Subgroups — C₃₇×#28289 #22649542

Order 9472.

794 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#476	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2331	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2326	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2066	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2065	C₂	1	2	yes	maximal
7	C₃₇×#1983	C₂	1	2	yes	maximal
8	C₃₇×#1948	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1843	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1804	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
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×#476	—	2	4	no	—
17	C₃₇×#475	—	2	4	no	—
18	C₂×#106×C₃₇	C₂²	1	2	yes	—
19	C₂×#106×C₃₇	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
24	C₂×#103×C₃₇	C₂²	1	2	yes	—
25	C₂×#103×C₃₇	C₂²	1	2	yes	—
26	C₂×#102×C₃₇	C₂²	1	2	yes	—
27	C₂×#102×C₃₇	C₂²	1	2	yes	—
28	C₃₇×#391	—	2	2	no	—
29	C₃₇×#391	C₂²	1	1	yes	characteristic
30	C₃₇×#390	C₂²	1	1	yes	characteristic
31	C₃₇×#389	C₂²	1	2	yes	—
32	C₃₇×#388	—	2	2	no	—
33	C₃₇×#387	—	2	2	no	—
34	C₃₇×#385	—	2	2	no	—
35	C₃₇×#384	C₂²	1	1	yes	characteristic
36	C₃₇×#382	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
38	C₃₇×#376	C₂²	1	1	yes	characteristic
39	C₃₇×#340	C₂²	1	2	yes	—
40	C₃₇×#340	C₂²	1	2	yes	—
41	C₂²×Q₈×C₃₇	—	2	1	no	—
42	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₃₇	—	2	1	no	—
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	D₄	1	4	yes	—
49	#124×C₃₇	—	2	2	no	—
50	#124×C₃₇	Q₈	1	4	yes	complemented
51	C₄×Q₈×C₃₇	—	2	2	no	—
52	C₄×Q₈×C₃₇	—	2	2	no	—
53	C₄×D₄×C₃₇	—	2	2	no	—
54	C₄×D₄×C₃₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
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	2	yes	—
63	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
66	C₂×C₄²×C₃₇	—	2	1	no	—
67	C₂×C₄²×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	#106×C₃₇	—	2	4	no	—
72	#106×C₃₇	—	2	4	no	—
73	C₄⋊C₈×C₃₇	—	2	2	no	—
74	C₄⋊C₈×C₃₇	—	2	2	no	—
75	C₄⋊C₈×C₃₇	—	2	4	no	—
76	C₄⋊C₈×C₃₇	—	4	2	no	—
77	#103×C₃₇	—	2	4	no	—
78	#103×C₃₇	—	4	2	no	—
79	#102×C₃₇	—	2	4	no	—
80	#102×C₃₇	—	4	2	no	—
81	#95×C₃₇	—	2	2	no	—
82	#95×C₃₇	—	2	1	no	—
83	#95×C₃₇	—	2	1	no	—
84	#95×C₃₇	—	2	2	no	—
85	#95×C₃₇	—	2	2	no	—
86	#95×C₃₇	D₄	1	2	yes	—
87	#95×C₃₇	D₄	1	2	yes	—
88	C₂⁴×C₃₇	—	2	1	no	—
89	C₂×Q₈×C₃₇	—	2	4	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	1	no	—
95	C₂×Q₈×C₃₇	—	8	2	no	—
96	C₂×Q₈×C₃₇	C₂×Q₈	1	2	yes	—
97	C₂×D₄×C₃₇	—	2	1	no	—
98	C₂×D₄×C₃₇	—	2	1	no	—
99	C₂×D₄×C₃₇	—	2	1	no	—
100	C₂×D₄×C₃₇	—	2	1	no	—
101	C₂×D₄×C₃₇	—	2	1	no	—
102	C₂×D₄×C₃₇	C₂×Q₈	1	2	yes	—
103	C₂²×C₄×C₃₇	—	2	1	no	—
104	C₂²×C₄×C₃₇	—	2	2	no	—
105	C₂²×C₄×C₃₇	—	2	2	no	—
106	C₂²×C₄×C₃₇	—	2	1	no	—
107	C₂²×C₄×C₃₇	—	2	1	no	—
108	C₂²×C₄×C₃₇	—	4	2	no	—
109	C₂²×C₄×C₃₇	—	8	2	no	—
110	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
