Subgroups — C₃₇×#28380 #22649633

Order 9472.

912 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#479	C₂	1	2	yes	maximal, complemented
2	C₂×C₃₇×#464	C₂	1	2	yes	maximal
3	C₃₇×#2861	C₂	1	1	yes	maximal, characteristic
4	C₄×C₄⋊Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2095	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2094	C₂	1	1	yes	maximal, characteristic
7	C₃₇×#2016	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2013	C₂	1	1	yes	maximal, characteristic
9	C₃₇×#1973	C₂	1	2	yes	maximal
10	C₃₇×#1971	C₂	1	2	yes	maximal, complemented
11	C₃₇×#1767	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	2	yes	—
18	C₃₇×#479	—	2	8	no	—
19	C₃₇×#464	—	2	8	no	—
20	C₂×#107×C₃₇	C₂²	1	2	yes	—
21	C₂×#106×C₃₇	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
23	C₂×#103×C₃₇	C₂²	1	2	yes	—
24	C₂×#103×C₃₇	C₂²	1	2	yes	—
25	C₂×#103×C₃₇	C₂²	1	2	yes	—
26	C₂×#102×C₃₇	C₂²	1	2	yes	—
27	C₂×#97×C₃₇	C₂²	1	2	yes	—
28	C₃₇×#391	C₂²	1	1	yes	characteristic
29	C₃₇×#391	C₂²	1	1	yes	characteristic
30	C₃₇×#391	C₂²	1	2	yes	—
31	C₃₇×#390	C₂²	1	1	yes	characteristic
32	C₃₇×#390	C₂²	1	1	yes	characteristic
33	C₃₇×#389	—	2	2	no	—
34	C₃₇×#388	—	2	2	no	—
35	C₃₇×#388	—	2	2	no	—
36	C₃₇×#384	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₃₇	—	2	2	no	—
38	C₄³×C₃₇	C₂²	1	1	yes	characteristic
39	C₃₇×#336	C₂²	1	1	yes	characteristic
40	C₃₇×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
42	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
43	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
44	C₂×Q₁₆×C₃₇	—	2	4	no	—
45	C₂×Q₁₆×C₃₇	—	2	4	no	—
46	C₂×Q₁₆×C₃₇	—	4	2	no	—
47	C₂×SD₁₆×C₃₇	—	2	4	no	—
48	C₂×SD₁₆×C₃₇	—	2	4	no	—
49	C₂×SD₁₆×C₃₇	—	4	2	no	—
50	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
51	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₃₇	—	2	4	no	—
53	#125×C₃₇	—	2	4	no	—
54	#124×C₃₇	—	2	4	no	—
55	C₄×Q₈×C₃₇	—	2	4	no	—
56	C₄×Q₈×C₃₇	—	2	4	no	—
57	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
69	C₂×C₄²×C₃₇	—	2	2	no	—
70	C₂×C₄²×C₃₇	D₄	1	2	yes	—
71	C₂×C₄²×C₃₇	D₄	1	2	yes	—
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	#107×C₃₇	—	2	4	no	—
76	#106×C₃₇	—	2	4	no	—
77	C₄⋊C₈×C₃₇	D₄	1	8	yes	—
78	#103×C₃₇	—	2	4	no	—
79	#103×C₃₇	—	2	4	no	—
80	#103×C₃₇	—	2	4	no	—
81	#102×C₃₇	—	2	4	no	—
82	#97×C₃₇	—	4	2	no	—
83	#95×C₃₇	—	2	4	no	—
84	#95×C₃₇	—	2	2	no	—
85	#95×C₃₇	—	2	2	no	—
86	C₂⁴×C₃₇	—	2	1	no	—
87	C₂×Q₈×C₃₇	—	2	2	no	—
88	C₂×Q₈×C₃₇	—	2	2	no	—
89	C₂×Q₈×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	1	no	—
94	C₂×Q₈×C₃₇	—	2	2	no	—
95	C₂×Q₈×C₃₇	—	2	1	no	—
96	C₂×Q₈×C₃₇	#41	1	4	yes	—
97	C₂×D₄×C₃₇	—	2	2	no	—
98	C₂×D₄×C₃₇	—	2	2	no	—
