Subgroups — C₃₇×#24902 #22646155

Order 9472.

932 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×#451	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#2421	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₂²⋊C₄×C₃₇	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2097	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2075	C₂	1	1	yes	maximal, characteristic
7	C₃₇×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2035	C₂	1	1	yes	maximal, characteristic
9	C₃₇×#1933	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1923	C₂	1	1	yes	maximal, characteristic
11	C₃₇×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#1878	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₇×#1865	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₇×#1787	C₂	1	1	yes	maximal, characteristic
16	C₂³×Q₈×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	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×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	C₃₇×#451	—	2	4	no	—
24	C₄×Q₁₆×C₃₇	—	2	4	no	—
25	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
26	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
28	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
29	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
32	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
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×C₂²⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
39	C₃₇×#400	—	2	1	no	—
40	C₃₇×#397	—	2	1	no	—
41	C₃₇×#391	—	2	1	no	—
42	C₃₇×#391	—	2	1	no	—
43	C₃₇×#391	C₂²	1	1	yes	characteristic
44	C₃₇×#391	C₂²	1	1	yes	characteristic
45	C₃₇×#391	C₂²	1	1	yes	characteristic
46	C₃₇×#389	C₂²	1	1	yes	characteristic
47	C₃₇×#388	—	2	1	no	—
48	C₃₇×#387	—	2	1	no	—
49	C₃₇×#382	C₂²	1	1	yes	characteristic
50	C₃₇×#380	—	2	1	no	—
51	C₃₇×#380	C₂²	1	1	yes	characteristic
52	C₃₇×#380	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊C₄×C₃₇	—	2	1	no	—
54	C₄×C₂²⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
55	C₃₇×#340	C₂²	1	1	yes	characteristic
56	C₃₇×#340	C₂²	1	1	yes	characteristic
57	C₃₇×#340	C₂²	1	1	yes	characteristic
58	C₃₇×#340	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	—	2	2	no	—
62	C₂²×Q₈×C₃₇	—	2	2	no	—
63	C₂²×Q₈×C₃₇	—	2	1	no	—
64	C₂²×Q₈×C₃₇	—	2	2	no	—
65	C₂²×Q₈×C₃₇	—	2	2	no	—
66	C₂²×Q₈×C₃₇	—	4	1	no	—
67	C₂²×Q₈×C₃₇	—	4	1	no	—
68	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₃₇	—	2	1	no	—
72	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
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	—	4	1	no	—
78	C₂×Q₁₆×C₃₇	D₄	1	4	yes	—
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	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
83	C₂²⋊Q₈×C₃₇	—	2	2	no	—
84	C₂²⋊Q₈×C₃₇	—	4	1	no	—
85	C₄×Q₈×C₃₇	—	2	2	no	—
86	C₄×Q₈×C₃₇	—	2	2	no	—
87	C₄×Q₈×C₃₇	—	2	2	no	—
88	C₄×Q₈×C₃₇	—	4	1	no	—
89	C₄×Q₈×C₃₇	—	4	1	no	—
90	C₄×Q₈×C₃₇	—	4	1	no	—
91	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
92	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
93	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
94	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
95	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
96	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₃₇	D₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₃₇	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₃₇	—	2	1	no	—
107	C₂×C₄²×C₃₇	—	2	1	no	—
