Subgroups — C₃₇×#21694 #22642947

Order 9472.

1110 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#495	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₇×#442	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₇×#441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×SD₁₆×C₃₇	C₂	1	2	yes	maximal, complemented
5	C₃₇×#2326	C₂	1	2	yes	maximal, complemented
6	C₃₇×#1972	C₂	1	1	yes	maximal, characteristic
7	C₃₇×#1971	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1968	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1959	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1844	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
14	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×#124×C₃₇	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₃₇	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₃₇	C₂²	1	2	yes	—
18	C₃₇×#495	C₄	1	8	yes	complemented
19	C₃₇×#442	—	2	4	no	—
20	C₃₇×#441	—	2	4	no	—
21	C₄×SD₁₆×C₃₇	—	2	8	no	—
22	C₂×#106×C₃₇	C₂²	1	2	yes	—
23	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
24	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×#103×C₃₇	C₂²	1	2	yes	—
26	C₂×#103×C₃₇	C₂²	1	2	yes	—
27	C₂×#102×C₃₇	C₂²	1	2	yes	—
28	C₂×#102×C₃₇	C₂²	1	2	yes	—
29	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
35	C₃₇×#391	C₂²	1	2	yes	—
36	C₃₇×#390	C₂²	1	2	yes	—
37	C₃₇×#388	—	2	4	no	—
38	C₃₇×#385	—	2	4	no	—
39	C₃₇×#384	C₂²	1	2	yes	—
40	C₃₇×#376	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
42	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₃₇	—	2	2	no	—
44	C₂×Q₁₆×C₃₇	—	2	2	no	—
45	C₂×Q₁₆×C₃₇	—	2	2	no	—
46	C₂×Q₁₆×C₃₇	C₂×C₄	1	4	yes	complemented
47	C₂×SD₁₆×C₃₇	—	2	4	no	—
48	C₂×SD₁₆×C₃₇	—	2	4	no	—
49	C₂×SD₁₆×C₃₇	C₂×C₄	1	8	yes	complemented
50	C₂×D₈×C₃₇	—	2	2	no	—
51	C₂×D₈×C₃₇	—	2	2	no	—
52	C₂×D₈×C₃₇	C₂×C₄	1	4	yes	—
53	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
57	#124×C₃₇	—	2	4	no	—
58	#124×C₃₇	C₂×C₄	1	8	yes	complemented
59	C₄×Q₈×C₃₇	—	2	4	no	—
60	C₄×Q₈×C₃₇	—	2	4	no	—
61	C₄×D₄×C₃₇	—	2	4	no	—
62	C₄×D₄×C₃₇	—	2	4	no	—
63	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₃₇	—	2	4	no	—
65	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
67	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
70	C₂×C₄²×C₃₇	—	2	2	no	—
71	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
74	#106×C₃₇	—	2	4	no	—
75	#106×C₃₇	—	2	2	no	—
76	#106×C₃₇	—	2	2	no	—
77	#103×C₃₇	—	2	4	no	—
78	#103×C₃₇	—	2	4	no	—
79	#102×C₃₇	—	2	4	no	—
80	#102×C₃₇	—	2	4	no	—
81	#97×C₃₇	—	2	2	no	—
82	#97×C₃₇	—	2	2	no	—