99	C₂×D₄×C₃₇	—	2	1	no	—
100	C₂×D₄×C₃₇	—	2	1	no	—
101	C₂²×C₄×C₃₇	—	2	2	no	—
102	C₂²×C₄×C₃₇	—	2	1	no	—
103	C₂²×C₄×C₃₇	—	2	2	no	—
104	C₂²×C₄×C₃₇	—	2	1	no	—
105	C₂²×C₄×C₃₇	—	2	1	no	—
106	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
111	Q₁₆×C₃₇	—	4	8	no	—
112	SD₁₆×C₃₇	—	4	8	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	C₂×D₄	1	4	yes	—
118	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
119	C₄⋊C₄×C₃₇	—	2	8	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	4	no	—
125	C₄⋊C₄×C₃₇	—	4	4	no	—
126	C₄⋊C₄×C₃₇	—	4	2	no	—
127	C₄⋊C₄×C₃₇	—	4	2	no	—
128	C₂²⋊C₄×C₃₇	—	4	4	no	—
129	C₂²⋊C₄×C₃₇	—	4	2	no	—
130	C₂²⋊C₄×C₃₇	—	4	2	no	—
131	C₂²⋊C₄×C₃₇	—	4	4	no	—
132	C₄²×C₃₇	—	2	4	no	—
133	C₄²×C₃₇	—	2	2	no	—
134	C₄²×C₃₇	—	2	1	no	—
135	C₄²×C₃₇	—	2	1	no	—
136	C₄²×C₃₇	—	4	2	no	—
137	C₄²×C₃₇	—	4	4	no	—
138	C₄²×C₃₇	C₂×D₄	1	4	yes	—
139	C₂³×C₃₇	—	4	1	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	—	2	4	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	—	4	2	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	4	no	—
158	C₂×C₄×C₃₇	—	2	2	no	—
159	C₂×C₄×C₃₇	—	2	2	no	—
160	C₂×C₄×C₃₇	—	2	2	no	—
161	C₂×C₄×C₃₇	—	4	2	no	—
162	C₂×C₄×C₃₇	—	4	2	no	—
163	C₂×C₄×C₃₇	—	4	1	no	—
164	C₂×C₄×C₃₇	—	4	2	no	—
165	C₂×C₄×C₃₇	—	4	1	no	—
166	C₂×C₄×C₃₇	—	4	1	no	—
167	C₂×C₄×C₃₇	—	4	1	no	—
168	C₂×C₄×C₃₇	—	4	1	no	—
169	C₂×C₄×C₃₇	—	4	2	no	—
170	C₂×C₄×C₃₇	—	4	2	no	—
171	C₂×C₄×C₃₇	—	4	4	no	—
172	C₂×C₄×C₃₇	#127	1	2	yes	—
173	C₂×C₄×C₃₇	#127	1	2	yes	—
174	C₂×C₄×C₃₇	#137	1	4	yes	—
175	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
176	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
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	—	2	4	no	—
180	C₈×C₃₇	—	2	4	no	—
181	#28380	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	8	1	no	—
187	C₂²×C₃₇	#525	1	1	yes	characteristic
188	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
189	C₂²×C₃₇	#537	1	1	yes	characteristic
190	C₂²×C₃₇	C₂×#137	1	2	yes	—
191	C₂²×C₃₇	#575	1	2	yes	—
192	C₄×C₃₇	—	2	4	no	—
193	C₄×C₃₇	—	2	2	no	—
194	C₄×C₃₇	—	2	2	no	—
195	C₄×C₃₇	—	4	2	no	—
196	C₄×C₃₇	—	4	4	no	—
197	C₄×C₃₇	—	8	2	no	—
198	C₄×C₃₇	—	8	1	no	—
199	C₄×C₃₇	—	8	1	no	—
200	C₄×C₃₇	—	8	1	no	—
201	C₄×C₃₇	#546	1	2	yes	—
202	C₄×C₃₇	#548	1	2	yes	—
203	C₂×#479	C₂×C₃₇	1	2	yes	complemented
204	C₂×#464	C₂×C₃₇	1	2	yes	—
205	#2861	C₂×C₃₇	1	1	yes	characteristic
206	C₄×C₄⋊Q₈	C₂×C₃₇	1	1	yes	characteristic, complemented
207	#2095	C₂×C₃₇	1	1	yes	characteristic, complemented
208	#2094	C₂×C₃₇	1	1	yes	characteristic
209	#2016	C₂×C₃₇	1	1	yes	characteristic, complemented
210	#2013	C₂×C₃₇	1	1	yes	characteristic
211	#1973	C₂×C₃₇	1	2	yes	—
