Subgroups — C₃₇×#28449 #22649702

Order 9472.

1110 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#497	C₂	1	2	yes	maximal
2	C₂×C₃₇×#462	C₂	1	2	yes	maximal, complemented
3	C₂×C₃₇×#461	C₂	1	2	yes	maximal
4	C₃₇×#2868	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#124×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₃₇×#2016	C₂	1	2	yes	maximal, complemented
7	C₃₇×#2013	C₂	1	2	yes	maximal
8	C₃₇×#1960	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₃₇	C₂²	1	4	yes	—
11	C₂²×SD₁₆×C₃₇	C₂²	1	4	yes	—
12	C₂×C₄⋊Q₈×C₃₇	C₂²	1	2	yes	—
13	C₂×C₄⋊Q₈×C₃₇	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₃₇	C₂²	1	2	yes	—
15	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
18	C₃₇×#497	—	2	8	no	—
19	C₃₇×#462	—	2	8	no	—
20	C₃₇×#461	—	2	8	no	—
21	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
22	C₂×#103×C₃₇	C₂²	1	4	yes	—
23	C₂×#103×C₃₇	C₂²	1	4	yes	—
24	C₂×#97×C₃₇	C₂²	1	2	yes	—
25	C₃₇×#391	C₂²	1	1	yes	characteristic
26	C₃₇×#390	C₂²	1	1	yes	characteristic
27	C₃₇×#388	—	2	2	no	—
28	C₃₇×#384	—	2	2	no	—
29	C₃₇×#384	—	2	2	no	—
30	C₃₇×#382	C₂²	1	1	yes	characteristic
31	C₄×C₂²⋊C₄×C₃₇	—	2	2	no	—
32	C₄³×C₃₇	C₂²	1	1	yes	characteristic
33	C₃₇×#336	C₂²	1	2	yes	—
34	C₂²×Q₈×C₃₇	C₂³	1	4	yes	—
35	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
36	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₃₇	—	2	1	no	—
38	C₂×Q₁₆×C₃₇	—	2	8	no	—
39	C₂×Q₁₆×C₃₇	—	2	8	no	—
40	C₂×Q₁₆×C₃₇	—	4	4	no	—
41	C₂×SD₁₆×C₃₇	—	2	8	no	—
42	C₂×SD₁₆×C₃₇	—	2	8	no	—
43	C₂×SD₁₆×C₃₇	—	4	4	no	—
44	C₂²×C₈×C₃₇	C₂³	1	4	yes	—
45	C₄⋊Q₈×C₃₇	—	2	4	no	—
46	C₄⋊Q₈×C₃₇	—	2	4	no	—
47	C₄⋊Q₈×C₃₇	—	2	4	no	—
48	C₄⋊Q₈×C₃₇	—	2	4	no	—
49	C₄⋊Q₈×C₃₇	—	4	4	no	—
50	#124×C₃₇	—	2	2	no	—
51	#124×C₃₇	D₄	1	4	yes	—
52	C₄×Q₈×C₃₇	—	2	4	no	—
53	C₄×D₄×C₃₇	—	2	4	no	—
54	C₂×C₄⋊C₄×C₃₇	—	2	4	no	—
55	C₂×C₄⋊C₄×C₃₇	—	2	4	no	—
56	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
61	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
64	C₂×C₄²×C₃₇	—	2	1	no	—
65	C₂×C₄²×C₃₇	D₄	1	2	yes	—
66	C₂×C₄²×C₃₇	D₄	1	2	yes	—
67	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₃₇	D₄	1	8	yes	—
71	#103×C₃₇	—	2	8	no	—
72	#103×C₃₇	—	2	8	no	—
73	#97×C₃₇	—	2	4	no	—
74	#95×C₃₇	—	2	2	no	—
75	#95×C₃₇	—	2	2	no	—
76	C₂⁴×C₃₇	—	2	1	no	—
77	C₂×Q₈×C₃₇	—	2	1	no	—
78	C₂×Q₈×C₃₇	—	2	2	no	—
79	C₂×Q₈×C₃₇	—	2	4	no	—
80	C₂×Q₈×C₃₇	—	2	4	no	—
81	C₂×Q₈×C₃₇	—	2	4	no	—
82	C₂×Q₈×C₃₇	—	2	4	no	—
83	C₂×Q₈×C₃₇	—	2	2	no	—
84	C₂×Q₈×C₃₇	—	2	4	no	—
85	C₂×Q₈×C₃₇	—	2	4	no	—
86	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
87	C₂×D₄×C₃₇	—	2	2	no	—
88	C₂×D₄×C₃₇	—	2	1	no	—
89	C₂×D₄×C₃₇	—	2	2	no	—
90	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₃₇	—	2	1	no	—
