Subgroups — C₃₇×#28477 #22649730

Order 9472.

1068 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#497	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₇×#497	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₇×#494	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#464	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₇×#441	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2546	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2545	C₂	1	1	yes	maximal, characteristic
9	C₃₇×#2016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#2016	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#2015	C₂	1	1	yes	maximal, characteristic
12	C₃₇×#2013	C₂	1	1	yes	maximal, characteristic
13	C₃₇×#1971	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#1968	C₂	1	1	yes	maximal, characteristic
15	C₃₇×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
20	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
21	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
22	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
23	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
24	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
29	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
33	C₃₇×#497	—	2	4	no	—
34	C₃₇×#497	—	2	4	no	—
35	C₃₇×#494	—	2	4	no	—
36	C₃₇×#464	—	2	4	no	—
37	C₃₇×#462	—	2	4	no	—
38	C₃₇×#441	—	2	4	no	—
39	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
41	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
42	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
43	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
44	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
45	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
46	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
47	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
48	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
50	C₃₇×#398	—	2	2	no	—
51	C₃₇×#396	—	2	2	no	—
52	C₃₇×#391	C₂²	1	1	yes	characteristic
53	C₃₇×#391	C₂²	1	1	yes	characteristic
54	C₃₇×#391	C₂²	1	1	yes	characteristic
55	C₃₇×#390	C₂²	1	1	yes	characteristic
56	C₃₇×#389	—	2	2	no	—
57	C₃₇×#388	—	2	2	no	—
58	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
59	C₃₇×#336	C₂²	1	1	yes	characteristic
60	C₃₇×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
65	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
67	C₂×Q₁₆×C₃₇	—	2	2	no	—
68	C₂×Q₁₆×C₃₇	—	2	2	no	—
69	C₂×Q₁₆×C₃₇	—	2	2	no	—
70	C₂×Q₁₆×C₃₇	—	2	2	no	—
71	C₂×Q₁₆×C₃₇	—	2	2	no	—
72	C₂×Q₁₆×C₃₇	—	2	2	no	—
73	C₂×Q₁₆×C₃₇	—	2	2	no	—
74	C₂×Q₁₆×C₃₇	—	2	2	no	—
75	C₂×Q₁₆×C₃₇	—	2	2	no	—
76	C₂×Q₁₆×C₃₇	—	2	2	no	—
77	C₂×Q₁₆×C₃₇	—	2	2	no	—
78	C₂×Q₁₆×C₃₇	—	2	2	no	—
79	C₂×Q₁₆×C₃₇	—	4	1	no	—
80	C₂×Q₁₆×C₃₇	—	4	1	no	—
81	C₂×Q₁₆×C₃₇	—	4	1	no	—
82	C₂×Q₁₆×C₃₇	—	4	1	no	—
83	C₂×Q₁₆×C₃₇	—	4	1	no	—
