Subgroups — C₃₇×#23759 #22645012

Order 9472.

752 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂²⋊Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#2283	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2097	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2085	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2077	C₂	1	1	yes	maximal, characteristic
7	C₃₇×#2075	C₂	1	1	yes	maximal, characteristic
8	C₃₇×#2074	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#2036	C₂	1	1	yes	maximal, characteristic
10	C₃₇×#2035	C₂	1	1	yes	maximal, characteristic
11	C₄×#107×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#106×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#103×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#103×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂²⋊C₈×C₃₇	C₂	1	1	yes	maximal, characteristic
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	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
20	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
21	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
24	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
26	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
31	C₃₇×#391	C₂²	1	1	yes	characteristic
32	C₃₇×#389	C₂²	1	1	yes	characteristic
33	C₃₇×#387	—	2	1	no	—
34	C₃₇×#385	—	2	1	no	—
35	C₃₇×#383	—	2	1	no	—
36	C₃₇×#382	C₂²	1	1	yes	characteristic
37	C₃₇×#382	C₂²	1	1	yes	characteristic
38	C₃₇×#381	—	2	1	no	—
39	C₃₇×#380	C₂²	1	1	yes	characteristic
40	C₃₇×#380	C₂²	1	1	yes	characteristic
41	C₃₇×#380	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₃₇	—	2	1	no	—
43	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊C₄×C₃₇	—	2	1	no	—
47	C₄×C₂²⋊C₄×C₃₇	—	2	1	no	—
48	C₃₇×#376	—	2	1	no	—
49	C₃₇×#340	C₂²	1	1	yes	characteristic
50	C₃₇×#340	C₂²	1	1	yes	characteristic
51	C₃₇×#340	C₂²	1	1	yes	characteristic
52	C₃₇×#340	C₂²	1	1	yes	characteristic
53	C₃₇×#340	C₂²	1	1	yes	characteristic
54	C₃₇×#340	C₂²	1	1	yes	characteristic
55	C₃₇×#340	C₂²	1	1	yes	characteristic
56	C₃₇×#340	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	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
67	C₂²⋊Q₈×C₃₇	—	2	2	no	—
68	C₂²⋊Q₈×C₃₇	—	2	2	no	—
69	C₄×Q₈×C₃₇	—	2	2	no	—
70	C₄×Q₈×C₃₇	—	2	2	no	—
71	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
72	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
73	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
74	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
85	C₂×C₄²×C₃₇	—	2	2	no	—
86	C₂×C₄²×C₃₇	—	2	2	no	—
87	C₂×C₄²×C₃₇	—	2	1	no	—
88	C₂×C₄²×C₃₇	—	2	1	no	—
89	C₂×C₄²×C₃₇	—	2	1	no	—
90	C₂×C₄²×C₃₇	—	2	1	no	—
91	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
95	#107×C₃₇	—	2	2	no	—
