Subgroups — C₃₇×#29944 #22651197

Order 9472.

696 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#2851	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#2285	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2100	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2084	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2083	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2077	C₂	1	2	yes	maximal
8	C₃₇×#2075	C₂	1	2	yes	maximal
9	C₃₇×#1989	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1949	C₂	1	2	yes	maximal, complemented
11	C₃₇×#1797	C₂	1	1	yes	maximal, characteristic
12	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×#117×C₃₇	—	2	1	no	—
14	C₂²×C₄²×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×#107×C₃₇	C₂²	1	2	yes	—
16	C₂×#106×C₃₇	C₂²	1	2	yes	—
17	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
18	C₂×C₂²⋊C₈×C₃₇	C₂²	1	2	yes	—
19	C₃₇×#389	C₂²	1	1	yes	characteristic
20	C₃₇×#389	C₂²	1	1	yes	characteristic
21	C₃₇×#387	—	2	1	no	—
22	C₃₇×#387	—	2	1	no	—
23	C₃₇×#385	—	2	1	no	—
24	C₃₇×#385	—	2	1	no	—
25	C₃₇×#384	C₂²	1	1	yes	characteristic
26	C₃₇×#384	C₂²	1	1	yes	characteristic
27	C₃₇×#382	—	2	1	no	—
28	C₃₇×#382	C₂²	1	1	yes	characteristic
29	C₃₇×#380	—	2	1	no	—
30	C₃₇×#380	C₂²	1	2	yes	—
31	C₃₇×#380	C₂²	1	1	yes	characteristic
32	C₃₇×#380	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₃₇	—	2	1	no	—
34	C₄×C₄⋊C₄×C₃₇	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×#340	C₂²	1	2	yes	—
39	C₃₇×#340	C₂²	1	2	yes	—
40	C₃₇×#340	C₂²	1	2	yes	—
41	C₃₇×#336	C₂²	1	1	yes	characteristic
42	C₃₇×#336	C₂²	1	1	yes	characteristic
43	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
47	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
48	#125×C₃₇	—	2	4	no	—
49	#117×C₃₇	—	4	4	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	1	no	—
54	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
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×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
67	C₂×C₄²×C₃₇	—	2	4	no	—
68	C₂×C₄²×C₃₇	—	2	2	no	—
69	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
73	#107×C₃₇	—	4	2	no	—
74	#106×C₃₇	—	4	2	no	—
75	C₄⋊C₈×C₃₇	—	2	4	no	—
76	C₂²⋊C₈×C₃₇	—	4	2	no	—
77	#95×C₃₇	—	2	2	no	—
78	#95×C₃₇	—	2	2	no	—
79	#95×C₃₇	—	2	1	no	—
80	#95×C₃₇	—	2	1	no	—
81	#95×C₃₇	—	2	1	no	—
82	#95×C₃₇	—	2	1	no	—
83	#95×C₃₇	—	2	1	no	—
84	#95×C₃₇	—	2	1	no	—
85	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₃₇	—	2	2	no	—
87	C₂²×C₄×C₃₇	—	2	2	no	—
88	C₂²×C₄×C₃₇	—	2	2	no	—
89	C₂²×C₄×C₃₇	—	2	2	no	—
90	C₂²×C₄×C₃₇	—	2	2	no	—
91	C₂²×C₄×C₃₇	—	2	2	no	—
92	C₂²×C₄×C₃₇	—	2	1	no	—
93	C₂²×C₄×C₃₇	—	2	2	no	—
94	C₂²×C₄×C₃₇	—	2	1	no	—
95	C₂²×C₄×C₃₇	—	2	1	no	—
