Subgroups — C₃₇×#28458 #22649711

Order 9472.

1470 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#493	C₂	1	2	yes	maximal, complemented
3	C₂×C₃₇×#459	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×D₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2541	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2011	C₂	1	4	yes	maximal, complemented
7	C₃₇×#1970	C₂	1	2	yes	maximal, complemented
8	C₈×C₄⋊C₄×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₈×C₃₇	C₂²	1	2	yes	—
10	C₂²×D₈×C₃₇	C₂²	1	4	yes	—
11	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
12	C₂²×D₈×C₃₇	C₂²	1	2	yes	—
13	C₂×#127×C₃₇	C₂²	1	2	yes	—
14	C₂×#127×C₃₇	C₂²	1	4	yes	—
15	C₂×#121×C₃₇	—	2	4	no	—
16	C₂×C₄×D₄×C₃₇	C₂²	1	2	yes	—
17	C₃₇×#493	—	2	8	no	—
18	C₃₇×#493	—	2	4	no	—
19	C₃₇×#459	—	2	8	no	—
20	C₄×D₈×C₃₇	—	2	4	no	—
21	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×#102×C₃₇	C₂²	1	2	yes	—
24	C₂×#102×C₃₇	C₂²	1	4	yes	—
25	C₂×C₄×C₈×C₃₇	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
27	C₃₇×#392	—	2	4	no	—
28	C₃₇×#390	C₂²	1	4	yes	—
29	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
30	C₃₇×#336	C₂²	1	2	yes	—
31	C₂²×D₄×C₃₇	—	2	2	no	—
32	C₂²×D₄×C₃₇	—	2	8	no	—
33	C₂²×D₄×C₃₇	—	2	2	no	—
34	C₂²×D₄×C₃₇	C₂³	1	4	yes	—
35	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
36	C₂³×C₄×C₃₇	—	2	2	no	—
37	C₂×D₈×C₃₇	—	2	8	no	—
38	C₂×D₈×C₃₇	—	2	2	no	—
39	C₂×D₈×C₃₇	—	2	8	no	—
40	C₂×D₈×C₃₇	—	2	4	no	—
41	C₂×D₈×C₃₇	—	2	4	no	—
42	C₂×D₈×C₃₇	—	2	4	no	—
43	C₂×D₈×C₃₇	—	2	2	no	—
44	C₂×D₈×C₃₇	—	2	4	no	—
45	C₂×D₈×C₃₇	—	4	4	no	—
46	C₂×D₈×C₃₇	—	4	2	no	—
47	C₂×D₈×C₃₇	—	4	2	no	—
48	C₂×D₈×C₃₇	D₄	1	4	yes	complemented
49	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
51	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
52	#127×C₃₇	—	2	8	no	—
53	#127×C₃₇	—	2	4	no	—
54	#127×C₃₇	—	2	4	no	—
55	#127×C₃₇	—	4	4	no	—
56	#121×C₃₇	—	4	16	no	—
57	C₄×D₄×C₃₇	—	2	4	no	—
58	C₄×D₄×C₃₇	—	2	4	no	—
59	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₃₇	—	2	8	no	—
62	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
63	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
64	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
65	#107×C₃₇	—	2	2	no	—
66	C₄⋊C₈×C₃₇	D₄	1	4	yes	complemented
67	#102×C₃₇	—	2	4	no	—
68	#102×C₃₇	—	2	8	no	—
69	C₄×C₈×C₃₇	—	2	4	no	—
70	C₄×C₈×C₃₇	D₄	1	4	yes	complemented
71	#95×C₃₇	D₄	1	2	yes	—
72	C₂⁴×C₃₇	—	2	2	no	—
73	C₂⁴×C₃₇	—	2	4	no	—
74	C₂×D₄×C₃₇	—	2	2	no	—
75	C₂×D₄×C₃₇	—	2	2	no	—
