Subgroups — C₃₇×#28517 #22649770

Order 9472.

854 conjugacy classes of subgroups.

The subgroup lattice has 396 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×#2097	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2092	C₂	1	2	yes	maximal
7	C₃₇×#1959	C₂	1	1	yes	maximal, characteristic
8	C₃₇×#1959	C₂	1	1	yes	maximal, characteristic
9	C₃₇×#1847	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1847	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1767	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×#97×C₃₇	C₂²	1	1	yes	characteristic
28	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
29	C₃₇×#391	C₂²	1	1	yes	characteristic
30	C₃₇×#390	C₂²	1	1	yes	characteristic
31	C₃₇×#389	—	2	2	no	—
32	C₃₇×#389	—	2	2	no	—
33	C₃₇×#388	—	2	2	no	—
34	C₃₇×#384	C₂²	1	1	yes	characteristic
35	C₃₇×#384	C₂²	1	1	yes	characteristic
36	C₃₇×#382	C₂²	1	2	yes	—
37	C₃₇×#382	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₃₇	—	2	2	no	—
39	C₄³×C₃₇	C₂²	1	1	yes	characteristic
40	C₃₇×#336	C₂²	1	2	yes	—
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	#97×C₃₇	—	2	2	no	—
80	#97×C₃₇	—	2	2	no	—
81	#95×C₃₇	—	2	2	no	—
82	#95×C₃₇	—	2	2	no	—
83	#95×C₃₇	—	2	4	no	—
84	C₂⁴×C₃₇	—	2	1	no	—
85	C₂×Q₈×C₃₇	—	2	1	no	—
86	C₂×Q₈×C₃₇	—	2	2	no	—
87	C₂×Q₈×C₃₇	—	2	2	no	—
88	C₂×Q₈×C₃₇	C₂×Q₈	1	2	yes	—
89	C₂×D₄×C₃₇	—	2	2	no	—
90	C₂×D₄×C₃₇	—	2	1	no	—
91	C₂×D₄×C₃₇	—	2	2	no	—
92	C₂×D₄×C₃₇	C₂×Q₈	1	2	yes	—
93	C₂²×C₄×C₃₇	—	2	1	no	—
94	C₂²×C₄×C₃₇	—	2	1	no	—
95	C₂²×C₄×C₃₇	—	2	1	no	—
96	C₂²×C₄×C₃₇	—	2	2	no	—
97	C₂²×C₄×C₃₇	—	2	2	no	—
98	C₂²×C₄×C₃₇	—	4	4	no	—
99	C₂²×C₄×C₃₇	—	4	2	no	—
100	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
109	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
110	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
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	—	2	2	no	—
117	C₄⋊C₄×C₃₇	—	4	4	no	—
118	C₄⋊C₄×C₃₇	—	4	4	no	—
119	C₄⋊C₄×C₃₇	—	4	2	no	—
120	C₄⋊C₄×C₃₇	—	4	4	no	—
121	C₄⋊C₄×C₃₇	—	4	4	no	—
122	C₂²⋊C₄×C₃₇	—	2	8	no	—
123	C₂²⋊C₄×C₃₇	—	4	4	no	—
124	C₂²⋊C₄×C₃₇	—	4	2	no	—
125	C₄²×C₃₇	—	2	2	no	—
126	C₄²×C₃₇	—	4	2	no	—
127	C₄²×C₃₇	—	4	2	no	—
128	C₄²×C₃₇	—	4	2	no	—
129	C₄²×C₃₇	C₂×D₄	1	4	yes	—
130	C₄²×C₃₇	C₂×Q₈	1	2	yes	—
131	C₄²×C₃₇	#41	1	2	yes	—
132	C₂³×C₃₇	—	2	2	no	—
133	C₂³×C₃₇	—	4	1	no	—
134	C₂³×C₃₇	—	4	1	no	—
135	C₂³×C₃₇	—	4	2	no	—
136	C₂³×C₃₇	—	4	2	no	—
137	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
138	Q₈×C₃₇	—	2	4	no	—
139	Q₈×C₃₇	—	4	2	no	—
140	D₄×C₃₇	—	2	4	no	—
141	D₄×C₃₇	—	4	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	—	2	2	no	—
149	C₂×C₄×C₃₇	—	2	2	no	—
150	C₂×C₄×C₃₇	—	4	1	no	—
151	C₂×C₄×C₃₇	—	4	1	no	—
152	C₂×C₄×C₃₇	—	4	1	no	—
153	C₂×C₄×C₃₇	—	4	1	no	—
154	C₂×C₄×C₃₇	—	4	2	no	—
155	C₂×C₄×C₃₇	—	4	2	no	—
156	C₂×C₄×C₃₇	—	4	2	no	—
157	C₂×C₄×C₃₇	—	4	4	no	—
158	C₂×C₄×C₃₇	—	4	4	no	—
159	C₂×C₄×C₃₇	—	4	2	no	—
160	C₂×C₄×C₃₇	—	8	4	no	—
161	C₂×C₄×C₃₇	C₂²⋊Q₈	1	4	yes	—
162	C₂×C₄×C₃₇	#127	1	2	yes	—
163	C₂×C₄×C₃₇	#127	1	2	yes	—
164	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
165	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
166	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₃₇	2₋¹⁺⁴	1	2	yes	—
168	C₈×C₃₇	—	2	4	no	—
169	C₈×C₃₇	—	2	4	no	—
