Subgroups — C₃₇×#28728 #22649981

Order 9472.

838 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#490	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₇×#486	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2660	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2328	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2073	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2071	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1991	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1804	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1802	C₂	1	2	yes	maximal, complemented
11	C₃₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₃₇	C₂²	1	2	yes	—
16	C₃₇×#490	—	2	4	no	—
17	C₃₇×#486	—	2	4	no	—
18	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
19	C₂×#102×C₃₇	C₂²	1	2	yes	—
20	C₂×#102×C₃₇	C₂²	1	2	yes	—
21	C₂×#102×C₃₇	C₂²	1	2	yes	—
22	C₂×#102×C₃₇	C₂²	1	2	yes	—
23	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
25	C₃₇×#398	—	2	2	no	—
26	C₃₇×#395	—	2	2	no	—
27	C₃₇×#390	C₂²	1	2	yes	—
28	C₃₇×#386	—	2	2	no	—
29	C₃₇×#386	—	2	2	no	—
30	C₃₇×#384	C₂²	1	1	yes	characteristic
31	C₃₇×#384	C₂²	1	1	yes	characteristic
32	C₃₇×#382	C₂²	1	1	yes	characteristic
33	C₃₇×#382	C₂²	1	1	yes	characteristic
34	C₃₇×#382	C₂²	1	1	yes	characteristic
35	C₃₇×#376	C₂²	1	1	yes	characteristic
36	C₃₇×#340	C₂²	1	2	yes	—
37	C₃₇×#340	C₂²	1	2	yes	—
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×D₄×C₃₇	—	2	1	no	—
43	C₂²×D₄×C₃₇	—	2	1	no	—
44	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
45	C₂³×C₄×C₃₇	—	2	2	no	—
46	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
47	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
48	C₄⋊Q₈×C₃₇	—	2	2	no	—
49	C₄⋊Q₈×C₃₇	—	2	2	no	—
50	#127×C₃₇	—	2	2	no	—
51	#127×C₃₇	D₄	1	4	yes	—
52	#125×C₃₇	—	2	2	no	—
53	#125×C₃₇	—	2	2	no	—
54	C₄×D₄×C₃₇	—	2	8	no	—
55	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
68	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₃₇	—	2	4	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	1	no	—
79	#95×C₃₇	—	2	1	no	—
80	#95×C₃₇	—	2	2	no	—
81	#95×C₃₇	—	2	2	no	—
82	#95×C₃₇	D₄	1	2	yes	—
83	#95×C₃₇	D₄	1	2	yes	—
84	C₂⁴×C₃₇	—	2	2	no	—
85	C₂×Q₈×C₃₇	—	4	2	no	—
86	C₂×Q₈×C₃₇	—	8	2	no	—
87	C₂×D₄×C₃₇	—	2	4	no	—
88	C₂×D₄×C₃₇	—	2	4	no	—
89	C₂×D₄×C₃₇	—	2	4	no	—
90	C₂×D₄×C₃₇	—	2	2	no	—
91	C₂×D₄×C₃₇	—	2	4	no	—
92	C₂×D₄×C₃₇	—	8	2	no	—
93	C₂×D₄×C₃₇	—	8	2	no	—
94	C₂×D₄×C₃₇	C₂×D₄	1	4	yes	—
95	C₂²×C₄×C₃₇	—	2	1	no	—
96	C₂²×C₄×C₃₇	—	2	2	no	—
97	C₂²×C₄×C₃₇	—	2	1	no	—
98	C₂²×C₄×C₃₇	—	2	1	no	—
99	C₂²×C₄×C₃₇	—	2	1	no	—
100	C₂²×C₄×C₃₇	—	4	4	no	—
101	C₂²×C₄×C₃₇	—	8	2	no	—
102	C₂²×C₄×C₃₇	—	8	2	no	—
103	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
114	C₄⋊C₄×C₃₇	—	2	1	no	—
115	C₄⋊C₄×C₃₇	—	2	1	no	—
116	C₄⋊C₄×C₃₇	—	2	1	no	—
117	C₄⋊C₄×C₃₇	—	2	1	no	—
118	C₄⋊C₄×C₃₇	—	2	4	no	—
119	C₄⋊C₄×C₃₇	—	2	1	no	—
120	C₄⋊C₄×C₃₇	—	2	1	no	—
121	C₄⋊C₄×C₃₇	—	2	1	no	—
122	C₄⋊C₄×C₃₇	—	2	1	no	—
123	C₄⋊C₄×C₃₇	—	4	2	no	—
124	C₄⋊C₄×C₃₇	—	4	2	no	—
125	C₄⋊C₄×C₃₇	—	4	2	no	—
126	C₄⋊C₄×C₃₇	—	8	2	no	—
127	C₄⋊C₄×C₃₇	—	8	2	no	—
128	C₂²⋊C₄×C₃₇	—	4	4	no	—
129	C₂²⋊C₄×C₃₇	—	8	2	no	—
130	C₂²⋊C₄×C₃₇	—	8	2	no	—
131	C₄²×C₃₇	—	2	2	no	—
132	C₄²×C₃₇	C₂×D₄	1	2	yes	—
133	C₄²×C₃₇	#41	1	2	yes	—
134	C₄²×C₃₇	#41	1	4	yes	—
135	C₂³×C₃₇	—	2	4	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	—	4	2	no	—
141	C₂³×C₃₇	—	4	2	no	—