76	C₂×D₄×C₃₇	—	2	4	no	—
77	C₂×D₄×C₃₇	—	2	4	no	—
78	C₂×D₄×C₃₇	—	2	4	no	—
79	C₂×D₄×C₃₇	—	2	2	no	—
80	C₂×D₄×C₃₇	—	2	4	no	—
81	C₂×D₄×C₃₇	—	2	2	no	—
82	C₂×D₄×C₃₇	—	2	2	no	—
83	C₂×D₄×C₃₇	—	2	4	no	—
84	C₂×D₄×C₃₇	—	2	4	no	—
85	C₂×D₄×C₃₇	—	4	16	no	—
86	C₂×D₄×C₃₇	—	4	4	no	—
87	C₂×D₄×C₃₇	—	4	4	no	—
88	C₂×D₄×C₃₇	—	4	16	no	—
89	C₂×D₄×C₃₇	—	4	8	no	—
90	C₂×D₄×C₃₇	—	8	8	no	—
91	C₂×D₄×C₃₇	—	8	4	no	—
92	C₂×D₄×C₃₇	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₃₇	—	2	2	no	—
94	C₂²×C₄×C₃₇	—	4	4	no	—
95	C₂²×C₄×C₃₇	—	4	8	no	—
96	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₃₇	C₂×D₄	1	4	yes	—
98	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
100	D₈×C₃₇	—	2	8	no	—
101	D₈×C₃₇	—	4	16	no	—
102	D₈×C₃₇	—	4	8	no	—
103	D₈×C₃₇	—	4	8	no	—
104	C₂×C₈×C₃₇	—	2	2	no	—
105	C₂×C₈×C₃₇	—	2	1	no	—
106	C₂×C₈×C₃₇	—	2	1	no	—
107	C₂×C₈×C₃₇	—	2	2	no	—
108	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
110	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₃₇	#41	1	2	yes	—
113	C₄⋊C₄×C₃₇	—	2	2	no	—
114	C₄⋊C₄×C₃₇	—	2	2	no	—
115	C₄⋊C₄×C₃₇	D₈	1	8	yes	complemented
116	C₂²⋊C₄×C₃₇	—	4	4	no	—
117	C₂²⋊C₄×C₃₇	—	4	16	no	—
118	C₄²×C₃₇	—	2	2	no	—
119	C₄²×C₃₇	—	2	2	no	—
120	C₄²×C₃₇	C₂×D₄	1	2	yes	—
121	C₄²×C₃₇	C₂×D₄	1	2	yes	—
122	C₂³×C₃₇	—	2	4	no	—
123	C₂³×C₃₇	—	4	2	no	—
124	C₂³×C₃₇	—	4	2	no	—
125	C₂³×C₃₇	—	4	4	no	—
126	C₂³×C₃₇	—	4	4	no	—
127	C₂³×C₃₇	—	4	4	no	—
128	C₂³×C₃₇	—	4	4	no	—
129	C₂³×C₃₇	—	4	4	no	—
130	C₂³×C₃₇	—	4	8	no	—
131	C₂³×C₃₇	—	4	8	no	—
132	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
133	D₄×C₃₇	—	2	4	no	—
134	D₄×C₃₇	—	2	4	no	—
135	D₄×C₃₇	—	4	4	no	—
136	D₄×C₃₇	—	4	2	no	—
137	D₄×C₃₇	—	4	4	no	—
138	D₄×C₃₇	—	4	4	no	—
139	D₄×C₃₇	—	4	2	no	—
140	D₄×C₃₇	—	4	4	no	—
141	D₄×C₃₇	—	8	32	no	—
142	D₄×C₃₇	—	8	8	no	—
143	D₄×C₃₇	—	8	8	no	—
144	C₂×C₄×C₃₇	—	2	4	no	—
145	C₂×C₄×C₃₇	—	2	2	no	—
146	C₂×C₄×C₃₇	—	2	4	no	—
147	C₂×C₄×C₃₇	—	4	2	no	—
148	C₂×C₄×C₃₇	—	4	4	no	—
149	C₂×C₄×C₃₇	—	8	8	no	—
150	C₂×C₄×C₃₇	#127	1	2	yes	—
151	C₂×C₄×C₃₇	#127	1	2	yes	—
152	C₂×C₄×C₃₇	C₂×D₈	1	8	yes	—
153	C₂×C₄×C₃₇	C₂×D₈	1	4	yes	—
154	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
159	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
160	C₈×C₃₇	—	2	2	no	—
161	C₈×C₃₇	—	2	4	no	—
162	C₈×C₃₇	#121	1	4	yes	complemented
163	#28458	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂²×C₃₇	—	4	8	no	—
165	C₂²×C₃₇	—	4	4	no	—
166	C₂²×C₃₇	—	8	4	no	—
167	C₂²×C₃₇	—	8	2	no	—
168	C₂²×C₃₇	—	8	2	no	—
169	C₂²×C₃₇	—	8	8	no	—
170	C₂²×C₃₇	—	8	4	no	—