212	#1971	C₂×C₃₇	1	2	yes	complemented
213	#1767	C₂×C₃₇	1	1	yes	characteristic, complemented
214	C₂×C₃₇	—	16	1	no	—
215	C₂×C₃₇	#2540	1	1	yes	characteristic
216	C₂×C₃₇	#3117	1	2	yes	—
217	C₂×C₃₇	#3150	1	1	yes	characteristic
218	C₂×C₃₇	#3152	1	1	yes	characteristic
219	C₂×C₃₇	#3252	1	2	yes	—
220	C₂²×Q₁₆	C₂²×C₃₇	1	2	yes	—
221	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
222	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
223	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
224	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
225	C₂×C₄×Q₈	C₂²×C₃₇	1	2	yes	—
226	#479	—	2	8	no	—
227	#464	—	2	8	no	—
228	C₂×#107	C₂²×C₃₇	1	2	yes	—
229	C₂×#106	C₂²×C₃₇	1	2	yes	—
230	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
231	C₂×#103	C₂²×C₃₇	1	2	yes	—
232	C₂×#103	C₂²×C₃₇	1	2	yes	—
233	C₂×#103	C₂²×C₃₇	1	2	yes	—
234	C₂×#102	C₂²×C₃₇	1	2	yes	—
235	C₂×#97	C₂²×C₃₇	1	2	yes	—
236	#391	C₂²×C₃₇	1	2	yes	—
237	#391	C₂²×C₃₇	1	1	yes	characteristic
238	#391	C₂²×C₃₇	1	1	yes	characteristic
239	#390	C₂²×C₃₇	1	1	yes	characteristic
240	#390	C₂²×C₃₇	1	1	yes	characteristic
241	#389	—	2	2	no	—
242	#388	—	2	2	no	—
243	#388	—	2	2	no	—
244	#384	C₂²×C₃₇	1	1	yes	characteristic
245	C₄×C₄⋊C₄	—	2	2	no	—
246	C₄³	C₂²×C₃₇	1	1	yes	characteristic
247	#336	C₂²×C₃₇	1	1	yes	characteristic
248	#336	C₂²×C₃₇	1	1	yes	characteristic
249	C₃₇	#28380	1	1	yes	characteristic, direct product factor, Sylow
250	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
251	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
252	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
253	C₂×Q₁₆	—	2	4	no	—
254	C₂×Q₁₆	—	2	4	no	—
255	C₂×Q₁₆	—	4	2	no	—
256	C₂×SD₁₆	—	2	4	no	—
257	C₂×SD₁₆	—	2	4	no	—
258	C₂×SD₁₆	—	4	2	no	—
259	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
260	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
261	C₄⋊Q₈	—	2	4	no	—
262	#125	—	2	4	no	—
263	#124	—	2	4	no	—
264	C₄×Q₈	—	2	4	no	—
265	C₄×Q₈	—	2	4	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	D₄×C₃₇	1	2	yes	—
280	C₂×C₄²	D₄×C₃₇	1	2	yes	—
281	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
284	#107	—	2	4	no	—
285	#106	—	2	4	no	—
286	C₄⋊C₈	D₄×C₃₇	1	8	yes	—
287	#103	—	2	4	no	—
288	#103	—	2	4	no	—
289	#103	—	2	4	no	—
290	#102	—	2	4	no	—
291	#97	—	4	2	no	—
292	#95	—	2	4	no	—
293	#95	—	2	2	no	—
294	#95	—	2	2	no	—
295	C₂⁴	—	2	1	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	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	#41×C₃₇	1	4	yes	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
319	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
320	Q₁₆	—	4	8	no	—