96	#107×C₃₇	—	2	2	no	—
97	#106×C₃₇	—	2	2	no	—
98	#106×C₃₇	—	2	2	no	—
99	#103×C₃₇	—	2	2	no	—
100	#103×C₃₇	—	2	2	no	—
101	#103×C₃₇	—	2	2	no	—
102	#103×C₃₇	—	2	2	no	—
103	C₂²⋊C₈×C₃₇	—	2	2	no	—
104	C₂²⋊C₈×C₃₇	—	2	2	no	—
105	C₄×C₈×C₃₇	—	2	2	no	—
106	C₄×C₈×C₃₇	—	2	2	no	—
107	#95×C₃₇	—	2	1	no	—
108	#95×C₃₇	—	2	1	no	—
109	#95×C₃₇	—	2	1	no	—
110	#95×C₃₇	—	2	1	no	—
111	#95×C₃₇	—	2	1	no	—
112	#95×C₃₇	—	2	1	no	—
113	#95×C₃₇	—	2	1	no	—
114	#95×C₃₇	—	2	1	no	—
115	#95×C₃₇	—	2	1	no	—
116	#95×C₃₇	—	2	1	no	—
117	#95×C₃₇	—	2	1	no	—
118	#95×C₃₇	—	2	1	no	—
119	#95×C₃₇	—	2	1	no	—
120	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
121	C₂×Q₈×C₃₇	—	2	1	no	—
122	C₂×Q₈×C₃₇	—	2	1	no	—
123	C₂×Q₈×C₃₇	—	2	1	no	—
124	C₂×Q₈×C₃₇	—	2	1	no	—
125	C₂×Q₈×C₃₇	—	2	1	no	—
126	C₂×Q₈×C₃₇	#41	1	2	yes	—
127	C₂²×C₄×C₃₇	—	2	2	no	—
128	C₂²×C₄×C₃₇	—	2	1	no	—
129	C₂²×C₄×C₃₇	—	2	1	no	—
130	C₂²×C₄×C₃₇	—	2	2	no	—
131	C₂²×C₄×C₃₇	—	2	2	no	—
132	C₂²×C₄×C₃₇	—	2	2	no	—
133	C₂²×C₄×C₃₇	—	2	2	no	—
134	C₂²×C₄×C₃₇	—	2	1	no	—
135	C₂²×C₄×C₃₇	—	2	1	no	—
136	C₂²×C₄×C₃₇	—	2	1	no	—
137	C₂²×C₄×C₃₇	—	2	1	no	—
138	C₂²×C₄×C₃₇	—	2	1	no	—
139	C₂²×C₄×C₃₇	—	2	1	no	—
140	C₂²×C₄×C₃₇	—	2	1	no	—
141	C₂²×C₄×C₃₇	—	2	1	no	—
142	C₂²×C₄×C₃₇	—	2	1	no	—
143	C₂²×C₄×C₃₇	—	2	1	no	—
144	C₂²×C₄×C₃₇	—	2	1	no	—
145	C₂²×C₄×C₃₇	—	2	1	no	—
146	C₂²×C₄×C₃₇	—	4	1	no	—
147	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
153	C₂×C₈×C₃₇	—	2	1	no	—
154	C₂×C₈×C₃₇	—	2	1	no	—
155	C₂×C₈×C₃₇	—	2	1	no	—
156	C₂×C₈×C₃₇	—	2	1	no	—
157	C₂×C₈×C₃₇	—	2	1	no	—
158	C₂×C₈×C₃₇	—	2	1	no	—
159	C₂×C₈×C₃₇	—	2	1	no	—
160	C₂×C₈×C₃₇	—	2	1	no	—
161	C₂×C₈×C₃₇	—	2	1	no	—
162	C₂×C₈×C₃₇	—	2	1	no	—
163	C₂×C₈×C₃₇	#41	1	2	yes	—
164	C₂×C₈×C₃₇	#41	1	2	yes	—
165	C₄⋊C₄×C₃₇	—	2	4	no	—
166	C₄⋊C₄×C₃₇	—	2	1	no	—
167	C₄⋊C₄×C₃₇	—	2	1	no	—
168	C₄⋊C₄×C₃₇	—	2	1	no	—
169	C₄⋊C₄×C₃₇	—	2	1	no	—
170	C₄⋊C₄×C₃₇	—	2	1	no	—
171	C₄⋊C₄×C₃₇	—	2	1	no	—
172	C₄⋊C₄×C₃₇	—	2	1	no	—
173	C₄⋊C₄×C₃₇	—	2	1	no	—
174	C₄⋊C₄×C₃₇	—	2	1	no	—
175	C₄⋊C₄×C₃₇	—	2	1	no	—
176	C₄⋊C₄×C₃₇	—	2	1	no	—
177	C₄⋊C₄×C₃₇	—	2	1	no	—
178	C₄⋊C₄×C₃₇	—	2	1	no	—
179	C₄⋊C₄×C₃₇	—	4	2	no	—
180	C₄⋊C₄×C₃₇	—	4	2	no	—
181	C₄⋊C₄×C₃₇	#41	1	2	yes	—
182	C₂²⋊C₄×C₃₇	—	2	4	no	—
183	C₂²⋊C₄×C₃₇	—	4	2	no	—
184	C₂²⋊C₄×C₃₇	—	4	2	no	—
185	C₂²⋊C₄×C₃₇	—	4	2	no	—
186	C₄²×C₃₇	—	2	2	no	—
187	C₄²×C₃₇	—	2	2	no	—
188	C₄²×C₃₇	—	2	1	no	—
189	C₄²×C₃₇	—	2	1	no	—
190	C₄²×C₃₇	—	4	2	no	—
191	C₄²×C₃₇	—	4	2	no	—
192	C₄²×C₃₇	—	4	2	no	—
193	C₄²×C₃₇	—	4	2	no	—
194	C₄²×C₃₇	#41	1	2	yes	—
195	C₄²×C₃₇	#41	1	2	yes	—
196	C₂³×C₃₇	—	2	1	no	—
197	C₂³×C₃₇	—	2	1	no	—
198	C₂³×C₃₇	—	2	1	no	—
199	C₂³×C₃₇	—	2	1	no	—
200	C₂³×C₃₇	—	2	1	no	—
201	C₂³×C₃₇	—	2	1	no	—
202	C₂³×C₃₇	#135	1	2	yes	—
203	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₃₇	—	2	2	no	—
205	Q₈×C₃₇	—	2	2	no	—