83	#97×C₃₇	D₄	1	4	yes	—
84	C₄×C₈×C₃₇	—	2	2	no	—
85	C₄×C₈×C₃₇	C₂×C₄	1	4	yes	complemented
86	C₄×C₈×C₃₇	D₄	1	4	yes	—
87	#95×C₃₇	—	2	4	no	—
88	#95×C₃₇	D₄	1	4	yes	—
89	C₂⁴×C₃₇	—	2	2	no	—
90	C₂×Q₈×C₃₇	—	2	2	no	—
91	C₂×Q₈×C₃₇	—	2	2	no	—
92	C₂×Q₈×C₃₇	—	2	2	no	—
93	C₂×Q₈×C₃₇	—	2	2	no	—
94	C₂×Q₈×C₃₇	—	2	2	no	—
95	C₂×Q₈×C₃₇	C₂²×C₄	1	4	yes	—
96	C₂×D₄×C₃₇	—	2	2	no	—
97	C₂×D₄×C₃₇	—	2	2	no	—
98	C₂×D₄×C₃₇	—	2	2	no	—
99	C₂×D₄×C₃₇	—	2	2	no	—
100	C₂×D₄×C₃₇	—	2	2	no	—
101	C₂×D₄×C₃₇	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₃₇	—	2	2	no	—
103	C₂²×C₄×C₃₇	—	2	2	no	—
104	C₂²×C₄×C₃₇	—	2	2	no	—
105	C₂²×C₄×C₃₇	—	4	4	no	—
106	C₂²×C₄×C₃₇	—	8	4	no	—
107	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
111	Q₁₆×C₃₇	—	2	8	no	—
112	SD₁₆×C₃₇	—	2	16	no	—
113	D₈×C₃₇	—	2	8	no	—
114	C₂×C₈×C₃₇	—	2	1	no	—
115	C₂×C₈×C₃₇	—	2	1	no	—
116	C₂×C₈×C₃₇	—	2	1	no	—
117	C₂×C₈×C₃₇	—	2	1	no	—
118	C₂×C₈×C₃₇	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₃₇	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₃₇	#41	1	2	yes	—
125	C₂×C₈×C₃₇	#41	1	2	yes	—
126	C₄⋊C₄×C₃₇	—	2	2	no	—
127	C₄⋊C₄×C₃₇	—	2	2	no	—
128	C₄⋊C₄×C₃₇	—	2	2	no	—
129	C₄⋊C₄×C₃₇	—	2	2	no	—
130	C₄⋊C₄×C₃₇	—	4	4	no	—
131	C₄⋊C₄×C₃₇	—	8	4	no	—
132	C₂²⋊C₄×C₃₇	—	2	16	no	—
133	C₂²⋊C₄×C₃₇	—	4	4	no	—
134	C₂²⋊C₄×C₃₇	—	8	4	no	—
135	C₄²×C₃₇	—	2	1	no	—
136	C₄²×C₃₇	—	2	1	no	—
137	C₄²×C₃₇	—	4	4	no	—
138	C₄²×C₃₇	C₂²×C₄	1	2	yes	—
139	C₄²×C₃₇	C₂×D₄	1	2	yes	—
140	C₄²×C₃₇	C₂×D₄	1	2	yes	—
141	C₄²×C₃₇	#41	1	2	yes	—
142	C₂³×C₃₇	—	2	4	no	—
143	C₂³×C₃₇	—	4	2	no	—
144	C₂³×C₃₇	—	4	2	no	—
145	C₂³×C₃₇	—	4	4	no	—
146	C₂³×C₃₇	—	4	4	no	—
147	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₃₇	—	2	4	no	—
149	Q₈×C₃₇	—	2	4	no	—
150	Q₈×C₃₇	—	4	2	no	—
151	Q₈×C₃₇	—	4	2	no	—
152	D₄×C₃₇	—	2	4	no	—
153	D₄×C₃₇	—	2	4	no	—
154	D₄×C₃₇	—	4	2	no	—
155	D₄×C₃₇	—	4	2	no	—
156	C₂×C₄×C₃₇	—	2	4	no	—
157	C₂×C₄×C₃₇	—	2	4	no	—
158	C₂×C₄×C₃₇	—	2	4	no	—
159	C₂×C₄×C₃₇	—	2	2	no	—
160	C₂×C₄×C₃₇	—	2	4	no	—
161	C₂×C₄×C₃₇	—	4	2	no	—
162	C₂×C₄×C₃₇	—	4	2	no	—
163	C₂×C₄×C₃₇	—	4	2	no	—
164	C₂×C₄×C₃₇	—	4	2	no	—
165	C₂×C₄×C₃₇	—	4	4	no	—
166	C₂×C₄×C₃₇	—	4	4	no	—
167	C₂×C₄×C₃₇	—	8	8	no	—
168	C₂×C₄×C₃₇	C₄×D₄	1	4	yes	—
169	C₂×C₄×C₃₇	#127	1	4	yes	—
170	C₂×C₄×C₃₇	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
176	C₈×C₃₇	—	2	2	no	—
177	C₈×C₃₇	—	2	2	no	—
178	C₈×C₃₇	C₄×D₄	1	4	yes	—
179	C₈×C₃₇	C₄×D₄	1	4	yes	—
180	#21694	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂²×C₃₇	—	4	4	no	—
182	C₂²×C₃₇	—	4	8	no	—
183	C₂²×C₃₇	—	8	2	no	—
184	C₂²×C₃₇	—	8	2	no	—
