Subgroups — C₃₇×#28581 #22649834

Order 9472.

892 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#470	C₂	1	2	yes	maximal
2	C₃₇×#2857	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂²⋊Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2084	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2072	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2043	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2016	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1927	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1894	C₂	1	2	yes	maximal
10	C₃₇×#1878	C₂	1	2	yes	maximal, complemented
11	C₃₇×#1728	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₃₇	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₃₇	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₃₇	C₂²	1	1	yes	characteristic
19	C₃₇×#470	—	2	8	no	—
20	C₂×#106×C₃₇	C₂²	1	2	yes	—
21	C₂×#103×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	C₃₇×#391	C₂²	1	2	yes	—
26	C₃₇×#391	C₂²	1	1	yes	characteristic
27	C₃₇×#389	—	2	1	no	—
28	C₃₇×#389	—	2	1	no	—
29	C₃₇×#389	C₂²	1	1	yes	characteristic
30	C₃₇×#387	—	2	1	no	—
31	C₃₇×#385	—	2	1	no	—
32	C₃₇×#384	C₂²	1	1	yes	characteristic
33	C₃₇×#380	—	2	1	no	—
34	C₃₇×#380	—	2	1	no	—
35	C₃₇×#380	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₃₇	—	2	1	no	—
37	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₃₇	—	2	1	no	—
39	C₃₇×#340	C₂²	1	2	yes	—
40	C₃₇×#340	C₂²	1	2	yes	—
41	C₃₇×#336	C₂²	1	2	yes	—
42	C₃₇×#336	C₂²	1	1	yes	characteristic
43	C₃₇×#336	C₂²	1	1	yes	characteristic
44	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
45	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
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	C₂×Q₁₆×C₃₇	—	2	4	no	—
50	C₂×Q₁₆×C₃₇	—	2	4	no	—
51	C₂×Q₁₆×C₃₇	—	4	2	no	—
52	C₂×M₁₆×C₃₇	—	2	4	no	—
53	C₂×M₁₆×C₃₇	—	2	4	no	—
54	C₂×M₁₆×C₃₇	—	4	2	no	—
55	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
56	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₃₇	—	4	2	no	—
58	C₂²⋊Q₈×C₃₇	—	2	2	no	—
59	C₂²⋊Q₈×C₃₇	—	2	4	no	—
60	C₂²⋊Q₈×C₃₇	—	2	4	no	—
61	C₂²⋊Q₈×C₃₇	D₄	1	4	yes	—
62	C₄×Q₈×C₃₇	—	4	2	no	—
63	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
68	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
78	C₂×C₄²×C₃₇	—	2	1	no	—
79	C₂×C₄²×C₃₇	—	2	1	no	—
80	C₂×C₄²×C₃₇	—	4	2	no	—
81	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
85	#106×C₃₇	—	2	4	no	—
86	#103×C₃₇	—	2	4	no	—
87	#103×C₃₇	—	2	4	no	—
88	#103×C₃₇	—	2	4	no	—
89	#103×C₃₇	—	4	2	no	—
90	#95×C₃₇	—	2	1	no	—
91	#95×C₃₇	—	2	1	no	—
92	#95×C₃₇	—	2	1	no	—
93	#95×C₃₇	—	2	1	no	—