108	C₂×C₄²×C₃₇	—	2	1	no	—
109	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
111	#107×C₃₇	—	2	2	no	—
112	#106×C₃₇	—	4	1	no	—
113	C₄⋊C₈×C₃₇	—	4	1	no	—
114	#103×C₃₇	—	2	2	no	—
115	#103×C₃₇	—	2	2	no	—
116	#103×C₃₇	—	2	2	no	—
117	#103×C₃₇	—	2	2	no	—
118	#103×C₃₇	—	2	2	no	—
119	#103×C₃₇	—	2	2	no	—
120	#103×C₃₇	—	4	1	no	—
121	#103×C₃₇	—	4	1	no	—
122	C₂²⋊C₈×C₃₇	—	2	2	no	—
123	C₂²⋊C₈×C₃₇	—	4	1	no	—
124	C₄×C₈×C₃₇	—	2	2	no	—
125	#95×C₃₇	—	2	1	no	—
126	#95×C₃₇	—	2	1	no	—
127	#95×C₃₇	—	2	1	no	—
128	#95×C₃₇	—	2	1	no	—
129	#95×C₃₇	—	2	1	no	—
130	#95×C₃₇	—	2	1	no	—
131	#95×C₃₇	—	2	1	no	—
132	#95×C₃₇	—	2	1	no	—
133	#95×C₃₇	—	2	1	no	—
134	#95×C₃₇	—	2	1	no	—
135	#95×C₃₇	—	2	1	no	—
136	#95×C₃₇	D₄	1	1	yes	characteristic
137	#95×C₃₇	D₄	1	1	yes	characteristic
138	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
139	C₂×Q₈×C₃₇	—	2	4	no	—
140	C₂×Q₈×C₃₇	—	2	1	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	—	4	2	no	—
154	C₂×Q₈×C₃₇	—	4	2	no	—
155	C₂×Q₈×C₃₇	—	4	4	no	—
156	C₂×Q₈×C₃₇	—	4	4	no	—
157	C₂×Q₈×C₃₇	—	4	4	no	—
158	C₂×Q₈×C₃₇	—	4	4	no	—
159	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
160	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
161	C₂×Q₈×C₃₇	#41	1	2	yes	—
162	C₂×Q₈×C₃₇	#41	1	2	yes	—
163	C₂×Q₈×C₃₇	#41	1	2	yes	—
164	C₂²×C₄×C₃₇	—	2	1	no	—
165	C₂²×C₄×C₃₇	—	2	4	no	—
166	C₂²×C₄×C₃₇	—	2	1	no	—
167	C₂²×C₄×C₃₇	—	2	1	no	—
168	C₂²×C₄×C₃₇	—	2	1	no	—
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	—	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	—	4	2	no	—
180	C₂²×C₄×C₃₇	—	4	2	no	—
181	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
187	Q₁₆×C₃₇	—	2	8	no	—
188	Q₁₆×C₃₇	—	4	4	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	—	2	1	no	—
194	C₂×C₈×C₃₇	—	2	1	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	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
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	—	4	2	no	—
212	C₄⋊C₄×C₃₇	—	4	2	no	—
213	C₄⋊C₄×C₃₇	—	4	2	no	—
214	C₄⋊C₄×C₃₇	—	4	2	no	—
215	C₄⋊C₄×C₃₇	—	4	2	no	—
216	C₂²⋊C₄×C₃₇	—	2	2	no	—
217	C₂²⋊C₄×C₃₇	—	2	2	no	—
218	C₂²⋊C₄×C₃₇	—	4	2	no	—
219	C₂²⋊C₄×C₃₇	—	4	2	no	—
220	C₂²⋊C₄×C₃₇	—	4	2	no	—
221	C₄²×C₃₇	—	2	1	no	—
222	C₄²×C₃₇	—	2	1	no	—
223	C₄²×C₃₇	—	2	1	no	—
224	C₄²×C₃₇	—	2	1	no	—
225	C₄²×C₃₇	—	4	2	no	—
226	C₄²×C₃₇	—	4	2	no	—
227	C₄²×C₃₇	—	4	2	no	—
228	C₂³×C₃₇	—	2	1	no	—
229	C₂³×C₃₇	—	2	1	no	—
230	C₂³×C₃₇	—	2	1	no	—
231	C₂³×C₃₇	—	2	1	no	—
232	C₂³×C₃₇	—	2	1	no	—
233	C₂³×C₃₇	—	2	1	no	—
234	C₂³×C₃₇	#135	1	2	yes	—
235	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
236	Q₈×C₃₇	—	2	2	no	—
237	Q₈×C₃₇	—	2	2	no	—
238	Q₈×C₃₇	—	2	2	no	—
239	Q₈×C₃₇	—	2	2	no	—
240	Q₈×C₃₇	—	2	2	no	—
241	Q₈×C₃₇	—	2	2	no	—
242	Q₈×C₃₇	—	2	2	no	—
243	Q₈×C₃₇	—	4	8	no	—
244	Q₈×C₃₇	—	4	1	no	—
245	Q₈×C₃₇	—	4	1	no	—
246	Q₈×C₃₇	—	4	1	no	—
247	Q₈×C₃₇	—	4	1	no	—
248	Q₈×C₃₇	#123	1	4	yes	—
249	C₂×C₄×C₃₇	—	2	2	no	—
250	C₂×C₄×C₃₇	—	2	1	no	—
251	C₂×C₄×C₃₇	—	2	2	no	—
252	C₂×C₄×C₃₇	—	2	2	no	—
253	C₂×C₄×C₃₇	—	2	1	no	—
254	C₂×C₄×C₃₇	—	2	2	no	—
255	C₂×C₄×C₃₇	—	2	1	no	—
256	C₂×C₄×C₃₇	—	2	1	no	—
257	C₂×C₄×C₃₇	—	2	2	no	—
258	C₂×C₄×C₃₇	—	2	1	no	—
259	C₂×C₄×C₃₇	—	2	1	no	—
260	C₂×C₄×C₃₇	—	2	1	no	—
261	C₂×C₄×C₃₇	—	2	1	no	—
262	C₂×C₄×C₃₇	—	2	1	no	—
263	C₂×C₄×C₃₇	—	2	1	no	—
264	C₂×C₄×C₃₇	—	2	1	no	—
265	C₂×C₄×C₃₇	—	2	1	no	—
266	C₂×C₄×C₃₇	—	2	1	no	—
267	C₂×C₄×C₃₇	—	2	1	no	—
