Subgroups — C₃₇×#32783 #22654036

Order 9472.

686 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#2629	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#2620	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2095	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2093	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2083	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2042	C₂	1	2	yes	maximal, complemented
7	C₃₇×#2036	C₂	1	2	yes	maximal, complemented
8	C₃₇×#2033	C₂	1	2	yes	maximal
9	C₃₇×#2026	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#2025	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1818	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×#121×C₃₇	C₂²	1	1	yes	characteristic
16	C₂×#117×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×#107×C₃₇	C₂²	1	2	yes	—
18	C₂×#107×C₃₇	C₂²	1	2	yes	—
19	C₂×#103×C₃₇	C₂²	1	2	yes	—
20	C₂×#103×C₃₇	C₂²	1	2	yes	—
21	C₂×#102×C₃₇	C₂²	1	2	yes	—
22	C₂×#102×C₃₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₃₇	C₂²	1	2	yes	—
24	C₃₇×#398	—	2	2	no	—
25	C₃₇×#396	—	2	2	no	—
26	C₃₇×#396	—	2	2	no	—
27	C₃₇×#394	—	2	2	no	—
28	C₃₇×#391	C₂²	1	1	yes	characteristic
29	C₃₇×#390	C₂²	1	1	yes	characteristic
30	C₃₇×#389	C₂²	1	2	yes	—
31	C₃₇×#384	C₂²	1	1	yes	characteristic
32	C₃₇×#384	C₂²	1	1	yes	characteristic
33	C₃₇×#380	C₂²	1	2	yes	—
34	C₃₇×#340	C₂²	1	2	yes	—
35	C₃₇×#340	C₂²	1	2	yes	—
36	C₃₇×#336	C₂²	1	1	yes	characteristic
37	C₃₇×#336	C₂²	1	1	yes	characteristic
38	C₃₇×#336	C₂²	1	2	yes	—
39	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₃₇	—	2	1	no	—
41	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
44	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
45	#125×C₃₇	—	4	2	no	—
46	#124×C₃₇	—	4	2	no	—
47	C₂²⋊Q₈×C₃₇	—	4	2	no	—
48	#121×C₃₇	—	4	2	no	—
49	#117×C₃₇	—	4	2	no	—
50	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
51	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₃₇	D₄	1	2	yes	—
66	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
68	#107×C₃₇	—	4	2	no	—
69	#107×C₃₇	—	4	2	no	—
70	#103×C₃₇	—	4	2	no	—
71	#103×C₃₇	—	4	2	no	—
72	#102×C₃₇	—	4	2	no	—
73	#102×C₃₇	—	4	2	no	—
74	C₂²⋊C₈×C₃₇	—	4	2	no	—
75	#95×C₃₇	—	2	2	no	—
76	#95×C₃₇	—	2	2	no	—
77	#95×C₃₇	—	2	2	no	—
78	C₂⁴×C₃₇	—	2	1	no	—
79	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
80	C₂×Q₈×C₃₇	—	2	2	no	—
81	C₂×Q₈×C₃₇	—	2	2	no	—
82	C₂×Q₈×C₃₇	—	2	1	no	—
83	C₂×Q₈×C₃₇	—	2	1	no	—
84	C₂×D₄×C₃₇	—	2	2	no	—
85	C₂×D₄×C₃₇	—	2	2	no	—
86	C₂×D₄×C₃₇	—	2	1	no	—
87	C₂×D₄×C₃₇	—	2	1	no	—
88	C₂×D₄×C₃₇	—	4	2	no	—
89	C₂×D₄×C₃₇	—	8	2	no	—
90	C₂²×C₄×C₃₇	—	2	2	no	—
91	C₂²×C₄×C₃₇	—	2	2	no	—
92	C₂²×C₄×C₃₇	—	2	1	no	—
