Subgroups — C₃₇×#28421 #22649674

Order 9472.

1122 conjugacy classes of subgroups.

The subgroup lattice has 678 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, complemented
2	C₂×C₃₇×#478	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#459	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#442	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2566	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2541	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2094	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2092	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#2011	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#2011	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1972	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#1970	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₇×#1961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#1957	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₇×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
20	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
21	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×#121×C₃₇	—	2	2	no	—
24	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
26	C₃₇×#490	—	2	4	no	—
27	C₃₇×#478	—	2	4	no	—
28	C₃₇×#459	—	2	4	no	—
29	C₃₇×#442	—	2	4	no	—
30	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
32	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
34	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
35	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
36	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
37	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
38	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
39	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
40	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
41	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
42	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
43	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
44	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
45	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
47	C₃₇×#396	—	2	2	no	—
48	C₃₇×#392	—	2	2	no	—
49	C₃₇×#390	C₂²	1	1	yes	characteristic
50	C₃₇×#390	C₂²	1	1	yes	characteristic
51	C₃₇×#390	C₂²	1	1	yes	characteristic
52	C₃₇×#390	C₂²	1	1	yes	characteristic
53	C₃₇×#385	—	2	2	no	—
54	C₃₇×#384	C₂²	1	1	yes	characteristic
55	C₃₇×#382	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
57	C₃₇×#336	C₂²	1	1	yes	characteristic
58	C₃₇×#336	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₃₇	—	2	1	no	—
60	C₂²×D₄×C₃₇	—	2	2	no	—
61	C₂²×D₄×C₃₇	—	2	2	no	—
62	C₂²×D₄×C₃₇	—	2	1	no	—
63	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₃₇	—	2	1	no	—
68	C₂³×C₄×C₃₇	—	2	1	no	—
69	C₂×D₈×C₃₇	—	2	2	no	—
70	C₂×D₈×C₃₇	—	2	2	no	—
71	C₂×D₈×C₃₇	—	2	2	no	—
72	C₂×D₈×C₃₇	—	2	2	no	—
73	C₂×D₈×C₃₇	—	2	2	no	—
74	C₂×D₈×C₃₇	—	2	2	no	—
75	C₂×D₈×C₃₇	—	2	2	no	—