206	Q₈×C₃₇	—	4	1	no	—
207	Q₈×C₃₇	—	4	1	no	—
208	C₂×C₄×C₃₇	—	2	1	no	—
209	C₂×C₄×C₃₇	—	2	1	no	—
210	C₂×C₄×C₃₇	—	2	1	no	—
211	C₂×C₄×C₃₇	—	2	1	no	—
212	C₂×C₄×C₃₇	—	2	1	no	—
213	C₂×C₄×C₃₇	—	2	2	no	—
214	C₂×C₄×C₃₇	—	2	2	no	—
215	C₂×C₄×C₃₇	—	2	1	no	—
216	C₂×C₄×C₃₇	—	2	1	no	—
217	C₂×C₄×C₃₇	—	2	1	no	—
218	C₂×C₄×C₃₇	—	2	1	no	—
219	C₂×C₄×C₃₇	—	2	1	no	—
220	C₂×C₄×C₃₇	—	2	1	no	—
221	C₂×C₄×C₃₇	—	4	4	no	—
222	C₂×C₄×C₃₇	—	4	1	no	—
223	C₂×C₄×C₃₇	—	4	1	no	—
224	C₂×C₄×C₃₇	—	4	1	no	—
225	C₂×C₄×C₃₇	—	4	1	no	—
226	C₂×C₄×C₃₇	—	4	1	no	—
227	C₂×C₄×C₃₇	—	4	1	no	—
228	C₂×C₄×C₃₇	—	4	1	no	—
229	C₂×C₄×C₃₇	—	4	1	no	—
230	C₂×C₄×C₃₇	—	4	4	no	—
231	C₂×C₄×C₃₇	—	4	1	no	—
232	C₂×C₄×C₃₇	—	4	1	no	—
233	C₂×C₄×C₃₇	—	4	1	no	—
234	C₂×C₄×C₃₇	—	4	1	no	—
235	C₂×C₄×C₃₇	—	4	1	no	—
236	C₂×C₄×C₃₇	—	4	1	no	—
237	C₂×C₄×C₃₇	—	4	1	no	—
238	C₂×C₄×C₃₇	—	4	1	no	—
239	C₂×C₄×C₃₇	—	4	1	no	—
240	C₂×C₄×C₃₇	—	4	1	no	—
241	C₂×C₄×C₃₇	—	4	1	no	—
242	C₂×C₄×C₃₇	—	4	1	no	—
243	C₂×C₄×C₃₇	—	4	1	no	—
244	C₂×C₄×C₃₇	—	4	1	no	—
245	C₂×C₄×C₃₇	—	4	1	no	—
246	C₂×C₄×C₃₇	—	4	1	no	—
247	C₂×C₄×C₃₇	—	4	1	no	—
248	C₂×C₄×C₃₇	—	4	1	no	—
249	C₂×C₄×C₃₇	#123	1	2	yes	—
250	C₂×C₄×C₃₇	#123	1	2	yes	—
251	C₂×C₄×C₃₇	#135	1	2	yes	—
252	C₂×C₄×C₃₇	#137	1	2	yes	—
253	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
256	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
257	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
259	C₈×C₃₇	—	2	2	no	—
260	C₈×C₃₇	—	2	2	no	—
261	C₈×C₃₇	—	4	1	no	—
262	C₈×C₃₇	—	4	1	no	—
263	#23759	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
264	C₂²×C₃₇	—	2	2	no	—
265	C₂²×C₃₇	—	2	2	no	—
266	C₂²×C₃₇	—	2	2	no	—
267	C₂²×C₃₇	—	4	1	no	—
268	C₂²×C₃₇	—	4	1	no	—
269	C₂²×C₃₇	—	4	1	no	—
270	C₂²×C₃₇	—	4	1	no	—
271	C₂²×C₃₇	C₂×#123	1	1	yes	characteristic
272	C₂²×C₃₇	#525	1	1	yes	characteristic
273	C₂²×C₃₇	#532	1	1	yes	characteristic
274	C₂²×C₃₇	C₂×#135	1	1	yes	characteristic
275	C₂²×C₃₇	C₂×#135	1	1	yes	characteristic
276	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
277	C₂²×C₃₇	#575	1	1	yes	characteristic
278	C₄×C₃₇	—	2	2	no	—
279	C₄×C₃₇	—	4	1	no	—
280	C₄×C₃₇	—	4	1	no	—
281	C₄×C₃₇	—	4	2	no	—
282	C₄×C₃₇	—	4	1	no	—
283	C₄×C₃₇	—	4	2	no	—
284	C₄×C₃₇	—	8	1	no	—
285	C₄×C₃₇	—	8	1	no	—
286	C₄×C₃₇	—	8	1	no	—
287	C₄×C₃₇	—	8	1	no	—
288	C₄×C₃₇	—	8	1	no	—
289	C₄×C₃₇	—	8	1	no	—
290	C₄×C₃₇	#485	1	4	yes	—
291	C₄×C₃₇	#529	1	1	yes	characteristic
292	C₄×C₃₇	#529	1	1	yes	characteristic
293	C₄×C₃₇	#529	1	1	yes	characteristic
294	C₄×C₃₇	#529	1	1	yes	characteristic
295	C₄×C₂²⋊Q₈	C₂×C₃₇	1	1	yes	characteristic
296	#2283	C₂×C₃₇	1	1	yes	characteristic
297	#2101	C₂×C₃₇	1	1	yes	characteristic, complemented
298	#2097	C₂×C₃₇	1	1	yes	characteristic, complemented
299	#2085	C₂×C₃₇	1	1	yes	characteristic, complemented