171	C₂²×C₃₇	—	8	4	no	—
172	C₂²×C₃₇	—	8	8	no	—
173	C₂²×C₃₇	—	8	4	no	—
174	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
175	C₂²×C₃₇	D₄²	1	1	yes	characteristic
176	C₂²×C₃₇	#550	1	1	yes	characteristic
177	C₂²×C₃₇	C₂²×D₈	1	2	yes	—
178	C₂²×C₃₇	#576	1	2	yes	—
179	C₄×C₃₇	—	2	2	no	—
180	C₄×C₃₇	—	2	8	no	—
181	C₄×C₃₇	—	8	2	no	—
182	C₄×C₃₇	#493	1	4	yes	complemented
183	C₄×C₃₇	C₂×#121	1	1	yes	characteristic
184	C₄×C₃₇	#535	1	1	yes	characteristic
185	C₄×C₃₇	D₄²	1	1	yes	characteristic
186	C₄×C₃₇	#550	1	1	yes	characteristic
187	C₂×#493	C₂×C₃₇	1	1	yes	characteristic, complemented
188	C₂×#493	C₂×C₃₇	1	2	yes	complemented
189	C₂×#459	C₂×C₃₇	1	2	yes	complemented
190	C₂×C₄×D₈	C₂×C₃₇	1	1	yes	characteristic, complemented
191	#2541	C₂×C₃₇	1	2	yes	complemented
192	#2011	C₂×C₃₇	1	4	yes	complemented
193	#1970	C₂×C₃₇	1	2	yes	complemented
194	C₈×C₄⋊C₄	C₂×C₃₇	1	1	yes	characteristic, complemented
195	C₂×C₃₇	—	8	4	no	—
196	C₂×C₃₇	—	16	4	no	—
197	C₂×C₃₇	#2541	1	1	yes	characteristic
198	C₂×C₃₇	C₂×#493	1	1	yes	characteristic
199	C₂×C₃₇	#3155	1	1	yes	characteristic
200	C₂×C₃₇	D₄×D₈	1	2	yes	—
201	C₂×C₃₇	#3391	1	2	yes	—
202	C₂²×D₈	C₂²×C₃₇	1	2	yes	—
203	C₂²×D₈	C₂²×C₃₇	1	4	yes	—
204	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
205	C₂²×D₈	C₂²×C₃₇	1	2	yes	—
206	C₂×#127	C₂²×C₃₇	1	2	yes	—
207	C₂×#127	C₂²×C₃₇	1	4	yes	—
208	C₂×#121	—	2	4	no	—
209	C₂×C₄×D₄	C₂²×C₃₇	1	2	yes	—
210	#493	—	2	8	no	—
211	#493	—	2	4	no	—
212	#459	—	2	8	no	—
213	C₄×D₈	—	2	4	no	—
214	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
215	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
216	C₂×#102	C₂²×C₃₇	1	2	yes	—
217	C₂×#102	C₂²×C₃₇	1	4	yes	—
218	C₂×C₄×C₈	C₂²×C₃₇	1	2	yes	—
219	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
220	#392	—	2	4	no	—
221	#390	C₂²×C₃₇	1	4	yes	—
222	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
223	#336	C₂²×C₃₇	1	2	yes	—
224	C₃₇	#28458	1	1	yes	characteristic, direct product factor, Sylow
225	C₂²×D₄	—	2	2	no	—
226	C₂²×D₄	—	2	8	no	—
227	C₂²×D₄	—	2	2	no	—
228	C₂²×D₄	C₂³×C₃₇	1	4	yes	—
229	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
230	C₂³×C₄	—	2	2	no	—
231	C₂×D₈	—	2	8	no	—
232	C₂×D₈	—	2	2	no	—
233	C₂×D₈	—	2	8	no	—
234	C₂×D₈	—	2	4	no	—
235	C₂×D₈	—	2	4	no	—
236	C₂×D₈	—	2	4	no	—
237	C₂×D₈	—	2	2	no	—
238	C₂×D₈	—	2	4	no	—
239	C₂×D₈	—	4	4	no	—
240	C₂×D₈	—	4	2	no	—
241	C₂×D₈	—	4	2	no	—
242	C₂×D₈	D₄×C₃₇	1	4	yes	complemented
243	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