93	C₂²×C₄×C₃₇	—	2	1	no	—
94	C₂²×C₄×C₃₇	—	2	1	no	—
95	C₂²×C₄×C₃₇	—	2	2	no	—
96	C₂²×C₄×C₃₇	—	2	2	no	—
97	C₂²×C₄×C₃₇	—	2	1	no	—
98	C₂²×C₄×C₃₇	—	2	1	no	—
99	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
103	C₂×C₈×C₃₇	—	2	2	no	—
104	C₂×C₈×C₃₇	—	2	2	no	—
105	C₂×C₈×C₃₇	—	2	2	no	—
106	C₂×C₈×C₃₇	—	2	2	no	—
107	C₂×C₈×C₃₇	—	2	2	no	—
108	C₂×C₈×C₃₇	—	2	2	no	—
109	C₄⋊C₄×C₃₇	—	2	2	no	—
110	C₄⋊C₄×C₃₇	—	2	2	no	—
111	C₄⋊C₄×C₃₇	—	2	2	no	—
112	C₄⋊C₄×C₃₇	—	2	2	no	—
113	C₄⋊C₄×C₃₇	—	2	2	no	—
114	C₄⋊C₄×C₃₇	—	2	2	no	—
115	C₄⋊C₄×C₃₇	—	4	2	no	—
116	C₄⋊C₄×C₃₇	—	4	2	no	—
117	C₄⋊C₄×C₃₇	—	4	4	no	—
118	C₄⋊C₄×C₃₇	—	8	2	no	—
119	C₄⋊C₄×C₃₇	—	8	2	no	—
120	C₄⋊C₄×C₃₇	—	8	2	no	—
121	C₂²⋊C₄×C₃₇	—	4	2	no	—
122	C₂²⋊C₄×C₃₇	—	4	2	no	—
123	C₂²⋊C₄×C₃₇	—	4	4	no	—
124	C₂²⋊C₄×C₃₇	—	4	2	no	—
125	C₂²⋊C₄×C₃₇	—	8	2	no	—
126	C₂²⋊C₄×C₃₇	—	8	2	no	—
127	C₄²×C₃₇	—	2	2	no	—
128	C₄²×C₃₇	—	2	2	no	—
129	C₂³×C₃₇	—	2	1	no	—
130	C₂³×C₃₇	—	2	1	no	—
131	C₂³×C₃₇	—	2	1	no	—
132	C₂³×C₃₇	—	2	2	no	—
133	C₂³×C₃₇	—	2	2	no	—
134	C₂³×C₃₇	—	4	1	no	—
135	C₂³×C₃₇	—	4	1	no	—
136	C₂³×C₃₇	—	4	1	no	—
137	C₂³×C₃₇	—	4	2	no	—
138	C₂³×C₃₇	—	4	2	no	—
139	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₃₇	—	4	2	no	—
141	Q₈×C₃₇	—	4	2	no	—
142	D₄×C₃₇	—	4	2	no	—
143	D₄×C₃₇	—	4	2	no	—
144	D₄×C₃₇	—	8	4	no	—
145	C₂×C₄×C₃₇	—	2	2	no	—
146	C₂×C₄×C₃₇	—	2	2	no	—
147	C₂×C₄×C₃₇	—	2	1	no	—
148	C₂×C₄×C₃₇	—	2	1	no	—
149	C₂×C₄×C₃₇	—	2	1	no	—
150	C₂×C₄×C₃₇	—	2	2	no	—
151	C₂×C₄×C₃₇	—	2	2	no	—
152	C₂×C₄×C₃₇	—	2	2	no	—
153	C₂×C₄×C₃₇	—	2	2	no	—
154	C₂×C₄×C₃₇	—	4	2	no	—
155	C₂×C₄×C₃₇	—	4	2	no	—
156	C₂×C₄×C₃₇	—	4	1	no	—
157	C₂×C₄×C₃₇	—	4	2	no	—
158	C₂×C₄×C₃₇	—	4	1	no	—
159	C₂×C₄×C₃₇	—	4	1	no	—
160	C₂×C₄×C₃₇	—	4	1	no	—
161	C₂×C₄×C₃₇	—	4	2	no	—
162	C₂×C₄×C₃₇	—	4	1	no	—
163	C₂×C₄×C₃₇	—	4	2	no	—
164	C₂×C₄×C₃₇	—	4	2	no	—
165	C₂×C₄×C₃₇	—	4	2	no	—
166	C₂×C₄×C₃₇	—	4	2	no	—
167	C₂×C₄×C₃₇	—	4	2	no	—
168	C₂×C₄×C₃₇	—	4	2	no	—
169	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
170	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
171	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
172	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
173	C₈×C₃₇	—	4	2	no	—
174	C₈×C₃₇	—	4	2	no	—
175	#32783	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂²×C₃₇	—	4	1	no	—
177	C₂²×C₃₇	—	4	2	no	—
178	C₂²×C₃₇	—	4	1	no	—
179	C₂²×C₃₇	—	4	1	no	—
180	C₂²×C₃₇	—	4	2	no	—
181	C₂²×C₃₇	—	8	1	no	—
182	C₂²×C₃₇	—	8	2	no	—
183	C₂²×C₃₇	—	8	1	no	—
184	C₂²×C₃₇	—	8	1	no	—
185	C₂²×C₃₇	—	8	2	no	—
186	C₂²×C₃₇	#534	1	1	yes	characteristic
187	C₂²×C₃₇	#535	1	1	yes	characteristic
188	C₂²×C₃₇	#536	1	1	yes	characteristic
189	C₂²×C₃₇	#576	1	2	yes	—
190	C₂²×C₃₇	#578	1	2	yes	—