76	C₂×D₈×C₃₇	—	4	1	no	—
77	C₂×D₈×C₃₇	—	4	1	no	—
78	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
82	#127×C₃₇	—	2	2	no	—
83	#127×C₃₇	—	2	2	no	—
84	#127×C₃₇	—	2	2	no	—
85	#127×C₃₇	—	2	2	no	—
86	#127×C₃₇	—	4	1	no	—
87	#127×C₃₇	—	4	1	no	—
88	#125×C₃₇	—	2	2	no	—
89	#125×C₃₇	—	2	2	no	—
90	#121×C₃₇	—	4	8	no	—
91	C₄×D₄×C₃₇	—	2	2	no	—
92	C₄×D₄×C₃₇	—	2	2	no	—
93	C₄×D₄×C₃₇	—	2	2	no	—
94	C₄×D₄×C₃₇	—	2	2	no	—
95	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
96	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
97	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
98	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
99	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
104	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
105	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
106	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
109	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
112	#107×C₃₇	—	2	2	no	—
113	#106×C₃₇	—	2	2	no	—
114	#106×C₃₇	—	2	2	no	—
115	C₄⋊C₈×C₃₇	D₄	1	4	yes	complemented
116	#102×C₃₇	—	2	2	no	—
117	#102×C₃₇	—	2	2	no	—
118	#102×C₃₇	—	2	2	no	—
119	#102×C₃₇	—	2	2	no	—
120	#102×C₃₇	—	2	2	no	—
121	#102×C₃₇	—	2	2	no	—
122	#102×C₃₇	—	2	2	no	—
123	#102×C₃₇	—	2	2	no	—
124	#102×C₃₇	—	2	2	no	—
125	#102×C₃₇	—	2	2	no	—
126	#97×C₃₇	—	4	1	no	—
127	#97×C₃₇	D₄	1	4	yes	complemented
128	C₄×C₈×C₃₇	—	4	1	no	—
129	#95×C₃₇	—	2	2	no	—
130	#95×C₃₇	D₄	1	2	yes	—
131	C₂⁴×C₃₇	—	2	1	no	—
132	C₂⁴×C₃₇	—	2	1	no	—
133	C₂⁴×C₃₇	—	2	1	no	—
134	C₂⁴×C₃₇	—	2	1	no	—
135	C₂×D₄×C₃₇	—	2	1	no	—
136	C₂×D₄×C₃₇	—	2	1	no	—
137	C₂×D₄×C₃₇	—	2	1	no	—
138	C₂×D₄×C₃₇	—	2	1	no	—
139	C₂×D₄×C₃₇	—	2	1	no	—
140	C₂×D₄×C₃₇	—	2	1	no	—
141	C₂×D₄×C₃₇	—	2	1	no	—
142	C₂×D₄×C₃₇	—	2	1	no	—
143	C₂×D₄×C₃₇	—	2	1	no	—
144	C₂×D₄×C₃₇	—	2	1	no	—
145	C₂×D₄×C₃₇	—	2	1	no	—
146	C₂×D₄×C₃₇	—	2	1	no	—
147	C₂×D₄×C₃₇	—	2	1	no	—
148	C₂×D₄×C₃₇	—	2	1	no	—
149	C₂×D₄×C₃₇	—	2	1	no	—
150	C₂×D₄×C₃₇	—	2	1	no	—
151	C₂×D₄×C₃₇	—	2	1	no	—
152	C₂×D₄×C₃₇	—	2	1	no	—
153	C₂×D₄×C₃₇	—	2	1	no	—
154	C₂×D₄×C₃₇	—	2	1	no	—
155	C₂×D₄×C₃₇	—	2	1	no	—
156	C₂×D₄×C₃₇	—	2	1	no	—
157	C₂×D₄×C₃₇	—	4	4	no	—
158	C₂×D₄×C₃₇	—	4	4	no	—
159	C₂×D₄×C₃₇	—	4	4	no	—
160	C₂×D₄×C₃₇	—	4	4	no	—
161	C₂×D₄×C₃₇	—	4	2	no	—
162	C₂×D₄×C₃₇	—	4	2	no	—
163	C₂×D₄×C₃₇	—	4	4	no	—
164	C₂×D₄×C₃₇	—	8	2	no	—
165	C₂×D₄×C₃₇	—	8	2	no	—
166	C₂×D₄×C₃₇	—	8	2	no	—
167	C₂×D₄×C₃₇	#41	1	2	yes	—
168	C₂×D₄×C₃₇	#41	1	2	yes	—
169	C₂²×C₄×C₃₇	—	2	1	no	—
170	C₂²×C₄×C₃₇	—	2	1	no	—
171	C₂²×C₄×C₃₇	—	2	1	no	—
172	C₂²×C₄×C₃₇	—	2	1	no	—
173	C₂²×C₄×C₃₇	—	4	4	no	—
174	C₂²×C₄×C₃₇	—	4	2	no	—
175	C₂²×C₄×C₃₇	—	4	2	no	—
176	C₂²×C₄×C₃₇	—	8	2	no	—
177	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
181	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
182	D₈×C₃₇	—	2	8	no	—
183	D₈×C₃₇	—	4	4	no	—
184	D₈×C₃₇	—	4	4	no	—
185	C₂×C₈×C₃₇	—	2	1	no	—
186	C₂×C₈×C₃₇	—	2	1	no	—
187	C₂×C₈×C₃₇	—	2	1	no	—
188	C₂×C₈×C₃₇	—	2	1	no	—