245	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
246	#127	—	2	8	no	—
247	#127	—	2	4	no	—
248	#127	—	2	4	no	—
249	#127	—	4	4	no	—
250	#121	—	4	16	no	—
251	C₄×D₄	—	2	4	no	—
252	C₄×D₄	—	2	4	no	—
253	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	8	no	—
257	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
258	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
259	#107	—	2	2	no	—
260	C₄⋊C₈	D₄×C₃₇	1	4	yes	complemented
261	#102	—	2	4	no	—
262	#102	—	2	8	no	—
263	C₄×C₈	—	2	4	no	—
264	C₄×C₈	D₄×C₃₇	1	4	yes	complemented
265	#95	D₄×C₃₇	1	2	yes	—
266	C₂⁴	—	2	2	no	—
267	C₂⁴	—	2	4	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	2	4	no	—
271	C₂×D₄	—	2	4	no	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	4	16	no	—
280	C₂×D₄	—	4	4	no	—
281	C₂×D₄	—	4	4	no	—
282	C₂×D₄	—	4	16	no	—
283	C₂×D₄	—	4	8	no	—
284	C₂×D₄	—	8	8	no	—
285	C₂×D₄	—	8	4	no	—
286	C₂×D₄	C₂×D₄×C₃₇	1	4	yes	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	4	4	no	—
289	C₂²×C₄	—	4	8	no	—
290	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₃₇	1	4	yes	—
292	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
293	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
294	D₈	—	2	8	no	—
295	D₈	—	4	16	no	—
296	D₈	—	4	8	no	—
297	D₈	—	4	8	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
303	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
304	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
305	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
306	C₂×C₈	#41×C₃₇	1	2	yes	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	D₈×C₃₇	1	8	yes	complemented
310	C₂²⋊C₄	—	4	4	no	—
311	C₂²⋊C₄	—	4	16	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	C₂×D₄×C₃₇	1	2	yes	—
315	C₄²	C₂×D₄×C₃₇	1	2	yes	—
316	C₂³	—	2	4	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	4	no	—
320	C₂³	—	4	4	no	—
321	C₂³	—	4	4	no	—
322	C₂³	—	4	4	no	—
323	C₂³	—	4	4	no	—
324	C₂³	—	4	8	no	—
325	C₂³	—	4	8	no	—
326	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
327	D₄	—	2	4	no	—
328	D₄	—	2	4	no	—
329	D₄	—	4	4	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	4	no	—
332	D₄	—	4	4	no	—
333	D₄	—	4	2	no	—
334	D₄	—	4	4	no	—
335	D₄	—	8	32	no	—
336	D₄	—	8	8	no	—
337	D₄	—	8	8	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	8	8	no	—
344	C₂×C₄	#127×C₃₇	1	2	yes	—
345	C₂×C₄	#127×C₃₇	1	2	yes	—
346	C₂×C₄	C₂×D₈×C₃₇	1	8	yes	—
347	C₂×C₄	C₂×D₈×C₃₇	1	4	yes	—
348	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