142	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₃₇	—	8	4	no	—
144	D₄×C₃₇	—	2	8	no	—
145	D₄×C₃₇	—	4	4	no	—
146	D₄×C₃₇	—	8	4	no	—
147	D₄×C₃₇	—	8	4	no	—
148	C₂×C₄×C₃₇	—	2	2	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	1	no	—
156	C₂×C₄×C₃₇	—	4	1	no	—
157	C₂×C₄×C₃₇	—	4	1	no	—
158	C₂×C₄×C₃₇	—	4	1	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	—	4	2	no	—
165	C₂×C₄×C₃₇	—	4	2	no	—
166	C₂×C₄×C₃₇	—	8	8	no	—
167	C₂×C₄×C₃₇	#121	1	2	yes	—
168	C₂×C₄×C₃₇	#121	1	2	yes	—
169	C₂×C₄×C₃₇	#124	1	4	yes	—
170	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
172	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₃₇	2₋¹⁺⁴	1	2	yes	—
174	C₈×C₃₇	—	4	2	no	—
175	C₈×C₃₇	—	4	2	no	—
176	#28728	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂²×C₃₇	—	4	4	no	—
178	C₂²×C₃₇	—	4	4	no	—
179	C₂²×C₃₇	—	4	4	no	—
180	C₂²×C₃₇	—	8	2	no	—
181	C₂²×C₃₇	—	8	2	no	—
182	C₂²×C₃₇	—	8	2	no	—
183	C₂²×C₃₇	—	8	2	no	—
184	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
185	C₂²×C₃₇	C₂×#124	1	1	yes	characteristic
186	C₂²×C₃₇	#536	1	1	yes	characteristic
187	C₂²×C₃₇	#576	1	2	yes	—
188	C₂²×C₃₇	#577	1	2	yes	—
189	C₄×C₃₇	—	2	4	no	—
190	C₄×C₃₇	—	2	2	no	—
191	C₄×C₃₇	—	2	2	no	—
192	C₄×C₃₇	—	4	2	no	—
193	C₄×C₃₇	—	8	2	no	—
194	C₄×C₃₇	—	8	1	no	—
195	C₄×C₃₇	—	8	1	no	—
196	C₄×C₃₇	—	8	1	no	—
197	C₄×C₃₇	—	8	1	no	—
198	C₄×C₃₇	#547	1	2	yes	—
199	C₄×C₃₇	#556	1	2	yes	—
200	C₂×#490	C₂×C₃₇	1	1	yes	characteristic
201	C₂×#486	C₂×C₃₇	1	1	yes	characteristic
202	#2660	C₂×C₃₇	1	1	yes	characteristic, complemented
203	#2328	C₂×C₃₇	1	1	yes	characteristic
204	#2073	C₂×C₃₇	1	2	yes	complemented
205	#2071	C₂×C₃₇	1	2	yes	complemented
206	#1993	C₂×C₃₇	1	1	yes	characteristic, complemented
207	#1991	C₂×C₃₇	1	1	yes	characteristic, complemented
208	#1804	C₂×C₃₇	1	2	yes	complemented
209	#1802	C₂×C₃₇	1	2	yes	complemented
210	#1768	C₂×C₃₇	1	1	yes	characteristic, complemented
211	C₂×C₃₇	—	8	4	no	—
212	C₂×C₃₇	#2547	1	1	yes	characteristic
213	C₂×C₃₇	#3041	1	1	yes	characteristic
214	C₂×C₃₇	#3042	1	1	yes	characteristic
215	C₂×C₃₇	#3136	1	2	yes	—
216	C₂×C₃₇	#3241	1	2	yes	—
217	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
218	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
219	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
220	C₂×C₄×D₄	C₂²×C₃₇	1	2	yes	—
221	#490	—	2	4	no	—
222	#486	—	2	4	no	—
223	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
224	C₂×#102	C₂²×C₃₇	1	2	yes	—
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×#97	C₂²×C₃₇	1	1	yes	characteristic
229	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
230	#398	—	2	2	no	—
231	#395	—	2	2	no	—
232	#390	C₂²×C₃₇	1	2	yes	—
233	#386	—	2	2	no	—
234	#386	—	2	2	no	—
235	#384	C₂²×C₃₇	1	1	yes	characteristic
236	#384	C₂²×C₃₇	1	1	yes	characteristic
237	#382	C₂²×C₃₇	1	1	yes	characteristic
238	#382	C₂²×C₃₇	1	1	yes	characteristic
239	#382	C₂²×C₃₇	1	1	yes	characteristic
240	#376	C₂²×C₃₇	1	1	yes	characteristic
241	#340	C₂²×C₃₇	1	2	yes	—
242	#340	C₂²×C₃₇	1	2	yes	—
243	#340	C₂²×C₃₇	1	2	yes	—
244	#340	C₂²×C₃₇	1	2	yes	—
245	#336	C₂²×C₃₇	1	2	yes	—
246	C₃₇	#28728	1	1	yes	characteristic, direct product factor, Sylow
247	C₂²×Q₈	—	2	1	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
251	C₂³×C₄	—	2	2	no	—
252	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
253	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
