Subgroups — C₃₇×#28658 #22649911

Order 9472.

792 conjugacy classes of subgroups.

The subgroup lattice has 486 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×#489	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2861	C₂	1	1	yes	maximal, characteristic
4	C₄×C₄⋊Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2067	C₂	1	2	yes	maximal
6	C₃₇×#2066	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1992	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1959	C₂	1	1	yes	maximal, characteristic
9	C₃₇×#1928	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1926	C₂	1	2	yes	maximal
11	C₃₇×#1767	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×#124×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₃₇	—	2	1	no	—
16	C₃₇×#501	—	2	4	no	—
17	C₃₇×#489	—	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×#103×C₃₇	C₂²	1	2	yes	—
22	C₂×#103×C₃₇	C₂²	1	2	yes	—
23	C₂×#102×C₃₇	C₂²	1	2	yes	—
24	C₂×#102×C₃₇	C₂²	1	2	yes	—
25	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
26	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
27	C₃₇×#391	—	2	1	no	—
28	C₃₇×#391	C₂²	1	1	yes	characteristic
29	C₃₇×#391	C₂²	1	1	yes	characteristic
30	C₃₇×#390	C₂²	1	1	yes	characteristic
31	C₃₇×#390	C₂²	1	1	yes	characteristic
32	C₃₇×#389	—	2	1	no	—
33	C₃₇×#389	C₂²	1	2	yes	—
34	C₃₇×#388	—	2	1	no	—
35	C₃₇×#388	—	2	1	no	—
36	C₃₇×#388	—	2	1	no	—
37	C₃₇×#388	—	2	1	no	—
38	C₃₇×#384	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₃₇	—	2	1	no	—
40	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
41	C₄³×C₃₇	C₂²	1	1	yes	characteristic
42	C₃₇×#340	C₂²	1	2	yes	—
43	C₃₇×#340	C₂²	1	2	yes	—
44	C₃₇×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₃₇	—	2	1	no	—
46	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
50	C₄⋊Q₈×C₃₇	—	2	2	no	—
51	C₄⋊Q₈×C₃₇	D₄	1	4	yes	—
52	#125×C₃₇	—	2	2	no	—
53	#125×C₃₇	—	2	2	no	—
54	#124×C₃₇	—	2	2	no	—
55	#124×C₃₇	—	2	2	no	—
56	C₄×Q₈×C₃₇	—	4	4	no	—
57	C₂×C₄⋊C₄×C₃₇	—	2	1	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	2	no	—
63	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
67	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₃₇	—	2	1	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	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
81	#107×C₃₇	—	2	4	no	—
82	#106×C₃₇	—	2	4	no	—
83	C₄⋊C₈×C₃₇	—	2	4	no	—
84	#103×C₃₇	—	2	4	no	—
85	#103×C₃₇	—	2	4	no	—
86	#102×C₃₇	—	2	4	no	—
87	#102×C₃₇	—	2	4	no	—
88	#97×C₃₇	—	2	2	no	—
89	#97×C₃₇	—	2	2	no	—
90	#95×C₃₇	—	2	2	no	—
91	#95×C₃₇	—	2	2	no	—
92	#95×C₃₇	—	2	1	no	—
93	#95×C₃₇	—	2	1	no	—
94	#95×C₃₇	—	2	1	no	—
95	#95×C₃₇	—	2	1	no	—
96	C₂⁴×C₃₇	—	2	1	no	—
97	C₂×Q₈×C₃₇	—	2	4	no	—
98	C₂×Q₈×C₃₇	—	2	1	no	—
99	C₂×Q₈×C₃₇	—	2	2	no	—
100	C₂×Q₈×C₃₇	—	2	1	no	—
101	C₂×Q₈×C₃₇	—	2	2	no	—
102	C₂×Q₈×C₃₇	—	4	2	no	—
103	C₂×Q₈×C₃₇	—	4	2	no	—
104	C₂×D₄×C₃₇	—	2	1	no	—
105	C₂×D₄×C₃₇	—	2	2	no	—
106	C₂×D₄×C₃₇	—	2	1	no	—
107	C₂×D₄×C₃₇	—	2	2	no	—
108	C₂²×C₄×C₃₇	—	2	2	no	—
109	C₂²×C₄×C₃₇	—	2	1	no	—
110	C₂²×C₄×C₃₇	—	2	2	no	—
