Subgroups — C₃₇×#28760 #22650013

Order 9472.

804 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#491	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#488	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2658	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2330	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2043	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2042	C₂	1	2	yes	maximal
7	C₃₇×#1983	C₂	1	2	yes	maximal
8	C₃₇×#1981	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1959	C₂	1	1	yes	maximal, characteristic
10	C₃₇×#1956	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
16	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
19	C₃₇×#491	—	2	4	no	—
20	C₃₇×#488	—	2	4	no	—
21	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
22	C₂×#103×C₃₇	C₂²	1	2	yes	—
23	C₂×#103×C₃₇	C₂²	1	2	yes	—
24	C₂×#103×C₃₇	C₂²	1	2	yes	—
25	C₂×#103×C₃₇	C₂²	1	2	yes	—
26	C₂×#103×C₃₇	C₂²	1	2	yes	—
27	C₂×#103×C₃₇	C₂²	1	2	yes	—
28	C₂×#102×C₃₇	C₂²	1	2	yes	—
29	C₂×#102×C₃₇	C₂²	1	2	yes	—
30	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
32	C₃₇×#399	—	2	2	no	—
33	C₃₇×#399	—	2	2	no	—
34	C₃₇×#389	—	2	2	no	—
35	C₃₇×#389	C₂²	1	2	yes	—
36	C₃₇×#387	—	2	2	no	—
37	C₃₇×#384	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
39	C₃₇×#376	C₂²	1	1	yes	characteristic
40	C₃₇×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
42	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
46	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
47	C₄⋊Q₈×C₃₇	—	2	2	no	—
48	C₄⋊Q₈×C₃₇	—	2	2	no	—
49	C₄⋊Q₈×C₃₇	—	2	4	no	—
50	C₄⋊Q₈×C₃₇	—	4	2	no	—
51	#125×C₃₇	—	2	2	no	—
52	#125×C₃₇	D₄	1	4	yes	—
53	#124×C₃₇	—	2	2	no	—
54	#124×C₃₇	—	2	2	no	—
55	#124×C₃₇	—	2	4	no	—
56	#124×C₃₇	—	4	2	no	—
57	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
70	C₂×C₄²×C₃₇	—	2	2	no	—
71	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₃₇	—	2	4	no	—
75	#103×C₃₇	—	2	4	no	—
76	#103×C₃₇	—	2	4	no	—
77	#103×C₃₇	—	2	4	no	—
78	#103×C₃₇	—	4	2	no	—
79	#103×C₃₇	—	4	2	no	—
80	#103×C₃₇	—	4	2	no	—
81	#102×C₃₇	—	2	4	no	—
82	#102×C₃₇	—	4	2	no	—
83	#97×C₃₇	—	2	2	no	—
84	C₄×C₈×C₃₇	—	2	2	no	—
85	#95×C₃₇	—	2	2	no	—
86	#95×C₃₇	—	2	2	no	—
87	#95×C₃₇	D₄	1	2	yes	—
88	#95×C₃₇	D₄	1	2	yes	—
89	C₂⁴×C₃₇	—	2	1	no	—
90	C₂×Q₈×C₃₇	—	2	1	no	—
91	C₂×Q₈×C₃₇	—	2	1	no	—
92	C₂×Q₈×C₃₇	—	2	1	no	—
93	C₂×Q₈×C₃₇	—	2	1	no	—
94	C₂×Q₈×C₃₇	—	2	2	no	—
95	C₂×Q₈×C₃₇	—	2	1	no	—
96	C₂×Q₈×C₃₇	—	2	1	no	—
97	C₂×Q₈×C₃₇	—	2	2	no	—
98	C₂×Q₈×C₃₇	—	2	2	no	—
99	C₂×Q₈×C₃₇	—	2	2	no	—
100	C₂×Q₈×C₃₇	—	2	2	no	—
101	C₂×Q₈×C₃₇	—	2	2	no	—
102	C₂×D₄×C₃₇	—	2	1	no	—
103	C₂×D₄×C₃₇	—	2	2	no	—
104	C₂×D₄×C₃₇	—	2	1	no	—
105	C₂×D₄×C₃₇	—	2	2	no	—
106	C₂²×C₄×C₃₇	—	2	2	no	—
