Subgroups — C₃₇×#28648 #22649901

Order 9472.

854 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#486	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#2548	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2065	C₂	1	4	yes	maximal, complemented
6	C₃₇×#1988	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#1982	C₂	1	1	yes	maximal, characteristic
8	C₃₇×#1936	C₂	1	4	yes	maximal, complemented
9	C₄×#106×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄⋊Q₈×C₃₇	—	2	1	no	—
11	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
12	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×#124×C₃₇	—	2	1	no	—
14	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₃₇×#486	—	2	4	no	—
16	C₃₇×#446	—	2	4	no	—
17	C₂×#106×C₃₇	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
20	C₂×#102×C₃₇	C₂²	1	2	yes	—
21	C₂×#102×C₃₇	C₂²	1	2	yes	—
22	C₂×#102×C₃₇	C₂²	1	4	yes	—
23	C₂×#97×C₃₇	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
25	C₃₇×#398	—	2	2	no	—
26	C₃₇×#394	—	2	2	no	—
27	C₃₇×#391	—	2	1	no	—
28	C₃₇×#390	—	2	1	no	—
29	C₃₇×#390	C₂²	1	4	yes	—
30	C₃₇×#389	C₂²	1	4	yes	—
31	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
33	C₃₇×#340	C₂²	1	2	yes	—
34	C₃₇×#340	C₂²	1	4	yes	—
35	C₂²×Q₈×C₃₇	—	2	1	no	—
36	C₂²×Q₈×C₃₇	D₄	1	1	yes	characteristic
37	C₂²×D₄×C₃₇	—	2	1	no	—
38	C₂²×D₄×C₃₇	—	2	1	no	—
39	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
40	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
41	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
43	C₄⋊Q₈×C₃₇	—	2	2	no	—
44	C₄⋊Q₈×C₃₇	—	2	2	no	—
45	C₄⋊Q₈×C₃₇	—	4	4	no	—
46	#127×C₃₇	—	2	2	no	—
47	#127×C₃₇	—	2	2	no	—
48	#124×C₃₇	—	4	4	no	—
49	C₄×Q₈×C₃₇	—	2	2	no	—
50	C₄×Q₈×C₃₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₃₇	—	2	4	no	—
52	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
58	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
60	C₂×C₄²×C₃₇	—	2	1	no	—
61	C₂×C₄²×C₃₇	—	2	1	no	—
62	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
63	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
64	#106×C₃₇	—	2	4	no	—
65	C₄⋊C₈×C₃₇	—	2	4	no	—
66	C₄⋊C₈×C₃₇	—	2	2	no	—
67	#102×C₃₇	—	2	4	no	—
68	#102×C₃₇	—	2	4	no	—
69	#102×C₃₇	—	2	8	no	—
70	#97×C₃₇	—	2	4	no	—
71	C₄×C₈×C₃₇	D₄	1	4	yes	—
72	#95×C₃₇	—	2	1	no	—
73	#95×C₃₇	—	2	1	no	—
74	#95×C₃₇	—	2	4	no	—
75	C₂⁴×C₃₇	—	2	2	no	—
76	C₂×Q₈×C₃₇	—	2	2	no	—
77	C₂×Q₈×C₃₇	—	2	2	no	—
78	C₂×Q₈×C₃₇	—	2	2	no	—
79	C₂×Q₈×C₃₇	—	4	2	no	—
80	C₂×Q₈×C₃₇	—	4	2	no	—
81	C₂×Q₈×C₃₇	—	4	2	no	—
82	C₂×D₄×C₃₇	—	2	2	no	—
83	C₂×D₄×C₃₇	—	2	4	no	—
84	C₂×D₄×C₃₇	—	2	2	no	—
85	C₂×D₄×C₃₇	—	2	4	no	—
86	C₂×D₄×C₃₇	—	4	2	no	—
87	C₂×D₄×C₃₇	—	4	2	no	—
88	C₂×D₄×C₃₇	—	4	2	no	—
89	C₂×D₄×C₃₇	—	4	2	no	—
90	C₂×D₄×C₃₇	—	8	2	no	—
91	C₂²×C₄×C₃₇	—	2	2	no	—
92	C₂²×C₄×C₃₇	—	2	2	no	—
93	C₂²×C₄×C₃₇	—	2	2	no	—
94	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
99	C₂×C₈×C₃₇	—	2	2	no	—
100	C₂×C₈×C₃₇	—	2	2	no	—
101	C₂×C₈×C₃₇	—	2	2	no	—
102	C₂×C₈×C₃₇	—	2	4	no	—
103	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