92	C₂²×C₄×C₃₇	—	2	1	no	—
93	C₂²×C₄×C₃₇	—	2	1	no	—
94	C₂²×C₄×C₃₇	—	2	4	no	—
95	C₂²×C₄×C₃₇	—	4	2	no	—
96	C₂²×C₄×C₃₇	—	4	4	no	—
97	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
102	Q₁₆×C₃₇	—	4	16	no	—
103	SD₁₆×C₃₇	—	4	16	no	—
104	C₂×C₈×C₃₇	—	2	4	no	—
105	C₂×C₈×C₃₇	—	2	4	no	—
106	C₂×C₈×C₃₇	C₂×D₄	1	8	yes	—
107	C₄⋊C₄×C₃₇	—	2	2	no	—
108	C₄⋊C₄×C₃₇	—	2	2	no	—
109	C₄⋊C₄×C₃₇	—	4	8	no	—
110	C₄⋊C₄×C₃₇	—	4	8	no	—
111	C₄⋊C₄×C₃₇	—	4	2	no	—
112	C₄⋊C₄×C₃₇	—	4	4	no	—
113	C₄⋊C₄×C₃₇	—	4	4	no	—
114	C₂²⋊C₄×C₃₇	—	2	8	no	—
115	C₂²⋊C₄×C₃₇	—	4	2	no	—
116	C₂²⋊C₄×C₃₇	—	4	4	no	—
117	C₄²×C₃₇	—	2	4	no	—
118	C₄²×C₃₇	—	2	4	no	—
119	C₄²×C₃₇	—	2	2	no	—
120	C₄²×C₃₇	—	4	2	no	—
121	C₄²×C₃₇	C₂×D₄	1	2	yes	—
122	C₄²×C₃₇	C₂×D₄	1	4	yes	—
123	C₄²×C₃₇	#41	1	2	yes	—
124	C₂³×C₃₇	—	2	2	no	—
125	C₂³×C₃₇	—	4	1	no	—
126	C₂³×C₃₇	—	4	1	no	—
127	C₂³×C₃₇	—	4	2	no	—
128	C₂³×C₃₇	—	4	2	no	—
129	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
130	Q₈×C₃₇	—	2	4	no	—
131	Q₈×C₃₇	—	4	2	no	—
132	Q₈×C₃₇	—	4	4	no	—
133	Q₈×C₃₇	—	4	4	no	—
134	Q₈×C₃₇	—	4	4	no	—
135	Q₈×C₃₇	—	4	4	no	—
136	D₄×C₃₇	—	2	4	no	—
137	D₄×C₃₇	—	4	2	no	—
138	C₂×C₄×C₃₇	—	2	2	no	—
139	C₂×C₄×C₃₇	—	2	2	no	—
140	C₂×C₄×C₃₇	—	2	2	no	—
141	C₂×C₄×C₃₇	—	2	2	no	—
142	C₂×C₄×C₃₇	—	2	2	no	—
143	C₂×C₄×C₃₇	—	2	2	no	—
144	C₂×C₄×C₃₇	—	4	1	no	—
145	C₂×C₄×C₃₇	—	4	1	no	—
146	C₂×C₄×C₃₇	—	4	4	no	—
147	C₂×C₄×C₃₇	—	4	1	no	—
148	C₂×C₄×C₃₇	—	4	1	no	—
149	C₂×C₄×C₃₇	—	4	4	no	—
150	C₂×C₄×C₃₇	—	4	4	no	—
151	C₂×C₄×C₃₇	—	4	2	no	—
152	C₂×C₄×C₃₇	—	4	2	no	—
153	C₂×C₄×C₃₇	—	8	4	no	—
154	C₂×C₄×C₃₇	#121	1	4	yes	—
155	C₂×C₄×C₃₇	#127	1	2	yes	—
156	C₂×C₄×C₃₇	#127	1	2	yes	—
157	C₂×C₄×C₃₇	#137	1	4	yes	—
158	C₂×C₄×C₃₇	#137	1	4	yes	—
159	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
161	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
163	C₈×C₃₇	—	2	8	no	—
164	#28449	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂²×C₃₇	—	4	4	no	—
166	C₂²×C₃₇	—	4	2	no	—
167	C₂²×C₃₇	—	8	1	no	—
168	C₂²×C₃₇	—	8	1	no	—
169	C₂²×C₃₇	—	8	2	no	—
170	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
171	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
172	C₂²×C₃₇	#535	1	1	yes	characteristic
173	C₂²×C₃₇	C₂×#137	1	2	yes	—
174	C₂²×C₃₇	C₂×#137	1	2	yes	—
175	C₄×C₃₇	—	2	2	no	—
176	C₄×C₃₇	—	2	4	no	—
177	C₄×C₃₇	—	2	4	no	—
178	C₄×C₃₇	—	4	2	no	—
179	C₄×C₃₇	—	8	1	no	—
180	C₄×C₃₇	—	8	1	no	—
181	C₄×C₃₇	—	8	4	no	—
182	C₄×C₃₇	#497	1	4	yes	complemented
183	C₄×C₃₇	D₄²	1	2	yes	—
184	C₄×C₃₇	#550	1	2	yes	—
185	C₂×#497	C₂×C₃₇	1	2	yes	—
186	C₂×#462	C₂×C₃₇	1	2	yes	complemented
187	C₂×#461	C₂×C₃₇	1	2	yes	—
188	#2868	C₂×C₃₇	1	1	yes	characteristic, complemented
189	C₄×#124	C₂×C₃₇	1	1	yes	characteristic