189	C₂×C₈×C₃₇	—	2	1	no	—
190	C₂×C₈×C₃₇	—	2	1	no	—
191	C₂×C₈×C₃₇	—	2	1	no	—
192	C₂×C₈×C₃₇	—	2	1	no	—
193	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
194	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
195	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
196	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
197	C₄⋊C₄×C₃₇	—	2	4	no	—
198	C₄⋊C₄×C₃₇	—	2	1	no	—
199	C₄⋊C₄×C₃₇	—	2	1	no	—
200	C₄⋊C₄×C₃₇	—	2	1	no	—
201	C₄⋊C₄×C₃₇	—	2	1	no	—
202	C₄⋊C₄×C₃₇	—	2	1	no	—
203	C₄⋊C₄×C₃₇	—	2	1	no	—
204	C₄⋊C₄×C₃₇	—	2	1	no	—
205	C₄⋊C₄×C₃₇	—	2	1	no	—
206	C₄⋊C₄×C₃₇	—	4	2	no	—
207	C₄⋊C₄×C₃₇	—	4	2	no	—
208	C₄⋊C₄×C₃₇	—	8	2	no	—
209	C₂²⋊C₄×C₃₇	—	4	4	no	—
210	C₂²⋊C₄×C₃₇	—	4	2	no	—
211	C₂²⋊C₄×C₃₇	—	4	2	no	—
212	C₂²⋊C₄×C₃₇	—	4	4	no	—
213	C₂²⋊C₄×C₃₇	—	4	4	no	—
214	C₂²⋊C₄×C₃₇	—	8	2	no	—
215	C₄²×C₃₇	—	2	1	no	—
216	C₄²×C₃₇	—	2	1	no	—
217	C₄²×C₃₇	—	2	1	no	—
218	C₄²×C₃₇	—	2	1	no	—
219	C₄²×C₃₇	C₂×D₄	1	2	yes	—
220	C₄²×C₃₇	C₂×D₄	1	2	yes	—
221	C₂³×C₃₇	—	2	2	no	—
222	C₂³×C₃₇	—	2	2	no	—
223	C₂³×C₃₇	—	4	1	no	—
224	C₂³×C₃₇	—	4	1	no	—
225	C₂³×C₃₇	—	4	1	no	—
226	C₂³×C₃₇	—	4	1	no	—
227	C₂³×C₃₇	—	4	2	no	—
228	C₂³×C₃₇	—	4	2	no	—
229	C₂³×C₃₇	—	4	2	no	—
230	C₂³×C₃₇	—	4	2	no	—
231	C₂³×C₃₇	—	4	1	no	—
232	C₂³×C₃₇	—	4	1	no	—
233	C₂³×C₃₇	—	4	1	no	—
234	C₂³×C₃₇	—	4	1	no	—
235	C₂³×C₃₇	—	4	1	no	—
236	C₂³×C₃₇	—	4	1	no	—
237	C₂³×C₃₇	—	4	2	no	—
238	C₂³×C₃₇	—	4	2	no	—
239	C₂³×C₃₇	—	4	2	no	—
240	C₂³×C₃₇	—	4	2	no	—
241	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
242	D₄×C₃₇	—	2	2	no	—
243	D₄×C₃₇	—	2	2	no	—
244	D₄×C₃₇	—	2	2	no	—
245	D₄×C₃₇	—	2	2	no	—
246	D₄×C₃₇	—	4	1	no	—
247	D₄×C₃₇	—	4	1	no	—
248	D₄×C₃₇	—	4	1	no	—
249	D₄×C₃₇	—	4	1	no	—
250	D₄×C₃₇	—	4	1	no	—
251	D₄×C₃₇	—	4	1	no	—
252	D₄×C₃₇	—	4	1	no	—
253	D₄×C₃₇	—	4	1	no	—
254	D₄×C₃₇	—	4	1	no	—
255	D₄×C₃₇	—	4	1	no	—
256	D₄×C₃₇	—	4	1	no	—
257	D₄×C₃₇	—	4	1	no	—
258	D₄×C₃₇	—	8	8	no	—
259	D₄×C₃₇	—	8	4	no	—
260	D₄×C₃₇	—	8	4	no	—
261	D₄×C₃₇	—	8	8	no	—
262	C₂×C₄×C₃₇	—	2	2	no	—
263	C₂×C₄×C₃₇	—	2	2	no	—
264	C₂×C₄×C₃₇	—	2	2	no	—
265	C₂×C₄×C₃₇	—	2	2	no	—
266	C₂×C₄×C₃₇	—	2	2	no	—
267	C₂×C₄×C₃₇	—	2	2	no	—
268	C₂×C₄×C₃₇	—	2	2	no	—
269	C₂×C₄×C₃₇	—	4	1	no	—
270	C₂×C₄×C₃₇	—	4	1	no	—
271	C₂×C₄×C₃₇	—	4	1	no	—
272	C₂×C₄×C₃₇	—	4	1	no	—
273	C₂×C₄×C₃₇	—	4	2	no	—
274	C₂×C₄×C₃₇	—	4	2	no	—
275	C₂×C₄×C₃₇	—	4	2	no	—
276	C₂×C₄×C₃₇	—	4	2	no	—
277	C₂×C₄×C₃₇	—	8	4	no	—
278	C₂×C₄×C₃₇	—	8	4	no	—
279	C₂×C₄×C₃₇	#127	1	2	yes	—
280	C₂×C₄×C₃₇	#127	1	2	yes	—
281	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	4	yes	—
282	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
285	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
286	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
287	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
288	C₈×C₃₇	—	2	2	no	—
289	C₈×C₃₇	—	2	2	no	—
290	C₈×C₃₇	—	2	2	no	—
291	C₈×C₃₇	—	2	2	no	—
292	#28421	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
293	C₂²×C₃₇	—	4	4	no	—
294	C₂²×C₃₇	—	4	2	no	—
