Subgroups — C₃₇×#28504 #22649757

Order 9472.

1126 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3155	C₂	1	2	yes	maximal, complemented
2	C₂×C₃₇×#493	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#472	C₂	1	2	yes	maximal, complemented
4	C₃₇×#3058	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₇×#443	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2002	C₂	1	4	yes	maximal, complemented
7	C₃₇×#1978	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1772	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	4	yes	—
10	C₂×#135×C₃₇	C₂²	1	1	yes	characteristic
11	C₂²×D₈×C₃₇	C₂²	1	2	yes	—
12	C₂²×D₈×C₃₇	C₂²	1	2	yes	—
13	C₂×#131×C₃₇	C₂²	1	2	yes	—
14	C₃₇×#535	C₂²	1	4	yes	—
15	C₂×#127×C₃₇	C₂²	1	2	yes	—
16	C₃₇×#496	—	2	4	no	—
17	C₃₇×#495	—	2	2	no	—
18	C₃₇×#493	—	2	2	no	—
19	C₃₇×#493	—	2	4	no	—
20	C₃₇×#472	—	2	8	no	—
21	C₃₇×#469	—	2	4	no	—
22	C₃₇×#466	—	2	4	no	—
23	C₃₇×#443	—	2	4	no	—
24	C₂×#108×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×#108×C₃₇	C₂²	1	1	yes	characteristic
26	C₃₇×#427	C₂²	1	1	yes	characteristic
27	C₂×#104×C₃₇	C₂²	1	2	yes	—
28	C₃₇×#418	C₂²	1	4	yes	—
29	C₂×#100×C₃₇	C₂²	1	4	yes	—
30	C₃₇×#405	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
32	C₃₇×#339	C₂²	1	2	yes	—
33	C₂×#41×C₃₇	C₂³	1	2	yes	—
34	C₂²×D₄×C₃₇	—	4	2	no	—
35	C₂²×D₄×C₃₇	C₂³	1	4	yes	—
36	AGL(1,ℤ/8)×C₃₇	—	2	8	no	—
37	AGL(1,ℤ/8)×C₃₇	—	4	4	no	—
38	#135×C₃₇	—	2	2	no	—
39	#135×C₃₇	—	2	2	no	—
40	C₂×Q₁₆×C₃₇	D₄	1	1	yes	characteristic, complemented
41	C₂×SD₁₆×C₃₇	—	2	4	no	—
42	C₂×SD₁₆×C₃₇	D₄	1	2	yes	complemented
43	C₂×D₈×C₃₇	—	2	4	no	—
44	C₂×D₈×C₃₇	—	2	2	no	—
45	C₂×D₈×C₃₇	—	2	2	no	—
46	C₂×D₈×C₃₇	—	2	4	no	—
47	C₂×D₈×C₃₇	—	2	4	no	—
48	C₂×D₈×C₃₇	—	2	4	no	—
49	C₂×D₈×C₃₇	—	2	2	no	—
50	C₂×D₈×C₃₇	—	2	2	no	—
51	C₂×D₈×C₃₇	—	2	4	no	—
52	C₂×D₈×C₃₇	D₄	1	1	yes	characteristic, complemented
53	#131×C₃₇	—	2	4	no	—
54	#131×C₃₇	—	2	4	no	—
55	C₂×M₁₆×C₃₇	—	2	2	no	—
56	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
57	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
58	C₂²×C₈×C₃₇	—	2	2	no	—
59	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
61	#127×C₃₇	—	2	4	no	—
62	#127×C₃₇	—	2	4	no	—
63	#127×C₃₇	—	4	2	no	—
64	#124×C₃₇	—	2	4	no	—
65	#121×C₃₇	—	2	8	no	—
66	#120×C₃₇	—	4	4	no	—
67	#117×C₃₇	C₂³	1	2	yes	—
68	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
69	#108×C₃₇	—	2	2	no	—
70	#108×C₃₇	D₄	1	4	yes	complemented
