Subgroups — C₃₇×#29883 #22651136

Order 9472.

754 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#432	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2857	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2851	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2088	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2087	C₂	1	2	yes	maximal, complemented
7	C₃₇×#2077	C₂	1	2	yes	maximal
8	C₃₇×#2075	C₂	1	2	yes	maximal
9	C₃₇×#1993	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1992	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1836	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₃₇	—	2	1	no	—
15	C₂²×C₄²×C₃₇	C₂²	1	1	yes	characteristic
16	C₃₇×#501	—	2	4	no	—
17	C₃₇×#432	—	2	4	no	—
18	C₂×#107×C₃₇	C₂²	1	2	yes	—
19	C₂×#106×C₃₇	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
21	C₂×C₂²⋊C₈×C₃₇	C₂²	1	2	yes	—
22	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
24	C₃₇×#391	—	2	1	no	—
25	C₃₇×#389	—	2	1	no	—
26	C₃₇×#389	C₂²	1	1	yes	characteristic
27	C₃₇×#389	C₂²	1	1	yes	characteristic
28	C₃₇×#389	C₂²	1	2	yes	—
29	C₃₇×#387	—	2	1	no	—
30	C₃₇×#387	—	2	1	no	—
31	C₃₇×#385	—	2	1	no	—
32	C₃₇×#385	—	2	1	no	—
33	C₃₇×#384	C₂²	1	1	yes	characteristic
34	C₃₇×#382	C₂²	1	1	yes	characteristic
35	C₃₇×#380	—	2	1	no	—
36	C₃₇×#380	C₂²	1	1	yes	characteristic
37	C₃₇×#380	C₂²	1	2	yes	—
38	C₃₇×#380	C₂²	1	1	yes	characteristic
39	C₃₇×#340	C₂²	1	2	yes	—
40	C₃₇×#340	C₂²	1	2	yes	—
41	C₃₇×#340	C₂²	1	2	yes	—
42	C₃₇×#340	C₂²	1	2	yes	—
43	C₃₇×#340	C₂²	1	2	yes	—
44	C₃₇×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₃₇	—	2	1	no	—
46	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
50	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₃₇	—	2	2	no	—
52	C₄⋊Q₈×C₃₇	—	2	2	no	—
53	#125×C₃₇	—	2	2	no	—
54	#125×C₃₇	—	2	2	no	—
55	C₂²⋊Q₈×C₃₇	—	4	4	no	—
56	C₂×C₄⋊C₄×C₃₇	—	2	1	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	1	no	—
61	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
73	C₂×C₄²×C₃₇	—	2	2	no	—
74	C₂×C₄²×C₃₇	—	2	2	no	—
75	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
79	#107×C₃₇	—	2	4	no	—
80	#106×C₃₇	—	2	4	no	—
81	C₄⋊C₈×C₃₇	—	2	4	no	—
82	C₂²⋊C₈×C₃₇	—	2	4	no	—
83	#97×C₃₇	—	2	2	no	—
84	#97×C₃₇	D₄	1	4	yes	—
85	#95×C₃₇	—	2	2	no	—
86	#95×C₃₇	—	2	1	no	—
87	#95×C₃₇	—	2	1	no	—
88	#95×C₃₇	—	2	2	no	—
89	#95×C₃₇	—	2	1	no	—
90	#95×C₃₇	—	2	1	no	—
91	#95×C₃₇	—	2	1	no	—
92	#95×C₃₇	—	2	1	no	—
93	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
94	C₂×Q₈×C₃₇	—	4	2	no	—
95	C₂×Q₈×C₃₇	—	4	2	no	—
96	C₂×Q₈×C₃₇	—	4	2	no	—
97	C₂²×C₄×C₃₇	—	2	2	no	—
98	C₂²×C₄×C₃₇	—	2	2	no	—
99	C₂²×C₄×C₃₇	—	2	2	no	—
100	C₂²×C₄×C₃₇	—	2	2	no	—
101	C₂²×C₄×C₃₇	—	2	1	no	—
102	C₂²×C₄×C₃₇	—	2	1	no	—
103	C₂²×C₄×C₃₇	—	2	2	no	—
104	C₂²×C₄×C₃₇	—	2	2	no	—
105	C₂²×C₄×C₃₇	—	2	1	no	—
106	C₂²×C₄×C₃₇	—	2	1	no	—
107	C₂²×C₄×C₃₇	—	2	1	no	—
108	C₂²×C₄×C₃₇	—	2	1	no	—
109	C₂²×C₄×C₃₇	—	2	2	no	—
110	C₂²×C₄×C₃₇	—	2	2	no	—
111	C₂²×C₄×C₃₇	—	4	1	no	—
112	C₂²×C₄×C₃₇	—	4	1	no	—
