Subgroups — C₃₇×#28494 #22649747

Order 9472.

1054 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	C₃₇×#3152	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3151	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₇×#492	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#471	C₂	1	4	yes	maximal, complemented
5	C₃₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2019	C₂	1	4	yes	maximal, complemented
7	C₃₇×#1966	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1965	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#108×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#137×C₃₇	C₂²	1	4	yes	—
11	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	4	yes	—
12	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
14	C₂×#131×C₃₇	C₂²	1	2	yes	—
15	C₃₇×#532	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
18	C₃₇×#497	—	2	2	no	—
19	C₃₇×#496	—	2	2	no	—
20	C₃₇×#494	—	2	1	no	—
21	C₃₇×#493	—	2	1	no	—
22	C₃₇×#492	—	2	1	no	—
23	C₃₇×#492	—	2	1	no	—
24	C₃₇×#492	—	2	2	no	—
25	C₃₇×#492	—	2	2	no	—
26	C₃₇×#471	—	2	16	no	—
27	C₃₇×#436	—	2	2	no	—
28	C₈×D₄×C₃₇	—	2	2	no	—
29	C₂×#108×C₃₇	C₂²	1	2	yes	—
30	C₃₇×#423	C₂²	1	1	yes	characteristic
31	C₂×#101×C₃₇	C₂²	1	4	yes	—
32	C₂×#100×C₃₇	C₂²	1	4	yes	—
33	C₃₇×#408	C₂²	1	2	yes	—
34	C₄×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
35	C₄×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
37	C₃₇×#341	C₂²	1	2	yes	—
38	C₂×#41×C₃₇	C₂³	1	2	yes	—
39	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
40	C₂²×D₄×C₃₇	—	2	2	no	—
41	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
42	#137×C₃₇	—	2	8	no	—
43	#137×C₃₇	—	4	4	no	—
44	AGL(1,ℤ/8)×C₃₇	—	2	8	no	—
45	AGL(1,ℤ/8)×C₃₇	—	4	4	no	—
46	C₂×Q₁₆×C₃₇	—	2	4	no	—
47	C₂×SD₁₆×C₃₇	—	2	4	no	—
48	C₂×SD₁₆×C₃₇	—	2	4	no	—
49	C₂×SD₁₆×C₃₇	—	2	8	no	—
50	C₂×SD₁₆×C₃₇	—	2	4	no	—
51	C₂×SD₁₆×C₃₇	—	2	2	no	—
52	C₂×SD₁₆×C₃₇	—	2	2	no	—
53	C₂×SD₁₆×C₃₇	—	4	4	no	—
54	C₂×D₈×C₃₇	—	2	4	no	—
55	#131×C₃₇	—	2	8	no	—
56	C₂×M₁₆×C₃₇	—	2	2	no	—
57	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
58	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
59	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
60	C₂²×C₈×C₃₇	—	2	2	no	—
61	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
63	C₄⋊Q₈×C₃₇	—	2	2	no	—
64	C₄⋊Q₈×C₃₇	—	2	1	no	—
65	C₄⋊Q₈×C₃₇	—	2	1	no	—
66	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
67	#127×C₃₇	—	2	2	no	—
68	#127×C₃₇	—	2	1	no	—
69	#127×C₃₇	—	2	1	no	—
70	#127×C₃₇	D₄	1	1	yes	characteristic
71	#124×C₃₇	D₄	1	2	yes	—
72	#121×C₃₇	—	2	2	no	—
73	C₄×D₄×C₃₇	—	2	2	no	—
74	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
75	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
76	#108×C₃₇	D₄	1	8	yes	complemented
77	C₄⋊C₈×C₃₇	—	2	2	no	—
78	#101×C₃₇	—	2	8	no	—
79	#100×C₃₇	—	2	8	no	—
80	C₂²⋊C₈×C₃₇	—	2	4	no	—
81	#97×C₃₇	—	2	1	no	—
82	#97×C₃₇	—	2	1	no	—
83	C₄×C₈×C₃₇	—	2	1	no	—
84	C₄×C₈×C₃₇	—	2	1	no	—
85	C₄×C₈×C₃₇	D₄	1	2	yes	—
86	C₄×C₈×C₃₇	D₄	1	2	yes	—
87	C₂⁴×C₃₇	—	2	2	no	—
88	#41×C₃₇	—	2	4	no	—