268	C₂×C₄×C₃₇	—	4	8	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	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	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	#137	1	2	yes	—
293	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
295	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
298	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
299	C₈×C₃₇	—	2	2	no	—
300	C₈×C₃₇	—	4	1	no	—
301	C₈×C₃₇	—	4	1	no	—
302	C₈×C₃₇	—	4	1	no	—
303	#24902	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
304	C₂²×C₃₇	—	2	2	no	—
305	C₂²×C₃₇	—	2	2	no	—
306	C₂²×C₃₇	—	2	2	no	—
307	C₂²×C₃₇	—	4	1	no	—
308	C₂²×C₃₇	—	4	1	no	—
309	C₂²×C₃₇	—	4	1	no	—
310	C₂²×C₃₇	—	4	1	no	—
311	C₂²×C₃₇	#525	1	1	yes	characteristic
312	C₂²×C₃₇	D₄²	1	1	yes	characteristic
313	C₂²×C₃₇	#546	1	1	yes	characteristic
314	C₂²×C₃₇	C₂×#135	1	1	yes	characteristic
315	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
316	C₂²×C₃₇	#578	1	1	yes	characteristic
317	C₂²×C₃₇	#578	1	1	yes	characteristic
318	C₄×C₃₇	—	2	4	no	—
319	C₄×C₃₇	—	2	2	no	—
320	C₄×C₃₇	—	4	1	no	—
321	C₄×C₃₇	—	4	1	no	—
322	C₄×C₃₇	—	4	2	no	—
323	C₄×C₃₇	—	4	2	no	—
324	C₄×C₃₇	—	4	1	no	—
325	C₄×C₃₇	—	4	1	no	—
326	C₄×C₃₇	—	8	1	no	—
327	C₄×C₃₇	—	8	1	no	—
328	C₄×C₃₇	—	8	1	no	—
329	C₄×C₃₇	—	8	1	no	—
330	C₄×C₃₇	—	8	1	no	—
331	C₄×C₃₇	C₂×#123	1	1	yes	characteristic
332	C₄×C₃₇	#538	1	1	yes	characteristic
333	C₄×C₃₇	#546	1	1	yes	characteristic
334	C₄×C₃₇	#551	1	1	yes	characteristic
335	C₂×#451	C₂×C₃₇	1	1	yes	characteristic
336	C₂×C₄×Q₁₆	C₂×C₃₇	1	1	yes	characteristic, complemented
337	#2421	C₂×C₃₇	1	1	yes	characteristic
338	Q₈×C₂²⋊C₄	C₂×C₃₇	1	1	yes	characteristic
339	#2097	C₂×C₃₇	1	1	yes	characteristic, complemented
340	#2075	C₂×C₃₇	1	1	yes	characteristic
341	#2056	C₂×C₃₇	1	1	yes	characteristic, complemented
342	#2035	C₂×C₃₇	1	1	yes	characteristic
343	#1933	C₂×C₃₇	1	1	yes	characteristic, complemented
344	#1923	C₂×C₃₇	1	1	yes	characteristic
345	#1878	C₂×C₃₇	1	1	yes	characteristic, complemented
346	#1878	C₂×C₃₇	1	1	yes	characteristic, complemented
347	#1865	C₂×C₃₇	1	1	yes	characteristic, complemented
348	#1805	C₂×C₃₇	1	1	yes	characteristic, complemented
349	#1787	C₂×C₃₇	1	1	yes	characteristic
350	C₂×C₃₇	—	4	2	no	—
351	C₂×C₃₇	#2418	1	1	yes	characteristic
352	C₂×C₃₇	#3108	1	1	yes	characteristic
353	C₂×C₃₇	#3127	1	1	yes	characteristic
354	C₂×C₃₇	#3270	1	1	yes	characteristic
355	C₂×C₃₇	#3285	1	1	yes	characteristic
356	C₂×C₃₇	#3300	1	1	yes	characteristic
357	C₂×C₃₇	#3328	1	1	yes	characteristic
358	C₂³×Q₈	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	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
362	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
363	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
364	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
365	#451	—	2	4	no	—
366	C₄×Q₁₆	—	2	4	no	—
367	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
368	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
369	C₂×C₄⋊C₈	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×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
379	C₂×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
380	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
381	#400	—	2	1	no	—
382	#397	—	2	1	no	—
383	#391	—	2	1	no	—
384	#391	—	2	1	no	—
385	#391	C₂²×C₃₇	1	1	yes	characteristic
386	#391	C₂²×C₃₇	1	1	yes	characteristic
387	#391	C₂²×C₃₇	1	1	yes	characteristic
388	#389	C₂²×C₃₇	1	1	yes	characteristic
