Subgroups — C₃₇×#28367 #22649620

Order 9472.

1064 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#485	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#468	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₇×#448	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₇×#419	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2500	C₂	1	1	yes	maximal, characteristic
6	C₃₇×#2434	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2097	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2095	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#2013	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#2013	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#1968	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₇×#1960	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#1956	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₇×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₃₇	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
24	C₂×#121×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×#117×C₃₇	C₂²	1	1	yes	characteristic
26	C₃₇×#485	—	2	4	no	—
27	C₃₇×#468	—	2	4	no	—
28	C₃₇×#448	—	2	4	no	—
29	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
32	C₃₇×#419	—	2	4	no	—
33	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
34	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
35	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
36	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
37	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
38	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
39	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
40	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
41	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
42	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
44	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
46	C₃₇×#395	—	2	2	no	—
47	C₃₇×#394	—	2	2	no	—
48	C₃₇×#391	C₂²	1	1	yes	characteristic
49	C₃₇×#391	C₂²	1	1	yes	characteristic
50	C₃₇×#390	C₂²	1	1	yes	characteristic
51	C₃₇×#390	C₂²	1	1	yes	characteristic
52	C₃₇×#388	—	2	2	no	—
53	C₃₇×#385	—	2	2	no	—
54	C₃₇×#384	C₂²	1	1	yes	characteristic
55	C₃₇×#382	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊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×Q₈×C₃₇	—	2	1	no	—
60	C₂²×Q₈×C₃₇	—	2	2	no	—
61	C₂²×Q₈×C₃₇	—	2	2	no	—
62	C₂²×Q₈×C₃₇	—	2	2	no	—
63	C₂²×Q₈×C₃₇	—	2	2	no	—
64	C₂²×Q₈×C₃₇	—	4	1	no	—
65	C₂²×Q₈×C₃₇	—	4	1	no	—
66	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₃₇	—	2	1	no	—
70	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₃₇	—	2	1	no	—
72	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
73	C₂×SD₁₆×C₃₇	—	2	2	no	—
74	C₂×SD₁₆×C₃₇	—	2	2	no	—
75	C₂×SD₁₆×C₃₇	—	2	2	no	—
76	C₂×SD₁₆×C₃₇	—	2	2	no	—
77	C₂×SD₁₆×C₃₇	—	2	2	no	—
78	C₂×SD₁₆×C₃₇	—	4	1	no	—
79	C₂×SD₁₆×C₃₇	—	4	1	no	—
80	C₂×SD₁₆×C₃₇	—	4	1	no	—
81	C₂×SD₁₆×C₃₇	—	4	1	no	—
82	C₂×M₁₆×C₃₇	—	4	1	no	—
83	C₂×M₁₆×C₃₇	—	4	1	no	—
84	C₂×M₁₆×C₃₇	D₄	1	4	yes	—
85	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
89	C₄⋊Q₈×C₃₇	—	2	2	no	—
90	C₄⋊Q₈×C₃₇	—	2	2	no	—
91	C₄⋊Q₈×C₃₇	—	4	1	no	—
92	C₄⋊Q₈×C₃₇	—	4	1	no	—
93	C₂²⋊Q₈×C₃₇	—	2	2	no	—