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	C₂⁴	1	1	yes	characteristic
115	C₂×C₈×C₃₇	—	2	2	no	—
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	C₄⋊C₄×C₃₇	—	2	4	no	—
122	C₄⋊C₄×C₃₇	—	2	2	no	—
123	C₄⋊C₄×C₃₇	—	2	1	no	—
124	C₄⋊C₄×C₃₇	—	2	1	no	—
125	C₄⋊C₄×C₃₇	—	2	1	no	—
126	C₄⋊C₄×C₃₇	—	2	1	no	—
127	C₄⋊C₄×C₃₇	—	2	2	no	—
128	C₄⋊C₄×C₃₇	—	2	2	no	—
129	C₄⋊C₄×C₃₇	—	4	2	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	—	2	8	no	—
134	C₂²⋊C₄×C₃₇	—	4	2	no	—
135	C₂²⋊C₄×C₃₇	—	8	2	no	—
136	C₄²×C₃₇	—	2	1	no	—
137	C₄²×C₃₇	—	2	1	no	—
138	C₄²×C₃₇	—	4	2	no	—
139	C₄²×C₃₇	—	8	2	no	—
140	C₄²×C₃₇	C₂×D₄	1	2	yes	—
141	C₄²×C₃₇	C₂×Q₈	1	2	yes	—
142	C₄²×C₃₇	#41	1	2	yes	—
143	C₄²×C₃₇	#41	1	2	yes	—
144	C₂³×C₃₇	—	2	2	no	—
145	C₂³×C₃₇	—	4	1	no	—
146	C₂³×C₃₇	—	4	1	no	—
147	C₂³×C₃₇	—	4	2	no	—
148	C₂³×C₃₇	—	4	2	no	—
149	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₃₇	—	2	2	no	—
151	Q₈×C₃₇	—	2	2	no	—
152	Q₈×C₃₇	—	4	1	no	—
153	Q₈×C₃₇	—	4	1	no	—
154	Q₈×C₃₇	—	8	4	no	—
155	D₄×C₃₇	—	2	2	no	—
156	D₄×C₃₇	—	2	2	no	—
157	D₄×C₃₇	—	4	1	no	—
158	D₄×C₃₇	—	4	1	no	—
159	C₂×C₄×C₃₇	—	2	2	no	—
160	C₂×C₄×C₃₇	—	2	2	no	—
161	C₂×C₄×C₃₇	—	2	2	no	—
162	C₂×C₄×C₃₇	—	2	2	no	—
163	C₂×C₄×C₃₇	—	2	4	no	—
164	C₂×C₄×C₃₇	—	2	2	no	—
165	C₂×C₄×C₃₇	—	2	2	no	—
166	C₂×C₄×C₃₇	—	2	2	no	—
167	C₂×C₄×C₃₇	—	2	2	no	—
168	C₂×C₄×C₃₇	—	4	1	no	—
169	C₂×C₄×C₃₇	—	4	1	no	—
170	C₂×C₄×C₃₇	—	4	2	no	—
171	C₂×C₄×C₃₇	—	4	2	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	2	no	—
176	C₂×C₄×C₃₇	—	4	2	no	—
177	C₂×C₄×C₃₇	—	4	2	no	—
178	C₂×C₄×C₃₇	—	4	2	no	—
179	C₂×C₄×C₃₇	—	8	4	no	—
180	C₂×C₄×C₃₇	#121	1	2	yes	—
181	C₂×C₄×C₃₇	#121	1	2	yes	—
182	C₂×C₄×C₃₇	C₂²⋊Q₈	1	4	yes	—
183	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
189	C₈×C₃₇	—	4	2	no	—
190	C₈×C₃₇	—	4	2	no	—
191	#28289	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂²×C₃₇	—	4	4	no	—
193	C₂²×C₃₇	—	4	2	no	—
194	C₂²×C₃₇	—	8	2	no	—
195	C₂²×C₃₇	—	8	1	no	—
196	C₂²×C₃₇	—	8	1	no	—
197	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
198	C₂²×C₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
199	C₂²×C₃₇	#537	1	1	yes	characteristic
200	C₂²×C₃₇	#577	1	2	yes	—
201	C₂²×C₃₇	#577	1	2	yes	—
202	C₄×C₃₇	—	2	4	no	—
203	C₄×C₃₇	—	2	2	no	—
204	C₄×C₃₇	—	2	2	no	—
205	C₄×C₃₇	—	4	2	no	—
206	C₄×C₃₇	—	4	4	no	—
207	C₄×C₃₇	—	4	2	no	—
208	C₄×C₃₇	—	8	2	no	—
209	C₄×C₃₇	—	8	1	no	—
210	C₄×C₃₇	—	8	1	no	—
211	C₄×C₃₇	D₄×Q₈	1	1	yes	characteristic
212	C₄×C₃₇	#550	1	1	yes	characteristic
213	C₄×C₃₇	#554	1	1	yes	characteristic
214	C₄×C₃₇	#556	1	1	yes	characteristic
215	C₂×#475	C₂×C₃₇	1	1	yes	characteristic, complemented
216	C₂×#476	C₂×C₃₇	1	1	yes	characteristic
217	#2331	C₂×C₃₇	1	1	yes	characteristic, complemented
218	#2326	C₂×C₃₇	1	1	yes	characteristic
219	#2066	C₂×C₃₇	1	2	yes	complemented
220	#2065	C₂×C₃₇	1	2	yes	—
221	#1983	C₂×C₃₇	1	2	yes	—
222	#1948	C₂×C₃₇	1	2	yes	complemented