300	#2077	C₂×C₃₇	1	1	yes	characteristic
301	#2075	C₂×C₃₇	1	1	yes	characteristic
302	#2074	C₂×C₃₇	1	1	yes	characteristic, complemented
303	#2036	C₂×C₃₇	1	1	yes	characteristic
304	#2035	C₂×C₃₇	1	1	yes	characteristic
305	C₄×#107	C₂×C₃₇	1	1	yes	characteristic, complemented
306	C₄×#106	C₂×C₃₇	1	1	yes	characteristic, complemented
307	C₄×#103	C₂×C₃₇	1	1	yes	characteristic, complemented
308	C₄×#103	C₂×C₃₇	1	1	yes	characteristic, complemented
309	C₄×C₂²⋊C₈	C₂×C₃₇	1	1	yes	characteristic
310	C₂×C₃₇	—	4	2	no	—
311	C₂×C₃₇	#2395	1	1	yes	characteristic
312	C₂×C₃₇	C₂×#485	1	1	yes	characteristic
313	C₂×C₃₇	#3091	1	1	yes	characteristic
314	C₂×C₃₇	#3102	1	1	yes	characteristic
315	C₂×C₃₇	#3108	1	1	yes	characteristic
316	C₂×C₃₇	#3168	1	1	yes	characteristic
317	C₂×C₃₇	#3172	1	1	yes	characteristic
318	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
319	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
320	C₂²×C₄²	C₂²×C₃₇	1	1	yes	characteristic
321	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
322	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
323	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
324	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
325	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
326	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
327	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
328	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
329	C₂×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
330	C₂×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
331	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
332	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
333	#391	C₂²×C₃₇	1	1	yes	characteristic
334	#389	C₂²×C₃₇	1	1	yes	characteristic
335	#387	—	2	1	no	—
336	#385	—	2	1	no	—
337	#383	—	2	1	no	—
338	#382	C₂²×C₃₇	1	1	yes	characteristic
339	#382	C₂²×C₃₇	1	1	yes	characteristic
340	#381	—	2	1	no	—
341	#380	C₂²×C₃₇	1	1	yes	characteristic
342	#380	C₂²×C₃₇	1	1	yes	characteristic
343	#380	C₂²×C₃₇	1	1	yes	characteristic
344	C₄×C₄⋊C₄	—	2	1	no	—
345	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
346	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
347	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
348	C₄×C₂²⋊C₄	—	2	1	no	—
349	C₄×C₂²⋊C₄	—	2	1	no	—
350	#376	—	2	1	no	—
351	#340	C₂²×C₃₇	1	1	yes	characteristic
352	#340	C₂²×C₃₇	1	1	yes	characteristic
353	#340	C₂²×C₃₇	1	1	yes	characteristic
354	#340	C₂²×C₃₇	1	1	yes	characteristic
355	#340	C₂²×C₃₇	1	1	yes	characteristic
356	#340	C₂²×C₃₇	1	1	yes	characteristic
357	#340	C₂²×C₃₇	1	1	yes	characteristic
358	#340	C₂²×C₃₇	1	1	yes	characteristic
359	#336	C₂²×C₃₇	1	1	yes	characteristic
360	#336	C₂²×C₃₇	1	1	yes	characteristic
