Subgroups — C₃₇×#28754 #22650007

Order 9472.

922 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×#489	C₂	1	2	yes	maximal, complemented
2	C₃₇×#2858	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2042	C₂	1	4	yes	maximal, complemented
5	C₃₇×#1982	C₂	1	2	yes	maximal
6	C₃₇×#1981	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1959	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
11	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
12	C₂×#124×C₃₇	C₂²	1	2	yes	—
13	C₂×#124×C₃₇	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₃₇	—	2	1	no	—
15	C₃₇×#489	—	2	8	no	—
16	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
17	C₂×#103×C₃₇	C₂²	1	4	yes	—
18	C₂×#103×C₃₇	C₂²	1	4	yes	—
19	C₂×#102×C₃₇	C₂²	1	4	yes	—
20	C₂×#102×C₃₇	C₂²	1	4	yes	—
21	C₂×#97×C₃₇	C₂²	1	2	yes	—
22	C₃₇×#391	—	2	1	no	—
23	C₃₇×#390	—	2	1	no	—
24	C₃₇×#390	—	2	1	no	—
25	C₃₇×#390	—	2	1	no	—
26	C₃₇×#390	—	2	1	no	—
27	C₃₇×#389	—	2	1	no	—
28	C₃₇×#389	C₂²	1	2	yes	—
29	C₃₇×#384	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₃₇	—	2	1	no	—
31	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
32	C₄³×C₃₇	C₂²	1	1	yes	characteristic
33	C₃₇×#336	C₂²	1	2	yes	—
34	C₂²×Q₈×C₃₇	—	2	1	no	—
35	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
36	C₂²×D₄×C₃₇	—	2	1	no	—
37	C₂²×D₄×C₃₇	—	2	1	no	—
38	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
39	C₂²×C₈×C₃₇	C₂³	1	4	yes	—
40	C₄⋊Q₈×C₃₇	—	2	2	no	—
41	C₄⋊Q₈×C₃₇	—	2	4	no	—
42	C₄⋊Q₈×C₃₇	D₄	1	4	yes	complemented
43	#127×C₃₇	—	2	4	no	—
44	#124×C₃₇	—	2	4	no	—
45	#124×C₃₇	—	2	4	no	—
46	#124×C₃₇	—	4	4	no	—
47	C₄×Q₈×C₃₇	—	4	4	no	—
48	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
49	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
50	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
51	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
52	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
56	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
60	C₂×C₄²×C₃₇	—	2	2	no	—
61	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₃₇	—	2	4	no	—
69	#103×C₃₇	—	2	8	no	—
70	#103×C₃₇	—	4	4	no	—
71	#102×C₃₇	—	2	8	no	—
72	#102×C₃₇	—	4	4	no	—
73	#97×C₃₇	—	2	4	no	—
74	#95×C₃₇	—	2	2	no	—
75	#95×C₃₇	—	2	2	no	—
76	C₂⁴×C₃₇	—	2	2	no	—
77	C₂×Q₈×C₃₇	—	2	4	no	—
78	C₂×Q₈×C₃₇	—	2	2	no	—
79	C₂×Q₈×C₃₇	—	2	2	no	—
80	C₂×Q₈×C₃₇	—	2	4	no	—
81	C₂×Q₈×C₃₇	—	2	4	no	—
82	C₂×Q₈×C₃₇	—	4	2	no	—
83	C₂×Q₈×C₃₇	—	4	2	no	—
84	C₂×D₄×C₃₇	—	2	2	no	—
85	C₂×D₄×C₃₇	—	2	2	no	—
86	C₂×D₄×C₃₇	—	2	4	no	—
87	C₂×D₄×C₃₇	—	2	4	no	—
88	C₂×D₄×C₃₇	—	4	2	no	—
89	C₂×D₄×C₃₇	—	4	2	no	—
90	C₂×D₄×C₃₇	—	4	2	no	—
91	C₂×D₄×C₃₇	—	4	2	no	—
92	C₂×D₄×C₃₇	—	4	2	no	—
93	C₂×D₄×C₃₇	—	4	2	no	—
94	C₂²×C₄×C₃₇	—	2	2	no	—
95	C₂²×C₄×C₃₇	—	2	2	no	—
96	C₂²×C₄×C₃₇	—	2	2	no	—