191	C₄×C₃₇	—	4	1	no	—
192	C₄×C₃₇	—	4	2	no	—
193	C₄×C₃₇	—	4	2	no	—
194	C₄×C₃₇	—	8	1	no	—
195	C₄×C₃₇	—	8	2	no	—
196	C₄×C₃₇	—	8	1	no	—
197	C₄×C₃₇	—	8	2	no	—
198	C₄×C₃₇	—	8	1	no	—
199	C₄×C₃₇	#562	1	2	yes	—
200	C₄×C₃₇	#562	1	2	yes	—
201	#2629	C₂×C₃₇	1	1	yes	characteristic, complemented
202	#2620	C₂×C₃₇	1	1	yes	characteristic
203	#2095	C₂×C₃₇	1	1	yes	characteristic, complemented
204	#2093	C₂×C₃₇	1	1	yes	characteristic, complemented
205	#2083	C₂×C₃₇	1	2	yes	complemented
206	#2042	C₂×C₃₇	1	2	yes	complemented
207	#2036	C₂×C₃₇	1	2	yes	complemented
208	#2033	C₂×C₃₇	1	2	yes	—
209	#2026	C₂×C₃₇	1	1	yes	characteristic, complemented
210	#2025	C₂×C₃₇	1	1	yes	characteristic, complemented
211	#1818	C₂×C₃₇	1	1	yes	characteristic, complemented
212	C₂×C₃₇	—	8	1	no	—
213	C₂×C₃₇	—	16	1	no	—
214	C₂×C₃₇	#2816	1	1	yes	characteristic
215	C₂×C₃₇	#3203	1	2	yes	—
216	C₂×C₃₇	#3220	1	1	yes	characteristic
217	C₂×C₃₇	#3223	1	1	yes	characteristic
218	C₂×C₃₇	#3243	1	2	yes	—
219	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
220	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
221	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
222	C₂×#121	C₂²×C₃₇	1	1	yes	characteristic
223	C₂×#117	C₂²×C₃₇	1	1	yes	characteristic
224	C₂×#107	C₂²×C₃₇	1	2	yes	—
225	C₂×#107	C₂²×C₃₇	1	2	yes	—
226	C₂×#103	C₂²×C₃₇	1	2	yes	—
227	C₂×#103	C₂²×C₃₇	1	2	yes	—
228	C₂×#102	C₂²×C₃₇	1	2	yes	—
229	C₂×#102	C₂²×C₃₇	1	2	yes	—
230	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	—
231	#398	—	2	2	no	—
232	#396	—	2	2	no	—
233	#396	—	2	2	no	—
234	#394	—	2	2	no	—
235	#391	C₂²×C₃₇	1	1	yes	characteristic
236	#390	C₂²×C₃₇	1	1	yes	characteristic
237	#389	C₂²×C₃₇	1	2	yes	—
238	#384	C₂²×C₃₇	1	1	yes	characteristic
239	#384	C₂²×C₃₇	1	1	yes	characteristic
240	#380	C₂²×C₃₇	1	2	yes	—
241	#340	C₂²×C₃₇	1	2	yes	—
242	#340	C₂²×C₃₇	1	2	yes	—
243	#336	C₂²×C₃₇	1	2	yes	—
244	#336	C₂²×C₃₇	1	1	yes	characteristic
245	#336	C₂²×C₃₇	1	1	yes	characteristic
246	C₃₇	#32783	1	1	yes	characteristic, direct product factor, Sylow
247	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
250	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
252	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
253	#125	—	4	2	no	—
254	#124	—	4	2	no	—
255	C₂²⋊Q₈	—	4	2	no	—
256	#121	—	4	2	no	—
257	#117	—	4	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
268	C₂×C₂²⋊C₄	—	2	1	no	—
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	D₄×C₃₇	1	2	yes	—
274	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
276	#107	—	4	2	no	—
277	#107	—	4	2	no	—
278	#103	—	4	2	no	—
279	#103	—	4	2	no	—
280	#102	—	4	2	no	—
281	#102	—	4	2	no	—