94	#95×C₃₇	—	2	1	no	—
95	#95×C₃₇	—	2	2	no	—
96	#95×C₃₇	—	2	2	no	—
97	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
98	C₂×Q₈×C₃₇	—	2	1	no	—
99	C₂×Q₈×C₃₇	—	2	2	no	—
100	C₂×Q₈×C₃₇	—	2	2	no	—
101	C₂×Q₈×C₃₇	—	2	2	no	—
102	C₂×Q₈×C₃₇	—	2	2	no	—
103	C₂×Q₈×C₃₇	—	2	2	no	—
104	C₂×Q₈×C₃₇	—	2	2	no	—
105	C₂×Q₈×C₃₇	—	2	2	no	—
106	C₂×Q₈×C₃₇	—	2	2	no	—
107	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₃₇	—	2	2	no	—
109	C₂²×C₄×C₃₇	—	2	2	no	—
110	C₂²×C₄×C₃₇	—	2	1	no	—
111	C₂²×C₄×C₃₇	—	2	1	no	—
112	C₂²×C₄×C₃₇	—	2	2	no	—
113	C₂²×C₄×C₃₇	—	2	2	no	—
114	C₂²×C₄×C₃₇	—	2	2	no	—
115	C₂²×C₄×C₃₇	—	2	1	no	—
116	C₂²×C₄×C₃₇	—	2	1	no	—
117	C₂²×C₄×C₃₇	—	2	2	no	—
118	C₂²×C₄×C₃₇	—	2	2	no	—
119	C₂²×C₄×C₃₇	—	4	1	no	—
120	C₂²×C₄×C₃₇	—	4	1	no	—
121	C₂²×C₄×C₃₇	—	4	1	no	—
122	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₃₇	#41	1	2	yes	—
129	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
130	Q₁₆×C₃₇	—	4	8	no	—
131	M₁₆×C₃₇	—	4	8	no	—
132	C₂×C₈×C₃₇	—	2	2	no	—
133	C₂×C₈×C₃₇	—	2	2	no	—
134	C₂×C₈×C₃₇	—	2	2	no	—
135	C₂×C₈×C₃₇	—	2	2	no	—
136	C₂×C₈×C₃₇	—	2	2	no	—
137	C₂×C₈×C₃₇	#41	1	4	yes	—
138	C₄⋊C₄×C₃₇	—	2	4	no	—
139	C₄⋊C₄×C₃₇	—	2	1	no	—
140	C₄⋊C₄×C₃₇	—	2	2	no	—
141	C₄⋊C₄×C₃₇	—	2	2	no	—
142	C₄⋊C₄×C₃₇	—	2	2	no	—
143	C₄⋊C₄×C₃₇	—	2	2	no	—
144	C₄⋊C₄×C₃₇	—	4	2	no	—
145	C₄⋊C₄×C₃₇	—	4	2	no	—
146	C₄⋊C₄×C₃₇	—	4	2	no	—
147	C₄⋊C₄×C₃₇	—	4	2	no	—
148	C₄⋊C₄×C₃₇	—	4	4	no	—
149	C₄⋊C₄×C₃₇	—	4	2	no	—
150	C₄⋊C₄×C₃₇	—	4	2	no	—
151	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
152	C₂²⋊C₄×C₃₇	—	2	4	no	—
153	C₂²⋊C₄×C₃₇	—	4	2	no	—
154	C₂²⋊C₄×C₃₇	—	4	4	no	—
155	C₄²×C₃₇	—	2	2	no	—
156	C₄²×C₃₇	—	2	2	no	—
157	C₄²×C₃₇	—	4	1	no	—
158	C₄²×C₃₇	—	4	1	no	—
159	C₄²×C₃₇	—	4	2	no	—
160	C₄²×C₃₇	—	4	2	no	—
161	C₂³×C₃₇	—	2	1	no	—
162	C₂³×C₃₇	—	2	1	no	—
163	C₂³×C₃₇	—	2	1	no	—
164	C₂³×C₃₇	—	2	1	no	—
165	C₂³×C₃₇	—	2	1	no	—
166	C₂³×C₃₇	—	2	1	no	—
167	C₂³×C₃₇	#121	1	2	yes	—
168	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
169	Q₈×C₃₇	—	2	4	no	—
170	Q₈×C₃₇	—	4	2	no	—
171	Q₈×C₃₇	—	4	2	no	—
172	Q₈×C₃₇	—	4	2	no	—
173	Q₈×C₃₇	—	4	2	no	—
174	Q₈×C₃₇	—	4	2	no	—
175	C₂×C₄×C₃₇	—	2	1	no	—
176	C₂×C₄×C₃₇	—	2	1	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	—	2	4	no	—
184	C₂×C₄×C₃₇	—	2	4	no	—
185	C₂×C₄×C₃₇	—	2	2	no	—
186	C₂×C₄×C₃₇	—	2	2	no	—
187	C₂×C₄×C₃₇	—	2	1	no	—
188	C₂×C₄×C₃₇	—	2	1	no	—
189	C₂×C₄×C₃₇	—	2	1	no	—
190	C₂×C₄×C₃₇	—	4	4	no	—
191	C₂×C₄×C₃₇	—	4	4	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	—	4	2	no	—
198	C₂×C₄×C₃₇	—	4	1	no	—
199	C₂×C₄×C₃₇	—	4	2	no	—
200	C₂×C₄×C₃₇	—	4	1	no	—
201	C₂×C₄×C₃₇	—	4	2	no	—
202	C₂×C₄×C₃₇	—	4	1	no	—
