	4	no	—
73	#106×C₃₇	—	2	4	no	—
74	C₄⋊C₈×C₃₇	D₄	1	8	yes	—
75	#103×C₃₇	—	2	4	no	—
76	#103×C₃₇	—	2	4	no	—
77	#102×C₃₇	—	2	4	no	—
78	#102×C₃₇	—	2	4	no	—
79	C₄×C₈×C₃₇	—	2	4	no	—
80	#95×C₃₇	—	2	2	no	—
81	#95×C₃₇	—	2	2	no	—
82	#95×C₃₇	—	2	4	no	—
83	C₂⁴×C₃₇	—	2	1	no	—
84	C₂×Q₈×C₃₇	—	2	1	no	—
85	C₂×Q₈×C₃₇	—	2	2	no	—
86	C₂×Q₈×C₃₇	—	2	2	no	—
87	C₂×Q₈×C₃₇	C₂×Q₈	1	2	yes	—
88	C₂×D₄×C₃₇	—	2	2	no	—
89	C₂×D₄×C₃₇	—	2	1	no	—
90	C₂×D₄×C₃₇	—	2	2	no	—
91	C₂×D₄×C₃₇	C₂×Q₈	1	2	yes	—
92	C₂²×C₄×C₃₇	—	2	1	no	—
93	C₂²×C₄×C₃₇	—	2	1	no	—
94	C₂²×C₄×C₃₇	—	2	1	no	—
95	C₂²×C₄×C₃₇	—	2	2	no	—
96	C₂²×C₄×C₃₇	—	2	2	no	—
97	C₂²×C₄×C₃₇	—	4	4	no	—
98	C₂²×C₄×C₃₇	—	4	2	no	—
99	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
104	C₂×C₈×C₃₇	—	2	2	no	—
105	C₂×C₈×C₃₇	—	2	2	no	—
106	C₂×C₈×C₃₇	—	2	2	no	—
107	C₂×C₈×C₃₇	—	2	2	no	—
108	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
109	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
110	C₄⋊C₄×C₃₇	—	2	2	no	—
111	C₄⋊C₄×C₃₇	—	2	2	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	—	4	4	no	—
117	C₄⋊C₄×C₃₇	—	4	2	no	—
118	C₄⋊C₄×C₃₇	—	4	4	no	—
119	C₄⋊C₄×C₃₇	—	4	4	no	—
120	C₄⋊C₄×C₃₇	—	4	4	no	—
121	C₂²⋊C₄×C₃₇	—	2	8	no	—
122	C₂²⋊C₄×C₃₇	—	4	2	no	—
123	C₂²⋊C₄×C₃₇	—	4	4	no	—
124	C₄²×C₃₇	—	2	4	no	—
125	C₄²×C₃₇	—	2	2	no	—
126	C₄²×C₃₇	—	4	2	no	—
127	C₄²×C₃₇	—	4	2	no	—
128	C₄²×C₃₇	C₂×D₄	1	4	yes	—
129	C₄²×C₃₇	C₂×Q₈	1	2	yes	—
130	C₄²×C₃₇	#41	1	2	yes	—
131	C₂³×C₃₇	—	2	2	no	—
132	C₂³×C₃₇	—	4	1	no	—
133	C₂³×C₃₇	—	4	1	no	—
134	C₂³×C₃₇	—	4	2	no	—
135	C₂³×C₃₇	—	4	2	no	—
136	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
137	Q₈×C₃₇	—	2	4	no	—
138	Q₈×C₃₇	—	4	2	no	—
139	D₄×C₃₇	—	2	4	no	—
140	D₄×C₃₇	—	4	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	—	2	2	no	—
148	C₂×C₄×C₃₇	—	4	1	no	—
149	C₂×C₄×C₃₇	—	4	1	no	—
150	C₂×C₄×C₃₇	—	4	1	no	—
151	C₂×C₄×C₃₇	—	4	1	no	—
152	C₂×C₄×C₃₇	—	4	2	no	—
153	C₂×C₄×C₃₇	—	4	2	no	—
154	C₂×C₄×C₃₇	—	4	2	no	—
155	C₂×C₄×C₃₇	—	4	4	no	—
156	C₂×C₄×C₃₇	—	4	4	no	—
157	C₂×C₄×C₃₇	—	4	2	no	—
158	C₂×C₄×C₃₇	—	8	4	no	—
159	C₂×C₄×C₃₇	C₂²⋊Q₈	1	4	yes	—
160	C₂×C₄×C₃₇	#127	1	2	yes	—
161	C₂×C₄×C₃₇	#127	1	2	yes	—
162	C₂×C₄×C₃₇	#135	1	4	yes	—
163	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
164	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
165	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₃₇	2₋¹⁺⁴	1	2	yes	—
167	C₈×C₃₇	—	2	4	no	—
168	C₈×C₃₇	—	2	4	no	—
169	#28513	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂²×C₃₇	—	4	4	no	—
171	C₂²×C₃₇	—	4	2	no	—
172	C₂²×C₃₇	—	8	1	no	—
173	C₂²×C₃₇	—	8	1	no	—
174	C₂²×C₃₇	—	8	2	no	—
175	C₂²×C₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
176	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
177	C₂²×C₃₇	#536	1	1	yes	characteristic
178	C₂²×C₃₇	C₂×#135	1	2	yes	—
179	C₂²×C₃₇	#575	1	2	yes	—
180	C₄×C₃₇	—	2	4	no	—
181	C₄×C₃₇	—	2	2	no	—
182	C₄×C₃₇	—	2	2	no	—
183	C₄×C₃₇	—	2	4	no	—
184	C₄×C₃₇	—	4	2	no	—