113	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
119	C₂×C₈×C₃₇	—	2	2	no	—
120	C₂×C₈×C₃₇	—	2	2	no	—
121	C₂×C₈×C₃₇	—	2	2	no	—
122	C₂×C₈×C₃₇	—	2	2	no	—
123	C₂×C₈×C₃₇	—	2	2	no	—
124	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
125	C₄⋊C₄×C₃₇	—	2	1	no	—
126	C₄⋊C₄×C₃₇	—	2	2	no	—
127	C₄⋊C₄×C₃₇	—	2	1	no	—
128	C₄⋊C₄×C₃₇	—	2	1	no	—
129	C₄⋊C₄×C₃₇	—	2	1	no	—
130	C₄⋊C₄×C₃₇	—	2	2	no	—
131	C₄⋊C₄×C₃₇	—	2	2	no	—
132	C₄⋊C₄×C₃₇	—	2	2	no	—
133	C₄⋊C₄×C₃₇	—	2	4	no	—
134	C₄⋊C₄×C₃₇	—	4	2	no	—
135	C₄⋊C₄×C₃₇	—	4	2	no	—
136	C₄⋊C₄×C₃₇	—	4	2	no	—
137	C₄⋊C₄×C₃₇	—	4	4	no	—
138	C₄⋊C₄×C₃₇	—	4	2	no	—
139	C₄⋊C₄×C₃₇	—	4	2	no	—
140	C₄⋊C₄×C₃₇	—	4	2	no	—
141	C₄⋊C₄×C₃₇	—	4	2	no	—
142	C₂²⋊C₄×C₃₇	—	4	2	no	—
143	C₂²⋊C₄×C₃₇	—	4	2	no	—
144	C₂²⋊C₄×C₃₇	—	4	4	no	—
145	C₄²×C₃₇	—	2	2	no	—
146	C₄²×C₃₇	—	2	2	no	—
147	C₄²×C₃₇	—	2	1	no	—
148	C₄²×C₃₇	—	2	1	no	—
149	C₄²×C₃₇	C₂×D₄	1	2	yes	—
150	C₄²×C₃₇	#41	1	2	yes	—
151	C₂³×C₃₇	—	2	1	no	—
152	C₂³×C₃₇	—	2	1	no	—
153	C₂³×C₃₇	—	2	1	no	—
154	C₂³×C₃₇	—	2	1	no	—
155	C₂³×C₃₇	—	2	1	no	—
156	C₂³×C₃₇	—	2	1	no	—
157	C₂³×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
158	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₃₇	—	8	4	no	—
160	C₂×C₄×C₃₇	—	2	1	no	—
161	C₂×C₄×C₃₇	—	2	1	no	—
162	C₂×C₄×C₃₇	—	2	1	no	—
163	C₂×C₄×C₃₇	—	2	1	no	—
164	C₂×C₄×C₃₇	—	2	1	no	—
165	C₂×C₄×C₃₇	—	2	1	no	—
166	C₂×C₄×C₃₇	—	2	1	no	—
167	C₂×C₄×C₃₇	—	2	1	no	—
168	C₂×C₄×C₃₇	—	2	1	no	—
169	C₂×C₄×C₃₇	—	2	1	no	—
170	C₂×C₄×C₃₇	—	2	1	no	—
171	C₂×C₄×C₃₇	—	2	1	no	—
172	C₂×C₄×C₃₇	—	4	4	no	—
173	C₂×C₄×C₃₇	—	4	4	no	—
174	C₂×C₄×C₃₇	—	4	2	no	—
175	C₂×C₄×C₃₇	—	4	2	no	—
176	C₂×C₄×C₃₇	—	4	1	no	—
177	C₂×C₄×C₃₇	—	4	1	no	—
178	C₂×C₄×C₃₇	—	4	2	no	—
179	C₂×C₄×C₃₇	—	4	2	no	—
180	C₂×C₄×C₃₇	—	4	1	no	—
181	C₂×C₄×C₃₇	—	4	1	no	—
182	C₂×C₄×C₃₇	—	4	2	no	—
183	C₂×C₄×C₃₇	—	4	2	no	—
184	C₂×C₄×C₃₇	—	4	1	no	—
185	C₂×C₄×C₃₇	—	4	1	no	—
186	C₂×C₄×C₃₇	—	4	1	no	—
187	C₂×C₄×C₃₇	—	4	1	no	—
188	C₂×C₄×C₃₇	—	4	1	no	—
189	C₂×C₄×C₃₇	—	4	1	no	—
190	C₂×C₄×C₃₇	—	4	2	no	—
191	C₂×C₄×C₃₇	—	4	1	no	—
192	C₂×C₄×C₃₇	—	4	1	no	—
193	C₂×C₄×C₃₇	—	4	2	no	—
194	C₂×C₄×C₃₇	#121	1	2	yes	—
195	C₂×C₄×C₃₇	#121	1	2	yes	—
196	C₂×C₄×C₃₇	#137	1	2	yes	—
197	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₃₇	2₋¹⁺⁴	1	2	yes	—
200	C₂×C₄×C₃₇	2₋¹⁺⁴	1	2	yes	—
201	C₈×C₃₇	—	2	4	no	—
202	C₈×C₃₇	—	4	2	no	—
203	#29883	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂²×C₃₇	—	2	2	no	—
205	C₂²×C₃₇	—	2	2	no	—
206	C₂²×C₃₇	—	2	2	no	—
207	C₂²×C₃₇	—	4	1	no	—
208	C₂²×C₃₇	—	4	1	no	—
209	C₂²×C₃₇	—	4	1	no	—
210	C₂²×C₃₇	—	4	1	no	—
211	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
212	C₂²×C₃₇	#536	1	1	yes	characteristic
213	C₂²×C₃₇	#536	1	1	yes	characteristic
214	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
215	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
216	C₂²×C₃₇	#575	1	1	yes	characteristic
217	C₂²×C₃₇	#575	1	1	yes	characteristic
218	C₄×C₃₇	—	2	2	no	—
219	C₄×C₃₇	—	2	2	no	—
220	C₄×C₃₇	—	2	2	no	—
221	C₄×C₃₇	—	4	1	no	—
222	C₄×C₃₇	—	4	1	no	—
223	C₄×C₃₇	—	8	2	no	—
