Subgroups — C₃₇×#29128 #22650381

Order 9472.

706 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#2864	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#124×C₃₇	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2101	C₂	1	2	yes	maximal, complemented
4	C₃₇×#2042	C₂	1	2	yes	maximal
5	C₃₇×#1936	C₂	1	2	yes	maximal
6	C₃₇×#1935	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1804	C₂	1	1	yes	maximal, characteristic
10	C₃₇×#1804	C₂	1	1	yes	maximal, characteristic
11	C₃₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×#103×C₃₇	C₂²	1	2	yes	—
18	C₂×#103×C₃₇	C₂²	1	2	yes	—
19	C₂×#102×C₃₇	C₂²	1	2	yes	—
20	C₂×#102×C₃₇	C₂²	1	2	yes	—
21	C₂×#97×C₃₇	C₂²	1	2	yes	—
22	C₃₇×#391	C₂²	1	1	yes	characteristic
23	C₃₇×#390	C₂²	1	1	yes	characteristic
24	C₃₇×#389	C₂²	1	2	yes	—
25	C₃₇×#389	C₂²	1	2	yes	—
26	C₃₇×#388	—	2	2	no	—
27	C₃₇×#387	—	2	2	no	—
28	C₃₇×#387	—	2	2	no	—
29	C₃₇×#382	C₂²	1	1	yes	characteristic
30	C₃₇×#382	C₂²	1	1	yes	characteristic
31	C₃₇×#382	C₂²	1	1	yes	characteristic
32	C₄×C₂²⋊C₄×C₃₇	—	2	2	no	—
33	C₄³×C₃₇	C₂²	1	1	yes	characteristic
34	C₃₇×#340	C₂²	1	2	yes	—
35	C₃₇×#340	C₂²	1	2	yes	—
36	C₃₇×#340	C₂²	1	2	yes	—
37	C₃₇×#340	C₂²	1	2	yes	—
38	C₃₇×#336	C₂²	1	2	yes	—
39	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₃₇	—	2	1	no	—
42	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
43	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
44	#124×C₃₇	—	2	2	no	—
45	#124×C₃₇	—	2	2	no	—
46	C₄×Q₈×C₃₇	—	2	2	no	—
47	C₄×Q₈×C₃₇	—	2	2	no	—
48	C₄×D₄×C₃₇	—	2	2	no	—
49	C₄×D₄×C₃₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
57	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
60	C₂×C₄²×C₃₇	—	2	1	no	—
61	C₂×C₄²×C₃₇	D₄	1	2	yes	—
62	C₂×C₄²×C₃₇	D₄	1	2	yes	—
63	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₃₇	—	2	2	no	—
67	C₄⋊C₈×C₃₇	—	2	2	no	—
68	#103×C₃₇	—	2	4	no	—
69	#103×C₃₇	—	4	2	no	—
70	#102×C₃₇	—	2	4	no	—
71	#102×C₃₇	—	4	2	no	—
72	#97×C₃₇	—	4	2	no	—
73	#95×C₃₇	—	2	2	no	—
74	#95×C₃₇	—	2	2	no	—
75	#95×C₃₇	—	2	1	no	—
76	#95×C₃₇	—	2	1	no	—
77	#95×C₃₇	—	2	1	no	—
78	#95×C₃₇	—	2	1	no	—
79	#95×C₃₇	—	2	2	no	—
80	#95×C₃₇	—	2	2	no	—
81	C₂⁴×C₃₇	—	2	1	no	—
82	C₂×Q₈×C₃₇	—	2	1	no	—
83	C₂×Q₈×C₃₇	—	2	1	no	—
84	C₂×Q₈×C₃₇	—	2	1	no	—
85	C₂×Q₈×C₃₇	—	2	1	no	—
86	C₂×Q₈×C₃₇	—	2	1	no	—
87	C₂×Q₈×C₃₇	#41	1	2	yes	—
88	C₂×D₄×C₃₇	—	2	1	no	—
89	C₂×D₄×C₃₇	—	2	1	no	—
90	C₂×D₄×C₃₇	—	2	1	no	—
91	C₂×D₄×C₃₇	—	2	1	no	—
92	C₂×D₄×C₃₇	—	2	1	no	—
93	C₂×D₄×C₃₇	#41	1	2	yes	—
94	C₂²×C₄×C₃₇	—	2	1	no	—
95	C₂²×C₄×C₃₇	—	2	1	no	—
96	C₂²×C₄×C₃₇	—	2	2	no	—
97	C₂²×C₄×C₃₇	—	2	2	no	—
98	C₂²×C₄×C₃₇	—	2	1	no	—
99	C₂²×C₄×C₃₇	—	4	4	no	—
100	C₂²×C₄×C₃₇	—	4	2	no	—
101	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