389	#388	—	2	1	no	—
390	#387	—	2	1	no	—
391	#382	C₂²×C₃₇	1	1	yes	characteristic
392	#380	—	2	1	no	—
393	#380	C₂²×C₃₇	1	1	yes	characteristic
394	#380	C₂²×C₃₇	1	1	yes	characteristic
395	C₄×C₂²⋊C₄	—	2	1	no	—
396	C₄×C₂²⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
397	#340	C₂²×C₃₇	1	1	yes	characteristic
398	#340	C₂²×C₃₇	1	1	yes	characteristic
399	#340	C₂²×C₃₇	1	1	yes	characteristic
400	#340	C₂²×C₃₇	1	1	yes	characteristic
401	#336	C₂²×C₃₇	1	1	yes	characteristic
402	#336	C₂²×C₃₇	1	1	yes	characteristic
403	C₃₇	#24902	1	1	yes	characteristic, direct product factor, Sylow
404	C₂²×Q₈	—	2	2	no	—
405	C₂²×Q₈	—	2	2	no	—
406	C₂²×Q₈	—	2	1	no	—
407	C₂²×Q₈	—	2	2	no	—
408	C₂²×Q₈	—	2	2	no	—
409	C₂²×Q₈	—	4	1	no	—
410	C₂²×Q₈	—	4	1	no	—
411	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
412	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
413	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
414	C₂³×C₄	—	2	1	no	—
415	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
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	—	4	1	no	—
421	C₂×Q₁₆	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	C₂²⋊Q₈	—	2	2	no	—
427	C₂²⋊Q₈	—	4	1	no	—
428	C₄×Q₈	—	2	2	no	—
429	C₄×Q₈	—	2	2	no	—
430	C₄×Q₈	—	2	2	no	—
431	C₄×Q₈	—	4	1	no	—
432	C₄×Q₈	—	4	1	no	—
433	C₄×Q₈	—	4	1	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	2	1	no	—
438	C₂×C₄⋊C₄	—	2	1	no	—
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×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	D₄×C₃₇	1	1	yes	characteristic
448	C₂×C₂²⋊C₄	D₄×C₃₇	1	1	yes	characteristic
449	C₂×C₄²	—	2	1	no	—
450	C₂×C₄²	—	2	1	no	—
451	C₂×C₄²	—	2	1	no	—
452	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
453	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
454	#107	—	2	2	no	—
455	#106	—	4	1	no	—
456	C₄⋊C₈	—	4	1	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	—	4	1	no	—
464	#103	—	4	1	no	—
465	C₂²⋊C₈	—	2	2	no	—
466	C₂²⋊C₈	—	4	1	no	—
467	C₄×C₈	—	2	2	no	—
468	#95	—	2	1	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	#95	—	2	1	no	—
475	#95	—	2	1	no	—
476	#95	—	2	1	no	—
477	#95	—	2	1	no	—
478	#95	—	2	1	no	—
479	#95	D₄×C₃₇	1	1	yes	characteristic
480	#95	D₄×C₃₇	1	1	yes	characteristic
481	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
482	C₂×Q₈	—	2	4	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	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	4	2	no	—
497	C₂×Q₈	—	4	2	no	—
498	C₂×Q₈	—	4	4	no	—
499	C₂×Q₈	—	4	4	no	—
500	C₂×Q₈	—	4	4	no	—
501	C₂×Q₈	—	4	4	no	—
502	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
503	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
504	C₂×Q₈	#41×C₃₇	1	2	yes	—
505	C₂×Q₈	#41×C₃₇	1	2	yes	—
506	C₂×Q₈	#41×C₃₇	1	2	yes	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	4	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	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	4	2	no	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
526	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
527	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
528	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
529	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
530	Q₁₆	—	2	8	no	—
531	Q₁₆	—	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	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