84	C₂×Q₁₆×C₃₇	D₄	1	4	yes	—
85	C₂×SD₁₆×C₃₇	—	2	2	no	—
86	C₂×SD₁₆×C₃₇	—	2	2	no	—
87	C₂×SD₁₆×C₃₇	—	2	2	no	—
88	C₂×SD₁₆×C₃₇	—	2	2	no	—
89	C₂×SD₁₆×C₃₇	—	2	2	no	—
90	C₂×SD₁₆×C₃₇	—	2	2	no	—
91	C₂×SD₁₆×C₃₇	—	4	1	no	—
92	C₂×SD₁₆×C₃₇	—	4	1	no	—
93	C₂×SD₁₆×C₃₇	—	4	1	no	—
94	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
98	C₄⋊Q₈×C₃₇	—	2	2	no	—
99	C₄⋊Q₈×C₃₇	—	2	2	no	—
100	C₄⋊Q₈×C₃₇	—	2	2	no	—
101	C₄⋊Q₈×C₃₇	—	2	2	no	—
102	C₄⋊Q₈×C₃₇	—	2	2	no	—
103	C₄⋊Q₈×C₃₇	—	4	1	no	—
104	C₄⋊Q₈×C₃₇	—	4	1	no	—
105	C₄⋊Q₈×C₃₇	—	4	1	no	—
106	#124×C₃₇	—	2	2	no	—
107	#124×C₃₇	—	2	2	no	—
108	#124×C₃₇	—	2	2	no	—
109	#124×C₃₇	—	4	1	no	—
110	C₄×Q₈×C₃₇	—	2	2	no	—
111	C₄×Q₈×C₃₇	—	2	2	no	—
112	C₄×Q₈×C₃₇	—	2	2	no	—
113	C₄×Q₈×C₃₇	—	2	2	no	—
114	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
115	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
116	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
117	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
118	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
119	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
120	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
121	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
122	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
126	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
128	C₂×C₄²×C₃₇	—	2	1	no	—
129	C₂×C₄²×C₃₇	—	2	1	no	—
130	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
133	#106×C₃₇	—	2	2	no	—
134	C₄⋊C₈×C₃₇	D₄	1	4	yes	—
135	#103×C₃₇	—	2	2	no	—
136	#103×C₃₇	—	2	2	no	—
137	#103×C₃₇	—	2	2	no	—
138	#103×C₃₇	—	2	2	no	—
139	#103×C₃₇	—	2	2	no	—
140	#102×C₃₇	—	2	2	no	—
141	#97×C₃₇	—	2	2	no	—
142	#97×C₃₇	D₄	1	4	yes	—
143	C₄×C₈×C₃₇	—	2	2	no	—
144	#95×C₃₇	—	2	2	no	—
145	#95×C₃₇	—	2	2	no	—
146	#95×C₃₇	—	2	2	no	—
147	#95×C₃₇	D₄	1	2	yes	—
148	C₂⁴×C₃₇	—	2	1	no	—
149	C₂×Q₈×C₃₇	—	2	1	no	—
150	C₂×Q₈×C₃₇	—	2	1	no	—
151	C₂×Q₈×C₃₇	—	2	1	no	—
152	C₂×Q₈×C₃₇	—	2	1	no	—
153	C₂×Q₈×C₃₇	—	2	1	no	—
154	C₂×Q₈×C₃₇	—	2	1	no	—
155	C₂×Q₈×C₃₇	—	2	1	no	—
156	C₂×Q₈×C₃₇	—	2	1	no	—
157	C₂×Q₈×C₃₇	—	2	1	no	—
158	C₂×Q₈×C₃₇	—	2	1	no	—
159	C₂×Q₈×C₃₇	—	2	1	no	—
160	C₂×Q₈×C₃₇	—	2	1	no	—
161	C₂×Q₈×C₃₇	—	2	1	no	—
162	C₂×Q₈×C₃₇	—	2	1	no	—
163	C₂×Q₈×C₃₇	—	2	1	no	—
164	C₂×Q₈×C₃₇	—	2	1	no	—
165	C₂×Q₈×C₃₇	—	2	1	no	—
166	C₂×Q₈×C₃₇	—	2	1	no	—
167	C₂×Q₈×C₃₇	—	2	1	no	—
168	C₂×Q₈×C₃₇	—	2	1	no	—
169	C₂×Q₈×C₃₇	—	2	1	no	—
170	C₂×Q₈×C₃₇	—	2	1	no	—
171	C₂×Q₈×C₃₇	—	2	1	no	—
172	C₂×Q₈×C₃₇	—	2	1	no	—
173	C₂×Q₈×C₃₇	—	2	1	no	—
174	C₂×Q₈×C₃₇	—	2	1	no	—
175	C₂×Q₈×C₃₇	—	2	1	no	—
176	C₂×Q₈×C₃₇	—	2	1	no	—
177	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
178	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
179	C₂×D₄×C₃₇	—	2	1	no	—
180	C₂×D₄×C₃₇	—	2	1	no	—
181	C₂×D₄×C₃₇	—	2	1	no	—
182	C₂×D₄×C₃₇	—	2	1	no	—
183	C₂×D₄×C₃₇	—	2	1	no	—
184	C₂×D₄×C₃₇	—	2	1	no	—
185	C₂²×C₄×C₃₇	—	2	1	no	—