96	C₂²×C₄×C₃₇	—	2	1	no	—
97	C₂²×C₄×C₃₇	—	2	2	no	—
98	C₂²×C₄×C₃₇	—	2	2	no	—
99	C₂²×C₄×C₃₇	—	2	1	no	—
100	C₂²×C₄×C₃₇	—	2	1	no	—
101	C₂²×C₄×C₃₇	—	4	1	no	—
102	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
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	C₂×C₈×C₃₇	—	2	2	no	—
113	C₂×C₈×C₃₇	—	2	2	no	—
114	C₄⋊C₄×C₃₇	—	2	2	no	—
115	C₄⋊C₄×C₃₇	—	2	2	no	—
116	C₄⋊C₄×C₃₇	—	2	1	no	—
117	C₄⋊C₄×C₃₇	—	2	2	no	—
118	C₄⋊C₄×C₃₇	—	2	1	no	—
119	C₄⋊C₄×C₃₇	—	2	4	no	—
120	C₄⋊C₄×C₃₇	—	2	2	no	—
121	C₄⋊C₄×C₃₇	—	2	1	no	—
122	C₄⋊C₄×C₃₇	—	2	1	no	—
123	C₄⋊C₄×C₃₇	—	4	2	no	—
124	C₄⋊C₄×C₃₇	—	4	2	no	—
125	C₄⋊C₄×C₃₇	—	4	2	no	—
126	C₄⋊C₄×C₃₇	—	4	2	no	—
127	C₄⋊C₄×C₃₇	—	4	2	no	—
128	C₄⋊C₄×C₃₇	—	4	2	no	—
129	C₄⋊C₄×C₃₇	—	4	2	no	—
130	C₄⋊C₄×C₃₇	—	4	2	no	—
131	C₂²⋊C₄×C₃₇	—	4	2	no	—
132	C₂²⋊C₄×C₃₇	—	4	2	no	—
133	C₂²⋊C₄×C₃₇	—	4	4	no	—
134	C₄²×C₃₇	—	2	2	no	—
135	C₄²×C₃₇	—	2	2	no	—
136	C₄²×C₃₇	—	2	2	no	—
137	C₄²×C₃₇	—	4	4	no	—
138	C₄²×C₃₇	#41	1	4	yes	—
139	C₂³×C₃₇	—	2	1	no	—
140	C₂³×C₃₇	—	2	1	no	—
141	C₂³×C₃₇	—	2	1	no	—
142	C₂³×C₃₇	—	2	1	no	—
143	C₂³×C₃₇	—	2	1	no	—
144	C₂³×C₃₇	—	2	1	no	—
145	C₂³×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
146	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₃₇	—	2	8	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	1	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	—	2	1	no	—
159	C₂×C₄×C₃₇	—	4	4	no	—
160	C₂×C₄×C₃₇	—	4	2	no	—
161	C₂×C₄×C₃₇	—	4	2	no	—
162	C₂×C₄×C₃₇	—	4	1	no	—
163	C₂×C₄×C₃₇	—	4	1	no	—
164	C₂×C₄×C₃₇	—	4	2	no	—
165	C₂×C₄×C₃₇	—	4	2	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	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	1	no	—
174	C₂×C₄×C₃₇	—	4	1	no	—
175	C₂×C₄×C₃₇	—	4	1	no	—
176	C₂×C₄×C₃₇	—	4	1	no	—
177	C₂×C₄×C₃₇	—	4	1	no	—
178	C₂×C₄×C₃₇	—	4	1	no	—
179	C₂×C₄×C₃₇	—	4	2	no	—
180	C₂×C₄×C₃₇	#123	1	2	yes	—
181	C₂×C₄×C₃₇	#123	1	2	yes	—
182	C₂×C₄×C₃₇	#135	1	2	yes	—
183	C₂×C₄×C₃₇	#137	1	2	yes	—
184	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
185	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
187	C₂×C₄×C₃₇	2₋¹⁺⁴	1	2	yes	—
188	C₈×C₃₇	—	4	2	no	—
189	C₈×C₃₇	—	4	2	no	—
190	#29944	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂²×C₃₇	—	2	2	no	—
192	C₂²×C₃₇	—	2	2	no	—
193	C₂²×C₃₇	—	2	2	no	—
194	C₂²×C₃₇	—	4	1	no	—
195	C₂²×C₃₇	—	4	1	no	—
196	C₂²×C₃₇	—	4	1	no	—
197	C₂²×C₃₇	—	4	1	no	—
198	C₂²×C₃₇	C₂×#123	1	1	yes	characteristic
199	C₂²×C₃₇	#536	1	1	yes	characteristic
200	C₂²×C₃₇	#537	1	1	yes	characteristic
201	C₂²×C₃₇	C₂×#135	1	1	yes	characteristic
202	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
204	C₂²×C₃₇	#575	1	1	yes	characteristic
205	C₄×C₃₇	—	2	2	no	—
206	C₄×C₃₇	—	2	2	no	—
207	C₄×C₃₇	—	2	2	no	—
208	C₄×C₃₇	—	2	2	no	—
209	C₄×C₃₇	—	4	1	no	—