185	C₄×C₃₇	—	8	1	no	—
186	C₄×C₃₇	—	8	2	no	—
187	C₄×C₃₇	—	8	2	no	—
188	C₄×C₃₇	—	8	1	no	—
189	C₄×C₃₇	#547	1	2	yes	—
190	C₄×C₃₇	D₄×Q₈	1	2	yes	—
191	C₂×#479	C₂×C₃₇	1	2	yes	complemented
192	C₂×#478	C₂×C₃₇	1	2	yes	—
193	#2859	C₂×C₃₇	1	1	yes	characteristic, complemented
194	C₄×#124	C₂×C₃₇	1	1	yes	characteristic
195	#2096	C₂×C₃₇	1	1	yes	characteristic, complemented
196	#2095	C₂×C₃₇	1	1	yes	characteristic, complemented
197	#2094	C₂×C₃₇	1	1	yes	characteristic
198	#2093	C₂×C₃₇	1	1	yes	characteristic
199	#1958	C₂×C₃₇	1	2	yes	—
200	#1846	C₂×C₃₇	1	2	yes	complemented
201	C₄×C₄⋊C₈	C₂×C₃₇	1	1	yes	characteristic, complemented
202	C₂×C₃₇	—	8	2	no	—
203	C₂×C₃₇	#2542	1	1	yes	characteristic
204	C₂×C₃₇	#3076	1	2	yes	—
205	C₂×C₃₇	#3147	1	1	yes	characteristic
206	C₂×C₃₇	#3153	1	1	yes	characteristic
207	C₂×C₃₇	#3232	1	2	yes	—
208	C₂×#125	C₂²×C₃₇	1	2	yes	—
209	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
210	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
211	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
212	#479	—	2	8	no	—
213	#478	—	2	8	no	—
214	C₂×#107	C₂²×C₃₇	1	2	yes	—
215	C₂×#107	C₂²×C₃₇	1	2	yes	—
216	C₂×#106	C₂²×C₃₇	1	2	yes	—
217	C₂×#106	C₂²×C₃₇	1	2	yes	—
218	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
219	C₂×#103	C₂²×C₃₇	1	2	yes	—
220	C₂×#103	C₂²×C₃₇	1	2	yes	—
221	C₂×#102	C₂²×C₃₇	1	2	yes	—
222	C₂×#102	C₂²×C₃₇	1	2	yes	—
223	C₂×C₄×C₈	C₂²×C₃₇	1	2	yes	—
224	#391	C₂²×C₃₇	1	1	yes	characteristic
225	#390	C₂²×C₃₇	1	1	yes	characteristic
226	#389	—	2	2	no	—
227	#389	—	2	2	no	—
228	#388	—	2	2	no	—
229	#384	C₂²×C₃₇	1	1	yes	characteristic
230	#384	C₂²×C₃₇	1	1	yes	characteristic
231	#382	C₂²×C₃₇	1	2	yes	—
232	#382	C₂²×C₃₇	1	1	yes	characteristic
233	C₄×C₂²⋊C₄	—	2	2	no	—
234	C₄³	C₂²×C₃₇	1	1	yes	characteristic
235	#336	C₂²×C₃₇	1	1	yes	characteristic
236	#336	C₂²×C₃₇	1	1	yes	characteristic
237	C₃₇	#28513	1	1	yes	characteristic, direct product factor, Sylow
238	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
239	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
240	C₂³×C₄	—	2	1	no	—
241	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
242	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
243	#125	—	2	4	no	—
244	#125	—	2	4	no	—
245	#124	—	2	2	no	—
246	#124	Q₈×C₃₇	1	4	yes	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×D₄	—	2	4	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	D₄×C₃₇	1	2	yes	—
263	C₂×C₄²	D₄×C₃₇	1	2	yes	—
264	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
267	#107	—	2	4	no	—
268	#107	—	2	4	no	—
269	#106	—	2	4	no	—
270	#106	—	2	4	no	—
271	C₄⋊C₈	D₄×C₃₇	1	8	yes	—
272	#103	—	2	4	no	—
273	#103	—	2	4	no	—
274	#102	—	2	4	no	—
275	#102	—	2	4	no	—
276	C₄×C₈	—	2	4	no	—
277	#95	—	2	2	no	—
278	#95	—	2	2	no	—
279	#95	—	2	4	no	—