186	C₂²×C₄×C₃₇	—	2	1	no	—
187	C₂²×C₄×C₃₇	—	2	1	no	—
188	C₂²×C₄×C₃₇	—	2	1	no	—
189	C₂²×C₄×C₃₇	—	2	1	no	—
190	C₂²×C₄×C₃₇	—	2	1	no	—
191	C₂²×C₄×C₃₇	—	2	1	no	—
192	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
193	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
196	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
197	Q₁₆×C₃₇	—	2	8	no	—
198	Q₁₆×C₃₇	—	4	4	no	—
199	Q₁₆×C₃₇	—	4	4	no	—
200	Q₁₆×C₃₇	—	4	4	no	—
201	Q₁₆×C₃₇	—	4	4	no	—
202	Q₁₆×C₃₇	—	4	4	no	—
203	SD₁₆×C₃₇	—	4	4	no	—
204	SD₁₆×C₃₇	—	4	4	no	—
205	SD₁₆×C₃₇	—	4	4	no	—
206	C₂×C₈×C₃₇	—	2	1	no	—
207	C₂×C₈×C₃₇	—	2	1	no	—
208	C₂×C₈×C₃₇	—	2	1	no	—
209	C₂×C₈×C₃₇	—	2	1	no	—
210	C₂×C₈×C₃₇	—	2	1	no	—
211	C₂×C₈×C₃₇	—	2	1	no	—
212	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
213	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
214	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
215	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
216	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
217	C₂×C₈×C₃₇	#41	1	2	yes	—
218	C₄⋊C₄×C₃₇	—	2	4	no	—
219	C₄⋊C₄×C₃₇	—	2	1	no	—
220	C₄⋊C₄×C₃₇	—	2	1	no	—
221	C₄⋊C₄×C₃₇	—	2	1	no	—
222	C₄⋊C₄×C₃₇	—	2	1	no	—
223	C₄⋊C₄×C₃₇	—	4	4	no	—
224	C₄⋊C₄×C₃₇	—	4	4	no	—
225	C₄⋊C₄×C₃₇	—	4	4	no	—
226	C₄⋊C₄×C₃₇	—	4	2	no	—
227	C₄⋊C₄×C₃₇	—	4	2	no	—
228	C₄⋊C₄×C₃₇	—	4	2	no	—
229	C₄⋊C₄×C₃₇	—	4	2	no	—
230	C₂²⋊C₄×C₃₇	—	4	4	no	—
231	C₂²⋊C₄×C₃₇	—	4	2	no	—
232	C₂²⋊C₄×C₃₇	—	4	2	no	—
233	C₂²⋊C₄×C₃₇	—	4	4	no	—
234	C₄²×C₃₇	—	2	1	no	—
235	C₄²×C₃₇	—	2	1	no	—
236	C₄²×C₃₇	—	2	1	no	—
237	C₄²×C₃₇	—	2	1	no	—
238	C₄²×C₃₇	—	4	2	no	—
239	C₄²×C₃₇	—	4	2	no	—
240	C₄²×C₃₇	C₂×D₄	1	2	yes	—
241	C₄²×C₃₇	C₂×D₄	1	2	yes	—
242	C₂³×C₃₇	—	4	1	no	—
243	C₂³×C₃₇	—	4	1	no	—
244	C₂³×C₃₇	—	4	1	no	—
245	C₂³×C₃₇	—	4	2	no	—
246	C₂³×C₃₇	—	4	2	no	—
247	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
248	Q₈×C₃₇	—	2	2	no	—
249	Q₈×C₃₇	—	2	2	no	—
250	Q₈×C₃₇	—	2	2	no	—
251	Q₈×C₃₇	—	2	2	no	—
252	Q₈×C₃₇	—	4	1	no	—
253	Q₈×C₃₇	—	4	1	no	—
254	Q₈×C₃₇	—	4	1	no	—
255	Q₈×C₃₇	—	4	1	no	—
256	Q₈×C₃₇	—	4	1	no	—
257	Q₈×C₃₇	—	4	1	no	—
258	Q₈×C₃₇	—	4	1	no	—
259	Q₈×C₃₇	—	4	1	no	—
260	Q₈×C₃₇	—	4	1	no	—
261	Q₈×C₃₇	—	4	1	no	—
262	Q₈×C₃₇	—	4	1	no	—
263	Q₈×C₃₇	—	4	1	no	—
264	Q₈×C₃₇	—	4	1	no	—
265	Q₈×C₃₇	—	4	1	no	—
266	Q₈×C₃₇	—	4	1	no	—
267	Q₈×C₃₇	—	4	1	no	—
268	D₄×C₃₇	—	4	1	no	—
269	D₄×C₃₇	—	4	1	no	—
270	D₄×C₃₇	—	4	1	no	—
271	D₄×C₃₇	—	4	1	no	—
272	C₂×C₄×C₃₇	—	2	2	no	—
273	C₂×C₄×C₃₇	—	2	2	no	—
274	C₂×C₄×C₃₇	—	2	2	no	—
275	C₂×C₄×C₃₇	—	2	2	no	—
276	C₂×C₄×C₃₇	—	2	2	no	—
277	C₂×C₄×C₃₇	—	2	2	no	—
278	C₂×C₄×C₃₇	—	2	2	no	—
279	C₂×C₄×C₃₇	—	2	2	no	—
280	C₂×C₄×C₃₇	—	2	2	no	—
281	C₂×C₄×C₃₇	—	4	1	no	—
282	C₂×C₄×C₃₇	—	4	1	no	—
283	C₂×C₄×C₃₇	—	4	1	no	—
284	C₂×C₄×C₃₇	—	4	1	no	—
285	C₂×C₄×C₃₇	—	4	1	no	—
286	C₂×C₄×C₃₇	—	4	1	no	—
287	C₂×C₄×C₃₇	—	4	1	no	—
288	C₂×C₄×C₃₇	—	4	1	no	—
289	C₂×C₄×C₃₇	—	4	1	no	—