106	C₂×C₈×C₃₇	—	2	2	no	—
107	C₂×C₈×C₃₇	—	2	2	no	—
108	C₂×C₈×C₃₇	—	2	2	no	—
109	C₂×C₈×C₃₇	—	2	2	no	—
110	C₂×C₈×C₃₇	—	2	2	no	—
111	C₂×C₈×C₃₇	—	2	2	no	—
112	C₄⋊C₄×C₃₇	—	2	2	no	—
113	C₄⋊C₄×C₃₇	—	2	2	no	—
114	C₄⋊C₄×C₃₇	—	2	1	no	—
115	C₄⋊C₄×C₃₇	—	2	1	no	—
116	C₄⋊C₄×C₃₇	—	2	1	no	—
117	C₄⋊C₄×C₃₇	—	2	1	no	—
118	C₄⋊C₄×C₃₇	—	2	2	no	—
119	C₄⋊C₄×C₃₇	—	2	2	no	—
120	C₄⋊C₄×C₃₇	—	4	4	no	—
121	C₄⋊C₄×C₃₇	—	4	4	no	—
122	C₄⋊C₄×C₃₇	—	4	2	no	—
123	C₂²⋊C₄×C₃₇	—	2	8	no	—
124	C₂²⋊C₄×C₃₇	—	4	4	no	—
125	C₂²⋊C₄×C₃₇	—	4	2	no	—
126	C₄²×C₃₇	—	2	1	no	—
127	C₄²×C₃₇	—	2	1	no	—
128	C₄²×C₃₇	—	2	1	no	—
129	C₄²×C₃₇	—	2	1	no	—
130	C₄²×C₃₇	—	4	2	no	—
131	C₄²×C₃₇	—	4	2	no	—
132	C₄²×C₃₇	—	4	2	no	—
133	C₄²×C₃₇	#41	1	2	yes	—
134	C₄²×C₃₇	#41	1	2	yes	—
135	C₂³×C₃₇	—	2	2	no	—
136	C₂³×C₃₇	—	4	1	no	—
137	C₂³×C₃₇	—	4	1	no	—
138	C₂³×C₃₇	—	4	2	no	—
139	C₂³×C₃₇	—	4	2	no	—
140	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₃₇	—	2	2	no	—
142	Q₈×C₃₇	—	2	2	no	—
143	Q₈×C₃₇	—	4	1	no	—
144	Q₈×C₃₇	—	4	1	no	—
145	D₄×C₃₇	—	2	2	no	—
146	D₄×C₃₇	—	2	2	no	—
147	D₄×C₃₇	—	4	1	no	—
148	D₄×C₃₇	—	4	1	no	—
149	C₂×C₄×C₃₇	—	2	2	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	—	2	2	no	—
155	C₂×C₄×C₃₇	—	2	2	no	—
156	C₂×C₄×C₃₇	—	2	2	no	—
157	C₂×C₄×C₃₇	—	2	2	no	—
158	C₂×C₄×C₃₇	—	4	1	no	—
159	C₂×C₄×C₃₇	—	4	1	no	—
160	C₂×C₄×C₃₇	—	4	2	no	—
161	C₂×C₄×C₃₇	—	4	1	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	—	4	2	no	—
170	C₂×C₄×C₃₇	—	8	4	no	—
171	C₂×C₄×C₃₇	#124	1	2	yes	—
172	C₂×C₄×C₃₇	#124	1	2	yes	—
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	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
179	C₈×C₃₇	—	4	2	no	—
180	C₈×C₃₇	—	4	2	no	—
181	#29128	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂²×C₃₇	—	4	2	no	—
183	C₂²×C₃₇	—	4	4	no	—
184	C₂²×C₃₇	—	8	1	no	—
185	C₂²×C₃₇	—	8	1	no	—
186	C₂²×C₃₇	—	8	2	no	—
187	C₂²×C₃₇	#525	1	1	yes	characteristic
188	C₂²×C₃₇	C₂×#124	1	1	yes	characteristic
189	C₂²×C₃₇	#537	1	1	yes	characteristic
190	C₂²×C₃₇	#575	1	2	yes	—
191	C₂²×C₃₇	#575	1	2	yes	—
192	C₄×C₃₇	—	2	2	no	—
193	C₄×C₃₇	—	2	2	no	—
194	C₄×C₃₇	—	4	2	no	—
195	C₄×C₃₇	—	4	2	no	—
196	C₄×C₃₇	—	4	2	no	—
197	C₄×C₃₇	—	8	2	no	—
198	C₄×C₃₇	—	8	1	no	—
199	C₄×C₃₇	—	8	1	no	—
200	C₄×C₃₇	—	8	2	no	—
201	C₄×C₃₇	#552	1	1	yes	characteristic
202	C₄×C₃₇	#552	1	1	yes	characteristic
203	C₄×C₃₇	#553	1	1	yes	characteristic
204	C₄×C₃₇	#553	1	1	yes	characteristic
205	#2864	C₂×C₃₇	1	1	yes	characteristic, complemented
206	C₄×#124	C₂×C₃₇	1	1	yes	characteristic
207	#2101	C₂×C₃₇	1	2	yes	complemented
208	#2042	C₂×C₃₇	1	2	yes	—
209	#1936	C₂×C₃₇	1	2	yes	—
210	#1935	C₂×C₃₇	1	2	yes	complemented
211	#1805	C₂×C₃₇	1	1	yes	characteristic, complemented