224	C₄×C₃₇	—	8	1	no	—
225	C₄×C₃₇	—	8	1	no	—
226	C₄×C₃₇	—	8	1	no	—
227	C₄×C₃₇	—	8	2	no	—
228	C₄×C₃₇	—	8	1	no	—
229	C₄×C₃₇	#536	1	2	yes	—
230	C₄×C₃₇	#541	1	2	yes	—
231	C₂×#501	C₂×C₃₇	1	1	yes	characteristic, complemented
232	C₂×#432	C₂×C₃₇	1	1	yes	characteristic
233	#2857	C₂×C₃₇	1	1	yes	characteristic
234	#2851	C₂×C₃₇	1	1	yes	characteristic
235	#2088	C₂×C₃₇	1	2	yes	complemented
236	#2087	C₂×C₃₇	1	2	yes	complemented
237	#2077	C₂×C₃₇	1	2	yes	—
238	#2075	C₂×C₃₇	1	2	yes	—
239	#1993	C₂×C₃₇	1	1	yes	characteristic, complemented
240	#1992	C₂×C₃₇	1	1	yes	characteristic, complemented
241	#1836	C₂×C₃₇	1	1	yes	characteristic, complemented
242	C₂×C₃₇	—	4	2	no	—
243	C₂×C₃₇	#2621	1	1	yes	characteristic
244	C₂×C₃₇	#3055	1	1	yes	characteristic
245	C₂×C₃₇	#3056	1	1	yes	characteristic
246	C₂×C₃₇	#3234	1	1	yes	characteristic
247	C₂×C₃₇	#3237	1	1	yes	characteristic
248	C₂×C₃₇	#3238	1	1	yes	characteristic
249	C₂×C₃₇	#3240	1	1	yes	characteristic
250	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
251	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
252	C₂×C₂²⋊Q₈	—	2	1	no	—
253	C₂²×C₄²	C₂²×C₃₇	1	1	yes	characteristic
254	#501	—	2	4	no	—
255	#432	—	2	4	no	—
256	C₂×#107	C₂²×C₃₇	1	2	yes	—
257	C₂×#106	C₂²×C₃₇	1	2	yes	—
258	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
259	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	—
260	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
261	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
262	#391	—	2	1	no	—
263	#389	—	2	1	no	—
264	#389	C₂²×C₃₇	1	1	yes	characteristic
265	#389	C₂²×C₃₇	1	1	yes	characteristic
266	#389	C₂²×C₃₇	1	2	yes	—
267	#387	—	2	1	no	—
268	#387	—	2	1	no	—
269	#385	—	2	1	no	—
270	#385	—	2	1	no	—
271	#384	C₂²×C₃₇	1	1	yes	characteristic
272	#382	C₂²×C₃₇	1	1	yes	characteristic
273	#380	—	2	1	no	—
274	#380	C₂²×C₃₇	1	1	yes	characteristic
275	#380	C₂²×C₃₇	1	2	yes	—
276	#380	C₂²×C₃₇	1	1	yes	characteristic
277	#340	C₂²×C₃₇	1	2	yes	—
278	#340	C₂²×C₃₇	1	2	yes	—
279	#340	C₂²×C₃₇	1	2	yes	—
280	#340	C₂²×C₃₇	1	2	yes	—
281	#340	C₂²×C₃₇	1	2	yes	—
282	#340	C₂²×C₃₇	1	2	yes	—
283	C₃₇	#29883	1	1	yes	characteristic, direct product factor, Sylow
284	C₂²×Q₈	—	2	1	no	—
285	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
286	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
287	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
289	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
290	C₄⋊Q₈	—	2	2	no	—
291	C₄⋊Q₈	—	2	2	no	—
292	#125	—	2	2	no	—
293	#125	—	2	2	no	—
294	C₂²⋊Q₈	—	4	4	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₄²	—	2	2	no	—
313	C₂×C₄²	—	2	2	no	—
314	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
315	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
316	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
317	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
318	#107	—	2	4	no	—
319	#106	—	2	4	no	—
320	C₄⋊C₈	—	2	4	no	—
321	C₂²⋊C₈	—	2	4	no	—
322	#97	—	2	2	no	—
323	#97	D₄×C₃₇	1	4	yes	—