185	C₂²×C₃₇	—	8	4	no	—
186	C₂²×C₃₇	C₂×C₄×D₄	1	1	yes	characteristic
187	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
188	C₂²×C₃₇	#532	1	1	yes	characteristic
189	C₂²×C₃₇	#577	1	4	yes	—
190	C₄×C₃₇	—	2	4	no	—
191	C₄×C₃₇	—	2	4	no	—
192	C₄×C₃₇	—	4	4	no	—
193	C₄×C₃₇	—	4	2	no	—
194	C₄×C₃₇	—	8	2	no	—
195	C₄×C₃₇	—	8	2	no	—
196	C₄×C₃₇	C₂×C₄×D₄	1	1	yes	characteristic
197	C₄×C₃₇	C₂×C₄×D₄	1	1	yes	characteristic
198	C₄×C₃₇	#532	1	1	yes	characteristic
199	C₄×C₃₇	#532	1	1	yes	characteristic
200	C₂×#495	C₂×C₃₇	1	1	yes	characteristic
201	C₂×#442	C₂×C₃₇	1	1	yes	characteristic
202	C₂×#441	C₂×C₃₇	1	1	yes	characteristic, complemented
203	C₂×C₄×SD₁₆	C₂×C₃₇	1	2	yes	complemented
204	#2326	C₂×C₃₇	1	2	yes	complemented
205	#1972	C₂×C₃₇	1	1	yes	characteristic
206	#1971	C₂×C₃₇	1	1	yes	characteristic, complemented
207	#1968	C₂×C₃₇	1	2	yes	complemented
208	#1959	C₂×C₃₇	1	2	yes	complemented
209	#1844	C₂×C₃₇	1	1	yes	characteristic, complemented
210	#1726	C₂×C₃₇	1	1	yes	characteristic, complemented
211	C₂×C₃₇	—	8	4	no	—
212	C₂×C₃₇	C₄×#127	1	1	yes	characteristic
213	C₂×C₃₇	#2952	1	2	yes	—
214	C₂×C₃₇	#3154	1	2	yes	—
215	C₂×C₃₇	#3173	1	2	yes	—
216	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
217	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
218	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
219	C₂×#124	C₂²×C₃₇	1	2	yes	—
220	C₂×C₄×Q₈	C₂²×C₃₇	1	2	yes	—
221	C₂×C₄×D₄	C₂²×C₃₇	1	2	yes	—
222	#495	C₄×C₃₇	1	8	yes	complemented
223	#442	—	2	4	no	—
224	#441	—	2	4	no	—
225	C₄×SD₁₆	—	2	8	no	—
226	C₂×#106	C₂²×C₃₇	1	2	yes	—
227	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
228	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
229	C₂×#103	C₂²×C₃₇	1	2	yes	—
230	C₂×#103	C₂²×C₃₇	1	2	yes	—
231	C₂×#102	C₂²×C₃₇	1	2	yes	—
232	C₂×#102	C₂²×C₃₇	1	2	yes	—
233	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
234	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
235	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
236	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
237	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
238	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
239	#391	C₂²×C₃₇	1	2	yes	—
240	#390	C₂²×C₃₇	1	2	yes	—
241	#388	—	2	4	no	—
242	#385	—	2	4	no	—
243	#384	C₂²×C₃₇	1	2	yes	—
244	#376	C₂²×C₃₇	1	1	yes	characteristic
245	C₃₇	#21694	1	1	yes	characteristic, direct product factor, Sylow
246	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
247	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
248	C₂³×C₄	—	2	2	no	—