321	SD₁₆	—	4	8	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
327	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	4	4	no	—
334	C₄⋊C₄	—	4	4	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	4	4	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	4	4	no	—
341	C₄²	—	2	4	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	4	2	no	—
346	C₄²	—	4	4	no	—
347	C₄²	C₂×D₄×C₃₇	1	4	yes	—
348	C₂³	—	4	1	no	—
349	C₂³	—	4	1	no	—
350	C₂³	—	4	1	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
354	Q₈	—	2	4	no	—
355	Q₈	—	2	4	no	—
356	Q₈	—	4	2	no	—
357	Q₈	—	4	2	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	4	2	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	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	4	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	#127×C₃₇	1	2	yes	—
382	C₂×C₄	#127×C₃₇	1	2	yes	—
383	C₂×C₄	#137×C₃₇	1	4	yes	—
384	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
385	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
386	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
387	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
388	C₈	—	2	4	no	—
389	C₈	—	2	4	no	—
390	C₂²	—	8	1	no	—
391	C₂²	—	8	1	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	1	no	—
394	C₂²	—	8	2	no	—
395	C₂²	C₃₇×#525	1	1	yes	characteristic
396	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
397	C₂²	C₃₇×#537	1	1	yes	characteristic
398	C₂²	C₂×#137×C₃₇	1	2	yes	—
399	C₂²	C₃₇×#575	1	2	yes	—
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	4	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	4	no	—
405	C₄	—	8	2	no	—
406	C₄	—	8	1	no	—
407	C₄	—	8	1	no	—
408	C₄	—	8	1	no	—
409	C₄	C₃₇×#546	1	2	yes	—
410	C₄	C₃₇×#548	1	2	yes	—
411	C₂	—	16	1	no	—
412	C₂	C₃₇×#2540	1	1	yes	characteristic
413	C₂	C₃₇×#3117	1	2	yes	—
414	C₂	C₃₇×#3150	1	1	yes	characteristic
415	C₂	C₃₇×#3152	1	1	yes	characteristic
416	C₂	C₃₇×#3252	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. C₂×C₃₇×#479	C₂	semidirect
4. C₄×C₄⋊Q₈×C₃₇	C₂	semidirect
5. C₃₇×#2095	C₂	semidirect
7. C₃₇×#2016	C₂	semidirect
10. C₃₇×#1971	C₂	semidirect
11. C₃₇×#1767	C₂	semidirect
181. #28380	C₃₇	direct (N × H)
203. C₂×#479	C₂×C₃₇	semidirect
206. C₄×C₄⋊Q₈	C₂×C₃₇	semidirect
207. #2095	C₂×C₃₇	semidirect
209. #2016	C₂×C₃₇	semidirect
212. #1971	C₂×C₃₇	semidirect
213. #1767	C₂×C₃₇	semidirect
249. C₃₇	#28380	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×#479	2
C₂×C₃₇×#464	2
C₃₇×#2861	2
C₄×C₄⋊Q₈×C₃₇	2
C₃₇×#2095	2
C₃₇×#2094	2
C₃₇×#2016	2
C₃₇×#2013	2
C₃₇×#1973	2
C₃₇×#1971	2
C₃₇×#1767	2
#28380	37

Subgroups — C37×#28380 #22649633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28380 #22649633