Subgroups — C₃₇×#29963 #22651216

Order 9472.

790 conjugacy classes of subgroups.

The subgroup lattice has 414 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
2	C₃₇×#2310	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2096	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2095	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2068	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2066	C₂	1	2	yes	maximal, complemented
7	C₃₇×#2026	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2026	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1854	C₂	1	2	yes	maximal
10	C₃₇×#1798	C₂	1	1	yes	maximal, characteristic
11	C₃₇×#1787	C₂	1	2	yes	maximal
12	C₂³×Q₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×#117×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×#117×C₃₇	C₂²	1	1	yes	characteristic
16	C₂×#107×C₃₇	C₂²	1	2	yes	—
17	C₂×#106×C₃₇	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
19	C₂×#103×C₃₇	C₂²	1	2	yes	—
20	C₂×#103×C₃₇	C₂²	1	2	yes	—
21	C₂×#103×C₃₇	C₂²	1	2	yes	—
22	C₂×#103×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×#391	—	2	2	no	—
27	C₃₇×#391	C₂²	1	1	yes	characteristic
28	C₃₇×#391	C₂²	1	1	yes	characteristic
29	C₃₇×#391	C₂²	1	1	yes	characteristic
30	C₃₇×#391	C₂²	1	1	yes	characteristic
31	C₃₇×#389	C₂²	1	2	yes	—
32	C₃₇×#384	C₂²	1	1	yes	characteristic
33	C₃₇×#381	—	2	2	no	—
34	C₃₇×#380	C₂²	1	2	yes	—
35	C₃₇×#340	C₂²	1	2	yes	—
36	C₃₇×#340	C₂²	1	2	yes	—
37	C₃₇×#336	C₂²	1	1	yes	characteristic
38	C₃₇×#336	C₂²	1	1	yes	characteristic
39	C₂²×Q₈×C₃₇	—	2	1	no	—
40	C₂²×Q₈×C₃₇	—	2	2	no	—
41	C₂²×Q₈×C₃₇	—	4	2	no	—
42	C₂²×Q₈×C₃₇	—	4	2	no	—
43	C₂²×Q₈×C₃₇	Q₈	1	4	yes	—
44	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₃₇	—	2	1	no	—
47	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
50	#125×C₃₇	—	4	2	no	—
51	#117×C₃₇	—	4	2	no	—
52	#117×C₃₇	—	4	2	no	—
53	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₃₇	D₄	1	2	yes	—
64	C₂×C₄²×C₃₇	—	2	1	no	—
65	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
67	#107×C₃₇	—	4	2	no	—
68	#106×C₃₇	—	4	2	no	—
69	C₄⋊C₈×C₃₇	—	4	2	no	—
70	#103×C₃₇	—	4	2	no	—
71	#103×C₃₇	—	4	2	no	—
72	#103×C₃₇	—	4	2	no	—
73	#103×C₃₇	—	4	2	no	—
74	C₂²⋊C₈×C₃₇	—	2	4	no	—
75	#95×C₃₇	—	2	2	no	—
76	#95×C₃₇	—	2	2	no	—
77	#95×C₃₇	—	2	2	no	—
78	#95×C₃₇	—	2	2	no	—
79	#95×C₃₇	—	2	2	no	—
80	#95×C₃₇	—	2	2	no	—
81	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
82	C₂×Q₈×C₃₇	—	2	4	no	—
83	C₂×Q₈×C₃₇	—	2	1	no	—
84	C₂×Q₈×C₃₇	—	2	1	no	—
85	C₂×Q₈×C₃₇	—	2	2	no	—
86	C₂×Q₈×C₃₇	—	2	2	no	—
87	C₂×Q₈×C₃₇	—	2	2	no	—
88	C₂×Q₈×C₃₇	—	2	2	no	—
89	C₂×Q₈×C₃₇	—	4	8	no	—
90	C₂×Q₈×C₃₇	—	4	2	no	—