89	#41×C₃₇	—	2	4	no	—
90	C₂×Q₈×C₃₇	—	2	4	no	—
91	C₂×Q₈×C₃₇	—	2	2	no	—
92	C₂×Q₈×C₃₇	—	2	2	no	—
93	C₂×Q₈×C₃₇	—	2	4	no	—
94	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
95	C₂×D₄×C₃₇	—	2	2	no	—
96	C₂×D₄×C₃₇	—	2	2	no	—
97	C₂×D₄×C₃₇	—	2	4	no	—
98	C₂×D₄×C₃₇	—	2	2	no	—
99	C₂×D₄×C₃₇	—	2	2	no	—
100	C₂×D₄×C₃₇	—	2	4	no	—
101	C₂×D₄×C₃₇	—	4	2	no	—
102	C₂×D₄×C₃₇	—	4	2	no	—
103	C₂×D₄×C₃₇	—	8	4	no	—
104	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₃₇	—	2	2	no	—
106	C₂²×C₄×C₃₇	—	2	2	no	—
107	C₂²×C₄×C₃₇	#41	1	2	yes	—
108	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
109	Q₁₆×C₃₇	—	4	8	no	—
110	SD₁₆×C₃₇	—	4	8	no	—
111	SD₁₆×C₃₇	—	4	8	no	—
112	SD₁₆×C₃₇	—	4	8	no	—
113	SD₁₆×C₃₇	—	4	4	no	—
114	SD₁₆×C₃₇	—	4	4	no	—
115	D₈×C₃₇	—	4	8	no	—
116	M₁₆×C₃₇	—	2	2	no	—
117	M₁₆×C₃₇	—	2	2	no	—
118	M₁₆×C₃₇	—	2	4	no	—
119	M₁₆×C₃₇	—	4	4	no	—
120	M₁₆×C₃₇	C₂×D₄	1	4	yes	—
121	M₁₆×C₃₇	C₂×D₄	1	4	yes	—
122	C₂×C₈×C₃₇	—	2	2	no	—
123	C₂×C₈×C₃₇	—	2	2	no	—
124	C₂×C₈×C₃₇	—	2	2	no	—
125	C₂×C₈×C₃₇	—	2	2	no	—
126	C₂×C₈×C₃₇	—	4	4	no	—
127	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
131	C₄⋊C₄×C₃₇	—	2	2	no	—
132	C₄⋊C₄×C₃₇	—	4	2	no	—
133	C₄⋊C₄×C₃₇	—	4	2	no	—
134	C₂²⋊C₄×C₃₇	—	2	4	no	—
135	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₃₇	C₂×D₄	1	2	yes	—
137	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
138	C₂³×C₃₇	—	2	2	no	—
139	C₂³×C₃₇	—	4	2	no	—
140	C₂³×C₃₇	—	4	4	no	—
141	C₂³×C₃₇	—	8	4	no	—
142	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
143	Q₈×C₃₇	—	2	4	no	—
144	Q₈×C₃₇	—	4	2	no	—
145	Q₈×C₃₇	—	4	2	no	—
146	Q₈×C₃₇	—	4	4	no	—
147	D₄×C₃₇	—	2	4	no	—
148	D₄×C₃₇	—	4	4	no	—
149	D₄×C₃₇	—	4	2	no	—
150	D₄×C₃₇	—	4	2	no	—
151	D₄×C₃₇	—	4	4	no	—
152	D₄×C₃₇	—	4	4	no	—
153	D₄×C₃₇	—	8	4	no	—
154	D₄×C₃₇	—	8	4	no	—
155	C₂×C₄×C₃₇	—	2	4	no	—
156	C₂×C₄×C₃₇	—	2	2	no	—
157	C₂×C₄×C₃₇	—	4	2	no	—
158	C₂×C₄×C₃₇	—	4	2	no	—
159	C₂×C₄×C₃₇	—	4	2	no	—
160	C₂×C₄×C₃₇	—	4	4	no	—
161	C₂×C₄×C₃₇	#121	1	2	yes	—
162	C₂×C₄×C₃₇	#121	1	2	yes	—
163	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
165	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
167	C₈×C₃₇	—	2	2	no	—
168	C₈×C₃₇	—	2	4	no	—
169	C₈×C₃₇	—	2	4	no	—
170	C₈×C₃₇	—	4	2	no	—
171	C₈×C₃₇	#127	1	2	yes	—
172	C₈×C₃₇	#127	1	2	yes	—
173	#28494	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂²×C₃₇	—	2	2	no	—
175	C₂²×C₃₇	—	4	2	no	—
176	C₂²×C₃₇	—	4	4	no	—
177	C₂²×C₃₇	—	8	2	no	—
178	C₂²×C₃₇	—	8	4	no	—
179	C₂²×C₃₇	—	16	4	no	—
180	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
181	C₂²×C₃₇	#550	1	2	yes	—
182	C₄×C₃₇	—	2	2	no	—
183	C₄×C₃₇	—	4	2	no	—
184	C₄×C₃₇	—	8	2	no	—
185	C₄×C₃₇	#471	1	4	yes	complemented
186	C₄×C₃₇	C₂×#127	1	1	yes	characteristic
187	C₄×C₃₇	#535	1	1	yes	characteristic
188	C₄×C₃₇	D₄²	1	2	yes	—
189	#3152	C₂×C₃₇	1	1	yes	characteristic, complemented
190	#3151	C₂×C₃₇	1	1	yes	characteristic
191	C₂×#492	C₂×C₃₇	1	1	yes	characteristic, complemented
192	C₂×#471	C₂×C₃₇	1	4	yes	complemented
193	#2931	C₂×C₃₇	1	1	yes	characteristic, complemented