97	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
104	C₂×C₈×C₃₇	—	2	4	no	—
105	C₂×C₈×C₃₇	—	2	4	no	—
106	C₂×C₈×C₃₇	—	2	4	no	—
107	C₄⋊C₄×C₃₇	—	2	4	no	—
108	C₄⋊C₄×C₃₇	—	2	2	no	—
109	C₄⋊C₄×C₃₇	—	2	2	no	—
110	C₄⋊C₄×C₃₇	—	2	2	no	—
111	C₄⋊C₄×C₃₇	—	4	2	no	—
112	C₄⋊C₄×C₃₇	—	4	2	no	—
113	C₄⋊C₄×C₃₇	—	4	4	no	—
114	C₄⋊C₄×C₃₇	—	4	2	no	—
115	C₄⋊C₄×C₃₇	—	4	2	no	—
116	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
117	C₂²⋊C₄×C₃₇	—	4	4	no	—
118	C₂²⋊C₄×C₃₇	—	4	4	no	—
119	C₂²⋊C₄×C₃₇	—	4	4	no	—
120	C₂²⋊C₄×C₃₇	—	4	4	no	—
121	C₄²×C₃₇	—	2	2	no	—
122	C₄²×C₃₇	—	2	2	no	—
123	C₄²×C₃₇	—	2	2	no	—
124	C₄²×C₃₇	—	4	1	no	—
125	C₄²×C₃₇	—	4	1	no	—
126	C₄²×C₃₇	—	4	4	no	—
127	C₄²×C₃₇	C₂×D₄	1	2	yes	—
128	C₄²×C₃₇	#41	1	2	yes	—
129	C₄²×C₃₇	#41	1	4	yes	—
130	C₂³×C₃₇	—	4	2	no	—
131	C₂³×C₃₇	—	4	2	no	—
132	C₂³×C₃₇	—	4	2	no	—
133	C₂³×C₃₇	—	4	2	no	—
134	C₂³×C₃₇	—	4	2	no	—
135	C₂³×C₃₇	—	4	2	no	—
136	C₂³×C₃₇	—	4	2	no	—
137	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
138	Q₈×C₃₇	—	4	8	no	—
139	Q₈×C₃₇	—	4	4	no	—
140	Q₈×C₃₇	—	4	4	no	—
141	D₄×C₃₇	—	4	4	no	—
142	D₄×C₃₇	—	4	4	no	—
143	D₄×C₃₇	—	8	4	no	—
144	D₄×C₃₇	—	8	4	no	—
145	C₂×C₄×C₃₇	—	2	1	no	—
146	C₂×C₄×C₃₇	—	2	1	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	1	no	—
151	C₂×C₄×C₃₇	—	2	4	no	—
152	C₂×C₄×C₃₇	—	2	1	no	—
153	C₂×C₄×C₃₇	—	2	1	no	—
154	C₂×C₄×C₃₇	—	2	1	no	—
155	C₂×C₄×C₃₇	—	2	1	no	—
156	C₂×C₄×C₃₇	—	2	1	no	—
157	C₂×C₄×C₃₇	—	2	1	no	—
158	C₂×C₄×C₃₇	—	4	2	no	—
159	C₂×C₄×C₃₇	—	4	2	no	—
160	C₂×C₄×C₃₇	—	4	2	no	—
161	C₂×C₄×C₃₇	—	4	2	no	—
162	C₂×C₄×C₃₇	—	4	2	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	#121	1	2	yes	—
167	C₂×C₄×C₃₇	#121	1	2	yes	—
168	C₂×C₄×C₃₇	#124	1	2	yes	—
169	C₂×C₄×C₃₇	#124	1	2	yes	—
170	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
171	C₂×C₄×C₃₇	#137	1	2	yes	—
172	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
174	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
176	C₈×C₃₇	—	4	4	no	—
177	#28754	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂²×C₃₇	—	8	2	no	—
179	C₂²×C₃₇	—	8	2	no	—
180	C₂²×C₃₇	—	8	2	no	—
181	C₂²×C₃₇	—	8	2	no	—
182	C₂²×C₃₇	—	8	2	no	—
183	C₂²×C₃₇	—	8	2	no	—
184	C₂²×C₃₇	—	8	2	no	—
185	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
186	C₂²×C₃₇	C₂×#124	1	1	yes	characteristic
187	C₂²×C₃₇	#535	1	1	yes	characteristic
188	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
190	C₂²×C₃₇	#575	1	1	yes	characteristic
191	C₂²×C₃₇	#575	1	1	yes	characteristic
192	C₄×C₃₇	—	2	2	no	—
193	C₄×C₃₇	—	2	2	no	—
194	C₄×C₃₇	—	2	2	no	—
195	C₄×C₃₇	—	4	1	no	—
196	C₄×C₃₇	—	4	1	no	—
197	C₄×C₃₇	—	4	4	no	—
198	C₄×C₃₇	—	8	2	no	—
199	C₄×C₃₇	—	8	2	no	—
200	C₄×C₃₇	#489	1	4	yes	complemented
201	C₄×C₃₇	#550	1	2	yes	—
202	C₄×C₃₇	#559	1	2	yes	—