295	C₂²×C₃₇	—	4	2	no	—
296	C₂²×C₃₇	—	4	4	no	—
297	C₂²×C₃₇	—	8	2	no	—
298	C₂²×C₃₇	—	8	1	no	—
299	C₂²×C₃₇	—	8	1	no	—
300	C₂²×C₃₇	—	8	1	no	—
301	C₂²×C₃₇	—	8	1	no	—
302	C₂²×C₃₇	—	8	2	no	—
303	C₂²×C₃₇	—	8	2	no	—
304	C₂²×C₃₇	—	8	2	no	—
305	C₂²×C₃₇	—	8	1	no	—
306	C₂²×C₃₇	—	8	1	no	—
307	C₂²×C₃₇	—	8	1	no	—
308	C₂²×C₃₇	—	8	1	no	—
309	C₂²×C₃₇	—	8	1	no	—
310	C₂²×C₃₇	—	8	1	no	—
311	C₂²×C₃₇	—	8	2	no	—
312	C₂²×C₃₇	—	8	2	no	—
313	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
314	C₂²×C₃₇	#546	1	1	yes	characteristic
315	C₂²×C₃₇	#548	1	1	yes	characteristic
316	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
317	C₂²×C₃₇	#576	1	2	yes	—
318	C₄×C₃₇	—	2	2	no	—
319	C₄×C₃₇	—	2	2	no	—
320	C₄×C₃₇	—	2	4	no	—
321	C₄×C₃₇	—	4	2	no	—
322	C₄×C₃₇	—	8	1	no	—
323	C₄×C₃₇	—	8	1	no	—
324	C₄×C₃₇	—	8	1	no	—
325	C₄×C₃₇	—	8	1	no	—
326	C₄×C₃₇	#525	1	1	yes	characteristic
327	C₄×C₃₇	#537	1	1	yes	characteristic
328	C₄×C₃₇	#546	1	1	yes	characteristic
329	C₄×C₃₇	#548	1	1	yes	characteristic
330	C₂×#490	C₂×C₃₇	1	1	yes	characteristic, complemented
331	C₂×#478	C₂×C₃₇	1	1	yes	characteristic, complemented
332	C₂×#459	C₂×C₃₇	1	1	yes	characteristic, complemented
333	C₂×#442	C₂×C₃₇	1	1	yes	characteristic, complemented
334	#2566	C₂×C₃₇	1	1	yes	characteristic, complemented
335	#2541	C₂×C₃₇	1	1	yes	characteristic, complemented
336	#2094	C₂×C₃₇	1	1	yes	characteristic, complemented
337	#2092	C₂×C₃₇	1	1	yes	characteristic, complemented
338	#2011	C₂×C₃₇	1	1	yes	characteristic, complemented
339	#2011	C₂×C₃₇	1	1	yes	characteristic, complemented
340	#1972	C₂×C₃₇	1	1	yes	characteristic, complemented
341	#1970	C₂×C₃₇	1	1	yes	characteristic, complemented
342	#1961	C₂×C₃₇	1	1	yes	characteristic, complemented
343	#1957	C₂×C₃₇	1	1	yes	characteristic, complemented
344	#1771	C₂×C₃₇	1	1	yes	characteristic, complemented
345	C₂×C₃₇	—	8	2	no	—
346	C₂×C₃₇	—	8	2	no	—
347	C₂×C₃₇	—	16	1	no	—
348	C₂×C₃₇	—	16	1	no	—
349	C₂×C₃₇	#2540	1	1	yes	characteristic
350	C₂×C₃₇	#3151	1	1	yes	characteristic
351	C₂×C₃₇	#3155	1	1	yes	characteristic
352	C₂×C₃₇	#3318	1	2	yes	—
353	C₂×C₃₇	#3366	1	2	yes	—
354	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
355	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
356	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
357	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
358	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
359	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
360	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
361	C₂×#121	—	2	2	no	—
362	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
363	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
364	#490	—	2	4	no	—
365	#478	—	2	4	no	—
366	#459	—	2	4	no	—
367	#442	—	2	4	no	—
368	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
369	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
370	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