190	#2016	C₂×C₃₇	1	2	yes	complemented
191	#2013	C₂×C₃₇	1	2	yes	—
192	#1960	C₂×C₃₇	1	2	yes	complemented
193	#1767	C₂×C₃₇	1	1	yes	characteristic, complemented
194	C₂×C₃₇	—	8	2	no	—
195	C₂×C₃₇	#2541	1	1	yes	characteristic
196	C₂×C₃₇	#3039	1	2	yes	—
197	C₂×C₃₇	C₂×#497	1	1	yes	characteristic
198	C₂×C₃₇	#3152	1	1	yes	characteristic
199	C₂×C₃₇	#3218	1	2	yes	—
200	C₂²×Q₁₆	C₂²×C₃₇	1	4	yes	—
201	C₂²×SD₁₆	C₂²×C₃₇	1	4	yes	—
202	C₂×C₄⋊Q₈	C₂²×C₃₇	1	2	yes	—
203	C₂×C₄⋊Q₈	C₂²×C₃₇	1	2	yes	—
204	C₂×C₄⋊Q₈	C₂²×C₃₇	1	2	yes	—
205	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
206	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
207	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
208	#497	—	2	8	no	—
209	#462	—	2	8	no	—
210	#461	—	2	8	no	—
211	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
212	C₂×#103	C₂²×C₃₇	1	4	yes	—
213	C₂×#103	C₂²×C₃₇	1	4	yes	—
214	C₂×#97	C₂²×C₃₇	1	2	yes	—
215	#391	C₂²×C₃₇	1	1	yes	characteristic
216	#390	C₂²×C₃₇	1	1	yes	characteristic
217	#388	—	2	2	no	—
218	#384	—	2	2	no	—
219	#384	—	2	2	no	—
220	#382	C₂²×C₃₇	1	1	yes	characteristic
221	C₄×C₂²⋊C₄	—	2	2	no	—
222	C₄³	C₂²×C₃₇	1	1	yes	characteristic
223	#336	C₂²×C₃₇	1	2	yes	—
224	C₃₇	#28449	1	1	yes	characteristic, direct product factor, Sylow
225	C₂²×Q₈	C₂³×C₃₇	1	4	yes	—
226	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
227	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
228	C₂³×C₄	—	2	1	no	—
229	C₂×Q₁₆	—	2	8	no	—
230	C₂×Q₁₆	—	2	8	no	—
231	C₂×Q₁₆	—	4	4	no	—
232	C₂×SD₁₆	—	2	8	no	—
233	C₂×SD₁₆	—	2	8	no	—
234	C₂×SD₁₆	—	4	4	no	—
235	C₂²×C₈	C₂³×C₃₇	1	4	yes	—
236	C₄⋊Q₈	—	2	4	no	—
237	C₄⋊Q₈	—	2	4	no	—
238	C₄⋊Q₈	—	2	4	no	—
239	C₄⋊Q₈	—	2	4	no	—
240	C₄⋊Q₈	—	4	4	no	—
241	#124	—	2	2	no	—
242	#124	D₄×C₃₇	1	4	yes	—
243	C₄×Q₈	—	2	4	no	—
244	C₄×D₄	—	2	4	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	4	no	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₂²⋊C₄	—	2	1	no	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	D₄×C₃₇	1	2	yes	—
257	C₂×C₄²	D₄×C₃₇	1	2	yes	—
258	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
261	C₄⋊C₈	D₄×C₃₇	1	8	yes	—
262	#103	—	2	8	no	—
263	#103	—	2	8	no	—
264	#97	—	2	4	no	—
265	#95	—	2	2	no	—
266	#95	—	2	2	no	—
267	C₂⁴	—	2	1	no	—
268	C₂×Q₈	—	2	1	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	2	4	no	—
271	C₂×Q₈	—	2	4	no	—
272	C₂×Q₈	—	2	4	no	—
273	C₂×Q₈	—	2	4	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	4	no	—
288	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
289	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
292	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
293	Q₁₆	—	4	16	no	—
294	SD₁₆	—	4	16	no	—