212	#1805	C₂×C₃₇	1	1	yes	characteristic, complemented
213	#1804	C₂×C₃₇	1	1	yes	characteristic
214	#1804	C₂×C₃₇	1	1	yes	characteristic
215	#1767	C₂×C₃₇	1	1	yes	characteristic, complemented
216	C₂×C₃₇	—	8	2	no	—
217	C₂×C₃₇	#2562	1	1	yes	characteristic
218	C₂×C₃₇	#3111	1	2	yes	—
219	C₂×C₃₇	#3135	1	1	yes	characteristic
220	C₂×C₃₇	#3140	1	1	yes	characteristic
221	C₂×C₃₇	#3256	1	2	yes	—
222	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
223	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
224	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
227	C₂×#103	C₂²×C₃₇	1	2	yes	—
228	C₂×#103	C₂²×C₃₇	1	2	yes	—
229	C₂×#102	C₂²×C₃₇	1	2	yes	—
230	C₂×#102	C₂²×C₃₇	1	2	yes	—
231	C₂×#97	C₂²×C₃₇	1	2	yes	—
232	#391	C₂²×C₃₇	1	1	yes	characteristic
233	#390	C₂²×C₃₇	1	1	yes	characteristic
234	#389	C₂²×C₃₇	1	2	yes	—
235	#389	C₂²×C₃₇	1	2	yes	—
236	#388	—	2	2	no	—
237	#387	—	2	2	no	—
238	#387	—	2	2	no	—
239	#382	C₂²×C₃₇	1	1	yes	characteristic
240	#382	C₂²×C₃₇	1	1	yes	characteristic
241	#382	C₂²×C₃₇	1	1	yes	characteristic
242	C₄×C₂²⋊C₄	—	2	2	no	—
243	C₄³	C₂²×C₃₇	1	1	yes	characteristic
244	#340	C₂²×C₃₇	1	2	yes	—
245	#340	C₂²×C₃₇	1	2	yes	—
246	#340	C₂²×C₃₇	1	2	yes	—
247	#340	C₂²×C₃₇	1	2	yes	—
248	#336	C₂²×C₃₇	1	2	yes	—
249	C₃₇	#29128	1	1	yes	characteristic, direct product factor, Sylow
250	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
251	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
252	C₂³×C₄	—	2	1	no	—
253	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
254	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
255	#124	—	2	2	no	—
256	#124	—	2	2	no	—
257	C₄×Q₈	—	2	2	no	—
258	C₄×Q₈	—	2	2	no	—
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
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	2	no	—
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	D₄×C₃₇	1	2	yes	—
273	C₂×C₄²	D₄×C₃₇	1	2	yes	—
274	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
276	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	2	2	no	—
279	#103	—	2	4	no	—
280	#103	—	4	2	no	—
281	#102	—	2	4	no	—
282	#102	—	4	2	no	—
283	#97	—	4	2	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	—	2	1	no	—
287	#95	—	2	1	no	—
288	#95	—	2	1	no	—
289	#95	—	2	1	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	C₂⁴	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	#41×C₃₇	1	2	yes	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	#41×C₃₇	1	2	yes	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	4	4	no	—
311	C₂²×C₄	—	4	2	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	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
316	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	4	no	—