203	C₂×C₄×C₃₇	—	4	1	no	—
204	C₂×C₄×C₃₇	—	4	2	no	—
205	C₂×C₄×C₃₇	—	4	1	no	—
206	C₂×C₄×C₃₇	—	4	1	no	—
207	C₂×C₄×C₃₇	—	4	2	no	—
208	C₂×C₄×C₃₇	#121	1	2	yes	—
209	C₂×C₄×C₃₇	#137	1	2	yes	—
210	C₂×C₄×C₃₇	#137	1	2	yes	—
211	C₂×C₄×C₃₇	#137	1	2	yes	—
212	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
214	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
216	C₈×C₃₇	—	2	4	no	—
217	C₈×C₃₇	—	4	2	no	—
218	#28581	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂²×C₃₇	—	2	2	no	—
220	C₂²×C₃₇	—	2	2	no	—
221	C₂²×C₃₇	—	2	2	no	—
222	C₂²×C₃₇	—	4	1	no	—
223	C₂²×C₃₇	—	4	1	no	—
224	C₂²×C₃₇	—	4	1	no	—
225	C₂²×C₃₇	—	4	1	no	—
226	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
227	C₂²×C₃₇	#532	1	1	yes	characteristic
228	C₂²×C₃₇	#534	1	1	yes	characteristic
229	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
230	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
231	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
232	C₂²×C₃₇	#575	1	1	yes	characteristic
233	C₄×C₃₇	—	2	2	no	—
234	C₄×C₃₇	—	2	2	no	—
235	C₄×C₃₇	—	2	2	no	—
236	C₄×C₃₇	—	2	2	no	—
237	C₄×C₃₇	—	4	1	no	—
238	C₄×C₃₇	—	4	2	no	—
239	C₄×C₃₇	—	4	2	no	—
240	C₄×C₃₇	—	8	1	no	—
241	C₄×C₃₇	—	8	1	no	—
242	C₄×C₃₇	—	8	2	no	—
243	C₄×C₃₇	—	8	2	no	—
244	C₄×C₃₇	#546	1	2	yes	—
245	C₄×C₃₇	#553	1	2	yes	—
246	C₂×#470	C₂×C₃₇	1	2	yes	—
247	#2857	C₂×C₃₇	1	1	yes	characteristic
248	C₄×C₂²⋊Q₈	C₂×C₃₇	1	1	yes	characteristic
249	#2084	C₂×C₃₇	1	1	yes	characteristic, complemented
250	#2072	C₂×C₃₇	1	1	yes	characteristic, complemented
251	#2043	C₂×C₃₇	1	1	yes	characteristic, complemented
252	#2016	C₂×C₃₇	1	1	yes	characteristic, complemented
253	#1927	C₂×C₃₇	1	2	yes	complemented
254	#1894	C₂×C₃₇	1	2	yes	—
255	#1878	C₂×C₃₇	1	2	yes	complemented
256	#1728	C₂×C₃₇	1	1	yes	characteristic
257	C₂×C₃₇	—	4	2	no	—
258	C₂×C₃₇	#2543	1	1	yes	characteristic
259	C₂×C₃₇	#3037	1	1	yes	characteristic
260	C₂×C₃₇	#3039	1	1	yes	characteristic
261	C₂×C₃₇	#3172	1	1	yes	characteristic
262	C₂×C₃₇	#3185	1	1	yes	characteristic
263	C₂×C₃₇	#3195	1	1	yes	characteristic
264	C₂×C₃₇	#3196	1	1	yes	characteristic
265	C₂²×Q₁₆	C₂²×C₃₇	1	2	yes	—
266	C₂²×M₁₆	C₂²×C₃₇	1	2	yes	—
267	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
268	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	2	yes	—
269	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
270	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
271	C₂²×C₄²	C₂²×C₃₇	1	1	yes	characteristic
272	#470	—	2	8	no	—
273	C₂×#106	C₂²×C₃₇	1	2	yes	—
274	C₂×#103	C₂²×C₃₇	1	2	yes	—
275	C₂×#103	C₂²×C₃₇	1	2	yes	—
276	C₂×#103	C₂²×C₃₇	1	2	yes	—