111	C₂²×C₄×C₃₇	—	2	1	no	—
112	C₂²×C₄×C₃₇	—	2	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	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
125	C₂×C₈×C₃₇	#41	1	4	yes	—
126	C₄⋊C₄×C₃₇	—	2	4	no	—
127	C₄⋊C₄×C₃₇	—	2	2	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	1	no	—
133	C₄⋊C₄×C₃₇	—	2	1	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	2	no	—
138	C₄⋊C₄×C₃₇	—	4	4	no	—
139	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
140	C₂²⋊C₄×C₃₇	—	4	2	no	—
141	C₂²⋊C₄×C₃₇	—	4	2	no	—
142	C₂²⋊C₄×C₃₇	—	4	2	no	—
143	C₂²⋊C₄×C₃₇	—	4	2	no	—
144	C₂²⋊C₄×C₃₇	—	4	2	no	—
145	C₂²⋊C₄×C₃₇	—	4	2	no	—
146	C₄²×C₃₇	—	2	2	no	—
147	C₄²×C₃₇	—	2	2	no	—
148	C₄²×C₃₇	—	2	2	no	—
149	C₄²×C₃₇	—	2	2	no	—
150	C₄²×C₃₇	—	4	1	no	—
151	C₄²×C₃₇	—	4	1	no	—
152	C₄²×C₃₇	—	4	4	no	—
153	C₄²×C₃₇	C₂×D₄	1	2	yes	—
154	C₄²×C₃₇	#41	1	2	yes	—
155	C₂³×C₃₇	—	4	1	no	—
156	C₂³×C₃₇	—	4	1	no	—
157	C₂³×C₃₇	—	4	1	no	—
158	C₂³×C₃₇	—	4	1	no	—
159	C₂³×C₃₇	—	4	1	no	—
160	C₂³×C₃₇	—	4	1	no	—
161	C₂³×C₃₇	—	4	1	no	—
162	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₃₇	—	4	8	no	—
164	Q₈×C₃₇	—	4	2	no	—
165	Q₈×C₃₇	—	4	2	no	—
166	D₄×C₃₇	—	4	2	no	—
167	D₄×C₃₇	—	4	2	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	—	2	1	no	—
173	C₂×C₄×C₃₇	—	2	1	no	—
174	C₂×C₄×C₃₇	—	2	1	no	—
175	C₂×C₄×C₃₇	—	2	1	no	—
176	C₂×C₄×C₃₇	—	2	4	no	—
177	C₂×C₄×C₃₇	—	2	1	no	—
178	C₂×C₄×C₃₇	—	2	1	no	—
179	C₂×C₄×C₃₇	—	2	1	no	—
180	C₂×C₄×C₃₇	—	2	1	no	—
181	C₂×C₄×C₃₇	—	2	1	no	—
182	C₂×C₄×C₃₇	—	2	1	no	—
183	C₂×C₄×C₃₇	—	4	2	no	—
184	C₂×C₄×C₃₇	—	4	2	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	2	no	—
189	C₂×C₄×C₃₇	—	4	1	no	—
190	C₂×C₄×C₃₇	—	4	1	no	—
191	C₂×C₄×C₃₇	—	4	2	no	—
192	C₂×C₄×C₃₇	—	4	1	no	—
193	C₂×C₄×C₃₇	—	4	1	no	—
194	C₂×C₄×C₃₇	—	4	1	no	—
195	C₂×C₄×C₃₇	—	4	1	no	—
196	C₂×C₄×C₃₇	—	4	2	no	—
197	C₂×C₄×C₃₇	#121	1	2	yes	—
198	C₂×C₄×C₃₇	#121	1	2	yes	—
199	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
200	C₂×C₄×C₃₇	#137	1	2	yes	—
201	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
203	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₃₇	2₋¹⁺⁴	1	2	yes	—
205	C₈×C₃₇	—	2	4	no	—
206	C₈×C₃₇	—	4	2	no	—
207	#28658	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂²×C₃₇	—	8	1	no	—
209	C₂²×C₃₇	—	8	1	no	—
210	C₂²×C₃₇	—	8	1	no	—
211	C₂²×C₃₇	—	8	1	no	—
212	C₂²×C₃₇	—	8	1	no	—
213	C₂²×C₃₇	—	8	1	no	—
214	C₂²×C₃₇	—	8	1	no	—
215	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
216	C₂²×C₃₇	#532	1	1	yes	characteristic
217	C₂²×C₃₇	#536	1	1	yes	characteristic
218	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
219	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
220	C₂²×C₃₇	#575	1	1	yes	characteristic
221	C₂²×C₃₇	#575	1	1	yes	characteristic
222	C₄×C₃₇	—	2	2	no	—
223	C₄×C₃₇	—	2	2	no	—
224	C₄×C₃₇	—	2	2	no	—
225	C₄×C₃₇	—	2	2	no	—
226	C₄×C₃₇	—	4	1	no	—
227	C₄×C₃₇	—	4	1	no	—
228	C₄×C₃₇	—	4	4	no	—
229	C₄×C₃₇	—	8	2	no	—
230	C₄×C₃₇	—	8	1	no	—
231	C₄×C₃₇	—	8	1	no	—
232	C₄×C₃₇	—	8	1	no	—
233	C₄×C₃₇	#548	1	2	yes	—
234	C₄×C₃₇	#556	1	2	yes	—