203	C₂×#489	C₂×C₃₇	1	2	yes	complemented
204	#2858	C₂×C₃₇	1	1	yes	characteristic
205	C₄×C₄⋊Q₈	C₂×C₃₇	1	1	yes	characteristic, complemented
206	#2042	C₂×C₃₇	1	4	yes	complemented
207	#1982	C₂×C₃₇	1	2	yes	—
208	#1981	C₂×C₃₇	1	2	yes	complemented
209	#1959	C₂×C₃₇	1	2	yes	complemented
210	#1767	C₂×C₃₇	1	1	yes	characteristic, complemented
211	C₂×C₃₇	—	16	2	no	—
212	C₂×C₃₇	#2548	1	1	yes	characteristic
213	C₂×C₃₇	#3036	1	1	yes	characteristic
214	C₂×C₃₇	#3037	1	1	yes	characteristic
215	C₂×C₃₇	C₂×#489	1	1	yes	characteristic
216	C₂×C₃₇	#3140	1	1	yes	characteristic
217	C₂×C₃₇	#3214	1	1	yes	characteristic
218	C₂×C₃₇	#3216	1	1	yes	characteristic
219	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
220	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
221	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
222	C₂×#124	C₂²×C₃₇	1	2	yes	—
223	C₂×#124	C₂²×C₃₇	1	2	yes	—
224	C₂×C₄×Q₈	—	2	1	no	—
225	#489	—	2	8	no	—
226	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
227	C₂×#103	C₂²×C₃₇	1	4	yes	—
228	C₂×#103	C₂²×C₃₇	1	4	yes	—
229	C₂×#102	C₂²×C₃₇	1	4	yes	—
230	C₂×#102	C₂²×C₃₇	1	4	yes	—
231	C₂×#97	C₂²×C₃₇	1	2	yes	—
232	#391	—	2	1	no	—
233	#390	—	2	1	no	—
234	#390	—	2	1	no	—
235	#390	—	2	1	no	—
236	#390	—	2	1	no	—
237	#389	—	2	1	no	—
238	#389	C₂²×C₃₇	1	2	yes	—
239	#384	C₂²×C₃₇	1	1	yes	characteristic
240	C₄×C₄⋊C₄	—	2	1	no	—
241	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
242	C₄³	C₂²×C₃₇	1	1	yes	characteristic
243	#336	C₂²×C₃₇	1	2	yes	—
244	C₃₇	#28754	1	1	yes	characteristic, direct product factor, Sylow
245	C₂²×Q₈	—	2	1	no	—
246	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
250	C₂²×C₈	C₂³×C₃₇	1	4	yes	—
251	C₄⋊Q₈	—	2	2	no	—
252	C₄⋊Q₈	—	2	4	no	—
253	C₄⋊Q₈	D₄×C₃₇	1	4	yes	complemented
254	#127	—	2	4	no	—
255	#124	—	2	4	no	—
256	#124	—	2	4	no	—
257	#124	—	4	4	no	—
258	C₄×Q₈	—	4	4	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
273	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
274	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
275	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
276	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
279	C₄⋊C₈	—	2	4	no	—
280	#103	—	2	8	no	—
281	#103	—	4	4	no	—
282	#102	—	2	8	no	—
283	#102	—	4	4	no	—
284	#97	—	2	4	no	—
285	#95	—	2	2	no	—
286	#95	—	2	2	no	—
287	C₂⁴	—	2	2	no	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	4	no	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	—	4	2	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
314	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	4	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
328	C₂²⋊C₄	—	4	4	no	—
329	C₂²⋊C₄	—	4	4	no	—
330	C₂²⋊C₄	—	4	4	no	—