223	#1843	C₂×C₃₇	1	1	yes	characteristic, complemented
224	#1805	C₂×C₃₇	1	1	yes	characteristic, complemented
225	#1804	C₂×C₃₇	1	1	yes	characteristic
226	C₂×C₃₇	—	8	2	no	—
227	C₂×C₃₇	#2538	1	1	yes	characteristic
228	C₂×C₃₇	#3042	1	1	yes	characteristic
229	C₂×C₃₇	#3043	1	1	yes	characteristic
230	C₂×C₃₇	#3084	1	2	yes	—
231	C₂×C₃₇	#3263	1	2	yes	—
232	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
233	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
234	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
236	#476	—	2	4	no	—
237	#475	—	2	4	no	—
238	C₂×#106	C₂²×C₃₇	1	2	yes	—
239	C₂×#106	C₂²×C₃₇	1	2	yes	—
240	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
241	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
242	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
243	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
244	C₂×#103	C₂²×C₃₇	1	2	yes	—
245	C₂×#103	C₂²×C₃₇	1	2	yes	—
246	C₂×#102	C₂²×C₃₇	1	2	yes	—
247	C₂×#102	C₂²×C₃₇	1	2	yes	—
248	#391	—	2	2	no	—
249	#391	C₂²×C₃₇	1	1	yes	characteristic
250	#390	C₂²×C₃₇	1	1	yes	characteristic
251	#389	C₂²×C₃₇	1	2	yes	—
252	#388	—	2	2	no	—
253	#387	—	2	2	no	—
254	#385	—	2	2	no	—
255	#384	C₂²×C₃₇	1	1	yes	characteristic
256	#382	C₂²×C₃₇	1	1	yes	characteristic
257	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
258	#376	C₂²×C₃₇	1	1	yes	characteristic
259	#340	C₂²×C₃₇	1	2	yes	—
260	#340	C₂²×C₃₇	1	2	yes	—
261	C₃₇	#28289	1	1	yes	characteristic, direct product factor, Sylow
262	C₂²×Q₈	—	2	1	no	—
263	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
264	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
265	C₂³×C₄	—	2	1	no	—
266	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
267	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
268	C₄⋊Q₈	—	2	2	no	—
269	C₄⋊Q₈	D₄×C₃₇	1	4	yes	—
270	#124	—	2	2	no	—
271	#124	Q₈×C₃₇	1	4	yes	complemented
272	C₄×Q₈	—	2	2	no	—
273	C₄×Q₈	—	2	2	no	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
292	#106	—	2	4	no	—
293	#106	—	2	4	no	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	—	2	2	no	—
296	C₄⋊C₈	—	2	4	no	—
297	C₄⋊C₈	—	4	2	no	—
298	#103	—	2	4	no	—
299	#103	—	4	2	no	—
300	#102	—	2	4	no	—
301	#102	—	4	2	no	—
302	#95	—	2	2	no	—
303	#95	—	2	1	no	—
304	#95	—	2	1	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	D₄×C₃₇	1	2	yes	—
308	#95	D₄×C₃₇	1	2	yes	—
309	C₂⁴	—	2	1	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	8	2	no	—
317	C₂×Q₈	C₂×Q₈×C₃₇	1	2	yes	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	C₂×Q₈×C₃₇	1	2	yes	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	8	2	no	—
331	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
335	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	8	2	no	—
352	C₄⋊C₄	—	8	2	no	—
353	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