332	C₄⋊C₄	—	4	4	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	2	8	no	—
335	C₂²⋊C₄	—	4	4	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	4	2	no	—
342	C₄²	—	4	2	no	—
343	C₄²	—	4	2	no	—
344	C₄²	#41×C₃₇	1	2	yes	—
345	C₄²	#41×C₃₇	1	2	yes	—
346	C₂³	—	2	2	no	—
347	C₂³	—	4	1	no	—
348	C₂³	—	4	1	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
352	Q₈	—	2	2	no	—
353	Q₈	—	2	2	no	—
354	Q₈	—	4	1	no	—
355	Q₈	—	4	1	no	—
356	D₄	—	2	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	4	1	no	—
359	D₄	—	4	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	8	4	no	—
382	C₂×C₄	#124×C₃₇	1	2	yes	—
383	C₂×C₄	#124×C₃₇	1	2	yes	—
384	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
385	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
386	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
387	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
388	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
389	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
390	C₈	—	4	2	no	—
391	C₈	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	8	1	no	—
395	C₂²	—	8	1	no	—
396	C₂²	—	8	2	no	—
397	C₂²	C₃₇×#525	1	1	yes	characteristic
398	C₂²	C₂×#124×C₃₇	1	1	yes	characteristic
399	C₂²	C₃₇×#537	1	1	yes	characteristic
400	C₂²	C₃₇×#575	1	2	yes	—
401	C₂²	C₃₇×#575	1	2	yes	—
402	C₄	—	2	2	no	—
403	C₄	—	2	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	8	1	no	—
408	C₄	—	8	1	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	2	no	—
411	C₄	C₃₇×#552	1	1	yes	characteristic
412	C₄	C₃₇×#552	1	1	yes	characteristic
413	C₄	C₃₇×#553	1	1	yes	characteristic
414	C₄	C₃₇×#553	1	1	yes	characteristic
415	C₂	—	8	2	no	—
416	C₂	C₃₇×#2562	1	1	yes	characteristic
417	C₂	C₃₇×#3111	1	2	yes	—
418	C₂	C₃₇×#3135	1	1	yes	characteristic
419	C₂	C₃₇×#3140	1	1	yes	characteristic
420	C₂	C₃₇×#3256	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂²×D₄×C₃₇	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₄³×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#2864	C₂	semidirect
3. C₃₇×#2101	C₂	semidirect
6. C₃₇×#1935	C₂	semidirect
7. C₃₇×#1805	C₂	semidirect
8. C₃₇×#1805	C₂	semidirect
11. C₃₇×#1767	C₂	semidirect
181. #29128	C₃₇	direct (N × H)
205. #2864	C₂×C₃₇	semidirect
207. #2101	C₂×C₃₇	semidirect
210. #1935	C₂×C₃₇	semidirect
211. #1805	C₂×C₃₇	semidirect
212. #1805	C₂×C₃₇	semidirect
215. #1767	C₂×C₃₇	semidirect
249. C₃₇	#29128	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×#2864	2
C₄×#124×C₃₇	2
C₃₇×#2101	2
C₃₇×#2042	2
C₃₇×#1936	2
C₃₇×#1935	2
C₃₇×#1805	2
C₃₇×#1804	2
C₃₇×#1767	2
#29128	37

Subgroups — C37×#29128 #22650381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#29128 #22650381