94	C₂²⋊Q₈×C₃₇	—	2	2	no	—
95	#121×C₃₇	—	2	2	no	—
96	#121×C₃₇	—	2	2	no	—
97	#117×C₃₇	—	2	2	no	—
98	#117×C₃₇	—	2	2	no	—
99	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
100	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
101	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
102	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
103	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
111	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
112	C₂×C₂²⋊C₄×C₃₇	D₄	1	2	yes	—
113	C₂×C₄²×C₃₇	—	2	1	no	—
114	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
116	#107×C₃₇	—	2	2	no	—
117	#107×C₃₇	—	2	2	no	—
118	#106×C₃₇	—	2	2	no	—
119	#103×C₃₇	—	2	2	no	—
120	#103×C₃₇	—	2	2	no	—
121	#103×C₃₇	—	2	2	no	—
122	#103×C₃₇	—	2	2	no	—
123	#103×C₃₇	—	2	2	no	—
124	#103×C₃₇	—	2	2	no	—
125	#103×C₃₇	—	2	2	no	—
126	#103×C₃₇	—	2	2	no	—
127	#103×C₃₇	—	2	2	no	—
128	#102×C₃₇	—	2	2	no	—
129	C₂²⋊C₈×C₃₇	D₄	1	4	yes	—
130	#97×C₃₇	—	4	1	no	—
131	C₄×C₈×C₃₇	—	4	1	no	—
132	#95×C₃₇	—	2	2	no	—
133	#95×C₃₇	—	2	2	no	—
134	#95×C₃₇	—	2	2	no	—
135	#95×C₃₇	D₄	1	2	yes	—
136	C₂⁴×C₃₇	—	2	1	no	—
137	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
138	C₂×Q₈×C₃₇	—	2	1	no	—
139	C₂×Q₈×C₃₇	—	2	1	no	—
140	C₂×Q₈×C₃₇	—	2	8	no	—
141	C₂×Q₈×C₃₇	—	2	1	no	—
142	C₂×Q₈×C₃₇	—	2	1	no	—
143	C₂×Q₈×C₃₇	—	2	1	no	—
144	C₂×Q₈×C₃₇	—	2	1	no	—
145	C₂×Q₈×C₃₇	—	2	1	no	—
146	C₂×Q₈×C₃₇	—	2	1	no	—
147	C₂×Q₈×C₃₇	—	2	1	no	—
148	C₂×Q₈×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	—	4	2	no	—
156	C₂×Q₈×C₃₇	—	4	2	no	—
157	C₂×Q₈×C₃₇	—	4	4	no	—
158	C₂×Q₈×C₃₇	—	4	4	no	—
159	C₂×Q₈×C₃₇	—	4	4	no	—
160	C₂×Q₈×C₃₇	—	4	2	no	—
161	C₂×Q₈×C₃₇	#41	1	2	yes	—
162	C₂×Q₈×C₃₇	#41	1	2	yes	—
163	C₂×D₄×C₃₇	—	2	1	no	—
164	C₂×D₄×C₃₇	—	2	1	no	—
165	C₂×D₄×C₃₇	—	2	1	no	—
166	C₂×D₄×C₃₇	—	2	1	no	—
167	C₂×D₄×C₃₇	—	2	1	no	—
168	C₂×D₄×C₃₇	—	2	1	no	—
169	C₂×D₄×C₃₇	—	4	2	no	—
170	C₂×D₄×C₃₇	—	8	2	no	—
171	C₂²×C₄×C₃₇	—	2	1	no	—
172	C₂²×C₄×C₃₇	—	2	1	no	—
173	C₂²×C₄×C₃₇	—	2	1	no	—
174	C₂²×C₄×C₃₇	—	2	1	no	—
175	C₂²×C₄×C₃₇	—	2	1	no	—
176	C₂²×C₄×C₃₇	—	2	1	no	—
177	C₂²×C₄×C₃₇	—	2	1	no	—
178	C₂²×C₄×C₃₇	—	2	1	no	—
179	C₂²×C₄×C₃₇	—	2	1	no	—
180	C₂²×C₄×C₃₇	—	2	1	no	—
181	C₂²×C₄×C₃₇	—	2	1	no	—
182	C₂²×C₄×C₃₇	—	4	2	no	—
183	C₂²×C₄×C₃₇	—	4	2	no	—
184	C₂²×C₄×C₃₇	—	4	2	no	—
185	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
186	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
189	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
190	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
191	SD₁₆×C₃₇	—	4	4	no	—
192	SD₁₆×C₃₇	—	4	4	no	—
193	SD₁₆×C₃₇	—	4	4	no	—
194	M₁₆×C₃₇	—	4	4	no	—
195	C₂×C₈×C₃₇	—	2	1	no	—
196	C₂×C₈×C₃₇	—	2	1	no	—
197	C₂×C₈×C₃₇	—	2	1	no	—
198	C₂×C₈×C₃₇	—	2	1	no	—
199	C₂×C₈×C₃₇	—	2	1	no	—
200	C₂×C₈×C₃₇	—	2	1	no	—
201	C₂×C₈×C₃₇	—	2	1	no	—
202	C₂×C₈×C₃₇	—	2	1	no	—
203	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
204	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
205	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
206	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
207	C₄⋊C₄×C₃₇	—	2	1	no	—
208	C₄⋊C₄×C₃₇	—	2	1	no	—
209	C₄⋊C₄×C₃₇	—	2	1	no	—
210	C₄⋊C₄×C₃₇	—	2	1	no	—
211	C₄⋊C₄×C₃₇	—	2	1	no	—
212	C₄⋊C₄×C₃₇	—	2	1	no	—