290	C₂×C₄×C₃₇	—	4	1	no	—
291	C₂×C₄×C₃₇	—	4	1	no	—
292	C₂×C₄×C₃₇	—	4	1	no	—
293	C₂×C₄×C₃₇	—	4	1	no	—
294	C₂×C₄×C₃₇	—	4	1	no	—
295	C₂×C₄×C₃₇	—	4	1	no	—
296	C₂×C₄×C₃₇	—	4	2	no	—
297	C₂×C₄×C₃₇	—	4	2	no	—
298	C₂×C₄×C₃₇	#127	1	2	yes	—
299	C₂×C₄×C₃₇	#127	1	2	yes	—
300	C₂×C₄×C₃₇	#137	1	4	yes	—
301	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
305	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
306	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
307	C₈×C₃₇	—	2	2	no	—
308	C₈×C₃₇	—	2	2	no	—
309	C₈×C₃₇	—	2	2	no	—
310	C₈×C₃₇	#121	1	4	yes	—
311	#28477	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
312	C₂²×C₃₇	—	8	2	no	—
313	C₂²×C₃₇	—	8	1	no	—
314	C₂²×C₃₇	—	8	1	no	—
315	C₂²×C₃₇	—	8	2	no	—
316	C₂²×C₃₇	—	8	1	no	—
317	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
318	C₂²×C₃₇	D₄²	1	1	yes	characteristic
319	C₂²×C₃₇	#550	1	1	yes	characteristic
320	C₂²×C₃₇	C₂×#137	1	2	yes	—
321	C₂²×C₃₇	#578	1	2	yes	—
322	C₄×C₃₇	—	2	2	no	—
323	C₄×C₃₇	—	2	2	no	—
324	C₄×C₃₇	—	2	4	no	—
325	C₄×C₃₇	—	4	2	no	—
326	C₄×C₃₇	—	4	2	no	—
327	C₄×C₃₇	—	4	2	no	—
328	C₄×C₃₇	—	8	1	no	—
329	C₄×C₃₇	—	8	1	no	—
330	C₄×C₃₇	—	8	1	no	—
331	C₄×C₃₇	—	8	1	no	—
332	C₄×C₃₇	—	8	1	no	—
333	C₄×C₃₇	C₂×#121	1	1	yes	characteristic
334	C₄×C₃₇	#535	1	1	yes	characteristic
335	C₄×C₃₇	D₄²	1	1	yes	characteristic
336	C₄×C₃₇	#550	1	1	yes	characteristic
337	C₂×#497	C₂×C₃₇	1	1	yes	characteristic
338	C₂×#497	C₂×C₃₇	1	1	yes	characteristic
339	C₂×#494	C₂×C₃₇	1	1	yes	characteristic, complemented
340	C₂×#464	C₂×C₃₇	1	1	yes	characteristic
341	C₂×#462	C₂×C₃₇	1	1	yes	characteristic, complemented
342	C₂×#441	C₂×C₃₇	1	1	yes	characteristic, complemented
343	#2546	C₂×C₃₇	1	1	yes	characteristic, complemented
344	#2545	C₂×C₃₇	1	1	yes	characteristic
345	#2016	C₂×C₃₇	1	1	yes	characteristic, complemented
346	#2016	C₂×C₃₇	1	1	yes	characteristic, complemented
347	#2015	C₂×C₃₇	1	1	yes	characteristic
348	#2013	C₂×C₃₇	1	1	yes	characteristic
349	#1971	C₂×C₃₇	1	1	yes	characteristic, complemented
350	#1968	C₂×C₃₇	1	1	yes	characteristic
351	#1771	C₂×C₃₇	1	1	yes	characteristic, complemented
352	C₂×C₃₇	—	16	1	no	—
353	C₂×C₃₇	#2541	1	1	yes	characteristic
354	C₂×C₃₇	#3152	1	1	yes	characteristic
355	C₂×C₃₇	#3156	1	1	yes	characteristic
356	C₂×C₃₇	#3270	1	2	yes	—
357	C₂×C₃₇	#3398	1	2	yes	—
358	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
359	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
360	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
361	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
362	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
363	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
364	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
365	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
366	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