249	C₂×Q₁₆	—	2	2	no	—
250	C₂×Q₁₆	—	2	2	no	—
251	C₂×Q₁₆	C₂×C₄×C₃₇	1	4	yes	complemented
252	C₂×SD₁₆	—	2	4	no	—
253	C₂×SD₁₆	—	2	4	no	—
254	C₂×SD₁₆	C₂×C₄×C₃₇	1	8	yes	complemented
255	C₂×D₈	—	2	2	no	—
256	C₂×D₈	—	2	2	no	—
257	C₂×D₈	C₂×C₄×C₃₇	1	4	yes	—
258	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
261	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
262	#124	—	2	4	no	—
263	#124	C₂×C₄×C₃₇	1	8	yes	complemented
264	C₄×Q₈	—	2	4	no	—
265	C₄×Q₈	—	2	4	no	—
266	C₄×D₄	—	2	4	no	—
267	C₄×D₄	—	2	4	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	4	no	—
270	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
272	C₂×C₂²⋊C₄	—	2	4	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	4	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
279	#106	—	2	4	no	—
280	#106	—	2	2	no	—
281	#106	—	2	2	no	—
282	#103	—	2	4	no	—
283	#103	—	2	4	no	—
284	#102	—	2	4	no	—
285	#102	—	2	4	no	—
286	#97	—	2	2	no	—
287	#97	—	2	2	no	—
288	#97	D₄×C₃₇	1	4	yes	—
289	C₄×C₈	—	2	2	no	—
290	C₄×C₈	C₂×C₄×C₃₇	1	4	yes	complemented
291	C₄×C₈	D₄×C₃₇	1	4	yes	—
292	#95	—	2	4	no	—
293	#95	D₄×C₃₇	1	4	yes	—
294	C₂⁴	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	C₂²×C₄×C₃₇	1	4	yes	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	C₂²×C₄×C₃₇	1	4	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	4	4	no	—
311	C₂²×C₄	—	8	4	no	—
312	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
315	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
316	Q₁₆	—	2	8	no	—
317	SD₁₆	—	2	16	no	—
318	D₈	—	2	8	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	C₂²×C₄×C₃₇	1	2	yes	—
324	C₂×C₈	C₂²×C₄×C₃₇	1	2	yes	—
325	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
326	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
327	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
328	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
329	C₂×C₈	#41×C₃₇	1	2	yes	—
330	C₂×C₈	#41×C₃₇	1	2	yes	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	4	4	no	—
336	C₄⋊C₄	—	8	4	no	—
337	C₂²⋊C₄	—	2	16	no	—
338	C₂²⋊C₄	—	4	4	no	—
339	C₂²⋊C₄	—	8	4	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	4	4	no	—
343	C₄²	C₂²×C₄×C₃₇	1	2	yes	—
344	C₄²	C₂×D₄×C₃₇	1	2	yes	—
345	C₄²	C₂×D₄×C₃₇	1	2	yes	—
346	C₄²	#41×C₃₇	1	2	yes	—
347	C₂³	—	2	4	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	4	no	—
351	C₂³	—	4	4	no	—
352	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
353	Q₈	—	2	4	no	—
354	Q₈	—	2	4	no	—
355	Q₈	—	4	2	no	—
356	Q₈	—	4	2	no	—
357	D₄	—	2	4	no	—