210	C₄×C₃₇	—	8	1	no	—
211	C₄×C₃₇	—	8	1	no	—
212	C₄×C₃₇	—	8	2	no	—
213	C₄×C₃₇	—	8	2	no	—
214	C₄×C₃₇	—	8	1	no	—
215	C₄×C₃₇	—	8	1	no	—
216	C₄×C₃₇	#541	1	2	yes	—
217	C₄×C₃₇	#542	1	2	yes	—
218	#2851	C₂×C₃₇	1	1	yes	characteristic
219	#2285	C₂×C₃₇	1	1	yes	characteristic
220	#2100	C₂×C₃₇	1	1	yes	characteristic, complemented
221	#2100	C₂×C₃₇	1	1	yes	characteristic, complemented
222	#2084	C₂×C₃₇	1	1	yes	characteristic, complemented
223	#2083	C₂×C₃₇	1	1	yes	characteristic, complemented
224	#2077	C₂×C₃₇	1	2	yes	—
225	#2075	C₂×C₃₇	1	2	yes	—
226	#1989	C₂×C₃₇	1	2	yes	complemented
227	#1949	C₂×C₃₇	1	2	yes	complemented
228	#1797	C₂×C₃₇	1	1	yes	characteristic
229	C₂×C₃₇	—	4	2	no	—
230	C₂×C₃₇	#2625	1	1	yes	characteristic
231	C₂×C₃₇	#3091	1	1	yes	characteristic
232	C₂×C₃₇	#3092	1	1	yes	characteristic
233	C₂×C₃₇	#3231	1	1	yes	characteristic
234	C₂×C₃₇	#3234	1	1	yes	characteristic
235	C₂×C₃₇	#3247	1	1	yes	characteristic
236	C₂×C₃₇	#3252	1	1	yes	characteristic
237	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
238	C₂×#117	—	2	1	no	—
239	C₂²×C₄²	C₂²×C₃₇	1	1	yes	characteristic
240	C₂×#107	C₂²×C₃₇	1	2	yes	—
241	C₂×#106	C₂²×C₃₇	1	2	yes	—
242	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
243	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	—
244	#389	C₂²×C₃₇	1	1	yes	characteristic
245	#389	C₂²×C₃₇	1	1	yes	characteristic
246	#387	—	2	1	no	—
247	#387	—	2	1	no	—
248	#385	—	2	1	no	—
249	#385	—	2	1	no	—
250	#384	C₂²×C₃₇	1	1	yes	characteristic
251	#384	C₂²×C₃₇	1	1	yes	characteristic
252	#382	—	2	1	no	—
253	#382	C₂²×C₃₇	1	1	yes	characteristic
254	#380	—	2	1	no	—
255	#380	C₂²×C₃₇	1	1	yes	characteristic
256	#380	C₂²×C₃₇	1	2	yes	—
257	#380	C₂²×C₃₇	1	1	yes	characteristic
258	C₄×C₄⋊C₄	—	2	1	no	—
259	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
260	#340	C₂²×C₃₇	1	2	yes	—
261	#340	C₂²×C₃₇	1	2	yes	—
262	#340	C₂²×C₃₇	1	2	yes	—
263	#340	C₂²×C₃₇	1	2	yes	—
264	#340	C₂²×C₃₇	1	2	yes	—
265	#340	C₂²×C₃₇	1	2	yes	—
266	#336	C₂²×C₃₇	1	1	yes	characteristic
267	#336	C₂²×C₃₇	1	1	yes	characteristic
268	C₃₇	#29944	1	1	yes	characteristic, direct product factor, Sylow
269	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
270	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
271	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
273	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
274	#125	—	2	4	no	—
275	#117	—	4	4	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₄²	—	2	4	no	—
294	C₂×C₄²	—	2	2	no	—
295	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
296	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
297	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
299	#107	—	4	2	no	—
300	#106	—	4	2	no	—