107	C₂²×C₄×C₃₇	—	2	2	no	—
108	C₂²×C₄×C₃₇	—	2	1	no	—
109	C₂²×C₄×C₃₇	—	2	1	no	—
110	C₂²×C₄×C₃₇	—	2	1	no	—
111	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₃₇	—	2	2	no	—
117	C₂×C₈×C₃₇	—	2	2	no	—
118	C₂×C₈×C₃₇	—	2	2	no	—
119	C₂×C₈×C₃₇	—	2	2	no	—
120	C₂×C₈×C₃₇	—	2	2	no	—
121	C₂×C₈×C₃₇	—	2	2	no	—
122	C₄⋊C₄×C₃₇	—	2	8	no	—
123	C₄⋊C₄×C₃₇	—	2	2	no	—
124	C₄⋊C₄×C₃₇	—	2	2	no	—
125	C₄⋊C₄×C₃₇	—	2	2	no	—
126	C₄⋊C₄×C₃₇	—	4	2	no	—
127	C₄⋊C₄×C₃₇	—	4	2	no	—
128	C₄⋊C₄×C₃₇	—	4	4	no	—
129	C₄⋊C₄×C₃₇	—	4	4	no	—
130	C₄⋊C₄×C₃₇	—	8	2	no	—
131	C₄⋊C₄×C₃₇	—	8	2	no	—
132	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
133	C₂²⋊C₄×C₃₇	—	4	2	no	—
134	C₂²⋊C₄×C₃₇	—	4	2	no	—
135	C₂²⋊C₄×C₃₇	—	4	4	no	—
136	C₂²⋊C₄×C₃₇	—	4	4	no	—
137	C₄²×C₃₇	—	2	2	no	—
138	C₄²×C₃₇	—	8	2	no	—
139	C₄²×C₃₇	C₂×D₄	1	2	yes	—
140	C₄²×C₃₇	#41	1	2	yes	—
141	C₄²×C₃₇	#41	1	4	yes	—
142	C₂³×C₃₇	—	4	1	no	—
143	C₂³×C₃₇	—	4	1	no	—
144	C₂³×C₃₇	—	4	1	no	—
145	C₂³×C₃₇	—	4	2	no	—
146	C₂³×C₃₇	—	4	2	no	—
147	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₃₇	—	4	2	no	—
149	Q₈×C₃₇	—	4	2	no	—
150	Q₈×C₃₇	—	4	2	no	—
151	Q₈×C₃₇	—	4	2	no	—
152	Q₈×C₃₇	—	4	2	no	—
153	Q₈×C₃₇	—	4	2	no	—
154	D₄×C₃₇	—	4	2	no	—
155	D₄×C₃₇	—	4	2	no	—
156	C₂×C₄×C₃₇	—	2	2	no	—
157	C₂×C₄×C₃₇	—	2	2	no	—
158	C₂×C₄×C₃₇	—	2	2	no	—
159	C₂×C₄×C₃₇	—	2	2	no	—
160	C₂×C₄×C₃₇	—	2	4	no	—
161	C₂×C₄×C₃₇	—	2	1	no	—
162	C₂×C₄×C₃₇	—	2	1	no	—
163	C₂×C₄×C₃₇	—	2	2	no	—
164	C₂×C₄×C₃₇	—	2	2	no	—
165	C₂×C₄×C₃₇	—	4	2	no	—
166	C₂×C₄×C₃₇	—	4	2	no	—
167	C₂×C₄×C₃₇	—	4	1	no	—
168	C₂×C₄×C₃₇	—	4	1	no	—
169	C₂×C₄×C₃₇	—	4	1	no	—
170	C₂×C₄×C₃₇	—	4	1	no	—
171	C₂×C₄×C₃₇	—	4	1	no	—
172	C₂×C₄×C₃₇	—	4	1	no	—
173	C₂×C₄×C₃₇	—	4	1	no	—
174	C₂×C₄×C₃₇	—	4	2	no	—
175	C₂×C₄×C₃₇	—	4	1	no	—
176	C₂×C₄×C₃₇	—	4	1	no	—
177	C₂×C₄×C₃₇	—	4	2	no	—
178	C₂×C₄×C₃₇	—	4	2	no	—
179	C₂×C₄×C₃₇	#121	1	4	yes	—
180	C₂×C₄×C₃₇	#124	1	4	yes	—
181	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
183	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
185	C₈×C₃₇	—	4	2	no	—
186	C₈×C₃₇	—	4	2	no	—
187	#28760	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂²×C₃₇	—	8	2	no	—
189	C₂²×C₃₇	—	8	1	no	—
190	C₂²×C₃₇	—	8	1	no	—
191	C₂²×C₃₇	—	8	2	no	—
192	C₂²×C₃₇	—	8	1	no	—
193	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
194	C₂²×C₃₇	C₂×#124	1	1	yes	characteristic
195	C₂²×C₃₇	#535	1	1	yes	characteristic
196	C₂²×C₃₇	#577	1	2	yes	—
197	C₂²×C₃₇	#578	1	2	yes	—
198	C₄×C₃₇	—	2	4	no	—
199	C₄×C₃₇	—	2	4	no	—
200	C₄×C₃₇	—	4	1	no	—
201	C₄×C₃₇	—	4	1	no	—
202	C₄×C₃₇	—	4	4	no	—
203	C₄×C₃₇	—	8	2	no	—
204	C₄×C₃₇	—	8	1	no	—
205	C₄×C₃₇	—	8	1	no	—
206	C₄×C₃₇	—	8	1	no	—
207	C₄×C₃₇	#550	1	2	yes	—
208	C₄×C₃₇	#559	1	2	yes	—
209	C₂×#491	C₂×C₃₇	1	1	yes	characteristic, complemented