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	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	4	2	no	—
555	C₄⋊C₄	—	4	2	no	—
556	C₄⋊C₄	—	4	2	no	—
557	C₄⋊C₄	—	4	2	no	—
558	C₄⋊C₄	—	4	2	no	—
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	4	2	no	—
562	C₂²⋊C₄	—	4	2	no	—
563	C₂²⋊C₄	—	4	2	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	2	1	no	—
568	C₄²	—	4	2	no	—
569	C₄²	—	4	2	no	—
570	C₄²	—	4	2	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	#135×C₃₇	1	2	yes	—
578	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
579	Q₈	—	2	2	no	—
580	Q₈	—	2	2	no	—
581	Q₈	—	2	2	no	—
582	Q₈	—	2	2	no	—
583	Q₈	—	2	2	no	—
584	Q₈	—	2	2	no	—
585	Q₈	—	2	2	no	—
586	Q₈	—	4	8	no	—
587	Q₈	—	4	1	no	—
588	Q₈	—	4	1	no	—
589	Q₈	—	4	1	no	—
590	Q₈	—	4	1	no	—
591	Q₈	#123×C₃₇	1	4	yes	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	4	8	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	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	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	#137×C₃₇	1	2	yes	—
636	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
637	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
638	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
639	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
640	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
641	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
642	C₈	—	2	2	no	—
643	C₈	—	4	1	no	—
644	C₈	—	4	1	no	—
645	C₈	—	4	1	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	1	no	—
653	C₂²	C₃₇×#525	1	1	yes	characteristic
654	C₂²	D₄²×C₃₇	1	1	yes	characteristic
655	C₂²	C₃₇×#546	1	1	yes	characteristic
656	C₂²	C₂×#135×C₃₇	1	1	yes	characteristic
657	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
658	C₂²	C₃₇×#578	1	1	yes	characteristic
659	C₂²	C₃₇×#578	1	1	yes	characteristic
660	C₄	—	2	4	no	—
661	C₄	—	2	2	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	1	no	—
668	C₄	—	8	1	no	—
669	C₄	—	8	1	no	—
670	C₄	—	8	1	no	—
671	C₄	—	8	1	no	—
672	C₄	—	8	1	no	—
673	C₄	C₂×#123×C₃₇	1	1	yes	characteristic
674	C₄	C₃₇×#538	1	1	yes	characteristic
675	C₄	C₃₇×#546	1	1	yes	characteristic
676	C₄	C₃₇×#551	1	1	yes	characteristic
677	C₂	—	4	2	no	—
678	C₂	C₃₇×#2418	1	1	yes	characteristic
679	C₂	C₃₇×#3108	1	1	yes	characteristic
680	C₂	C₃₇×#3127	1	1	yes	characteristic
681	C₂	C₃₇×#3270	1	1	yes	characteristic
682	C₂	C₃₇×#3285	1	1	yes	characteristic
683	C₂	C₃₇×#3300	1	1	yes	characteristic
684	C₂	C₃₇×#3328	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 ◁ C₄×C₂²⋊C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₁₆×C₃₇	C₂	semidirect
5. C₃₇×#2097	C₂	semidirect
7. C₃₇×#2056	C₂	semidirect
9. C₃₇×#1933	C₂	semidirect
11. C₃₇×#1878	C₂	semidirect
12. C₃₇×#1878	C₂	semidirect
13. C₃₇×#1865	C₂	semidirect
14. C₃₇×#1805	C₂	semidirect
303. #24902	C₃₇	direct (N × H)
336. C₂×C₄×Q₁₆	C₂×C₃₇	semidirect
339. #2097	C₂×C₃₇	semidirect
341. #2056	C₂×C₃₇	semidirect
343. #1933	C₂×C₃₇	semidirect
345. #1878	C₂×C₃₇	semidirect
346. #1878	C₂×C₃₇	semidirect
347. #1865	C₂×C₃₇	semidirect
348. #1805	C₂×C₃₇	semidirect
403. C₃₇	#24902	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×#451	2
C₂×C₄×Q₁₆×C₃₇	2
C₃₇×#2421	2
Q₈×C₂²⋊C₄×C₃₇	2
C₃₇×#2097	2
C₃₇×#2075	2
C₃₇×#2056	2
C₃₇×#2035	2
C₃₇×#1933	2
C₃₇×#1923	2
C₃₇×#1878	2
C₃₇×#1865	2
C₃₇×#1805	2
C₃₇×#1787	2
#24902	37

Subgroups — C37×#24902 #22646155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#24902 #22646155