194	#2019	C₂×C₃₇	1	4	yes	complemented
195	#1966	C₂×C₃₇	1	1	yes	characteristic, complemented
196	#1965	C₂×C₃₇	1	1	yes	characteristic, complemented
197	C₄×#108	C₂×C₃₇	1	1	yes	characteristic, complemented
198	C₂×C₃₇	—	2	2	no	—
199	C₂×C₃₇	—	8	2	no	—
200	C₂×C₃₇	—	16	2	no	—
201	C₂×C₃₇	#2541	1	1	yes	characteristic
202	C₂×C₃₇	C₂×#471	1	2	yes	—
203	C₂×#137	C₂²×C₃₇	1	4	yes	—
204	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	4	yes	—
205	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
206	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
207	C₂×#131	C₂²×C₃₇	1	2	yes	—
208	#532	C₂²×C₃₇	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
210	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
211	#497	—	2	2	no	—
212	#496	—	2	2	no	—
213	#494	—	2	1	no	—
214	#493	—	2	1	no	—
215	#492	—	2	1	no	—
216	#492	—	2	1	no	—
217	#492	—	2	2	no	—
218	#492	—	2	2	no	—
219	#471	—	2	16	no	—
220	#436	—	2	2	no	—
221	C₈×D₄	—	2	2	no	—
222	C₂×#108	C₂²×C₃₇	1	2	yes	—
223	#423	C₂²×C₃₇	1	1	yes	characteristic
224	C₂×#101	C₂²×C₃₇	1	4	yes	—
225	C₂×#100	C₂²×C₃₇	1	4	yes	—
226	#408	C₂²×C₃₇	1	2	yes	—
227	C₄×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
228	C₄×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
229	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
230	#341	C₂²×C₃₇	1	2	yes	—
231	C₃₇	#28494	1	1	yes	characteristic, direct product factor, Sylow
232	C₂×#41	C₂³×C₃₇	1	2	yes	—
233	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
234	C₂²×D₄	—	2	2	no	—
235	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
236	#137	—	2	8	no	—
237	#137	—	4	4	no	—
238	AGL(1,ℤ/8)	—	2	8	no	—
239	AGL(1,ℤ/8)	—	4	4	no	—
240	C₂×Q₁₆	—	2	4	no	—
241	C₂×SD₁₆	—	2	4	no	—
242	C₂×SD₁₆	—	2	4	no	—
243	C₂×SD₁₆	—	2	8	no	—
244	C₂×SD₁₆	—	2	4	no	—
245	C₂×SD₁₆	—	2	2	no	—
246	C₂×SD₁₆	—	2	2	no	—
247	C₂×SD₁₆	—	4	4	no	—
248	C₂×D₈	—	2	4	no	—
249	#131	—	2	8	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
252	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
253	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
257	C₄⋊Q₈	—	2	2	no	—
258	C₄⋊Q₈	—	2	1	no	—
259	C₄⋊Q₈	—	2	1	no	—
260	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
261	#127	—	2	2	no	—
262	#127	—	2	1	no	—
263	#127	—	2	1	no	—
264	#127	D₄×C₃₇	1	1	yes	characteristic
265	#124	D₄×C₃₇	1	2	yes	—
266	#121	—	2	2	no	—
267	C₄×D₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
270	#108	D₄×C₃₇	1	8	yes	complemented
271	C₄⋊C₈	—	2	2	no	—
272	#101	—	2	8	no	—
273	#100	—	2	8	no	—
274	C₂²⋊C₈	—	2	4	no	—
275	#97	—	2	1	no	—
276	#97	—	2	1	no	—
277	C₄×C₈	—	2	1	no	—
278	C₄×C₈	—	2	1	no	—
279	C₄×C₈	D₄×C₃₇	1	2	yes	—
280	C₄×C₈	D₄×C₃₇	1	2	yes	—
281	C₂⁴	—	2	2	no	—
282	#41	—	2	4	no	—
283	#41	—	2	4	no	—
284	C₂×Q₈	—	2	4	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	8	4	no	—
298	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	#41×C₃₇	1	2	yes	—
302	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
303	Q₁₆	—	4	8	no	—
304	SD₁₆	—	4	8	no	—
305	SD₁₆	—	4	8	no	—