277	C₂×#103	C₂²×C₃₇	1	2	yes	—
278	#391	C₂²×C₃₇	1	1	yes	characteristic
279	#391	C₂²×C₃₇	1	2	yes	—
280	#389	—	2	1	no	—
281	#389	—	2	1	no	—
282	#389	C₂²×C₃₇	1	1	yes	characteristic
283	#387	—	2	1	no	—
284	#385	—	2	1	no	—
285	#384	C₂²×C₃₇	1	1	yes	characteristic
286	#380	—	2	1	no	—
287	#380	—	2	1	no	—
288	#380	C₂²×C₃₇	1	1	yes	characteristic
289	C₄×C₄⋊C₄	—	2	1	no	—
290	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
291	C₄×C₂²⋊C₄	—	2	1	no	—
292	#340	C₂²×C₃₇	1	2	yes	—
293	#340	C₂²×C₃₇	1	2	yes	—
294	#336	C₂²×C₃₇	1	1	yes	characteristic
295	#336	C₂²×C₃₇	1	1	yes	characteristic
296	#336	C₂²×C₃₇	1	2	yes	—
297	C₃₇	#28581	1	1	yes	characteristic, direct product factor, Sylow
298	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
299	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
300	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
301	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
302	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
303	C₂×Q₁₆	—	2	4	no	—
304	C₂×Q₁₆	—	2	4	no	—
305	C₂×Q₁₆	—	4	2	no	—
306	C₂×M₁₆	—	2	4	no	—
307	C₂×M₁₆	—	2	4	no	—
308	C₂×M₁₆	—	4	2	no	—
309	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
310	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
311	C₄⋊Q₈	—	4	2	no	—
312	C₂²⋊Q₈	—	2	2	no	—
313	C₂²⋊Q₈	—	2	4	no	—
314	C₂²⋊Q₈	—	2	4	no	—
315	C₂²⋊Q₈	D₄×C₃₇	1	4	yes	—
316	C₄×Q₈	—	4	2	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	—	4	2	no	—
335	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
336	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
337	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
338	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
339	#106	—	2	4	no	—
340	#103	—	2	4	no	—
341	#103	—	2	4	no	—
342	#103	—	2	4	no	—
343	#103	—	4	2	no	—
344	#95	—	2	1	no	—
345	#95	—	2	1	no	—
346	#95	—	2	1	no	—
347	#95	—	2	1	no	—
348	#95	—	2	1	no	—
349	#95	—	2	2	no	—
350	#95	—	2	2	no	—
351	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	4	1	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	—	4	1	no	—
376	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
379	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
382	C₂²×C₄	#41×C₃₇	1	2	yes	—
383	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
384	Q₁₆	—	4	8	no	—
385	M₁₆	—	4	8	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	#41×C₃₇	1	4	yes	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	4	2	no	—
399	C₄⋊C₄	—	4	2	no	—
400	C₄⋊C₄	—	4	2	no	—
401	C₄⋊C₄	—	4	2	no	—
402	C₄⋊C₄	—	4	4	no	—
403	C₄⋊C₄	—	4	2	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	4	2	no	—