91	C₂×Q₈×C₃₇	—	4	2	no	—
92	C₂×Q₈×C₃₇	—	4	8	no	—
93	C₂×Q₈×C₃₇	C₂×Q₈	1	2	yes	—
94	C₂×Q₈×C₃₇	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₃₇	—	2	2	no	—
96	C₂²×C₄×C₃₇	—	2	2	no	—
97	C₂²×C₄×C₃₇	—	2	4	no	—
98	C₂²×C₄×C₃₇	—	2	1	no	—
99	C₂²×C₄×C₃₇	—	2	1	no	—
100	C₂²×C₄×C₃₇	—	2	1	no	—
101	C₂²×C₄×C₃₇	—	2	1	no	—
102	C₂²×C₄×C₃₇	—	2	2	no	—
103	C₂²×C₄×C₃₇	—	2	2	no	—
104	C₂²×C₄×C₃₇	—	4	2	no	—
105	C₂²×C₄×C₃₇	—	4	2	no	—
106	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₃₇	C₂×Q₈	1	2	yes	—
110	C₂²×C₄×C₃₇	#41	1	2	yes	—
111	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
112	C₂×C₈×C₃₇	—	2	2	no	—
113	C₂×C₈×C₃₇	—	2	2	no	—
114	C₂×C₈×C₃₇	—	2	2	no	—
115	C₂×C₈×C₃₇	—	2	2	no	—
116	C₂×C₈×C₃₇	—	2	2	no	—
117	C₂×C₈×C₃₇	—	2	2	no	—
118	C₄⋊C₄×C₃₇	—	2	2	no	—
119	C₄⋊C₄×C₃₇	—	2	2	no	—
120	C₄⋊C₄×C₃₇	—	2	2	no	—
121	C₄⋊C₄×C₃₇	—	2	2	no	—
122	C₄⋊C₄×C₃₇	—	2	2	no	—
123	C₄⋊C₄×C₃₇	—	2	2	no	—
124	C₄⋊C₄×C₃₇	—	4	2	no	—
125	C₄⋊C₄×C₃₇	—	4	4	no	—
126	C₄⋊C₄×C₃₇	—	8	2	no	—
127	C₄⋊C₄×C₃₇	—	8	2	no	—
128	C₂²⋊C₄×C₃₇	—	4	2	no	—
129	C₂²⋊C₄×C₃₇	—	4	2	no	—
130	C₂²⋊C₄×C₃₇	—	8	2	no	—
131	C₄²×C₃₇	—	2	2	no	—
132	C₄²×C₃₇	—	2	2	no	—
133	C₄²×C₃₇	—	4	2	no	—
134	C₂³×C₃₇	—	2	1	no	—
135	C₂³×C₃₇	—	2	1	no	—
136	C₂³×C₃₇	—	2	2	no	—
137	C₂³×C₃₇	—	2	2	no	—
138	C₂³×C₃₇	C₂²⋊Q₈	1	2	yes	—
139	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₃₇	—	2	4	no	—
141	Q₈×C₃₇	—	2	4	no	—
142	Q₈×C₃₇	—	4	8	no	—
143	Q₈×C₃₇	—	4	2	no	—
144	Q₈×C₃₇	—	4	2	no	—
145	C₂×C₄×C₃₇	—	2	1	no	—
146	C₂×C₄×C₃₇	—	2	1	no	—
147	C₂×C₄×C₃₇	—	2	4	no	—
148	C₂×C₄×C₃₇	—	2	4	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	—	4	8	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	1	no	—
162	C₂×C₄×C₃₇	—	4	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	2	no	—
169	C₂×C₄×C₃₇	—	4	2	no	—
170	C₂×C₄×C₃₇	—	4	2	no	—
171	C₂×C₄×C₃₇	—	4	2	no	—
172	C₂×C₄×C₃₇	C₂²⋊Q₈	1	2	yes	—
173	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
176	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
177	C₈×C₃₇	—	4	2	no	—
178	C₈×C₃₇	—	4	2	no	—
179	#29963	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂²×C₃₇	—	2	4	no	—
181	C₂²×C₃₇	—	2	2	no	—
182	C₂²×C₃₇	—	4	2	no	—
183	C₂²×C₃₇	—	4	1	no	—
184	C₂²×C₃₇	—	4	1	no	—
185	C₂²×C₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
186	C₂²×C₃₇	#534	1	1	yes	characteristic
187	C₂²×C₃₇	#535	1	1	yes	characteristic
188	C₂²×C₃₇	#577	1	2	yes	—
189	C₂²×C₃₇	#578	1	2	yes	—
190	C₄×C₃₇	—	2	2	no	—
191	C₄×C₃₇	—	4	2	no	—
192	C₄×C₃₇	—	4	2	no	—
193	C₄×C₃₇	—	4	2	no	—
194	C₄×C₃₇	—	4	2	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	#538	1	2	yes	—
200	C₄×C₃₇	#543	1	2	yes	—
201	#2629	C₂×C₃₇	1	1	yes	characteristic