71	#107×C₃₇	D₄	1	2	yes	complemented
72	#106×C₃₇	D₄	1	2	yes	complemented
73	#104×C₃₇	—	2	4	no	—
74	#102×C₃₇	—	2	8	no	—
75	#100×C₃₇	—	2	8	no	—
76	#97×C₃₇	—	2	2	no	—
77	C₄×C₈×C₃₇	—	2	2	no	—
78	C₄×C₈×C₃₇	D₄	1	4	yes	complemented
79	C₂⁴×C₃₇	—	2	4	no	—
80	#41×C₃₇	—	2	2	no	—
81	#41×C₃₇	—	2	2	no	—
82	#41×C₃₇	—	2	2	no	—
83	#41×C₃₇	—	2	2	no	—
84	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
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	—	2	4	no	—
89	C₂×D₄×C₃₇	—	2	4	no	—
90	C₂×D₄×C₃₇	—	2	4	no	—
91	C₂×D₄×C₃₇	—	2	4	no	—
92	C₂×D₄×C₃₇	—	4	8	no	—
93	C₂×D₄×C₃₇	—	4	8	no	—
94	C₂×D₄×C₃₇	—	8	8	no	—
95	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₃₇	—	2	1	no	—
97	C₂²×C₄×C₃₇	—	2	2	no	—
98	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
99	Q₁₆×C₃₇	—	2	2	no	—
100	SD₁₆×C₃₇	—	2	4	no	—
101	SD₁₆×C₃₇	—	4	8	no	—
102	D₈×C₃₇	—	2	2	no	—
103	D₈×C₃₇	—	4	8	no	—
104	D₈×C₃₇	—	4	4	no	—
105	D₈×C₃₇	—	4	4	no	—
106	D₈×C₃₇	—	4	4	no	—
107	D₈×C₃₇	—	4	4	no	—
108	M₁₆×C₃₇	—	2	2	no	—
109	M₁₆×C₃₇	—	2	2	no	—
110	M₁₆×C₃₇	—	2	2	no	—
111	M₁₆×C₃₇	—	4	4	no	—
112	M₁₆×C₃₇	C₂×D₄	1	4	yes	—
113	C₂×C₈×C₃₇	—	2	2	no	—
114	C₂×C₈×C₃₇	—	2	2	no	—
115	C₂×C₈×C₃₇	—	4	4	no	—
116	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₃₇	#41	1	2	yes	—
124	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
125	C₂²⋊C₄×C₃₇	—	2	2	no	—
126	C₂²⋊C₄×C₃₇	—	4	8	no	—
127	C₄²×C₃₇	—	2	2	no	—
128	C₄²×C₃₇	—	2	1	no	—
129	C₄²×C₃₇	C₂×D₄	1	2	yes	—
130	C₂³×C₃₇	—	2	2	no	—
131	C₂³×C₃₇	—	4	4	no	—
132	C₂³×C₃₇	—	4	4	no	—
133	C₂³×C₃₇	—	4	4	no	—
134	C₂³×C₃₇	—	8	8	no	—
135	C₂³×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
136	Q₈×C₃₇	—	2	2	no	—
137	Q₈×C₃₇	—	2	2	no	—
138	D₄×C₃₇	—	2	2	no	—
139	D₄×C₃₇	—	2	2	no	—
140	D₄×C₃₇	—	4	2	no	—
141	D₄×C₃₇	—	4	2	no	—
142	D₄×C₃₇	—	4	4	no	—
143	D₄×C₃₇	—	4	4	no	—
144	D₄×C₃₇	—	4	4	no	—
145	D₄×C₃₇	—	4	4	no	—
146	D₄×C₃₇	—	8	16	no	—
147	D₄×C₃₇	—	16	8	no	—
148	C₂×C₄×C₃₇	—	2	4	no	—
149	C₂×C₄×C₃₇	—	2	2	no	—
150	C₂×C₄×C₃₇	—	2	4	no	—
151	C₂×C₄×C₃₇	—	2	2	no	—
152	C₂×C₄×C₃₇	—	4	2	no	—
153	C₂×C₄×C₃₇	—	4	2	no	—
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	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
160	C₈×C₃₇	—	2	4	no	—
161	C₈×C₃₇	—	4	2	no	—
162	C₈×C₃₇	#121	1	2	yes	—
163	C₈×C₃₇	#121	1	2	yes	—
164	C₈×C₃₇	#127	1	2	yes	—
165	C₈×C₃₇	#127	1	2	yes	—
166	#28504	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂²×C₃₇	—	2	2	no	—