235	C₂×#501	C₂×C₃₇	1	1	yes	characteristic, complemented
236	C₂×#489	C₂×C₃₇	1	1	yes	characteristic
237	#2861	C₂×C₃₇	1	1	yes	characteristic
238	C₄×C₄⋊Q₈	C₂×C₃₇	1	1	yes	characteristic, complemented
239	#2067	C₂×C₃₇	1	2	yes	—
240	#2066	C₂×C₃₇	1	2	yes	complemented
241	#1992	C₂×C₃₇	1	1	yes	characteristic, complemented
242	#1959	C₂×C₃₇	1	1	yes	characteristic
243	#1928	C₂×C₃₇	1	2	yes	complemented
244	#1926	C₂×C₃₇	1	2	yes	—
245	#1767	C₂×C₃₇	1	1	yes	characteristic, complemented
246	C₂×C₃₇	—	16	1	no	—
247	C₂×C₃₇	#2545	1	1	yes	characteristic
248	C₂×C₃₇	#3036	1	1	yes	characteristic
249	C₂×C₃₇	#3037	1	1	yes	characteristic
250	C₂×C₃₇	#3172	1	1	yes	characteristic
251	C₂×C₃₇	#3180	1	1	yes	characteristic
252	C₂×C₃₇	#3239	1	1	yes	characteristic
253	C₂×C₃₇	#3240	1	1	yes	characteristic
254	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
255	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
256	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
257	C₂×C₄×Q₈	—	2	1	no	—
258	#501	—	2	4	no	—
259	#489	—	2	4	no	—
260	C₂×#107	C₂²×C₃₇	1	2	yes	—
261	C₂×#106	C₂²×C₃₇	1	2	yes	—
262	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
263	C₂×#103	C₂²×C₃₇	1	2	yes	—
264	C₂×#103	C₂²×C₃₇	1	2	yes	—
265	C₂×#102	C₂²×C₃₇	1	2	yes	—
266	C₂×#102	C₂²×C₃₇	1	2	yes	—
267	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
268	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
269	#391	—	2	1	no	—
270	#391	C₂²×C₃₇	1	1	yes	characteristic
271	#391	C₂²×C₃₇	1	1	yes	characteristic
272	#390	C₂²×C₃₇	1	1	yes	characteristic
273	#390	C₂²×C₃₇	1	1	yes	characteristic
274	#389	—	2	1	no	—
275	#389	C₂²×C₃₇	1	2	yes	—
276	#388	—	2	1	no	—
277	#388	—	2	1	no	—
278	#388	—	2	1	no	—
279	#388	—	2	1	no	—
280	#384	C₂²×C₃₇	1	1	yes	characteristic
281	C₄×C₄⋊C₄	—	2	1	no	—
282	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
283	C₄³	C₂²×C₃₇	1	1	yes	characteristic
284	#340	C₂²×C₃₇	1	2	yes	—
285	#340	C₂²×C₃₇	1	2	yes	—
286	#336	C₂²×C₃₇	1	2	yes	—
287	C₃₇	#28658	1	1	yes	characteristic, direct product factor, Sylow
288	C₂²×Q₈	—	2	1	no	—
289	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
290	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
292	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
293	C₄⋊Q₈	—	2	2	no	—
294	C₄⋊Q₈	D₄×C₃₇	1	4	yes	—
295	#125	—	2	2	no	—
296	#125	—	2	2	no	—
297	#124	—	2	2	no	—
298	#124	—	2	2	no	—
299	C₄×Q₈	—	4	4	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
318	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
319	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
320	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
323	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
324	#107	—	2	4	no	—
325	#106	—	2	4	no	—
326	C₄⋊C₈	—	2	4	no	—
327	#103	—	2	4	no	—
328	#103	—	2	4	no	—
329	#102	—	2	4	no	—
330	#102	—	2	4	no	—
331	#97	—	2	2	no	—
332	#97	—	2	2	no	—
333	#95	—	2	2	no	—
334	#95	—	2	2	no	—
335	#95	—	2	1	no	—
336	#95	—	2	1	no	—
337	#95	—	2	1	no	—
338	#95	—	2	1	no	—