202	#2310	C₂×C₃₇	1	1	yes	characteristic
203	#2096	C₂×C₃₇	1	1	yes	characteristic, complemented
204	#2095	C₂×C₃₇	1	1	yes	characteristic, complemented
205	#2068	C₂×C₃₇	1	2	yes	complemented
206	#2066	C₂×C₃₇	1	2	yes	complemented
207	#2026	C₂×C₃₇	1	1	yes	characteristic, complemented
208	#2026	C₂×C₃₇	1	1	yes	characteristic, complemented
209	#1854	C₂×C₃₇	1	2	yes	—
210	#1798	C₂×C₃₇	1	1	yes	characteristic
211	#1787	C₂×C₃₇	1	2	yes	—
212	C₂×C₃₇	—	4	2	no	—
213	C₂×C₃₇	#2626	1	1	yes	characteristic
214	C₂×C₃₇	#3082	1	2	yes	—
215	C₂×C₃₇	#3201	1	2	yes	—
216	C₂×C₃₇	#3221	1	1	yes	characteristic
217	C₂×C₃₇	#3223	1	1	yes	characteristic
218	C₂³×Q₈	C₂²×C₃₇	1	1	yes	characteristic
219	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
220	C₂×#117	C₂²×C₃₇	1	1	yes	characteristic
221	C₂×#117	C₂²×C₃₇	1	1	yes	characteristic
222	C₂×#107	C₂²×C₃₇	1	2	yes	—
223	C₂×#106	C₂²×C₃₇	1	2	yes	—
224	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
225	C₂×#103	C₂²×C₃₇	1	2	yes	—
226	C₂×#103	C₂²×C₃₇	1	2	yes	—
227	C₂×#103	C₂²×C₃₇	1	2	yes	—
228	C₂×#103	C₂²×C₃₇	1	2	yes	—
229	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	—
230	#398	—	2	2	no	—
231	#396	—	2	2	no	—
232	#391	—	2	2	no	—
233	#391	C₂²×C₃₇	1	1	yes	characteristic
234	#391	C₂²×C₃₇	1	1	yes	characteristic
235	#391	C₂²×C₃₇	1	1	yes	characteristic
236	#391	C₂²×C₃₇	1	1	yes	characteristic
237	#389	C₂²×C₃₇	1	2	yes	—
238	#384	C₂²×C₃₇	1	1	yes	characteristic
239	#381	—	2	2	no	—
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	1	yes	characteristic
244	#336	C₂²×C₃₇	1	1	yes	characteristic
245	C₃₇	#29963	1	1	yes	characteristic, direct product factor, Sylow
246	C₂²×Q₈	—	2	1	no	—
247	C₂²×Q₈	—	2	2	no	—
248	C₂²×Q₈	—	4	2	no	—
249	C₂²×Q₈	—	4	2	no	—
250	C₂²×Q₈	Q₈×C₃₇	1	4	yes	—
251	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
252	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
253	C₂³×C₄	—	2	1	no	—
254	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
256	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
257	#125	—	4	2	no	—
258	#117	—	4	2	no	—
259	#117	—	4	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	2	no	—
270	C₂×C₂²⋊C₄	D₄×C₃₇	1	2	yes	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
274	#107	—	4	2	no	—
275	#106	—	4	2	no	—
276	C₄⋊C₈	—	4	2	no	—
277	#103	—	4	2	no	—
278	#103	—	4	2	no	—
279	#103	—	4	2	no	—
280	#103	—	4	2	no	—
281	C₂²⋊C₈	—	2	4	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	4	8	no	—
297	C₂×Q₈	—	4	2	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂×Q₈	—	4	8	no	—
300	C₂×Q₈	C₂×Q₈×C₃₇	1	2	yes	—
301	C₂×Q₈	C₂×Q₈×C₃₇	1	2	yes	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	—	4	2	no	—