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	C₂×D₄×C₃₇	1	8	yes	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	4	8	no	—
301	C₄⋊C₄	—	4	8	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄⋊C₄	—	4	4	no	—
304	C₄⋊C₄	—	4	4	no	—
305	C₂²⋊C₄	—	2	8	no	—
306	C₂²⋊C₄	—	4	2	no	—
307	C₂²⋊C₄	—	4	4	no	—
308	C₄²	—	2	4	no	—
309	C₄²	—	2	4	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	4	2	no	—
312	C₄²	C₂×D₄×C₃₇	1	2	yes	—
313	C₄²	C₂×D₄×C₃₇	1	4	yes	—
314	C₄²	#41×C₃₇	1	2	yes	—
315	C₂³	—	2	2	no	—
316	C₂³	—	4	1	no	—
317	C₂³	—	4	1	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
321	Q₈	—	2	4	no	—
322	Q₈	—	4	2	no	—
323	Q₈	—	4	4	no	—
324	Q₈	—	4	4	no	—
325	Q₈	—	4	4	no	—
326	Q₈	—	4	4	no	—
327	D₄	—	2	4	no	—
328	D₄	—	4	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	8	4	no	—
345	C₂×C₄	#121×C₃₇	1	4	yes	—
346	C₂×C₄	#127×C₃₇	1	2	yes	—
347	C₂×C₄	#127×C₃₇	1	2	yes	—
348	C₂×C₄	#137×C₃₇	1	4	yes	—
349	C₂×C₄	#137×C₃₇	1	4	yes	—
350	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
351	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
352	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
353	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
354	C₈	—	2	8	no	—
355	C₂²	—	4	4	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	8	1	no	—
358	C₂²	—	8	1	no	—
359	C₂²	—	8	2	no	—
360	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
361	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
362	C₂²	C₃₇×#535	1	1	yes	characteristic
363	C₂²	C₂×#137×C₃₇	1	2	yes	—
364	C₂²	C₂×#137×C₃₇	1	2	yes	—
365	C₄	—	2	2	no	—
366	C₄	—	2	4	no	—
367	C₄	—	2	4	no	—
368	C₄	—	4	2	no	—
369	C₄	—	8	1	no	—
370	C₄	—	8	1	no	—
371	C₄	—	8	4	no	—
372	C₄	C₃₇×#497	1	4	yes	complemented
373	C₄	D₄²×C₃₇	1	2	yes	—
374	C₄	C₃₇×#550	1	2	yes	—
375	C₂	—	8	2	no	—
376	C₂	C₃₇×#2541	1	1	yes	characteristic
377	C₂	C₃₇×#3039	1	2	yes	—
378	C₂	C₂×C₃₇×#497	1	1	yes	characteristic
379	C₂	C₃₇×#3152	1	1	yes	characteristic
380	C₂	C₃₇×#3218	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
2. C₂×C₃₇×#462	C₂	semidirect
4. C₃₇×#2868	C₂	semidirect
6. C₃₇×#2016	C₂	semidirect
8. C₃₇×#1960	C₂	semidirect
9. C₃₇×#1767	C₂	semidirect
164. #28449	C₃₇	direct (N × H)
182. C₄×C₃₇	#497	semidirect
186. C₂×#462	C₂×C₃₇	semidirect
188. #2868	C₂×C₃₇	semidirect
190. #2016	C₂×C₃₇	semidirect
192. #1960	C₂×C₃₇	semidirect
193. #1767	C₂×C₃₇	semidirect
224. C₃₇	#28449	direct (N × H)
372. C₄	C₃₇×#497	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#497	2
C₂×C₃₇×#462	2
C₂×C₃₇×#461	2
C₃₇×#2868	2
C₄×#124×C₃₇	2
C₃₇×#2016	2
C₃₇×#2013	2
C₃₇×#1960	2
C₃₇×#1767	2
#28449	37

Subgroups — C37×#28449 #22649702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28449 #22649702