367	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
368	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
369	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
370	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
371	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
372	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
373	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
374	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
375	#497	—	2	4	no	—
376	#497	—	2	4	no	—
377	#494	—	2	4	no	—
378	#464	—	2	4	no	—
379	#462	—	2	4	no	—
380	#441	—	2	4	no	—
381	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
382	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
383	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
384	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
385	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
386	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
387	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
388	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
389	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
390	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
391	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
392	#398	—	2	2	no	—
393	#396	—	2	2	no	—
394	#391	C₂²×C₃₇	1	1	yes	characteristic
395	#391	C₂²×C₃₇	1	1	yes	characteristic
396	#391	C₂²×C₃₇	1	1	yes	characteristic
397	#390	C₂²×C₃₇	1	1	yes	characteristic
398	#389	—	2	2	no	—
399	#388	—	2	2	no	—
400	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
401	#336	C₂²×C₃₇	1	1	yes	characteristic
402	#336	C₂²×C₃₇	1	1	yes	characteristic
403	C₃₇	#28477	1	1	yes	characteristic, direct product factor, Sylow
404	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
405	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
406	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
407	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
408	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
409	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
410	C₂×Q₁₆	—	2	2	no	—
411	C₂×Q₁₆	—	2	2	no	—
412	C₂×Q₁₆	—	2	2	no	—
413	C₂×Q₁₆	—	2	2	no	—
414	C₂×Q₁₆	—	2	2	no	—
415	C₂×Q₁₆	—	2	2	no	—
416	C₂×Q₁₆	—	2	2	no	—
417	C₂×Q₁₆	—	2	2	no	—
418	C₂×Q₁₆	—	2	2	no	—
419	C₂×Q₁₆	—	2	2	no	—
420	C₂×Q₁₆	—	2	2	no	—
421	C₂×Q₁₆	—	2	2	no	—
422	C₂×Q₁₆	—	4	1	no	—
423	C₂×Q₁₆	—	4	1	no	—
424	C₂×Q₁₆	—	4	1	no	—
425	C₂×Q₁₆	—	4	1	no	—
426	C₂×Q₁₆	—	4	1	no	—
427	C₂×Q₁₆	D₄×C₃₇	1	4	yes	—
428	C₂×SD₁₆	—	2	2	no	—
429	C₂×SD₁₆	—	2	2	no	—
430	C₂×SD₁₆	—	2	2	no	—
431	C₂×SD₁₆	—	2	2	no	—
432	C₂×SD₁₆	—	2	2	no	—
433	C₂×SD₁₆	—	2	2	no	—
434	C₂×SD₁₆	—	4	1	no	—
435	C₂×SD₁₆	—	4	1	no	—
436	C₂×SD₁₆	—	4	1	no	—
437	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
438	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
