Subgroups — C₃₇×#28629 #22649882

Order 9472.

838 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	C₂×C₃₇×#497	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₇×#488	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2642	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2326	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2056	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2055	C₂	1	2	yes	maximal
7	C₃₇×#1992	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1878	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1877	C₂	1	2	yes	maximal
11	C₃₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₃₇	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
16	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
19	C₃₇×#497	—	2	4	no	—
20	C₃₇×#488	—	2	4	no	—
21	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
22	C₂×#103×C₃₇	C₂²	1	2	yes	—
23	C₂×#103×C₃₇	C₂²	1	2	yes	—
24	C₂×#103×C₃₇	C₂²	1	2	yes	—
25	C₂×#102×C₃₇	C₂²	1	2	yes	—
26	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
28	C₃₇×#400	—	2	2	no	—
29	C₃₇×#400	—	2	2	no	—
30	C₃₇×#391	C₂²	1	2	yes	—
31	C₃₇×#391	C₂²	1	2	yes	—
32	C₃₇×#391	C₂²	1	1	yes	characteristic
33	C₃₇×#390	C₂²	1	1	yes	characteristic
34	C₃₇×#388	—	2	2	no	—
35	C₃₇×#385	—	2	2	no	—
36	C₃₇×#384	C₂²	1	1	yes	characteristic
37	C₃₇×#376	C₂²	1	1	yes	characteristic
38	C₃₇×#340	C₂²	1	2	yes	—
39	C₃₇×#340	C₂²	1	2	yes	—
40	C₃₇×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
42	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₃₇	—	2	1	no	—
45	C₂×Q₁₆×C₃₇	—	2	4	no	—
46	C₂×Q₁₆×C₃₇	—	2	4	no	—
47	C₂×Q₁₆×C₃₇	—	4	2	no	—
48	C₂×SD₁₆×C₃₇	—	2	4	no	—
49	C₂×SD₁₆×C₃₇	—	2	4	no	—
50	C₂×SD₁₆×C₃₇	—	4	2	no	—
51	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
52	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
53	C₄⋊Q₈×C₃₇	—	2	2	no	—
54	C₄⋊Q₈×C₃₇	—	2	2	no	—
55	#125×C₃₇	—	2	2	no	—
56	#125×C₃₇	—	2	2	no	—
57	#124×C₃₇	—	2	2	no	—
58	#124×C₃₇	D₄	1	4	yes	—
59	C₄×Q₈×C₃₇	—	4	2	no	—
60	C₄×D₄×C₃₇	—	4	2	no	—
61	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
71	C₂×C₄²×C₃₇	—	2	1	no	—
72	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₃₇	—	2	4	no	—
76	#103×C₃₇	—	2	4	no	—
77	#103×C₃₇	—	4	2	no	—
78	#103×C₃₇	—	4	2	no	—
79	#102×C₃₇	—	2	4	no	—
80	#97×C₃₇	—	2	2	no	—
81	C₄×C₈×C₃₇	—	2	2	no	—
82	#95×C₃₇	—	2	2	no	—
83	#95×C₃₇	—	2	4	no	—
84	#95×C₃₇	—	2	2	no	—
85	#95×C₃₇	—	2	2	no	—
86	#95×C₃₇	D₄	1	2	yes	—
87	#95×C₃₇	D₄	1	2	yes	—
88	C₂⁴×C₃₇	—	2	1	no	—
89	C₂×Q₈×C₃₇	—	2	1	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	—	2	2	no	—
96	C₂×Q₈×C₃₇	—	2	2	no	—
97	C₂×Q₈×C₃₇	—	2	2	no	—
98	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
99	C₂×D₄×C₃₇	—	2	2	no	—
100	C₂×D₄×C₃₇	—	2	1	no	—
101	C₂×D₄×C₃₇	—	2	2	no	—