168	C₂²×C₃₇	—	4	4	no	—
169	C₂²×C₃₇	—	4	2	no	—
170	C₂²×C₃₇	—	8	8	no	—
171	C₂²×C₃₇	—	8	8	no	—
172	C₂²×C₃₇	—	8	4	no	—
173	C₂²×C₃₇	—	16	4	no	—
174	C₂²×C₃₇	#535	1	1	yes	characteristic
175	C₂²×C₃₇	D₄²	1	1	yes	characteristic
176	C₂²×C₃₇	#550	1	1	yes	characteristic
177	C₄×C₃₇	—	2	4	no	—
178	C₄×C₃₇	—	4	4	no	—
179	C₄×C₃₇	—	4	2	no	—
180	C₄×C₃₇	C₂×#121	1	1	yes	characteristic
181	C₄×C₃₇	C₂×#127	1	1	yes	characteristic
182	C₄×C₃₇	D₄²	1	1	yes	characteristic
183	C₄×C₃₇	#550	1	1	yes	characteristic
184	#3155	C₂×C₃₇	1	2	yes	complemented
185	C₂×#493	C₂×C₃₇	1	1	yes	characteristic, complemented
186	C₂×#472	C₂×C₃₇	1	2	yes	complemented
187	#3058	C₂×C₃₇	1	2	yes	complemented
188	C₂×#443	C₂×C₃₇	1	1	yes	characteristic, complemented
189	#2002	C₂×C₃₇	1	4	yes	complemented
190	#1978	C₂×C₃₇	1	2	yes	complemented
191	#1772	C₂×C₃₇	1	1	yes	characteristic, complemented
192	C₂×C₃₇	—	2	1	no	—
193	C₂×C₃₇	—	2	1	no	—
194	C₂×C₃₇	—	8	2	no	—
195	C₂×C₃₇	—	16	4	no	—
196	C₂×C₃₇	#2541	1	1	yes	characteristic
197	C₂×C₃₇	#3292	1	2	yes	—
198	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	4	yes	—
199	C₂×#135	C₂²×C₃₇	1	1	yes	characteristic
200	C₂²×D₈	C₂²×C₃₇	1	2	yes	—
201	C₂²×D₈	C₂²×C₃₇	1	2	yes	—
202	C₂×#131	C₂²×C₃₇	1	2	yes	—
203	#535	C₂²×C₃₇	1	4	yes	—
204	C₂×#127	C₂²×C₃₇	1	2	yes	—
205	#496	—	2	4	no	—
206	#495	—	2	2	no	—
207	#493	—	2	2	no	—
208	#493	—	2	4	no	—
209	#472	—	2	8	no	—
210	#469	—	2	4	no	—
211	#466	—	2	4	no	—
212	#443	—	2	4	no	—
213	C₂×#108	C₂²×C₃₇	1	1	yes	characteristic
214	C₂×#108	C₂²×C₃₇	1	1	yes	characteristic
215	#427	C₂²×C₃₇	1	1	yes	characteristic
216	C₂×#104	C₂²×C₃₇	1	2	yes	—
217	#418	C₂²×C₃₇	1	4	yes	—
218	C₂×#100	C₂²×C₃₇	1	4	yes	—
219	#405	C₂²×C₃₇	1	2	yes	—
220	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
221	#339	C₂²×C₃₇	1	2	yes	—
222	C₃₇	#28504	1	1	yes	characteristic, direct product factor, Sylow
223	C₂×#41	C₂³×C₃₇	1	2	yes	—
224	C₂²×D₄	—	4	2	no	—
225	C₂²×D₄	C₂³×C₃₇	1	4	yes	—
226	AGL(1,ℤ/8)	—	2	8	no	—
227	AGL(1,ℤ/8)	—	4	4	no	—
228	#135	—	2	2	no	—
229	#135	—	2	2	no	—
230	C₂×Q₁₆	D₄×C₃₇	1	1	yes	characteristic, complemented
231	C₂×SD₁₆	—	2	4	no	—
232	C₂×SD₁₆	D₄×C₃₇	1	2	yes	complemented
233	C₂×D₈	—	2	4	no	—
234	C₂×D₈	—	2	2	no	—
235	C₂×D₈	—	2	2	no	—
236	C₂×D₈	—	2	4	no	—
237	C₂×D₈	—	2	4	no	—
238	C₂×D₈	—	2	4	no	—
239	C₂×D₈	—	2	2	no	—
240	C₂×D₈	—	2	2	no	—
241	C₂×D₈	—	2	4	no	—