408	C₂²⋊C₄	—	4	4	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	4	1	no	—
412	C₄²	—	4	1	no	—
413	C₄²	—	4	2	no	—
414	C₄²	—	4	2	no	—
415	C₂³	—	2	1	no	—
416	C₂³	—	2	1	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	#121×C₃₇	1	2	yes	—
422	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
423	Q₈	—	2	4	no	—
424	Q₈	—	4	2	no	—
425	Q₈	—	4	2	no	—
426	Q₈	—	4	2	no	—
427	Q₈	—	4	2	no	—
428	Q₈	—	4	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	#121×C₃₇	1	2	yes	—
463	C₂×C₄	#137×C₃₇	1	2	yes	—
464	C₂×C₄	#137×C₃₇	1	2	yes	—
465	C₂×C₄	#137×C₃₇	1	2	yes	—
466	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
467	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
468	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
469	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
470	C₈	—	2	4	no	—
471	C₈	—	4	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	—	4	1	no	—
478	C₂²	—	4	1	no	—
479	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
480	C₂²	C₃₇×#532	1	1	yes	characteristic
481	C₂²	C₃₇×#534	1	1	yes	characteristic
482	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
483	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
484	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
485	C₂²	C₃₇×#575	1	1	yes	characteristic
486	C₄	—	2	2	no	—
487	C₄	—	2	2	no	—
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	4	1	no	—
491	C₄	—	4	2	no	—
492	C₄	—	4	2	no	—
493	C₄	—	8	1	no	—
494	C₄	—	8	1	no	—
495	C₄	—	8	2	no	—
496	C₄	—	8	2	no	—
497	C₄	C₃₇×#546	1	2	yes	—
498	C₄	C₃₇×#553	1	2	yes	—
499	C₂	—	4	2	no	—
500	C₂	C₃₇×#2543	1	1	yes	characteristic
501	C₂	C₃₇×#3037	1	1	yes	characteristic
502	C₂	C₃₇×#3039	1	1	yes	characteristic
503	C₂	C₃₇×#3172	1	1	yes	characteristic
504	C₂	C₃₇×#3185	1	1	yes	characteristic
505	C₂	C₃₇×#3195	1	1	yes	characteristic
506	C₂	C₃₇×#3196	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
4. C₃₇×#2084	C₂	semidirect
5. C₃₇×#2072	C₂	semidirect
6. C₃₇×#2043	C₂	semidirect
7. C₃₇×#2016	C₂	semidirect
8. C₃₇×#1927	C₂	semidirect
10. C₃₇×#1878	C₂	semidirect
218. #28581	C₃₇	direct (N × H)
249. #2084	C₂×C₃₇	semidirect
250. #2072	C₂×C₃₇	semidirect
251. #2043	C₂×C₃₇	semidirect
252. #2016	C₂×C₃₇	semidirect
253. #1927	C₂×C₃₇	semidirect
255. #1878	C₂×C₃₇	semidirect
297. C₃₇	#28581	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×#470	2
C₃₇×#2857	2
C₄×C₂²⋊Q₈×C₃₇	2
C₃₇×#2084	2
C₃₇×#2072	2
C₃₇×#2043	2
C₃₇×#2016	2
C₃₇×#1927	2
C₃₇×#1894	2
C₃₇×#1878	2
C₃₇×#1728	2
#28581	37

Subgroups — C37×#28581 #22649834

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28581 #22649834