313	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
316	C₂²×C₄	C₂×Q₈×C₃₇	1	2	yes	—
317	C₂²×C₄	#41×C₃₇	1	2	yes	—
318	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
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	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	4	no	—
333	C₄⋊C₄	—	8	2	no	—
334	C₄⋊C₄	—	8	2	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	8	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	4	2	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	C₂²⋊Q₈×C₃₇	1	2	yes	—
346	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
347	Q₈	—	2	4	no	—
348	Q₈	—	2	4	no	—
349	Q₈	—	4	8	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	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	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	4	8	no	—
365	C₂×C₄	—	4	1	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	1	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	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	C₂²⋊Q₈×C₃₇	1	2	yes	—
380	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
381	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
382	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
383	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	C₂×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
392	C₂²	C₃₇×#534	1	1	yes	characteristic
393	C₂²	C₃₇×#535	1	1	yes	characteristic
394	C₂²	C₃₇×#577	1	2	yes	—
395	C₂²	C₃₇×#578	1	2	yes	—
396	C₄	—	2	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	2	no	—
401	C₄	—	8	2	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	2	no	—
404	C₄	—	8	1	no	—
405	C₄	C₃₇×#538	1	2	yes	—
406	C₄	C₃₇×#543	1	2	yes	—
407	C₂	—	4	2	no	—
408	C₂	C₃₇×#2626	1	1	yes	characteristic
409	C₂	C₃₇×#3082	1	2	yes	—
410	C₂	C₃₇×#3201	1	2	yes	—
411	C₂	C₃₇×#3221	1	1	yes	characteristic
412	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	C₂⁴×C₃₇	C₂×D₄
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
3. C₃₇×#2096	C₂	semidirect
4. C₃₇×#2095	C₂	semidirect
5. C₃₇×#2068	C₂	semidirect
6. C₃₇×#2066	C₂	semidirect
7. C₃₇×#2026	C₂	semidirect
8. C₃₇×#2026	C₂	semidirect
179. #29963	C₃₇	direct (N × H)
203. #2096	C₂×C₃₇	semidirect
204. #2095	C₂×C₃₇	semidirect
205. #2068	C₂×C₃₇	semidirect
206. #2066	C₂×C₃₇	semidirect
207. #2026	C₂×C₃₇	semidirect
208. #2026	C₂×C₃₇	semidirect
245. C₃₇	#29963	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×#2310	2
C₃₇×#2096	2
C₃₇×#2095	2
C₃₇×#2068	2
C₃₇×#2066	2
C₃₇×#2026	2
C₃₇×#1854	2
C₃₇×#1798	2
C₃₇×#1787	2
#29963	37

Subgroups — C37×#29963 #22651216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#29963 #22651216