439	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
440	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
441	C₄⋊Q₈	—	2	2	no	—
442	C₄⋊Q₈	—	2	2	no	—
443	C₄⋊Q₈	—	2	2	no	—
444	C₄⋊Q₈	—	2	2	no	—
445	C₄⋊Q₈	—	2	2	no	—
446	C₄⋊Q₈	—	4	1	no	—
447	C₄⋊Q₈	—	4	1	no	—
448	C₄⋊Q₈	—	4	1	no	—
449	#124	—	2	2	no	—
450	#124	—	2	2	no	—
451	#124	—	2	2	no	—
452	#124	—	4	1	no	—
453	C₄×Q₈	—	2	2	no	—
454	C₄×Q₈	—	2	2	no	—
455	C₄×Q₈	—	2	2	no	—
456	C₄×Q₈	—	2	2	no	—
457	C₂×C₄⋊C₄	—	2	1	no	—
458	C₂×C₄⋊C₄	—	2	1	no	—
459	C₂×C₄⋊C₄	—	2	2	no	—
460	C₂×C₄⋊C₄	—	2	1	no	—
461	C₂×C₄⋊C₄	—	2	2	no	—
462	C₂×C₄⋊C₄	—	2	2	no	—
463	C₂×C₄⋊C₄	—	2	1	no	—
464	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₂²⋊C₄	—	2	2	no	—
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₂²⋊C₄	—	2	2	no	—
471	C₂×C₄²	—	2	1	no	—
472	C₂×C₄²	—	2	1	no	—
473	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
474	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
475	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
476	#106	—	2	2	no	—
477	C₄⋊C₈	D₄×C₃₇	1	4	yes	—
478	#103	—	2	2	no	—
479	#103	—	2	2	no	—
480	#103	—	2	2	no	—
481	#103	—	2	2	no	—
482	#103	—	2	2	no	—
483	#102	—	2	2	no	—
484	#97	—	2	2	no	—
485	#97	D₄×C₃₇	1	4	yes	—
486	C₄×C₈	—	2	2	no	—
487	#95	—	2	2	no	—
488	#95	—	2	2	no	—
489	#95	—	2	2	no	—
490	#95	D₄×C₃₇	1	2	yes	—
491	C₂⁴	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
521	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	2	1	no	—
527	C₂×D₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
536	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
537	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
538	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
539	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
540	Q₁₆	—	2	8	no	—
541	Q₁₆	—	4	4	no	—
542	Q₁₆	—	4	4	no	—
543	Q₁₆	—	4	4	no	—
544	Q₁₆	—	4	4	no	—
545	Q₁₆	—	4	4	no	—
546	SD₁₆	—	4	4	no	—
547	SD₁₆	—	4	4	no	—
548	SD₁₆	—	4	4	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
556	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
557	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
558	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
559	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
560	C₂×C₈	#41×C₃₇	1	2	yes	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	4	4	no	—
567	C₄⋊C₄	—	4	4	no	—
568	C₄⋊C₄	—	4	4	no	—
569	C₄⋊C₄	—	4	2	no	—
570	C₄⋊C₄	—	4	2	no	—
571	C₄⋊C₄	—	4	2	no	—
572	C₄⋊C₄	—	4	2	no	—
573	C₂²⋊C₄	—	4	4	no	—
574	C₂²⋊C₄	—	4	2	no	—
575	C₂²⋊C₄	—	4	2	no	—
576	C₂²⋊C₄	—	4	4	no	—
577	C₄²	—	2	1	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	4	2	no	—
582	C₄²	—	4	2	no	—
583	C₄²	C₂×D₄×C₃₇	1	2	yes	—
584	C₄²	C₂×D₄×C₃₇	1	2	yes	—
585	C₂³	—	4	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	4	2	no	—
589	C₂³	—	4	2	no	—
590	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
591	Q₈	—	2	2	no	—