254	C₄⋊Q₈	—	2	2	no	—
255	C₄⋊Q₈	—	2	2	no	—
256	#127	—	2	2	no	—
257	#127	D₄×C₃₇	1	4	yes	—
258	#125	—	2	2	no	—
259	#125	—	2	2	no	—
260	C₄×D₄	—	2	8	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
276	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
277	C₄⋊C₈	—	2	4	no	—
278	#102	—	2	4	no	—
279	#102	—	2	4	no	—
280	#102	—	2	4	no	—
281	#102	—	2	4	no	—
282	#97	—	2	2	no	—
283	C₄×C₈	—	2	2	no	—
284	#95	—	2	1	no	—
285	#95	—	2	1	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	#95	D₄×C₃₇	1	2	yes	—
289	#95	D₄×C₃₇	1	2	yes	—
290	C₂⁴	—	2	2	no	—
291	C₂×Q₈	—	4	2	no	—
292	C₂×Q₈	—	8	2	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	8	2	no	—
299	C₂×D₄	—	8	2	no	—
300	C₂×D₄	C₂×D₄×C₃₇	1	4	yes	—
301	C₂²×C₄	—	2	1	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	—	4	4	no	—
307	C₂²×C₄	—	8	2	no	—
308	C₂²×C₄	—	8	2	no	—
309	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
313	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	8	2	no	—
333	C₄⋊C₄	—	8	2	no	—
334	C₂²⋊C₄	—	4	4	no	—
335	C₂²⋊C₄	—	8	2	no	—
336	C₂²⋊C₄	—	8	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	C₂×D₄×C₃₇	1	2	yes	—
339	C₄²	#41×C₃₇	1	2	yes	—
340	C₄²	#41×C₃₇	1	4	yes	—
341	C₂³	—	2	4	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
349	Q₈	—	8	4	no	—
350	D₄	—	2	8	no	—
351	D₄	—	4	4	no	—
352	D₄	—	8	4	no	—
353	D₄	—	8	4	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	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	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	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	8	8	no	—
373	C₂×C₄	#121×C₃₇	1	2	yes	—
374	C₂×C₄	#121×C₃₇	1	2	yes	—
375	C₂×C₄	#124×C₃₇	1	4	yes	—
376	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
377	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
378	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
379	C₂×C₄	2₋¹⁺⁴×C₃₇	1	2	yes	—
380	C₈	—	4	2	no	—
381	C₈	—	4	2	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
390	C₂²	C₂×#124×C₃₇	1	1	yes	characteristic
391	C₂²	C₃₇×#536	1	1	yes	characteristic
392	C₂²	C₃₇×#576	1	2	yes	—
393	C₂²	C₃₇×#577	1	2	yes	—
394	C₄	—	2	4	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	8	2	no	—
399	C₄	—	8	1	no	—
400	C₄	—	8	1	no	—
401	C₄	—	8	1	no	—
402	C₄	—	8	1	no	—
403	C₄	C₃₇×#547	1	2	yes	—
404	C₄	C₃₇×#556	1	2	yes	—
405	C₂	—	8	4	no	—
406	C₂	C₃₇×#2547	1	1	yes	characteristic
407	C₂	C₃₇×#3041	1	1	yes	characteristic
408	C₂	C₃₇×#3042	1	1	yes	characteristic
409	C₂	C₃₇×#3136	1	2	yes	—
410	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
3. C₃₇×#2660	C₂	semidirect
5. C₃₇×#2073	C₂	semidirect
6. C₃₇×#2071	C₂	semidirect
7. C₃₇×#1993	C₂	semidirect
8. C₃₇×#1991	C₂	semidirect
9. C₃₇×#1804	C₂	semidirect
10. C₃₇×#1802	C₂	semidirect
11. C₃₇×#1768	C₂	semidirect
176. #28728	C₃₇	direct (N × H)
202. #2660	C₂×C₃₇	semidirect
204. #2073	C₂×C₃₇	semidirect
205. #2071	C₂×C₃₇	semidirect
206. #1993	C₂×C₃₇	semidirect
207. #1991	C₂×C₃₇	semidirect
208. #1804	C₂×C₃₇	semidirect
209. #1802	C₂×C₃₇	semidirect
210. #1768	C₂×C₃₇	semidirect
246. C₃₇	#28728	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×#490	2
C₂×C₃₇×#486	2
C₃₇×#2660	2
C₃₇×#2328	2
C₃₇×#2073	2
C₃₇×#2071	2
C₃₇×#1993	2
C₃₇×#1991	2
C₃₇×#1804	2
C₃₇×#1802	2
C₃₇×#1768	2
#28728	37

Subgroups — C37×#28728 #22649981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28728 #22649981