324	#95	—	2	2	no	—
325	#95	—	2	1	no	—
326	#95	—	2	1	no	—
327	#95	—	2	2	no	—
328	#95	—	2	1	no	—
329	#95	—	2	1	no	—
330	#95	—	2	1	no	—
331	#95	—	2	1	no	—
332	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
333	C₂×Q₈	—	4	2	no	—
334	C₂×Q₈	—	4	2	no	—
335	C₂×Q₈	—	4	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	4	1	no	—
351	C₂²×C₄	—	4	1	no	—
352	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	—	4	4	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₄⋊C₄	—	4	2	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	4	2	no	—
382	C₂²⋊C₄	—	4	2	no	—
383	C₂²⋊C₄	—	4	4	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	C₂×D₄×C₃₇	1	2	yes	—
389	C₄²	#41×C₃₇	1	2	yes	—
390	C₂³	—	2	1	no	—
391	C₂³	—	2	1	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
397	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
398	Q₈	—	8	4	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	#121×C₃₇	1	2	yes	—
434	C₂×C₄	#121×C₃₇	1	2	yes	—
435	C₂×C₄	#137×C₃₇	1	2	yes	—
436	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
437	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
438	C₂×C₄	2₋¹⁺⁴×C₃₇	1	2	yes	—
439	C₂×C₄	2₋¹⁺⁴×C₃₇	1	2	yes	—
440	C₈	—	2	4	no	—
441	C₈	—	4	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	1	no	—
449	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
450	C₂²	C₃₇×#536	1	1	yes	characteristic
451	C₂²	C₃₇×#536	1	1	yes	characteristic
452	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
453	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
454	C₂²	C₃₇×#575	1	1	yes	characteristic
455	C₂²	C₃₇×#575	1	1	yes	characteristic
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	1	no	—
461	C₄	—	8	2	no	—
462	C₄	—	8	1	no	—
463	C₄	—	8	1	no	—
464	C₄	—	8	2	no	—
465	C₄	—	8	1	no	—
466	C₄	—	8	1	no	—
467	C₄	C₃₇×#536	1	2	yes	—
468	C₄	C₃₇×#541	1	2	yes	—
469	C₂	—	4	2	no	—
470	C₂	C₃₇×#2621	1	1	yes	characteristic
471	C₂	C₃₇×#3055	1	1	yes	characteristic
472	C₂	C₃₇×#3056	1	1	yes	characteristic
473	C₂	C₃₇×#3234	1	1	yes	characteristic
474	C₂	C₃₇×#3237	1	1	yes	characteristic
475	C₂	C₃₇×#3238	1	1	yes	characteristic
476	C₂	C₃₇×#3240	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂⁴×C₃₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂²×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#501	C₂	semidirect
5. C₃₇×#2088	C₂	semidirect
6. C₃₇×#2087	C₂	semidirect
9. C₃₇×#1993	C₂	semidirect
10. C₃₇×#1992	C₂	semidirect
11. C₃₇×#1836	C₂	semidirect
203. #29883	C₃₇	direct (N × H)
231. C₂×#501	C₂×C₃₇	semidirect
235. #2088	C₂×C₃₇	semidirect
236. #2087	C₂×C₃₇	semidirect
239. #1993	C₂×C₃₇	semidirect
240. #1992	C₂×C₃₇	semidirect
241. #1836	C₂×C₃₇	semidirect
283. C₃₇	#29883	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×#501	2
C₂×C₃₇×#432	2
C₃₇×#2857	2
C₃₇×#2851	2
C₃₇×#2088	2
C₃₇×#2087	2
C₃₇×#2077	2
C₃₇×#2075	2
C₃₇×#1993	2
C₃₇×#1992	2
C₃₇×#1836	2
#29883	37

Subgroups — C37×#29883 #22651136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#29883 #22651136