306	SD₁₆	—	4	8	no	—
307	SD₁₆	—	4	4	no	—
308	SD₁₆	—	4	4	no	—
309	D₈	—	4	8	no	—
310	M₁₆	—	2	2	no	—
311	M₁₆	—	2	2	no	—
312	M₁₆	—	2	4	no	—
313	M₁₆	—	4	4	no	—
314	M₁₆	C₂×D₄×C₃₇	1	4	yes	—
315	M₁₆	C₂×D₄×C₃₇	1	4	yes	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	4	4	no	—
321	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
322	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
323	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
324	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
330	C₄²	C₂×D₄×C₃₇	1	2	yes	—
331	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
332	C₂³	—	2	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	4	no	—
335	C₂³	—	8	4	no	—
336	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
337	Q₈	—	2	4	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	4	2	no	—
340	Q₈	—	4	4	no	—
341	D₄	—	2	4	no	—
342	D₄	—	4	4	no	—
343	D₄	—	4	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	4	4	no	—
346	D₄	—	4	4	no	—
347	D₄	—	8	4	no	—
348	D₄	—	8	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	#121×C₃₇	1	2	yes	—
356	C₂×C₄	#121×C₃₇	1	2	yes	—
357	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
359	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
360	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
361	C₈	—	2	2	no	—
362	C₈	—	2	4	no	—
363	C₈	—	2	4	no	—
364	C₈	—	4	2	no	—
365	C₈	#127×C₃₇	1	2	yes	—
366	C₈	#127×C₃₇	1	2	yes	—
367	C₂²	—	2	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	4	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	4	no	—
372	C₂²	—	16	4	no	—
373	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
374	C₂²	C₃₇×#550	1	2	yes	—
375	C₄	—	2	2	no	—
376	C₄	—	4	2	no	—
377	C₄	—	8	2	no	—
378	C₄	C₃₇×#471	1	4	yes	complemented
379	C₄	C₂×#127×C₃₇	1	1	yes	characteristic
380	C₄	C₃₇×#535	1	1	yes	characteristic
381	C₄	D₄²×C₃₇	1	2	yes	—
382	C₂	—	2	2	no	—
383	C₂	—	8	2	no	—
384	C₂	—	16	2	no	—
385	C₂	C₃₇×#2541	1	1	yes	characteristic
386	C₂	C₂×C₃₇×#471	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#3151	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3152	C₂	semidirect
3. C₂×C₃₇×#492	C₂	semidirect
4. C₂×C₃₇×#471	C₂	semidirect
5. C₃₇×#2931	C₂	semidirect
6. C₃₇×#2019	C₂	semidirect
7. C₃₇×#1966	C₂	semidirect
8. C₃₇×#1965	C₂	semidirect
9. C₄×#108×C₃₇	C₂	semidirect
76. #108×C₃₇	D₄	semidirect
173. #28494	C₃₇	direct (N × H)
185. C₄×C₃₇	#471	semidirect
189. #3152	C₂×C₃₇	semidirect
191. C₂×#492	C₂×C₃₇	semidirect
192. C₂×#471	C₂×C₃₇	semidirect
193. #2931	C₂×C₃₇	semidirect
194. #2019	C₂×C₃₇	semidirect
195. #1966	C₂×C₃₇	semidirect
196. #1965	C₂×C₃₇	semidirect
197. C₄×#108	C₂×C₃₇	semidirect
231. C₃₇	#28494	direct (N × H)
270. #108	D₄×C₃₇	semidirect
378. C₄	C₃₇×#471	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#3152	2
C₃₇×#3151	2
C₂×C₃₇×#492	2
C₂×C₃₇×#471	2
C₃₇×#2931	2
C₃₇×#2019	2
C₃₇×#1966	2
C₃₇×#1965	2
C₄×#108×C₃₇	2
#28494	37

Subgroups — C37×#28494 #22649747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28494 #22649747