170	#28517	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂²×C₃₇	—	4	4	no	—
172	C₂²×C₃₇	—	4	2	no	—
173	C₂²×C₃₇	—	8	1	no	—
174	C₂²×C₃₇	—	8	1	no	—
175	C₂²×C₃₇	—	8	2	no	—
176	C₂²×C₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
177	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
178	C₂²×C₃₇	#536	1	1	yes	characteristic
179	C₂²×C₃₇	#575	1	2	yes	—
180	C₂²×C₃₇	#575	1	2	yes	—
181	C₄×C₃₇	—	2	4	no	—
182	C₄×C₃₇	—	2	2	no	—
183	C₄×C₃₇	—	2	2	no	—
184	C₄×C₃₇	—	4	2	no	—
185	C₄×C₃₇	—	4	2	no	—
186	C₄×C₃₇	—	8	1	no	—
187	C₄×C₃₇	—	8	2	no	—
188	C₄×C₃₇	—	8	2	no	—
189	C₄×C₃₇	—	8	1	no	—
190	C₄×C₃₇	#547	1	2	yes	—
191	C₄×C₃₇	D₄×Q₈	1	2	yes	—
192	C₂×#479	C₂×C₃₇	1	2	yes	complemented
193	C₂×#478	C₂×C₃₇	1	2	yes	—
194	#2859	C₂×C₃₇	1	1	yes	characteristic, complemented
195	C₄×#124	C₂×C₃₇	1	1	yes	characteristic
196	#2097	C₂×C₃₇	1	2	yes	complemented
197	#2092	C₂×C₃₇	1	2	yes	—
198	#1959	C₂×C₃₇	1	1	yes	characteristic
199	#1959	C₂×C₃₇	1	1	yes	characteristic
200	#1847	C₂×C₃₇	1	1	yes	characteristic, complemented
201	#1847	C₂×C₃₇	1	1	yes	characteristic, complemented
202	#1767	C₂×C₃₇	1	1	yes	characteristic, complemented
203	C₂×C₃₇	—	8	2	no	—
204	C₂×C₃₇	#2542	1	1	yes	characteristic
205	C₂×C₃₇	#3080	1	2	yes	—
206	C₂×C₃₇	#3150	1	1	yes	characteristic
207	C₂×C₃₇	#3153	1	1	yes	characteristic
208	C₂×C₃₇	#3240	1	2	yes	—
209	C₂×#125	C₂²×C₃₇	1	2	yes	—
210	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
211	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
212	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
213	#479	—	2	8	no	—
214	#478	—	2	8	no	—
215	C₂×#107	C₂²×C₃₇	1	2	yes	—
216	C₂×#107	C₂²×C₃₇	1	2	yes	—
217	C₂×#106	C₂²×C₃₇	1	2	yes	—
218	C₂×#106	C₂²×C₃₇	1	2	yes	—
219	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
220	C₂×#103	C₂²×C₃₇	1	2	yes	—
221	C₂×#103	C₂²×C₃₇	1	2	yes	—
222	C₂×#102	C₂²×C₃₇	1	2	yes	—
223	C₂×#102	C₂²×C₃₇	1	2	yes	—
224	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
225	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
226	#391	C₂²×C₃₇	1	1	yes	characteristic
227	#390	C₂²×C₃₇	1	1	yes	characteristic
228	#389	—	2	2	no	—
229	#389	—	2	2	no	—
230	#388	—	2	2	no	—
231	#384	C₂²×C₃₇	1	1	yes	characteristic
232	#384	C₂²×C₃₇	1	1	yes	characteristic
233	#382	C₂²×C₃₇	1	2	yes	—
234	#382	C₂²×C₃₇	1	1	yes	characteristic
235	C₄×C₂²⋊C₄	—	2	2	no	—
236	C₄³	C₂²×C₃₇	1	1	yes	characteristic
237	#336	C₂²×C₃₇	1	2	yes	—
238	C₃₇	#28517	1	1	yes	characteristic, direct product factor, Sylow
239	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
240	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
241	C₂³×C₄	—	2	1	no	—
242	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
243	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
244	#125	—	2	4	no	—
245	#125	—	2	4	no	—
246	#124	—	2	2	no	—
247	#124	Q₈×C₃₇	1	4	yes	—
248	C₄×Q₈	—	2	4	no	—
249	C₄×D₄	—	2	4	no	—
250	C₂×C₄⋊C₄	—	2	1	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	—	2	2	no	—
255	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	1	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₄²	—	2	1	no	—
263	C₂×C₄²	D₄×C₃₇	1	2	yes	—
264	C₂×C₄²	D₄×C₃₇	1	2	yes	—
265	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
268	#107	—	2	4	no	—