354	C₂²⋊C₄	—	2	8	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₂²⋊C₄	—	8	2	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	4	2	no	—
360	C₄²	—	8	2	no	—
361	C₄²	C₂×D₄×C₃₇	1	2	yes	—
362	C₄²	C₂×Q₈×C₃₇	1	2	yes	—
363	C₄²	#41×C₃₇	1	2	yes	—
364	C₄²	#41×C₃₇	1	2	yes	—
365	C₂³	—	2	2	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	2	no	—
369	C₂³	—	4	2	no	—
370	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
371	Q₈	—	2	2	no	—
372	Q₈	—	2	2	no	—
373	Q₈	—	4	1	no	—
374	Q₈	—	4	1	no	—
375	Q₈	—	8	4	no	—
376	D₄	—	2	2	no	—
377	D₄	—	2	2	no	—
378	D₄	—	4	1	no	—
379	D₄	—	4	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	8	4	no	—
401	C₂×C₄	#121×C₃₇	1	2	yes	—
402	C₂×C₄	#121×C₃₇	1	2	yes	—
403	C₂×C₄	C₂²⋊Q₈×C₃₇	1	4	yes	—
404	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
405	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
406	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
407	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
408	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
409	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
410	C₈	—	4	2	no	—
411	C₈	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	4	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	1	no	—
417	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
418	C₂²	C₂×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
419	C₂²	C₃₇×#537	1	1	yes	characteristic
420	C₂²	C₃₇×#577	1	2	yes	—
421	C₂²	C₃₇×#577	1	2	yes	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	4	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	2	no	—
428	C₄	—	8	2	no	—
429	C₄	—	8	1	no	—
430	C₄	—	8	1	no	—
431	C₄	D₄×Q₈×C₃₇	1	1	yes	characteristic
432	C₄	C₃₇×#550	1	1	yes	characteristic
433	C₄	C₃₇×#554	1	1	yes	characteristic
434	C₄	C₃₇×#556	1	1	yes	characteristic
435	C₂	—	8	2	no	—
436	C₂	C₃₇×#2538	1	1	yes	characteristic
437	C₂	C₃₇×#3042	1	1	yes	characteristic
438	C₂	C₃₇×#3043	1	1	yes	characteristic
439	C₂	C₃₇×#3084	1	2	yes	—
440	C₂	C₃₇×#3263	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 ◁ C₃₇×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#475	C₂	semidirect
3. C₃₇×#2331	C₂	semidirect
5. C₃₇×#2066	C₂	semidirect
8. C₃₇×#1948	C₂	semidirect
9. C₃₇×#1843	C₂	semidirect
10. C₃₇×#1805	C₂	semidirect
50. #124×C₃₇	Q₈	semidirect
191. #28289	C₃₇	direct (N × H)
215. C₂×#475	C₂×C₃₇	semidirect
217. #2331	C₂×C₃₇	semidirect
219. #2066	C₂×C₃₇	semidirect
222. #1948	C₂×C₃₇	semidirect
223. #1843	C₂×C₃₇	semidirect
224. #1805	C₂×C₃₇	semidirect
261. C₃₇	#28289	direct (N × H)
271. #124	Q₈×C₃₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃₇×#475	2
C₂×C₃₇×#476	2
C₃₇×#2331	2
C₃₇×#2326	2
C₃₇×#2066	2
C₃₇×#2065	2
C₃₇×#1983	2
C₃₇×#1948	2
C₃₇×#1843	2
C₃₇×#1805	2
C₃₇×#1804	2
#28289	37

Subgroups — C37×#28289 #22649542

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28289 #22649542