592	Q₈	—	2	2	no	—
593	Q₈	—	2	2	no	—
594	Q₈	—	2	2	no	—
595	Q₈	—	4	1	no	—
596	Q₈	—	4	1	no	—
597	Q₈	—	4	1	no	—
598	Q₈	—	4	1	no	—
599	Q₈	—	4	1	no	—
600	Q₈	—	4	1	no	—
601	Q₈	—	4	1	no	—
602	Q₈	—	4	1	no	—
603	Q₈	—	4	1	no	—
604	Q₈	—	4	1	no	—
605	Q₈	—	4	1	no	—
606	Q₈	—	4	1	no	—
607	Q₈	—	4	1	no	—
608	Q₈	—	4	1	no	—
609	Q₈	—	4	1	no	—
610	Q₈	—	4	1	no	—
611	D₄	—	4	1	no	—
612	D₄	—	4	1	no	—
613	D₄	—	4	1	no	—
614	D₄	—	4	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	#127×C₃₇	1	2	yes	—
642	C₂×C₄	#127×C₃₇	1	2	yes	—
643	C₂×C₄	#137×C₃₇	1	4	yes	—
644	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
645	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
646	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
647	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
648	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
649	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
650	C₈	—	2	2	no	—
651	C₈	—	2	2	no	—
652	C₈	—	2	2	no	—
653	C₈	#121×C₃₇	1	4	yes	—
654	C₂²	—	8	2	no	—
655	C₂²	—	8	1	no	—
656	C₂²	—	8	1	no	—
657	C₂²	—	8	2	no	—
658	C₂²	—	8	1	no	—
659	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
660	C₂²	D₄²×C₃₇	1	1	yes	characteristic
661	C₂²	C₃₇×#550	1	1	yes	characteristic
662	C₂²	C₂×#137×C₃₇	1	2	yes	—
663	C₂²	C₃₇×#578	1	2	yes	—
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	4	no	—
667	C₄	—	4	2	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	2	no	—
670	C₄	—	8	1	no	—
671	C₄	—	8	1	no	—
672	C₄	—	8	1	no	—
673	C₄	—	8	1	no	—
674	C₄	—	8	1	no	—
675	C₄	C₂×#121×C₃₇	1	1	yes	characteristic
676	C₄	C₃₇×#535	1	1	yes	characteristic
677	C₄	D₄²×C₃₇	1	1	yes	characteristic
678	C₄	C₃₇×#550	1	1	yes	characteristic
679	C₂	—	16	1	no	—
680	C₂	C₃₇×#2541	1	1	yes	characteristic
681	C₂	C₃₇×#3152	1	1	yes	characteristic
682	C₂	C₃₇×#3156	1	1	yes	characteristic
683	C₂	C₃₇×#3270	1	2	yes	—
684	C₂	C₃₇×#3398	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 ◁ C₄×C₄⋊C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₃₇×#494	C₂	semidirect
5. C₂×C₃₇×#462	C₂	semidirect
6. C₂×C₃₇×#441	C₂	semidirect
7. C₃₇×#2546	C₂	semidirect
9. C₃₇×#2016	C₂	semidirect
10. C₃₇×#2016	C₂	semidirect
13. C₃₇×#1971	C₂	semidirect
15. C₃₇×#1771	C₂	semidirect
311. #28477	C₃₇	direct (N × H)
339. C₂×#494	C₂×C₃₇	semidirect
341. C₂×#462	C₂×C₃₇	semidirect
342. C₂×#441	C₂×C₃₇	semidirect
343. #2546	C₂×C₃₇	semidirect
345. #2016	C₂×C₃₇	semidirect
346. #2016	C₂×C₃₇	semidirect
349. #1971	C₂×C₃₇	semidirect
351. #1771	C₂×C₃₇	semidirect
403. C₃₇	#28477	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×#497	2
C₂×C₃₇×#494	2
C₂×C₃₇×#464	2
C₂×C₃₇×#462	2
C₂×C₃₇×#441	2
C₃₇×#2546	2
C₃₇×#2545	2
C₃₇×#2016	2
C₃₇×#2015	2
C₃₇×#2013	2
C₃₇×#1971	2
C₃₇×#1968	2
C₃₇×#1771	2
#28477	37

Subgroups — C37×#28477 #22649730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28477 #22649730