102	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₃₇	—	2	1	no	—
104	C₂²×C₄×C₃₇	—	2	2	no	—
105	C₂²×C₄×C₃₇	—	2	2	no	—
106	C₂²×C₄×C₃₇	—	2	1	no	—
107	C₂²×C₄×C₃₇	—	2	1	no	—
108	C₂²×C₄×C₃₇	—	4	2	no	—
109	C₂²×C₄×C₃₇	—	8	2	no	—
110	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
115	Q₁₆×C₃₇	—	4	8	no	—
116	SD₁₆×C₃₇	—	4	8	no	—
117	C₂×C₈×C₃₇	—	2	2	no	—
118	C₂×C₈×C₃₇	—	2	2	no	—
119	C₂×C₈×C₃₇	—	2	2	no	—
120	C₂×C₈×C₃₇	—	2	2	no	—
121	C₂×C₈×C₃₇	—	2	2	no	—
122	C₂×C₈×C₃₇	#41	1	4	yes	—
123	C₄⋊C₄×C₃₇	—	2	2	no	—
124	C₄⋊C₄×C₃₇	—	2	2	no	—
125	C₄⋊C₄×C₃₇	—	2	2	no	—
126	C₄⋊C₄×C₃₇	—	2	2	no	—
127	C₄⋊C₄×C₃₇	—	4	2	no	—
128	C₄⋊C₄×C₃₇	—	4	4	no	—
129	C₄⋊C₄×C₃₇	—	4	4	no	—
130	C₄⋊C₄×C₃₇	—	8	2	no	—
131	C₂²⋊C₄×C₃₇	—	2	8	no	—
132	C₂²⋊C₄×C₃₇	—	4	2	no	—
133	C₂²⋊C₄×C₃₇	—	8	2	no	—
134	C₄²×C₃₇	—	2	2	no	—
135	C₄²×C₃₇	—	2	2	no	—
136	C₄²×C₃₇	—	4	2	no	—
137	C₄²×C₃₇	C₂×D₄	1	2	yes	—
138	C₄²×C₃₇	#41	1	2	yes	—
139	C₂³×C₃₇	—	2	2	no	—
140	C₂³×C₃₇	—	4	1	no	—
141	C₂³×C₃₇	—	4	1	no	—
142	C₂³×C₃₇	—	4	2	no	—
143	C₂³×C₃₇	—	4	2	no	—
144	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
145	Q₈×C₃₇	—	2	4	no	—
146	Q₈×C₃₇	—	4	2	no	—
147	Q₈×C₃₇	—	4	2	no	—
148	Q₈×C₃₇	—	4	2	no	—
149	Q₈×C₃₇	—	4	2	no	—
150	Q₈×C₃₇	—	4	2	no	—
151	D₄×C₃₇	—	2	4	no	—
152	D₄×C₃₇	—	4	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	1	no	—
158	C₂×C₄×C₃₇	—	2	1	no	—
159	C₂×C₄×C₃₇	—	2	2	no	—
160	C₂×C₄×C₃₇	—	2	2	no	—
161	C₂×C₄×C₃₇	—	2	2	no	—
162	C₂×C₄×C₃₇	—	2	2	no	—
163	C₂×C₄×C₃₇	—	4	1	no	—
164	C₂×C₄×C₃₇	—	4	1	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	1	no	—
169	C₂×C₄×C₃₇	—	4	1	no	—
170	C₂×C₄×C₃₇	—	4	2	no	—
171	C₂×C₄×C₃₇	—	4	2	no	—
172	C₂×C₄×C₃₇	—	4	2	no	—
173	C₂×C₄×C₃₇	—	4	2	no	—
174	C₂×C₄×C₃₇	—	4	2	no	—
175	C₂×C₄×C₃₇	—	8	4	no	—
176	C₂×C₄×C₃₇	#121	1	4	yes	—
177	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
179	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
181	C₈×C₃₇	—	2	4	no	—
182	C₈×C₃₇	—	4	2	no	—
183	#28629	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂²×C₃₇	—	4	4	no	—
185	C₂²×C₃₇	—	4	2	no	—
186	C₂²×C₃₇	—	8	2	no	—
187	C₂²×C₃₇	—	8	1	no	—
188	C₂²×C₃₇	—	8	1	no	—
189	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
190	C₂²×C₃₇	#532	1	1	yes	characteristic
191	C₂²×C₃₇	#535	1	1	yes	characteristic
192	C₂²×C₃₇	#577	1	2	yes	—
193	C₂²×C₃₇	#578	1	2	yes	—
194	C₄×C₃₇	—	2	4	no	—
195	C₄×C₃₇	—	4	2	no	—
196	C₄×C₃₇	—	4	1	no	—
197	C₄×C₃₇	—	4	1	no	—
198	C₄×C₃₇	—	4	2	no	—
199	C₄×C₃₇	—	8	1	no	—
200	C₄×C₃₇	—	8	1	no	—
201	C₄×C₃₇	—	8	2	no	—
202	C₄×C₃₇	—	8	2	no	—
203	C₄×C₃₇	#546	1	2	yes	—
204	C₄×C₃₇	#559	1	2	yes	—
205	C₂×#497	C₂×C₃₇	1	1	yes	characteristic
206	C₂×#488	C₂×C₃₇	1	1	yes	characteristic
207	#2642	C₂×C₃₇	1	1	yes	characteristic, complemented
208	#2326	C₂×C₃₇	1	1	yes	characteristic