210	C₂×#488	C₂×C₃₇	1	1	yes	characteristic
211	#2658	C₂×C₃₇	1	1	yes	characteristic
212	#2330	C₂×C₃₇	1	1	yes	characteristic, complemented
213	#2043	C₂×C₃₇	1	2	yes	complemented
214	#2042	C₂×C₃₇	1	2	yes	—
215	#1983	C₂×C₃₇	1	2	yes	—
216	#1981	C₂×C₃₇	1	2	yes	complemented
217	#1959	C₂×C₃₇	1	1	yes	characteristic
218	#1956	C₂×C₃₇	1	1	yes	characteristic, complemented
219	#1768	C₂×C₃₇	1	1	yes	characteristic, complemented
220	C₂×C₃₇	—	16	1	no	—
221	C₂×C₃₇	#2548	1	1	yes	characteristic
222	C₂×C₃₇	#3046	1	2	yes	—
223	C₂×C₃₇	#3137	1	2	yes	—
224	C₂×C₃₇	#3221	1	1	yes	characteristic
225	C₂×C₃₇	#3223	1	1	yes	characteristic
226	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
227	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
228	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
229	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
230	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
231	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
232	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
233	#491	—	2	4	no	—
234	#488	—	2	4	no	—
235	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
236	C₂×#103	C₂²×C₃₇	1	2	yes	—
237	C₂×#103	C₂²×C₃₇	1	2	yes	—
238	C₂×#103	C₂²×C₃₇	1	2	yes	—
239	C₂×#103	C₂²×C₃₇	1	2	yes	—
240	C₂×#103	C₂²×C₃₇	1	2	yes	—
241	C₂×#103	C₂²×C₃₇	1	2	yes	—
242	C₂×#102	C₂²×C₃₇	1	2	yes	—
243	C₂×#102	C₂²×C₃₇	1	2	yes	—
244	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
245	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
246	#399	—	2	2	no	—
247	#399	—	2	2	no	—
248	#389	—	2	2	no	—
249	#389	C₂²×C₃₇	1	2	yes	—
250	#387	—	2	2	no	—
251	#384	C₂²×C₃₇	1	1	yes	characteristic
252	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
253	#376	C₂²×C₃₇	1	1	yes	characteristic
254	#336	C₂²×C₃₇	1	2	yes	—
255	C₃₇	#28760	1	1	yes	characteristic, direct product factor, Sylow
256	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
257	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
258	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
259	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
261	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
262	C₄⋊Q₈	—	2	2	no	—
263	C₄⋊Q₈	—	2	2	no	—
264	C₄⋊Q₈	—	2	4	no	—
265	C₄⋊Q₈	—	4	2	no	—
266	#125	—	2	2	no	—
267	#125	D₄×C₃₇	1	4	yes	—
268	#124	—	2	2	no	—
269	#124	—	2	2	no	—
270	#124	—	2	4	no	—
271	#124	—	4	2	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
289	C₄⋊C₈	—	2	4	no	—
290	#103	—	2	4	no	—
291	#103	—	2	4	no	—
292	#103	—	2	4	no	—
293	#103	—	4	2	no	—
294	#103	—	4	2	no	—
295	#103	—	4	2	no	—
296	#102	—	2	4	no	—
297	#102	—	4	2	no	—
298	#97	—	2	2	no	—