361	C₃₇	#23759	1	1	yes	characteristic, direct product factor, Sylow
362	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
363	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
364	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
365	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
366	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
367	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
368	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
369	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
370	C₂²⋊Q₈	—	2	2	no	—
371	C₂²⋊Q₈	—	2	2	no	—
372	C₄×Q₈	—	2	2	no	—
373	C₄×Q₈	—	2	2	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₄²	—	2	2	no	—
389	C₂×C₄²	—	2	2	no	—
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	—	2	1	no	—
393	C₂×C₄²	—	2	1	no	—
394	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
395	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
396	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
397	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
398	#107	—	2	2	no	—
399	#107	—	2	2	no	—
400	#106	—	2	2	no	—
401	#106	—	2	2	no	—
402	#103	—	2	2	no	—
403	#103	—	2	2	no	—
404	#103	—	2	2	no	—
405	#103	—	2	2	no	—
406	C₂²⋊C₈	—	2	2	no	—
407	C₂²⋊C₈	—	2	2	no	—
408	C₄×C₈	—	2	2	no	—
409	C₄×C₈	—	2	2	no	—
410	#95	—	2	1	no	—
411	#95	—	2	1	no	—
412	#95	—	2	1	no	—
413	#95	—	2	1	no	—
414	#95	—	2	1	no	—
415	#95	—	2	1	no	—
416	#95	—	2	1	no	—
417	#95	—	2	1	no	—
418	#95	—	2	1	no	—
419	#95	—	2	1	no	—
420	#95	—	2	1	no	—
421	#95	—	2	1	no	—
422	#95	—	2	1	no	—
423	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	#41×C₃₇	1	2	yes	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	4	1	no	—
450	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
455	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	#41×C₃₇	1	2	yes	—
467	C₂×C₈	#41×C₃₇	1	2	yes	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	4	2	no	—
483	C₄⋊C₄	—	4	2	no	—
484	C₄⋊C₄	#41×C₃₇	1	2	yes	—
485	C₂²⋊C₄	—	2	4	no	—
486	C₂²⋊C₄	—	4	2	no	—
487	C₂²⋊C₄	—	4	2	no	—
488	C₂²⋊C₄	—	4	2	no	—
489	C₄²	—	2	2	no	—
490	C₄²	—	2	2	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	4	2	no	—
494	C₄²	—	4	2	no	—
495	C₄²	—	4	2	no	—
496	C₄²	—	4	2	no	—
497	C₄²	#41×C₃₇	1	2	yes	—
498	C₄²	#41×C₃₇	1	2	yes	—
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	2	1	no	—
503	C₂³	—	2	1	no	—
504	C₂³	—	2	1	no	—
505	C₂³	#135×C₃₇	1	2	yes	—
506	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
507	Q₈	—	2	2	no	—
508	Q₈	—	2	2	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	4	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	4	4	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	4	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	#123×C₃₇	1	2	yes	—