213	C₄⋊C₄×C₃₇	—	2	1	no	—
214	C₄⋊C₄×C₃₇	—	2	1	no	—
215	C₄⋊C₄×C₃₇	—	4	4	no	—
216	C₄⋊C₄×C₃₇	—	4	4	no	—
217	C₄⋊C₄×C₃₇	—	4	2	no	—
218	C₄⋊C₄×C₃₇	—	8	2	no	—
219	C₂²⋊C₄×C₃₇	—	2	4	no	—
220	C₂²⋊C₄×C₃₇	—	4	2	no	—
221	C₂²⋊C₄×C₃₇	—	4	2	no	—
222	C₂²⋊C₄×C₃₇	—	4	2	no	—
223	C₂²⋊C₄×C₃₇	—	4	4	no	—
224	C₂²⋊C₄×C₃₇	—	8	2	no	—
225	C₄²×C₃₇	—	2	1	no	—
226	C₄²×C₃₇	—	2	1	no	—
227	C₄²×C₃₇	—	2	1	no	—
228	C₄²×C₃₇	—	2	1	no	—
229	C₄²×C₃₇	—	4	2	no	—
230	C₂³×C₃₇	—	2	1	no	—
231	C₂³×C₃₇	—	2	1	no	—
232	C₂³×C₃₇	—	2	2	no	—
233	C₂³×C₃₇	—	2	2	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	#127	1	2	yes	—
240	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
241	Q₈×C₃₇	—	2	2	no	—
242	Q₈×C₃₇	—	2	2	no	—
243	Q₈×C₃₇	—	2	2	no	—
244	Q₈×C₃₇	—	2	2	no	—
245	Q₈×C₃₇	—	4	8	no	—
246	Q₈×C₃₇	—	4	1	no	—
247	Q₈×C₃₇	—	4	1	no	—
248	Q₈×C₃₇	—	4	1	no	—
249	Q₈×C₃₇	—	4	1	no	—
250	Q₈×C₃₇	—	4	1	no	—
251	Q₈×C₃₇	—	4	1	no	—
252	Q₈×C₃₇	—	4	1	no	—
253	Q₈×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	4	no	—
259	C₂×C₄×C₃₇	—	2	2	no	—
260	C₂×C₄×C₃₇	—	2	1	no	—
261	C₂×C₄×C₃₇	—	2	1	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	—	2	2	no	—
270	C₂×C₄×C₃₇	—	2	2	no	—
271	C₂×C₄×C₃₇	—	2	2	no	—
272	C₂×C₄×C₃₇	—	4	8	no	—
273	C₂×C₄×C₃₇	—	4	1	no	—
274	C₂×C₄×C₃₇	—	4	1	no	—
275	C₂×C₄×C₃₇	—	4	1	no	—
276	C₂×C₄×C₃₇	—	4	1	no	—
277	C₂×C₄×C₃₇	—	4	1	no	—
278	C₂×C₄×C₃₇	—	4	1	no	—
279	C₂×C₄×C₃₇	—	4	1	no	—
280	C₂×C₄×C₃₇	—	4	1	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	2	no	—
285	C₂×C₄×C₃₇	—	4	2	no	—
286	C₂×C₄×C₃₇	—	4	2	no	—
287	C₂×C₄×C₃₇	—	4	2	no	—
288	C₂×C₄×C₃₇	#127	1	2	yes	—
289	C₂×C₄×C₃₇	#137	1	4	yes	—
290	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
293	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
294	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
295	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
296	C₈×C₃₇	—	2	2	no	—
297	C₈×C₃₇	—	2	2	no	—
298	C₈×C₃₇	—	2	2	no	—
299	C₈×C₃₇	—	2	2	no	—
300	#28367	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
301	C₂²×C₃₇	—	2	2	no	—
302	C₂²×C₃₇	—	2	2	no	—
303	C₂²×C₃₇	—	2	2	no	—
304	C₂²×C₃₇	—	4	2	no	—
305	C₂²×C₃₇	—	4	2	no	—
306	C₂²×C₃₇	—	8	2	no	—
307	C₂²×C₃₇	—	8	1	no	—
308	C₂²×C₃₇	—	8	1	no	—
309	C₂²×C₃₇	—	8	1	no	—
310	C₂²×C₃₇	—	8	2	no	—
311	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
312	C₂²×C₃₇	#546	1	1	yes	characteristic
313	C₂²×C₃₇	#546	1	1	yes	characteristic
314	C₂²×C₃₇	C₂×#137	1	2	yes	—
315	C₂²×C₃₇	#577	1	2	yes	—
316	C₄×C₃₇	—	2	2	no	—
317	C₄×C₃₇	—	2	4	no	—
318	C₄×C₃₇	—	4	2	no	—
319	C₄×C₃₇	—	4	2	no	—
320	C₄×C₃₇	—	4	2	no	—
321	C₄×C₃₇	—	8	1	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	#534	1	1	yes	characteristic
328	C₄×C₃₇	#546	1	1	yes	characteristic
329	C₄×C₃₇	#546	1	1	yes	characteristic
330	C₂×#485	C₂×C₃₇	1	1	yes	characteristic, complemented
331	C₂×#468	C₂×C₃₇	1	1	yes	characteristic
332	C₂×#448	C₂×C₃₇	1	1	yes	characteristic
333	C₂×#419	C₂×C₃₇	1	1	yes	characteristic, complemented
334	#2500	C₂×C₃₇	1	1	yes	characteristic
335	#2434	C₂×C₃₇	1	1	yes	characteristic, complemented
336	#2097	C₂×C₃₇	1	1	yes	characteristic, complemented
337	#2095	C₂×C₃₇	1	1	yes	characteristic, complemented
338	#2013	C₂×C₃₇	1	1	yes	characteristic, complemented