301	C₄⋊C₈	—	2	4	no	—
302	C₂²⋊C₈	—	4	2	no	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	—	2	1	no	—
306	#95	—	2	1	no	—
307	#95	—	2	1	no	—
308	#95	—	2	1	no	—
309	#95	—	2	1	no	—
310	#95	—	2	1	no	—
311	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
333	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₂²⋊C₄	—	4	2	no	—
358	C₂²⋊C₄	—	4	2	no	—
359	C₂²⋊C₄	—	4	4	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	4	4	no	—
364	C₄²	#41×C₃₇	1	4	yes	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
372	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
373	C₂×C₄	—	2	8	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	#123×C₃₇	1	2	yes	—
407	C₂×C₄	#123×C₃₇	1	2	yes	—
408	C₂×C₄	#135×C₃₇	1	2	yes	—
409	C₂×C₄	#137×C₃₇	1	2	yes	—
410	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
411	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
412	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
413	C₂×C₄	2₋¹⁺⁴×C₃₇	1	2	yes	—
414	C₈	—	4	2	no	—
415	C₈	—	4	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	C₂×#123×C₃₇	1	1	yes	characteristic
424	C₂²	C₃₇×#536	1	1	yes	characteristic
425	C₂²	C₃₇×#537	1	1	yes	characteristic
426	C₂²	C₂×#135×C₃₇	1	1	yes	characteristic
427	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
428	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
429	C₂²	C₃₇×#575	1	1	yes	characteristic
430	C₄	—	2	2	no	—
431	C₄	—	2	2	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	4	1	no	—
435	C₄	—	8	2	no	—
436	C₄	—	8	2	no	—
437	C₄	—	8	1	no	—
438	C₄	—	8	1	no	—
439	C₄	—	8	1	no	—
440	C₄	—	8	1	no	—
441	C₄	C₃₇×#541	1	2	yes	—
442	C₄	C₃₇×#542	1	2	yes	—
443	C₂	—	4	2	no	—
444	C₂	C₃₇×#2625	1	1	yes	characteristic
445	C₂	C₃₇×#3091	1	1	yes	characteristic
446	C₂	C₃₇×#3092	1	1	yes	characteristic
447	C₂	C₃₇×#3231	1	1	yes	characteristic
448	C₂	C₃₇×#3234	1	1	yes	characteristic
449	C₂	C₃₇×#3247	1	1	yes	characteristic
450	C₂	C₃₇×#3252	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 ◁ C₂²×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₇×#2100	C₂	semidirect
4. C₃₇×#2100	C₂	semidirect
5. C₃₇×#2084	C₂	semidirect
6. C₃₇×#2083	C₂	semidirect
9. C₃₇×#1989	C₂	semidirect
10. C₃₇×#1949	C₂	semidirect
190. #29944	C₃₇	direct (N × H)
220. #2100	C₂×C₃₇	semidirect
221. #2100	C₂×C₃₇	semidirect
222. #2084	C₂×C₃₇	semidirect
223. #2083	C₂×C₃₇	semidirect
226. #1989	C₂×C₃₇	semidirect
227. #1949	C₂×C₃₇	semidirect
268. C₃₇	#29944	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×#2851	2
C₃₇×#2285	2
C₃₇×#2100	2
C₃₇×#2084	2
C₃₇×#2083	2
C₃₇×#2077	2
C₃₇×#2075	2
C₃₇×#1989	2
C₃₇×#1949	2
C₃₇×#1797	2
#29944	37

Subgroups — C37×#29944 #22651197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#29944 #22651197