269	#107	—	2	4	no	—
270	#106	—	2	4	no	—
271	#106	—	2	4	no	—
272	C₄⋊C₈	D₄×C₃₇	1	8	yes	—
273	#103	—	2	4	no	—
274	#103	—	2	4	no	—
275	#102	—	2	4	no	—
276	#102	—	2	4	no	—
277	#97	—	2	2	no	—
278	#97	—	2	2	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	#95	—	2	4	no	—
282	C₂⁴	—	2	1	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	C₂×Q₈×C₃₇	1	2	yes	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	C₂×Q₈×C₃₇	1	2	yes	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	4	4	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
300	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
302	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
308	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
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	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	4	4	no	—
316	C₄⋊C₄	—	4	4	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	4	no	—
319	C₄⋊C₄	—	4	4	no	—
320	C₂²⋊C₄	—	2	8	no	—
321	C₂²⋊C₄	—	4	4	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	4	2	no	—
325	C₄²	—	4	2	no	—
326	C₄²	—	4	2	no	—
327	C₄²	C₂×D₄×C₃₇	1	4	yes	—
328	C₄²	C₂×Q₈×C₃₇	1	2	yes	—
329	C₄²	#41×C₃₇	1	2	yes	—
330	C₂³	—	2	2	no	—
331	C₂³	—	4	1	no	—
332	C₂³	—	4	1	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
336	Q₈	—	2	4	no	—
337	Q₈	—	4	2	no	—
338	D₄	—	2	4	no	—
339	D₄	—	4	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	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	8	4	no	—
359	C₂×C₄	C₂²⋊Q₈×C₃₇	1	4	yes	—
360	C₂×C₄	#127×C₃₇	1	2	yes	—
361	C₂×C₄	#127×C₃₇	1	2	yes	—
362	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
363	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
364	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
365	C₂×C₄	2₋¹⁺⁴×C₃₇	1	2	yes	—
366	C₈	—	2	4	no	—
367	C₈	—	2	4	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	4	no	—
370	C₂²	—	8	1	no	—
371	C₂²	—	8	1	no	—
372	C₂²	—	8	2	no	—
373	C₂²	C₂×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
374	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
375	C₂²	C₃₇×#536	1	1	yes	characteristic
376	C₂²	C₃₇×#575	1	2	yes	—
377	C₂²	C₃₇×#575	1	2	yes	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	4	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	8	1	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	1	no	—
386	C₄	—	8	2	no	—
387	C₄	C₃₇×#547	1	2	yes	—
388	C₄	D₄×Q₈×C₃₇	1	2	yes	—
389	C₂	—	8	2	no	—
390	C₂	C₃₇×#2542	1	1	yes	characteristic
391	C₂	C₃₇×#3080	1	2	yes	—
392	C₂	C₃₇×#3150	1	1	yes	characteristic
393	C₂	C₃₇×#3153	1	1	yes	characteristic
394	C₂	C₃₇×#3240	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×#2097	C₂	semidirect
9. C₃₇×#1847	C₂	semidirect
10. C₃₇×#1847	C₂	semidirect
11. C₃₇×#1767	C₂	semidirect
170. #28517	C₃₇	direct (N × H)
192. C₂×#479	C₂×C₃₇	semidirect
194. #2859	C₂×C₃₇	semidirect
196. #2097	C₂×C₃₇	semidirect
200. #1847	C₂×C₃₇	semidirect
201. #1847	C₂×C₃₇	semidirect
202. #1767	C₂×C₃₇	semidirect
238. C₃₇	#28517	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×#2097	2
C₃₇×#2092	2
C₃₇×#1959	2
C₃₇×#1847	2
C₃₇×#1767	2
#28517	37

Subgroups — C37×#28517 #22649770

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28517 #22649770