242	C₂×D₈	D₄×C₃₇	1	1	yes	characteristic, complemented
243	#131	—	2	4	no	—
244	#131	—	2	4	no	—
245	C₂×M₁₆	—	2	2	no	—
246	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
247	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
251	#127	—	2	4	no	—
252	#127	—	2	4	no	—
253	#127	—	4	2	no	—
254	#124	—	2	4	no	—
255	#121	—	2	8	no	—
256	#120	—	4	4	no	—
257	#117	C₂³×C₃₇	1	2	yes	—
258	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
259	#108	—	2	2	no	—
260	#108	D₄×C₃₇	1	4	yes	complemented
261	#107	D₄×C₃₇	1	2	yes	complemented
262	#106	D₄×C₃₇	1	2	yes	complemented
263	#104	—	2	4	no	—
264	#102	—	2	8	no	—
265	#100	—	2	8	no	—
266	#97	—	2	2	no	—
267	C₄×C₈	—	2	2	no	—
268	C₄×C₈	D₄×C₃₇	1	4	yes	complemented
269	C₂⁴	—	2	4	no	—
270	#41	—	2	2	no	—
271	#41	—	2	2	no	—
272	#41	—	2	2	no	—
273	#41	—	2	2	no	—
274	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	2	4	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	4	8	no	—
283	C₂×D₄	—	4	8	no	—
284	C₂×D₄	—	8	8	no	—
285	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
289	Q₁₆	—	2	2	no	—
290	SD₁₆	—	2	4	no	—
291	SD₁₆	—	4	8	no	—
292	D₈	—	2	2	no	—
293	D₈	—	4	8	no	—
294	D₈	—	4	4	no	—
295	D₈	—	4	4	no	—
296	D₈	—	4	4	no	—
297	D₈	—	4	4	no	—
298	M₁₆	—	2	2	no	—
299	M₁₆	—	2	2	no	—
300	M₁₆	—	2	2	no	—
301	M₁₆	—	4	4	no	—
302	M₁₆	C₂×D₄×C₃₇	1	4	yes	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	4	4	no	—
306	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
307	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
308	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
309	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
310	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
311	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
312	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
313	C₂×C₈	#41×C₃₇	1	2	yes	—
314	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	4	8	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	1	no	—
319	C₄²	C₂×D₄×C₃₇	1	2	yes	—
320	C₂³	—	2	2	no	—
321	C₂³	—	4	4	no	—
322	C₂³	—	4	4	no	—
323	C₂³	—	4	4	no	—
324	C₂³	—	8	8	no	—
325	C₂³	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
326	Q₈	—	2	2	no	—
327	Q₈	—	2	2	no	—
328	D₄	—	2	2	no	—
329	D₄	—	2	2	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	4	no	—
333	D₄	—	4	4	no	—
334	D₄	—	4	4	no	—
335	D₄	—	4	4	no	—
336	D₄	—	8	16	no	—
337	D₄	—	16	8	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