339	#2013	C₂×C₃₇	1	1	yes	characteristic, complemented
340	#1973	C₂×C₃₇	1	1	yes	characteristic, complemented
341	#1968	C₂×C₃₇	1	1	yes	characteristic, complemented
342	#1960	C₂×C₃₇	1	1	yes	characteristic, complemented
343	#1956	C₂×C₃₇	1	1	yes	characteristic, complemented
344	#1753	C₂×C₃₇	1	1	yes	characteristic, complemented
345	C₂×C₃₇	—	4	2	no	—
346	C₂×C₃₇	—	16	1	no	—
347	C₂×C₃₇	#2539	1	1	yes	characteristic
348	C₂×C₃₇	#3152	1	1	yes	characteristic
349	C₂×C₃₇	#3154	1	1	yes	characteristic
350	C₂×C₃₇	#3320	1	2	yes	—
351	C₂×C₃₇	#3329	1	2	yes	—
352	C₂³×Q₈	C₂²×C₃₇	1	1	yes	characteristic
353	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
354	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
355	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
356	C₂²×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
357	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
358	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
359	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
360	C₂×#121	C₂²×C₃₇	1	1	yes	characteristic
361	C₂×#117	C₂²×C₃₇	1	1	yes	characteristic
362	#485	—	2	4	no	—
363	#468	—	2	4	no	—
364	#448	—	2	4	no	—
365	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
366	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
367	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
368	#419	—	2	4	no	—
369	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
370	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
371	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
372	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
373	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
374	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
375	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
376	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
377	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
378	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
379	C₂×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
380	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
381	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
382	#395	—	2	2	no	—
383	#394	—	2	2	no	—
384	#391	C₂²×C₃₇	1	1	yes	characteristic
385	#391	C₂²×C₃₇	1	1	yes	characteristic
386	#390	C₂²×C₃₇	1	1	yes	characteristic
387	#390	C₂²×C₃₇	1	1	yes	characteristic
388	#388	—	2	2	no	—
389	#385	—	2	2	no	—
390	#384	C₂²×C₃₇	1	1	yes	characteristic
391	#382	C₂²×C₃₇	1	1	yes	characteristic
392	C₄×C₂²⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
393	#336	C₂²×C₃₇	1	1	yes	characteristic
394	#336	C₂²×C₃₇	1	1	yes	characteristic
395	C₃₇	#28367	1	1	yes	characteristic, direct product factor, Sylow
396	C₂²×Q₈	—	2	1	no	—
397	C₂²×Q₈	—	2	2	no	—
398	C₂²×Q₈	—	2	2	no	—
399	C₂²×Q₈	—	2	2	no	—
400	C₂²×Q₈	—	2	2	no	—
401	C₂²×Q₈	—	4	1	no	—
402	C₂²×Q₈	—	4	1	no	—
403	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
404	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
405	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
406	C₂²×D₄	—	2	1	no	—
407	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
408	C₂³×C₄	—	2	1	no	—
409	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
410	C₂×SD₁₆	—	2	2	no	—