331	C₂²⋊C₄	—	4	4	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	4	1	no	—
336	C₄²	—	4	1	no	—
337	C₄²	—	4	4	no	—
338	C₄²	C₂×D₄×C₃₇	1	2	yes	—
339	C₄²	#41×C₃₇	1	2	yes	—
340	C₄²	#41×C₃₇	1	4	yes	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
349	Q₈	—	4	8	no	—
350	Q₈	—	4	4	no	—
351	Q₈	—	4	4	no	—
352	D₄	—	4	4	no	—
353	D₄	—	4	4	no	—
354	D₄	—	8	4	no	—
355	D₄	—	8	4	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	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	#121×C₃₇	1	2	yes	—
378	C₂×C₄	#121×C₃₇	1	2	yes	—
379	C₂×C₄	#124×C₃₇	1	2	yes	—
380	C₂×C₄	#124×C₃₇	1	2	yes	—
381	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
382	C₂×C₄	#137×C₃₇	1	2	yes	—
383	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
384	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
385	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
386	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
387	C₈	—	4	4	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	8	2	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
396	C₂²	C₂×#124×C₃₇	1	1	yes	characteristic
397	C₂²	C₃₇×#535	1	1	yes	characteristic
398	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
399	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
400	C₂²	C₃₇×#575	1	1	yes	characteristic
401	C₂²	C₃₇×#575	1	1	yes	characteristic
402	C₄	—	2	2	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	—	4	1	no	—
406	C₄	—	4	1	no	—
407	C₄	—	4	4	no	—
408	C₄	—	8	2	no	—
409	C₄	—	8	2	no	—
410	C₄	C₃₇×#489	1	4	yes	complemented
411	C₄	C₃₇×#550	1	2	yes	—
412	C₄	C₃₇×#559	1	2	yes	—
413	C₂	—	16	2	no	—
414	C₂	C₃₇×#2548	1	1	yes	characteristic
415	C₂	C₃₇×#3036	1	1	yes	characteristic
416	C₂	C₃₇×#3037	1	1	yes	characteristic
417	C₂	C₂×C₃₇×#489	1	1	yes	characteristic
418	C₂	C₃₇×#3140	1	1	yes	characteristic
419	C₂	C₃₇×#3214	1	1	yes	characteristic
420	C₂	C₃₇×#3216	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×#127×C₃₇	C₂²
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×#489	C₂	semidirect
3. C₄×C₄⋊Q₈×C₃₇	C₂	semidirect
4. C₃₇×#2042	C₂	semidirect
6. C₃₇×#1981	C₂	semidirect
7. C₃₇×#1959	C₂	semidirect
8. C₃₇×#1767	C₂	semidirect
42. C₄⋊Q₈×C₃₇	D₄	semidirect
177. #28754	C₃₇	direct (N × H)
200. C₄×C₃₇	#489	semidirect
203. C₂×#489	C₂×C₃₇	semidirect
205. C₄×C₄⋊Q₈	C₂×C₃₇	semidirect
206. #2042	C₂×C₃₇	semidirect
208. #1981	C₂×C₃₇	semidirect
209. #1959	C₂×C₃₇	semidirect
210. #1767	C₂×C₃₇	semidirect
244. C₃₇	#28754	direct (N × H)
253. C₄⋊Q₈	D₄×C₃₇	semidirect
410. C₄	C₃₇×#489	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#489	2
C₃₇×#2858	2
C₄×C₄⋊Q₈×C₃₇	2
C₃₇×#2042	2
C₃₇×#1982	2
C₃₇×#1981	2
C₃₇×#1959	2
C₃₇×#1767	2
#28754	37

Subgroups — C37×#28754 #22650007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28754 #22650007