553	C₂×C₄	#123×C₃₇	1	2	yes	—
554	C₂×C₄	#135×C₃₇	1	2	yes	—
555	C₂×C₄	#137×C₃₇	1	2	yes	—
556	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
557	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
558	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
559	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
560	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
561	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
562	C₈	—	2	2	no	—
563	C₈	—	2	2	no	—
564	C₈	—	4	1	no	—
565	C₈	—	4	1	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	C₂×#123×C₃₇	1	1	yes	characteristic
574	C₂²	C₃₇×#525	1	1	yes	characteristic
575	C₂²	C₃₇×#532	1	1	yes	characteristic
576	C₂²	C₂×#135×C₃₇	1	1	yes	characteristic
577	C₂²	C₂×#135×C₃₇	1	1	yes	characteristic
578	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
579	C₂²	C₃₇×#575	1	1	yes	characteristic
580	C₄	—	2	2	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	2	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	2	no	—
586	C₄	—	8	1	no	—
587	C₄	—	8	1	no	—
588	C₄	—	8	1	no	—
589	C₄	—	8	1	no	—
590	C₄	—	8	1	no	—
591	C₄	—	8	1	no	—
592	C₄	C₃₇×#485	1	4	yes	—
593	C₄	C₃₇×#529	1	1	yes	characteristic
594	C₄	C₃₇×#529	1	1	yes	characteristic
595	C₄	C₃₇×#529	1	1	yes	characteristic
596	C₄	C₃₇×#529	1	1	yes	characteristic
597	C₂	—	4	2	no	—
598	C₂	C₃₇×#2395	1	1	yes	characteristic
599	C₂	C₂×C₃₇×#485	1	1	yes	characteristic
600	C₂	C₃₇×#3091	1	1	yes	characteristic
601	C₂	C₃₇×#3102	1	1	yes	characteristic
602	C₂	C₃₇×#3108	1	1	yes	characteristic
603	C₂	C₃₇×#3168	1	1	yes	characteristic
604	C₂	C₃₇×#3172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₇	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
socle	C₂³×C₃₇	C₂²×D₄
prime radical	C₂⁴×C₃₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₇ ◁ C₂²×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₇×#2101	C₂	semidirect
4. C₃₇×#2097	C₂	semidirect
5. C₃₇×#2085	C₂	semidirect
8. C₃₇×#2074	C₂	semidirect
11. C₄×#107×C₃₇	C₂	semidirect
12. C₄×#106×C₃₇	C₂	semidirect
13. C₄×#103×C₃₇	C₂	semidirect
14. C₄×#103×C₃₇	C₂	semidirect
263. #23759	C₃₇	direct (N × H)
297. #2101	C₂×C₃₇	semidirect
298. #2097	C₂×C₃₇	semidirect
299. #2085	C₂×C₃₇	semidirect
302. #2074	C₂×C₃₇	semidirect
305. C₄×#107	C₂×C₃₇	semidirect
306. C₄×#106	C₂×C₃₇	semidirect
307. C₄×#103	C₂×C₃₇	semidirect
308. C₄×#103	C₂×C₃₇	semidirect
361. C₃₇	#23759	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₂²⋊Q₈×C₃₇	2
C₃₇×#2283	2
C₃₇×#2101	2
C₃₇×#2097	2
C₃₇×#2085	2
C₃₇×#2077	2
C₃₇×#2075	2
C₃₇×#2074	2
C₃₇×#2036	2
C₃₇×#2035	2
C₄×#107×C₃₇	2
C₄×#106×C₃₇	2
C₄×#103×C₃₇	2
C₄×C₂²⋊C₈×C₃₇	2
#23759	37

Subgroups — C37×#23759 #22645012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#23759 #22645012