411	C₂×SD₁₆	—	2	2	no	—
412	C₂×SD₁₆	—	2	2	no	—
413	C₂×SD₁₆	—	2	2	no	—
414	C₂×SD₁₆	—	2	2	no	—
415	C₂×SD₁₆	—	4	1	no	—
416	C₂×SD₁₆	—	4	1	no	—
417	C₂×SD₁₆	—	4	1	no	—
418	C₂×SD₁₆	—	4	1	no	—
419	C₂×M₁₆	—	4	1	no	—
420	C₂×M₁₆	—	4	1	no	—
421	C₂×M₁₆	D₄×C₃₇	1	4	yes	—
422	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
423	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
424	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
425	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
426	C₄⋊Q₈	—	2	2	no	—
427	C₄⋊Q₈	—	2	2	no	—
428	C₄⋊Q₈	—	4	1	no	—
429	C₄⋊Q₈	—	4	1	no	—
430	C₂²⋊Q₈	—	2	2	no	—
431	C₂²⋊Q₈	—	2	2	no	—
432	#121	—	2	2	no	—
433	#121	—	2	2	no	—
434	#117	—	2	2	no	—
435	#117	—	2	2	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	2	2	no	—
438	C₂×C₄⋊C₄	—	2	2	no	—
439	C₂×C₄⋊C₄	—	2	2	no	—
440	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	2	no	—
448	C₂×C₂²⋊C₄	—	2	2	no	—
449	C₂×C₂²⋊C₄	D₄×C₃₇	1	2	yes	—
450	C₂×C₄²	—	2	1	no	—
451	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
452	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
453	#107	—	2	2	no	—
454	#107	—	2	2	no	—
455	#106	—	2	2	no	—
456	#103	—	2	2	no	—
457	#103	—	2	2	no	—
458	#103	—	2	2	no	—
459	#103	—	2	2	no	—
460	#103	—	2	2	no	—
461	#103	—	2	2	no	—
462	#103	—	2	2	no	—
463	#103	—	2	2	no	—
464	#103	—	2	2	no	—
465	#102	—	2	2	no	—
466	C₂²⋊C₈	D₄×C₃₇	1	4	yes	—
467	#97	—	4	1	no	—
468	C₄×C₈	—	4	1	no	—
469	#95	—	2	2	no	—
470	#95	—	2	2	no	—
471	#95	—	2	2	no	—
472	#95	D₄×C₃₇	1	2	yes	—
473	C₂⁴	—	2	1	no	—
474	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	8	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	4	2	no	—
493	C₂×Q₈	—	4	2	no	—
494	C₂×Q₈	—	4	4	no	—
495	C₂×Q₈	—	4	4	no	—
496	C₂×Q₈	—	4	4	no	—
497	C₂×Q₈	—	4	2	no	—
498	C₂×Q₈	#41×C₃₇	1	2	yes	—
499	C₂×Q₈	#41×C₃₇	1	2	yes	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	4	2	no	—
507	C₂×D₄	—	8	2	no	—
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	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	4	2	no	—
520	C₂²×C₄	—	4	2	no	—
521	C₂²×C₄	—	4	2	no	—
522	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
523	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
525	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
526	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
528	SD₁₆	—	4	4	no	—
529	SD₁₆	—	4	4	no	—
530	SD₁₆	—	4	4	no	—
531	M₁₆	—	4	4	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
541	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
542	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
543	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	4	4	no	—
553	C₄⋊C₄	—	4	4	no	—
554	C₄⋊C₄	—	4	2	no	—
555	C₄⋊C₄	—	8	2	no	—
556	C₂²⋊C₄	—	2	4	no	—
557	C₂²⋊C₄	—	4	2	no	—
558	C₂²⋊C₄	—	4	2	no	—
559	C₂²⋊C₄	—	4	2	no	—
560	C₂²⋊C₄	—	4	4	no	—
561	C₂²⋊C₄	—	8	2	no	—
562	C₄²	—	2	1	no	—
563	C₄²	—	2	1	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	4	2	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	—	2	2	no	—
570	C₂³	—	2	2	no	—
571	C₂³	—	4	1	no	—
572	C₂³	—	4	1	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	2	no	—
575	C₂³	—	4	2	no	—
576	C₂³	#127×C₃₇	1	2	yes	—
577	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