371	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
372	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
373	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
374	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
375	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
376	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
377	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
378	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
379	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
380	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
381	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
382	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
383	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
384	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
385	#396	—	2	2	no	—
386	#392	—	2	2	no	—
387	#390	C₂²×C₃₇	1	1	yes	characteristic
388	#390	C₂²×C₃₇	1	1	yes	characteristic
389	#390	C₂²×C₃₇	1	1	yes	characteristic
390	#390	C₂²×C₃₇	1	1	yes	characteristic
391	#385	—	2	2	no	—
392	#384	C₂²×C₃₇	1	1	yes	characteristic
393	#382	C₂²×C₃₇	1	1	yes	characteristic
394	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
395	#336	C₂²×C₃₇	1	1	yes	characteristic
396	#336	C₂²×C₃₇	1	1	yes	characteristic
397	C₃₇	#28421	1	1	yes	characteristic, direct product factor, Sylow
398	C₂²×D₄	—	2	1	no	—
399	C₂²×D₄	—	2	2	no	—
400	C₂²×D₄	—	2	2	no	—
401	C₂²×D₄	—	2	1	no	—
402	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
403	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
404	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
405	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
406	C₂³×C₄	—	2	1	no	—
407	C₂³×C₄	—	2	1	no	—
408	C₂×D₈	—	2	2	no	—
409	C₂×D₈	—	2	2	no	—
410	C₂×D₈	—	2	2	no	—
411	C₂×D₈	—	2	2	no	—
412	C₂×D₈	—	2	2	no	—
413	C₂×D₈	—	2	2	no	—
414	C₂×D₈	—	2	2	no	—
415	C₂×D₈	—	4	1	no	—
416	C₂×D₈	—	4	1	no	—
417	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
418	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
419	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
420	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
421	#127	—	2	2	no	—
422	#127	—	2	2	no	—
423	#127	—	2	2	no	—
424	#127	—	2	2	no	—
425	#127	—	4	1	no	—
426	#127	—	4	1	no	—
427	#125	—	2	2	no	—
428	#125	—	2	2	no	—
429	#121	—	4	8	no	—
430	C₄×D₄	—	2	2	no	—
431	C₄×D₄	—	2	2	no	—
432	C₄×D₄	—	2	2	no	—
433	C₄×D₄	—	2	2	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	—	2	2	no	—
437	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
438	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	2	no	—
445	C₂×C₂²⋊C₄	—	2	2	no	—
446	C₂×C₂²⋊C₄	—	2	2	no	—
447	C₂×C₂²⋊C₄	—	2	2	no	—
448	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
449	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
450	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
451	#107	—	2	2	no	—
452	#106	—	2	2	no	—
453	#106	—	2	2	no	—