345	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
346	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
347	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
348	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
349	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
350	C₈	—	2	4	no	—
351	C₈	—	4	2	no	—
352	C₈	#121×C₃₇	1	2	yes	—
353	C₈	#121×C₃₇	1	2	yes	—
354	C₈	#127×C₃₇	1	2	yes	—
355	C₈	#127×C₃₇	1	2	yes	—
356	C₂²	—	2	2	no	—
357	C₂²	—	4	4	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	8	8	no	—
360	C₂²	—	8	8	no	—
361	C₂²	—	8	4	no	—
362	C₂²	—	16	4	no	—
363	C₂²	C₃₇×#535	1	1	yes	characteristic
364	C₂²	D₄²×C₃₇	1	1	yes	characteristic
365	C₂²	C₃₇×#550	1	1	yes	characteristic
366	C₄	—	2	4	no	—
367	C₄	—	4	4	no	—
368	C₄	—	4	2	no	—
369	C₄	C₂×#121×C₃₇	1	1	yes	characteristic
370	C₄	C₂×#127×C₃₇	1	1	yes	characteristic
371	C₄	D₄²×C₃₇	1	1	yes	characteristic
372	C₄	C₃₇×#550	1	1	yes	characteristic
373	C₂	—	2	1	no	—
374	C₂	—	2	1	no	—
375	C₂	—	8	2	no	—
376	C₂	—	16	4	no	—
377	C₂	C₃₇×#2541	1	1	yes	characteristic
378	C₂	C₃₇×#3292	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₇	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3155	C₂	semidirect
2. C₂×C₃₇×#493	C₂	semidirect
3. C₂×C₃₇×#472	C₂	semidirect
4. C₃₇×#3058	C₂	semidirect
5. C₂×C₃₇×#443	C₂	semidirect
6. C₃₇×#2002	C₂	semidirect
7. C₃₇×#1978	C₂	semidirect
8. C₃₇×#1772	C₂	semidirect
40. C₂×Q₁₆×C₃₇	D₄	semidirect
42. C₂×SD₁₆×C₃₇	D₄	semidirect
52. C₂×D₈×C₃₇	D₄	semidirect
70. #108×C₃₇	D₄	semidirect
71. #107×C₃₇	D₄	semidirect
72. #106×C₃₇	D₄	semidirect
78. C₄×C₈×C₃₇	D₄	semidirect
166. #28504	C₃₇	direct (N × H)
184. #3155	C₂×C₃₇	semidirect
185. C₂×#493	C₂×C₃₇	semidirect
186. C₂×#472	C₂×C₃₇	semidirect
187. #3058	C₂×C₃₇	semidirect
188. C₂×#443	C₂×C₃₇	semidirect
189. #2002	C₂×C₃₇	semidirect
190. #1978	C₂×C₃₇	semidirect
191. #1772	C₂×C₃₇	semidirect
222. C₃₇	#28504	direct (N × H)
230. C₂×Q₁₆	D₄×C₃₇	semidirect
232. C₂×SD₁₆	D₄×C₃₇	semidirect
242. C₂×D₈	D₄×C₃₇	semidirect
260. #108	D₄×C₃₇	semidirect
261. #107	D₄×C₃₇	semidirect
262. #106	D₄×C₃₇	semidirect
268. C₄×C₈	D₄×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#3155	2
C₂×C₃₇×#493	2
C₂×C₃₇×#472	2
C₃₇×#3058	2
C₂×C₃₇×#443	2
C₃₇×#2002	2
C₃₇×#1978	2
C₃₇×#1772	2
#28504	37

Subgroups — C37×#28504 #22649757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28504 #22649757