339	C₂⁴	—	2	1	no	—
340	C₂×Q₈	—	2	4	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	4	2	no	—
346	C₂×Q₈	—	4	2	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	#41×C₃₇	1	4	yes	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	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	C₄⋊C₄	—	4	4	no	—
382	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₂²⋊C₄	—	4	2	no	—
385	C₂²⋊C₄	—	4	2	no	—
386	C₂²⋊C₄	—	4	2	no	—
387	C₂²⋊C₄	—	4	2	no	—
388	C₂²⋊C₄	—	4	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	4	1	no	—
394	C₄²	—	4	1	no	—
395	C₄²	—	4	4	no	—
396	C₄²	C₂×D₄×C₃₇	1	2	yes	—
397	C₄²	#41×C₃₇	1	2	yes	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
406	Q₈	—	4	8	no	—
407	Q₈	—	4	2	no	—
408	Q₈	—	4	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	#121×C₃₇	1	2	yes	—
441	C₂×C₄	#121×C₃₇	1	2	yes	—
442	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
443	C₂×C₄	#137×C₃₇	1	2	yes	—
444	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
445	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
446	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
447	C₂×C₄	2₋¹⁺⁴×C₃₇	1	2	yes	—
448	C₈	—	2	4	no	—
449	C₈	—	4	2	no	—
450	C₂²	—	8	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	1	no	—
453	C₂²	—	8	1	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
458	C₂²	C₃₇×#532	1	1	yes	characteristic
459	C₂²	C₃₇×#536	1	1	yes	characteristic
460	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
461	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
462	C₂²	C₃₇×#575	1	1	yes	characteristic
463	C₂²	C₃₇×#575	1	1	yes	characteristic
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	2	2	no	—
467	C₄	—	2	2	no	—
468	C₄	—	4	1	no	—
469	C₄	—	4	1	no	—
470	C₄	—	4	4	no	—
471	C₄	—	8	2	no	—
472	C₄	—	8	1	no	—
473	C₄	—	8	1	no	—
474	C₄	—	8	1	no	—
475	C₄	C₃₇×#548	1	2	yes	—
476	C₄	C₃₇×#556	1	2	yes	—
477	C₂	—	16	1	no	—
478	C₂	C₃₇×#2545	1	1	yes	characteristic
479	C₂	C₃₇×#3036	1	1	yes	characteristic
480	C₂	C₃₇×#3037	1	1	yes	characteristic
481	C₂	C₃₇×#3172	1	1	yes	characteristic
482	C₂	C₃₇×#3180	1	1	yes	characteristic
483	C₂	C₃₇×#3239	1	1	yes	characteristic
484	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	C₂²×D₄×C₃₇	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₄³×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#501	C₂	semidirect
4. C₄×C₄⋊Q₈×C₃₇	C₂	semidirect
6. C₃₇×#2066	C₂	semidirect
7. C₃₇×#1992	C₂	semidirect
9. C₃₇×#1928	C₂	semidirect
11. C₃₇×#1767	C₂	semidirect
207. #28658	C₃₇	direct (N × H)
235. C₂×#501	C₂×C₃₇	semidirect
238. C₄×C₄⋊Q₈	C₂×C₃₇	semidirect
240. #2066	C₂×C₃₇	semidirect
241. #1992	C₂×C₃₇	semidirect
243. #1928	C₂×C₃₇	semidirect
245. #1767	C₂×C₃₇	semidirect
287. C₃₇	#28658	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×#489	2
C₃₇×#2861	2
C₄×C₄⋊Q₈×C₃₇	2
C₃₇×#2067	2
C₃₇×#2066	2
C₃₇×#1992	2
C₃₇×#1959	2
C₃₇×#1928	2
C₃₇×#1926	2
C₃₇×#1767	2
#28658	37

Subgroups — C37×#28658 #22649911

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28658 #22649911