578	Q₈	—	2	2	no	—
579	Q₈	—	2	2	no	—
580	Q₈	—	2	2	no	—
581	Q₈	—	2	2	no	—
582	Q₈	—	4	8	no	—
583	Q₈	—	4	1	no	—
584	Q₈	—	4	1	no	—
585	Q₈	—	4	1	no	—
586	Q₈	—	4	1	no	—
587	Q₈	—	4	1	no	—
588	Q₈	—	4	1	no	—
589	Q₈	—	4	1	no	—
590	Q₈	—	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	—	8	4	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	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	—	2	2	no	—
609	C₂×C₄	—	4	8	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	2	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	#127×C₃₇	1	2	yes	—
626	C₂×C₄	#137×C₃₇	1	4	yes	—
627	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
628	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
629	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
630	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
631	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
632	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
633	C₈	—	2	2	no	—
634	C₈	—	2	2	no	—
635	C₈	—	2	2	no	—
636	C₈	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	4	2	no	—
642	C₂²	—	8	1	no	—
643	C₂²	—	8	1	no	—
644	C₂²	—	8	1	no	—
645	C₂²	—	8	2	no	—
646	C₂²	—	8	2	no	—
647	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
648	C₂²	C₃₇×#546	1	1	yes	characteristic
649	C₂²	C₃₇×#546	1	1	yes	characteristic
650	C₂²	C₂×#137×C₃₇	1	2	yes	—
651	C₂²	C₃₇×#577	1	2	yes	—
652	C₄	—	2	2	no	—
653	C₄	—	2	4	no	—
654	C₄	—	4	2	no	—
655	C₄	—	4	2	no	—
656	C₄	—	4	2	no	—
657	C₄	—	8	1	no	—
658	C₄	—	8	1	no	—
659	C₄	—	8	1	no	—
660	C₄	—	8	1	no	—
661	C₄	—	8	1	no	—
662	C₄	C₃₇×#525	1	1	yes	characteristic
663	C₄	C₃₇×#534	1	1	yes	characteristic
664	C₄	C₃₇×#546	1	1	yes	characteristic
665	C₄	C₃₇×#546	1	1	yes	characteristic
666	C₂	—	4	2	no	—
667	C₂	—	16	1	no	—
668	C₂	C₃₇×#2539	1	1	yes	characteristic
669	C₂	C₃₇×#3152	1	1	yes	characteristic
670	C₂	C₃₇×#3154	1	1	yes	characteristic
671	C₂	C₃₇×#3320	1	2	yes	—
672	C₂	C₃₇×#3329	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×#121×C₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₄×C₂²⋊C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#485	C₂	semidirect
4. C₂×C₃₇×#419	C₂	semidirect
6. C₃₇×#2434	C₂	semidirect
7. C₃₇×#2097	C₂	semidirect
8. C₃₇×#2095	C₂	semidirect
9. C₃₇×#2013	C₂	semidirect
10. C₃₇×#2013	C₂	semidirect
11. C₃₇×#1973	C₂	semidirect
12. C₃₇×#1968	C₂	semidirect
13. C₃₇×#1960	C₂	semidirect
14. C₃₇×#1956	C₂	semidirect
15. C₃₇×#1753	C₂	semidirect
300. #28367	C₃₇	direct (N × H)
330. C₂×#485	C₂×C₃₇	semidirect
333. C₂×#419	C₂×C₃₇	semidirect
335. #2434	C₂×C₃₇	semidirect
336. #2097	C₂×C₃₇	semidirect
337. #2095	C₂×C₃₇	semidirect
338. #2013	C₂×C₃₇	semidirect
339. #2013	C₂×C₃₇	semidirect
340. #1973	C₂×C₃₇	semidirect
341. #1968	C₂×C₃₇	semidirect
342. #1960	C₂×C₃₇	semidirect
343. #1956	C₂×C₃₇	semidirect
344. #1753	C₂×C₃₇	semidirect
395. C₃₇	#28367	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×#485	2
C₂×C₃₇×#468	2
C₂×C₃₇×#448	2
C₂×C₃₇×#419	2
C₃₇×#2500	2
C₃₇×#2434	2
C₃₇×#2097	2
C₃₇×#2095	2
C₃₇×#2013	2
C₃₇×#1973	2
C₃₇×#1968	2
C₃₇×#1960	2
C₃₇×#1956	2
C₃₇×#1753	2
#28367	37

Subgroups — C37×#28367 #22649620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28367 #22649620