454	C₄⋊C₈	D₄×C₃₇	1	4	yes	complemented
455	#102	—	2	2	no	—
456	#102	—	2	2	no	—
457	#102	—	2	2	no	—
458	#102	—	2	2	no	—
459	#102	—	2	2	no	—
460	#102	—	2	2	no	—
461	#102	—	2	2	no	—
462	#102	—	2	2	no	—
463	#102	—	2	2	no	—
464	#102	—	2	2	no	—
465	#97	—	4	1	no	—
466	#97	D₄×C₃₇	1	4	yes	complemented
467	C₄×C₈	—	4	1	no	—
468	#95	—	2	2	no	—
469	#95	D₄×C₃₇	1	2	yes	—
470	C₂⁴	—	2	1	no	—
471	C₂⁴	—	2	1	no	—
472	C₂⁴	—	2	1	no	—
473	C₂⁴	—	2	1	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	4	4	no	—
497	C₂×D₄	—	4	4	no	—
498	C₂×D₄	—	4	4	no	—
499	C₂×D₄	—	4	4	no	—
500	C₂×D₄	—	4	2	no	—
501	C₂×D₄	—	4	2	no	—
502	C₂×D₄	—	4	4	no	—
503	C₂×D₄	—	8	2	no	—
504	C₂×D₄	—	8	2	no	—
505	C₂×D₄	—	8	2	no	—
506	C₂×D₄	#41×C₃₇	1	2	yes	—
507	C₂×D₄	#41×C₃₇	1	2	yes	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	4	4	no	—
513	C₂²×C₄	—	4	2	no	—
514	C₂²×C₄	—	4	2	no	—
515	C₂²×C₄	—	8	2	no	—
516	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
517	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
518	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
519	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
521	D₈	—	2	8	no	—
522	D₈	—	4	4	no	—
523	D₈	—	4	4	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
533	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
534	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
535	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	4	2	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	—	8	2	no	—
548	C₂²⋊C₄	—	4	4	no	—
549	C₂²⋊C₄	—	4	2	no	—
550	C₂²⋊C₄	—	4	2	no	—
551	C₂²⋊C₄	—	4	4	no	—
552	C₂²⋊C₄	—	4	4	no	—
553	C₂²⋊C₄	—	8	2	no	—
554	C₄²	—	2	1	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	2	1	no	—
558	C₄²	C₂×D₄×C₃₇	1	2	yes	—
559	C₄²	C₂×D₄×C₃₇	1	2	yes	—
560	C₂³	—	2	2	no	—
561	C₂³	—	2	2	no	—
562	C₂³	—	4	1	no	—
563	C₂³	—	4	1	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	2	no	—
567	C₂³	—	4	2	no	—
568	C₂³	—	4	2	no	—
569	C₂³	—	4	2	no	—
570	C₂³	—	4	1	no	—
571	C₂³	—	4	1	no	—
572	C₂³	—	4	1	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	4	2	no	—
577	C₂³	—	4	2	no	—
578	C₂³	—	4	2	no	—
579	C₂³	—	4	2	no	—
580	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
581	D₄	—	2	2	no	—
582	D₄	—	2	2	no	—
583	D₄	—	2	2	no	—
584	D₄	—	2	2	no	—
585	D₄	—	4	1	no	—
586	D₄	—	4	1	no	—
587	D₄	—	4	1	no	—
588	D₄	—	4	1	no	—
589	D₄	—	4	1	no	—
590	D₄	—	4	1	no	—
591	D₄	—	4	1	no	—
592	D₄	—	4	1	no	—
593	D₄	—	4	1	no	—
594	D₄	—	4	1	no	—
595	D₄	—	4	1	no	—
596	D₄	—	4	1	no	—
597	D₄	—	8	8	no	—
598	D₄	—	8	4	no	—
599	D₄	—	8	4	no	—
600	D₄	—	8	8	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	4	2	no	—
614	C₂×C₄	—	4	2	no	—
615	C₂×C₄	—	4	2	no	—
616	C₂×C₄	—	8	4	no	—
617	C₂×C₄	—	8	4	no	—
618	C₂×C₄	#127×C₃₇	1	2	yes	—
619	C₂×C₄	#127×C₃₇	1	2	yes	—
620	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	4	yes	—
621	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
622	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