299	C₄×C₈	—	2	2	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	#95	D₄×C₃₇	1	2	yes	—
303	#95	D₄×C₃₇	1	2	yes	—
304	C₂⁴	—	2	1	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
330	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₄⋊C₄	—	2	8	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	—	4	4	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₄⋊C₄	—	8	2	no	—
346	C₄⋊C₄	—	8	2	no	—
347	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	4	4	no	—
351	C₂²⋊C₄	—	4	4	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	8	2	no	—
354	C₄²	C₂×D₄×C₃₇	1	2	yes	—
355	C₄²	#41×C₃₇	1	2	yes	—
356	C₄²	#41×C₃₇	1	4	yes	—
357	C₂³	—	4	1	no	—
358	C₂³	—	4	1	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
363	Q₈	—	4	2	no	—
364	Q₈	—	4	2	no	—
365	Q₈	—	4	2	no	—
366	Q₈	—	4	2	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	4	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	#121×C₃₇	1	4	yes	—
395	C₂×C₄	#124×C₃₇	1	4	yes	—
396	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
397	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
398	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
399	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
400	C₈	—	4	2	no	—
401	C₈	—	4	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	1	no	—
407	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
408	C₂²	C₂×#124×C₃₇	1	1	yes	characteristic
409	C₂²	C₃₇×#535	1	1	yes	characteristic
410	C₂²	C₃₇×#577	1	2	yes	—
411	C₂²	C₃₇×#578	1	2	yes	—
412	C₄	—	2	4	no	—
413	C₄	—	2	4	no	—
414	C₄	—	4	1	no	—
415	C₄	—	4	1	no	—
416	C₄	—	4	4	no	—
417	C₄	—	8	2	no	—
418	C₄	—	8	1	no	—
419	C₄	—	8	1	no	—
420	C₄	—	8	1	no	—
421	C₄	C₃₇×#550	1	2	yes	—
422	C₄	C₃₇×#559	1	2	yes	—
423	C₂	—	16	1	no	—
424	C₂	C₃₇×#2548	1	1	yes	characteristic
425	C₂	C₃₇×#3046	1	2	yes	—
426	C₂	C₃₇×#3137	1	2	yes	—
427	C₂	C₃₇×#3221	1	1	yes	characteristic
428	C₂	C₃₇×#3223	1	1	yes	characteristic

	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 ◁ C₃₇×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#491	C₂	semidirect
4. C₃₇×#2330	C₂	semidirect
5. C₃₇×#2043	C₂	semidirect
8. C₃₇×#1981	C₂	semidirect
10. C₃₇×#1956	C₂	semidirect
11. C₃₇×#1768	C₂	semidirect
187. #28760	C₃₇	direct (N × H)
209. C₂×#491	C₂×C₃₇	semidirect
212. #2330	C₂×C₃₇	semidirect
213. #2043	C₂×C₃₇	semidirect
216. #1981	C₂×C₃₇	semidirect
218. #1956	C₂×C₃₇	semidirect
219. #1768	C₂×C₃₇	semidirect
255. C₃₇	#28760	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×#491	2
C₂×C₃₇×#488	2
C₃₇×#2658	2
C₃₇×#2330	2
C₃₇×#2043	2
C₃₇×#2042	2
C₃₇×#1983	2
C₃₇×#1981	2
C₃₇×#1959	2
C₃₇×#1956	2
C₃₇×#1768	2
#28760	37

Subgroups — C37×#28760 #22650013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28760 #22650013