209	#2056	C₂×C₃₇	1	2	yes	complemented
210	#2055	C₂×C₃₇	1	2	yes	—
211	#1992	C₂×C₃₇	1	1	yes	characteristic, complemented
212	#1956	C₂×C₃₇	1	1	yes	characteristic, complemented
213	#1878	C₂×C₃₇	1	2	yes	complemented
214	#1877	C₂×C₃₇	1	2	yes	—
215	#1768	C₂×C₃₇	1	1	yes	characteristic, complemented
216	C₂×C₃₇	—	8	2	no	—
217	C₂×C₃₇	#2544	1	1	yes	characteristic
218	C₂×C₃₇	#3046	1	2	yes	—
219	C₂×C₃₇	#3178	1	2	yes	—
220	C₂×C₃₇	#3222	1	1	yes	characteristic
221	C₂×C₃₇	#3223	1	1	yes	characteristic
222	C₂²×Q₁₆	C₂²×C₃₇	1	2	yes	—
223	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
224	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
225	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
226	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
228	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
229	#497	—	2	4	no	—
230	#488	—	2	4	no	—
231	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
232	C₂×#103	C₂²×C₃₇	1	2	yes	—
233	C₂×#103	C₂²×C₃₇	1	2	yes	—
234	C₂×#103	C₂²×C₃₇	1	2	yes	—
235	C₂×#102	C₂²×C₃₇	1	2	yes	—
236	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
237	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
238	#400	—	2	2	no	—
239	#400	—	2	2	no	—
240	#391	C₂²×C₃₇	1	2	yes	—
241	#391	C₂²×C₃₇	1	1	yes	characteristic
242	#391	C₂²×C₃₇	1	2	yes	—
243	#390	C₂²×C₃₇	1	1	yes	characteristic
244	#388	—	2	2	no	—
245	#385	—	2	2	no	—
246	#384	C₂²×C₃₇	1	1	yes	characteristic
247	#376	C₂²×C₃₇	1	1	yes	characteristic
248	#340	C₂²×C₃₇	1	2	yes	—
249	#340	C₂²×C₃₇	1	2	yes	—
250	#336	C₂²×C₃₇	1	2	yes	—
251	C₃₇	#28629	1	1	yes	characteristic, direct product factor, Sylow
252	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
253	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
254	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
255	C₂³×C₄	—	2	1	no	—
256	C₂×Q₁₆	—	2	4	no	—
257	C₂×Q₁₆	—	2	4	no	—
258	C₂×Q₁₆	—	4	2	no	—
259	C₂×SD₁₆	—	2	4	no	—
260	C₂×SD₁₆	—	2	4	no	—
261	C₂×SD₁₆	—	4	2	no	—
262	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
263	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
264	C₄⋊Q₈	—	2	2	no	—
265	C₄⋊Q₈	—	2	2	no	—
266	#125	—	2	2	no	—
267	#125	—	2	2	no	—
268	#124	—	2	2	no	—
269	#124	D₄×C₃₇	1	4	yes	—
270	C₄×Q₈	—	4	2	no	—
271	C₄×D₄	—	4	2	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
284	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
286	C₄⋊C₈	—	2	4	no	—
287	#103	—	2	4	no	—
288	#103	—	4	2	no	—
289	#103	—	4	2	no	—
290	#102	—	2	4	no	—
291	#97	—	2	2	no	—
292	C₄×C₈	—	2	2	no	—
293	#95	—	2	2	no	—
294	#95	—	2	4	no	—
295	#95	—	2	2	no	—
296	#95	—	2	2	no	—
297	#95	D₄×C₃₇	1	2	yes	—
298	#95	D₄×C₃₇	1	2	yes	—
299	C₂⁴	—	2	1	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	4	2	no	—
320	C₂²×C₄	—	8	2	no	—