349	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
350	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
351	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
352	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
353	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
354	C₈	—	2	2	no	—
355	C₈	—	2	4	no	—
356	C₈	#121×C₃₇	1	4	yes	complemented
357	C₂²	—	4	8	no	—
358	C₂²	—	4	4	no	—
359	C₂²	—	8	4	no	—
360	C₂²	—	8	2	no	—
361	C₂²	—	8	2	no	—
362	C₂²	—	8	8	no	—
363	C₂²	—	8	4	no	—
364	C₂²	—	8	4	no	—
365	C₂²	—	8	8	no	—
366	C₂²	—	8	4	no	—
367	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
368	C₂²	D₄²×C₃₇	1	1	yes	characteristic
369	C₂²	C₃₇×#550	1	1	yes	characteristic
370	C₂²	C₂²×D₈×C₃₇	1	2	yes	—
371	C₂²	C₃₇×#576	1	2	yes	—
372	C₄	—	2	2	no	—
373	C₄	—	2	8	no	—
374	C₄	—	8	2	no	—
375	C₄	C₃₇×#493	1	4	yes	complemented
376	C₄	C₂×#121×C₃₇	1	1	yes	characteristic
377	C₄	C₃₇×#535	1	1	yes	characteristic
378	C₄	D₄²×C₃₇	1	1	yes	characteristic
379	C₄	C₃₇×#550	1	1	yes	characteristic
380	C₂	—	8	4	no	—
381	C₂	—	16	4	no	—
382	C₂	C₃₇×#2541	1	1	yes	characteristic
383	C₂	C₂×C₃₇×#493	1	1	yes	characteristic
384	C₂	C₃₇×#3155	1	1	yes	characteristic
385	C₂	D₄×D₈×C₃₇	1	2	yes	—
386	C₂	C₃₇×#3391	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₄×C₄⋊C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#493	C₂	semidirect
2. C₂×C₃₇×#493	C₂	semidirect
3. C₂×C₃₇×#459	C₂	semidirect
4. C₂×C₄×D₈×C₃₇	C₂	semidirect
5. C₃₇×#2541	C₂	semidirect
6. C₃₇×#2011	C₂	semidirect
7. C₃₇×#1970	C₂	semidirect
8. C₈×C₄⋊C₄×C₃₇	C₂	semidirect
48. C₂×D₈×C₃₇	D₄	semidirect
66. C₄⋊C₈×C₃₇	D₄	semidirect
70. C₄×C₈×C₃₇	D₄	semidirect
115. C₄⋊C₄×C₃₇	D₈	semidirect
162. C₈×C₃₇	#121	semidirect
163. #28458	C₃₇	direct (N × H)
182. C₄×C₃₇	#493	semidirect
187. C₂×#493	C₂×C₃₇	semidirect
188. C₂×#493	C₂×C₃₇	semidirect
189. C₂×#459	C₂×C₃₇	semidirect
190. C₂×C₄×D₈	C₂×C₃₇	semidirect
191. #2541	C₂×C₃₇	semidirect
192. #2011	C₂×C₃₇	semidirect
193. #1970	C₂×C₃₇	semidirect
194. C₈×C₄⋊C₄	C₂×C₃₇	semidirect
224. C₃₇	#28458	direct (N × H)
242. C₂×D₈	D₄×C₃₇	semidirect
260. C₄⋊C₈	D₄×C₃₇	semidirect
264. C₄×C₈	D₄×C₃₇	semidirect
309. C₄⋊C₄	D₈×C₃₇	semidirect
356. C₈	#121×C₃₇	semidirect
375. C₄	C₃₇×#493	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#493	2
C₂×C₃₇×#459	2
C₂×C₄×D₈×C₃₇	2
C₃₇×#2541	2
C₃₇×#2011	2
C₃₇×#1970	2
C₈×C₄⋊C₄×C₃₇	2
#28458	37

Subgroups — C37×#28458 #22649711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28458 #22649711