280	C₂⁴	—	2	1	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	C₂×Q₈×C₃₇	1	2	yes	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	C₂×Q₈×C₃₇	1	2	yes	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	4	4	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
300	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
306	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
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	2	no	—
315	C₄⋊C₄	—	4	4	no	—
316	C₄⋊C₄	—	4	4	no	—
317	C₄⋊C₄	—	4	4	no	—
318	C₂²⋊C₄	—	2	8	no	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	4	4	no	—
321	C₄²	—	2	4	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	4	2	no	—
324	C₄²	—	4	2	no	—
325	C₄²	C₂×D₄×C₃₇	1	4	yes	—
326	C₄²	C₂×Q₈×C₃₇	1	2	yes	—
327	C₄²	#41×C₃₇	1	2	yes	—
328	C₂³	—	2	2	no	—
329	C₂³	—	4	1	no	—
330	C₂³	—	4	1	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
334	Q₈	—	2	4	no	—
335	Q₈	—	4	2	no	—
336	D₄	—	2	4	no	—
337	D₄	—	4	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	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	8	4	no	—
356	C₂×C₄	C₂²⋊Q₈×C₃₇	1	4	yes	—
357	C₂×C₄	#127×C₃₇	1	2	yes	—
358	C₂×C₄	#127×C₃₇	1	2	yes	—
359	C₂×C₄	#135×C₃₇	1	4	yes	—
360	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
361	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
362	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
363	C₂×C₄	2₋¹⁺⁴×C₃₇	1	2	yes	—
364	C₈	—	2	4	no	—
365	C₈	—	2	4	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	8	1	no	—
369	C₂²	—	8	1	no	—
370	C₂²	—	8	2	no	—
371	C₂²	C₂×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
372	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
373	C₂²	C₃₇×#536	1	1	yes	characteristic
374	C₂²	C₂×#135×C₃₇	1	2	yes	—
375	C₂²	C₃₇×#575	1	2	yes	—
376	C₄	—	2	2	no	—
377	C₄	—	2	2	no	—
378	C₄	—	2	4	no	—
379	C₄	—	2	4	no	—
380	C₄	—	4	2	no	—
381	C₄	—	8	1	no	—
382	C₄	—	8	2	no	—
383	C₄	—	8	1	no	—
384	C₄	—	8	2	no	—
385	C₄	C₃₇×#547	1	2	yes	—
386	C₄	D₄×Q₈×C₃₇	1	2	yes	—
387	C₂	—	8	2	no	—
388	C₂	C₃₇×#2542	1	1	yes	characteristic
389	C₂	C₃₇×#3076	1	2	yes	—
390	C₂	C₃₇×#3147	1	1	yes	characteristic
391	C₂	C₃₇×#3153	1	1	yes	characteristic
392	C₂	C₃₇×#3232	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 ◁ C₄³×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#479	C₂	semidirect
3. C₃₇×#2859	C₂	semidirect
5. C₃₇×#2096	C₂	semidirect
6. C₃₇×#2095	C₂	semidirect
10. C₃₇×#1846	C₂	semidirect
11. C₄×C₄⋊C₈×C₃₇	C₂	semidirect
169. #28513	C₃₇	direct (N × H)
191. C₂×#479	C₂×C₃₇	semidirect
193. #2859	C₂×C₃₇	semidirect
195. #2096	C₂×C₃₇	semidirect
196. #2095	C₂×C₃₇	semidirect
200. #1846	C₂×C₃₇	semidirect
201. C₄×C₄⋊C₈	C₂×C₃₇	semidirect
237. C₃₇	#28513	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×#479	2
C₂×C₃₇×#478	2
C₃₇×#2859	2
C₄×#124×C₃₇	2
C₃₇×#2096	2
C₃₇×#2095	2
C₃₇×#2094	2
C₃₇×#2093	2
C₃₇×#1958	2
C₃₇×#1846	2
C₄×C₄⋊C₈×C₃₇	2
#28513	37

Subgroups — C37×#28513 #22649766

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28513 #22649766