321	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
325	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
326	Q₁₆	—	4	8	no	—
327	SD₁₆	—	4	8	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	#41×C₃₇	1	4	yes	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	4	4	no	—
340	C₄⋊C₄	—	4	4	no	—
341	C₄⋊C₄	—	8	2	no	—
342	C₂²⋊C₄	—	2	8	no	—
343	C₂²⋊C₄	—	4	2	no	—
344	C₂²⋊C₄	—	8	2	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	4	2	no	—
348	C₄²	C₂×D₄×C₃₇	1	2	yes	—
349	C₄²	#41×C₃₇	1	2	yes	—
350	C₂³	—	2	2	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	4	1	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
356	Q₈	—	2	4	no	—
357	Q₈	—	4	2	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	4	2	no	—
361	Q₈	—	4	2	no	—
362	D₄	—	2	4	no	—
363	D₄	—	4	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	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	8	4	no	—
387	C₂×C₄	#121×C₃₇	1	4	yes	—
388	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
389	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
390	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
391	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
392	C₈	—	2	4	no	—
393	C₈	—	4	2	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	1	no	—
398	C₂²	—	8	1	no	—
399	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
400	C₂²	C₃₇×#532	1	1	yes	characteristic
401	C₂²	C₃₇×#535	1	1	yes	characteristic
402	C₂²	C₃₇×#577	1	2	yes	—
403	C₂²	C₃₇×#578	1	2	yes	—
404	C₄	—	2	4	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	1	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	2	no	—
409	C₄	—	8	1	no	—
410	C₄	—	8	1	no	—
411	C₄	—	8	2	no	—
412	C₄	—	8	2	no	—
413	C₄	C₃₇×#546	1	2	yes	—
414	C₄	C₃₇×#559	1	2	yes	—
415	C₂	—	8	2	no	—
416	C₂	C₃₇×#2544	1	1	yes	characteristic
417	C₂	C₃₇×#3046	1	2	yes	—
418	C₂	C₃₇×#3178	1	2	yes	—
419	C₂	C₃₇×#3222	1	1	yes	characteristic
420	C₂	C₃₇×#3223	1	1	yes	characteristic

	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 ◁ C₃₇×#376 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₇×#2642	C₂	semidirect
5. C₃₇×#2056	C₂	semidirect
7. C₃₇×#1992	C₂	semidirect
8. C₃₇×#1956	C₂	semidirect
9. C₃₇×#1878	C₂	semidirect
11. C₃₇×#1768	C₂	semidirect
183. #28629	C₃₇	direct (N × H)
207. #2642	C₂×C₃₇	semidirect
209. #2056	C₂×C₃₇	semidirect
211. #1992	C₂×C₃₇	semidirect
212. #1956	C₂×C₃₇	semidirect
213. #1878	C₂×C₃₇	semidirect
215. #1768	C₂×C₃₇	semidirect
251. C₃₇	#28629	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×#497	2
C₂×C₃₇×#488	2
C₃₇×#2642	2
C₃₇×#2326	2
C₃₇×#2056	2
C₃₇×#2055	2
C₃₇×#1992	2
C₃₇×#1956	2
C₃₇×#1878	2
C₃₇×#1877	2
C₃₇×#1768	2
#28629	37

Subgroups — C37×#28629 #22649882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28629 #22649882