282	C₂²⋊C₈	—	4	2	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	C₂⁴	—	2	1	no	—
287	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	8	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
310	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	—	4	4	no	—
326	C₄⋊C₄	—	8	2	no	—
327	C₄⋊C₄	—	8	2	no	—
328	C₄⋊C₄	—	8	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	4	2	no	—
331	C₂²⋊C₄	—	4	4	no	—
332	C₂²⋊C₄	—	4	2	no	—
333	C₂²⋊C₄	—	8	2	no	—
334	C₂²⋊C₄	—	8	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	4	1	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
348	Q₈	—	4	2	no	—
349	Q₈	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	8	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
378	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
379	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
380	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
381	C₈	—	4	2	no	—
382	C₈	—	4	2	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	1	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	1	no	—
393	C₂²	C₃₇×#534	1	1	yes	characteristic
394	C₂²	C₃₇×#535	1	1	yes	characteristic
395	C₂²	C₃₇×#536	1	1	yes	characteristic
396	C₂²	C₃₇×#576	1	2	yes	—
397	C₂²	C₃₇×#578	1	2	yes	—
398	C₄	—	4	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	1	no	—
401	C₄	—	8	2	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	1	no	—
404	C₄	—	8	2	no	—
405	C₄	—	8	1	no	—
406	C₄	C₃₇×#562	1	2	yes	—
407	C₄	C₃₇×#562	1	2	yes	—
408	C₂	—	8	1	no	—
409	C₂	—	16	1	no	—
410	C₂	C₃₇×#2816	1	1	yes	characteristic
411	C₂	C₃₇×#3203	1	2	yes	—
412	C₂	C₃₇×#3220	1	1	yes	characteristic
413	C₂	C₃₇×#3223	1	1	yes	characteristic
414	C₂	C₃₇×#3243	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 ◁ C₂×#117×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#2629	C₂	semidirect
3. C₃₇×#2095	C₂	semidirect
4. C₃₇×#2093	C₂	semidirect
5. C₃₇×#2083	C₂	semidirect
6. C₃₇×#2042	C₂	semidirect
7. C₃₇×#2036	C₂	semidirect
9. C₃₇×#2026	C₂	semidirect
10. C₃₇×#2025	C₂	semidirect
11. C₃₇×#1818	C₂	semidirect
175. #32783	C₃₇	direct (N × H)
201. #2629	C₂×C₃₇	semidirect
203. #2095	C₂×C₃₇	semidirect
204. #2093	C₂×C₃₇	semidirect
205. #2083	C₂×C₃₇	semidirect
206. #2042	C₂×C₃₇	semidirect
207. #2036	C₂×C₃₇	semidirect
209. #2026	C₂×C₃₇	semidirect
210. #2025	C₂×C₃₇	semidirect
211. #1818	C₂×C₃₇	semidirect
246. C₃₇	#32783	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₇×#2629	2
C₃₇×#2620	2
C₃₇×#2095	2
C₃₇×#2093	2
C₃₇×#2083	2
C₃₇×#2042	2
C₃₇×#2036	2
C₃₇×#2033	2
C₃₇×#2026	2
C₃₇×#2025	2
C₃₇×#1818	2
#32783	37

Subgroups — C37×#32783 #22654036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#32783 #22654036