623	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
624	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
625	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
626	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
627	C₈	—	2	2	no	—
628	C₈	—	2	2	no	—
629	C₈	—	2	2	no	—
630	C₈	—	2	2	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	4	2	no	—
633	C₂²	—	4	4	no	—
634	C₂²	—	4	4	no	—
635	C₂²	—	8	1	no	—
636	C₂²	—	8	1	no	—
637	C₂²	—	8	1	no	—
638	C₂²	—	8	1	no	—
639	C₂²	—	8	2	no	—
640	C₂²	—	8	2	no	—
641	C₂²	—	8	1	no	—
642	C₂²	—	8	1	no	—
643	C₂²	—	8	1	no	—
644	C₂²	—	8	1	no	—
645	C₂²	—	8	1	no	—
646	C₂²	—	8	1	no	—
647	C₂²	—	8	2	no	—
648	C₂²	—	8	2	no	—
649	C₂²	—	8	2	no	—
650	C₂²	—	8	2	no	—
651	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
652	C₂²	C₃₇×#546	1	1	yes	characteristic
653	C₂²	C₃₇×#548	1	1	yes	characteristic
654	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	2	yes	—
655	C₂²	C₃₇×#576	1	2	yes	—
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	4	no	—
659	C₄	—	4	2	no	—
660	C₄	—	8	1	no	—
661	C₄	—	8	1	no	—
662	C₄	—	8	1	no	—
663	C₄	—	8	1	no	—
664	C₄	C₃₇×#525	1	1	yes	characteristic
665	C₄	C₃₇×#537	1	1	yes	characteristic
666	C₄	C₃₇×#546	1	1	yes	characteristic
667	C₄	C₃₇×#548	1	1	yes	characteristic
668	C₂	—	8	2	no	—
669	C₂	—	8	2	no	—
670	C₂	—	16	1	no	—
671	C₂	—	16	1	no	—
672	C₂	C₃₇×#2540	1	1	yes	characteristic
673	C₂	C₃₇×#3151	1	1	yes	characteristic
674	C₂	C₃₇×#3155	1	1	yes	characteristic
675	C₂	C₃₇×#3318	1	2	yes	—
676	C₂	C₃₇×#3366	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#490	C₂	semidirect
2. C₂×C₃₇×#478	C₂	semidirect
3. C₂×C₃₇×#459	C₂	semidirect
4. C₂×C₃₇×#442	C₂	semidirect
5. C₃₇×#2566	C₂	semidirect
6. C₃₇×#2541	C₂	semidirect
7. C₃₇×#2094	C₂	semidirect
8. C₃₇×#2092	C₂	semidirect
9. C₃₇×#2011	C₂	semidirect
10. C₃₇×#2011	C₂	semidirect
11. C₃₇×#1972	C₂	semidirect
12. C₃₇×#1970	C₂	semidirect
13. C₃₇×#1961	C₂	semidirect
14. C₃₇×#1957	C₂	semidirect
15. C₃₇×#1771	C₂	semidirect
115. C₄⋊C₈×C₃₇	D₄	semidirect
127. #97×C₃₇	D₄	semidirect
292. #28421	C₃₇	direct (N × H)
330. C₂×#490	C₂×C₃₇	semidirect
331. C₂×#478	C₂×C₃₇	semidirect
332. C₂×#459	C₂×C₃₇	semidirect
333. C₂×#442	C₂×C₃₇	semidirect
334. #2566	C₂×C₃₇	semidirect
335. #2541	C₂×C₃₇	semidirect
336. #2094	C₂×C₃₇	semidirect
337. #2092	C₂×C₃₇	semidirect
338. #2011	C₂×C₃₇	semidirect
339. #2011	C₂×C₃₇	semidirect
340. #1972	C₂×C₃₇	semidirect
341. #1970	C₂×C₃₇	semidirect
342. #1961	C₂×C₃₇	semidirect
343. #1957	C₂×C₃₇	semidirect
344. #1771	C₂×C₃₇	semidirect
397. C₃₇	#28421	direct (N × H)
454. C₄⋊C₈	D₄×C₃₇	semidirect
466. #97	D₄×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×#490	2
C₂×C₃₇×#478	2
C₂×C₃₇×#459	2
C₂×C₃₇×#442	2
C₃₇×#2566	2
C₃₇×#2541	2
C₃₇×#2094	2
C₃₇×#2092	2
C₃₇×#2011	2
C₃₇×#1972	2
C₃₇×#1970	2
C₃₇×#1961	2
C₃₇×#1957	2
C₃₇×#1771	2
#28421	37

Subgroups — C37×#28421 #22649674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28421 #22649674