358	D₄	—	2	4	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	8	8	no	—
373	C₂×C₄	C₄×D₄×C₃₇	1	4	yes	—
374	C₂×C₄	#127×C₃₇	1	4	yes	—
375	C₂×C₄	C₂³×C₄×C₃₇	1	1	yes	characteristic
376	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
378	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
379	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
380	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
381	C₈	—	2	2	no	—
382	C₈	—	2	2	no	—
383	C₈	C₄×D₄×C₃₇	1	4	yes	—
384	C₈	C₄×D₄×C₃₇	1	4	yes	—
385	C₂²	—	4	8	no	—
386	C₂²	—	4	4	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	8	4	no	—
390	C₂²	C₂×C₄×D₄×C₃₇	1	1	yes	characteristic
391	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
392	C₂²	C₃₇×#532	1	1	yes	characteristic
393	C₂²	C₃₇×#577	1	4	yes	—
394	C₄	—	2	4	no	—
395	C₄	—	2	4	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	4	no	—
398	C₄	—	8	2	no	—
399	C₄	—	8	2	no	—
400	C₄	C₂×C₄×D₄×C₃₇	1	1	yes	characteristic
401	C₄	C₂×C₄×D₄×C₃₇	1	1	yes	characteristic
402	C₄	C₃₇×#532	1	1	yes	characteristic
403	C₄	C₃₇×#532	1	1	yes	characteristic
404	C₂	—	8	4	no	—
405	C₂	C₄×#127×C₃₇	1	1	yes	characteristic
406	C₂	C₃₇×#2952	1	2	yes	—
407	C₂	C₃₇×#3154	1	2	yes	—
408	C₂	C₃₇×#3173	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂²×D₈×C₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₃₇×#376 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₃₇×#441	C₂	semidirect
4. C₂×C₄×SD₁₆×C₃₇	C₂	semidirect
5. C₃₇×#2326	C₂	semidirect
7. C₃₇×#1971	C₂	semidirect
8. C₃₇×#1968	C₂	semidirect
9. C₃₇×#1959	C₂	semidirect
10. C₃₇×#1844	C₂	semidirect
11. C₃₇×#1726	C₂	semidirect
18. C₃₇×#495	C₄	semidirect
46. C₂×Q₁₆×C₃₇	C₂×C₄	semidirect
49. C₂×SD₁₆×C₃₇	C₂×C₄	semidirect
58. #124×C₃₇	C₂×C₄	semidirect
85. C₄×C₈×C₃₇	C₂×C₄	semidirect
180. #21694	C₃₇	direct (N × H)
202. C₂×#441	C₂×C₃₇	semidirect
203. C₂×C₄×SD₁₆	C₂×C₃₇	semidirect
204. #2326	C₂×C₃₇	semidirect
206. #1971	C₂×C₃₇	semidirect
207. #1968	C₂×C₃₇	semidirect
208. #1959	C₂×C₃₇	semidirect
209. #1844	C₂×C₃₇	semidirect
210. #1726	C₂×C₃₇	semidirect
222. #495	C₄×C₃₇	semidirect
245. C₃₇	#21694	direct (N × H)
251. C₂×Q₁₆	C₂×C₄×C₃₇	semidirect
254. C₂×SD₁₆	C₂×C₄×C₃₇	semidirect
263. #124	C₂×C₄×C₃₇	semidirect
290. C₄×C₈	C₂×C₄×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#495	2
C₂×C₃₇×#442	2
C₂×C₃₇×#441	2
C₂×C₄×SD₁₆×C₃₇	2
C₃₇×#2326	2
C₃₇×#1972	2
C₃₇×#1971	2
C₃₇×#1968	2
C₃₇×#1959	2
C₃₇×#1844	2
C₃₇×#1726	2
#21694	37

Subgroups — C37×#21694 #22642947

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#21694 #22642947