104	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
105	C₄⋊C₄×C₃₇	—	2	2	no	—
106	C₄⋊C₄×C₃₇	—	2	4	no	—
107	C₄⋊C₄×C₃₇	—	2	2	no	—
108	C₄⋊C₄×C₃₇	—	2	2	no	—
109	C₄⋊C₄×C₃₇	—	2	2	no	—
110	C₄⋊C₄×C₃₇	—	2	2	no	—
111	C₄⋊C₄×C₃₇	—	2	2	no	—
112	C₄⋊C₄×C₃₇	—	4	8	no	—
113	C₄⋊C₄×C₃₇	—	4	2	no	—
114	C₄⋊C₄×C₃₇	#41	1	4	yes	—
115	C₂²⋊C₄×C₃₇	—	4	8	no	—
116	C₂²⋊C₄×C₃₇	—	8	4	no	—
117	C₄²×C₃₇	—	2	2	no	—
118	C₄²×C₃₇	—	2	2	no	—
119	C₄²×C₃₇	—	4	2	no	—
120	C₄²×C₃₇	—	4	2	no	—
121	C₄²×C₃₇	C₂×D₄	1	2	yes	—
122	C₄²×C₃₇	#41	1	2	yes	—
123	C₂³×C₃₇	—	4	2	no	—
124	C₂³×C₃₇	—	4	4	no	—
125	C₂³×C₃₇	—	4	2	no	—
126	C₂³×C₃₇	—	4	2	no	—
127	C₂³×C₃₇	—	4	4	no	—
128	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
129	Q₈×C₃₇	—	4	4	no	—
130	Q₈×C₃₇	—	8	4	no	—
131	D₄×C₃₇	—	4	2	no	—
132	D₄×C₃₇	—	4	2	no	—
133	D₄×C₃₇	—	4	4	no	—
134	D₄×C₃₇	—	8	4	no	—
135	D₄×C₃₇	—	8	4	no	—
136	C₂×C₄×C₃₇	—	2	2	no	—
137	C₂×C₄×C₃₇	—	2	2	no	—
138	C₂×C₄×C₃₇	—	2	2	no	—
139	C₂×C₄×C₃₇	—	2	4	no	—
140	C₂×C₄×C₃₇	—	2	2	no	—
141	C₂×C₄×C₃₇	—	2	2	no	—
142	C₂×C₄×C₃₇	—	2	4	no	—
143	C₂×C₄×C₃₇	—	4	2	no	—
144	C₂×C₄×C₃₇	—	4	2	no	—
145	C₂×C₄×C₃₇	—	4	2	no	—
146	C₂×C₄×C₃₇	—	4	2	no	—
147	C₂×C₄×C₃₇	—	4	2	no	—
148	C₂×C₄×C₃₇	—	4	2	no	—
149	C₂×C₄×C₃₇	—	4	2	no	—
150	C₂×C₄×C₃₇	—	4	2	no	—
151	C₂×C₄×C₃₇	#121	1	2	yes	—
152	C₂×C₄×C₃₇	#121	1	2	yes	—
153	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
154	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
155	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
157	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₃₇	2₋¹⁺⁴	1	2	yes	—
159	C₈×C₃₇	—	2	2	no	—
160	C₈×C₃₇	—	2	2	no	—
161	C₈×C₃₇	—	4	2	no	—
162	#28648	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂²×C₃₇	—	8	4	no	—
164	C₂²×C₃₇	—	8	4	no	—
165	C₂²×C₃₇	—	8	2	no	—
166	C₂²×C₃₇	—	8	2	no	—
167	C₂²×C₃₇	—	8	2	no	—
168	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
169	C₂²×C₃₇	#548	1	2	yes	—
170	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
172	C₂²×C₃₇	#577	1	2	yes	—
173	C₄×C₃₇	—	2	2	no	—
174	C₄×C₃₇	—	4	4	no	—
175	C₄×C₃₇	—	4	2	no	—
176	C₄×C₃₇	—	4	2	no	—
177	C₄×C₃₇	—	8	2	no	—
178	C₄×C₃₇	—	8	2	no	—
179	C₄×C₃₇	#469	1	4	yes	—
180	C₄×C₃₇	#532	1	1	yes	characteristic
181	C₄×C₃₇	#536	1	1	yes	characteristic
182	C₄×C₃₇	#556	1	2	yes	—
183	C₂×#486	C₂×C₃₇	1	1	yes	characteristic
184	C₂×#446	C₂×C₃₇	1	1	yes	characteristic, complemented
185	#2548	C₂×C₃₇	1	1	yes	characteristic
186	#2546	C₂×C₃₇	1	1	yes	characteristic, complemented
187	#2065	C₂×C₃₇	1	4	yes	complemented
188	#1988	C₂×C₃₇	1	1	yes	characteristic, complemented
189	#1982	C₂×C₃₇	1	1	yes	characteristic
190	#1936	C₂×C₃₇	1	4	yes	complemented
191	C₄×#106	C₂×C₃₇	1	1	yes	characteristic, complemented
192	C₂×C₃₇	—	16	2	no	—
193	C₂×C₃₇	#2545	1	1	yes	characteristic
194	C₂×C₃₇	C₂×#469	1	1	yes	characteristic
195	C₂×C₃₇	#3057	1	1	yes	characteristic
196	C₂×C₃₇	#3368	1	2	yes	—
197	C₂×C₃₇	#3373	1	2	yes	—
198	C₂×C₄⋊Q₈	—	2	1	no	—
199	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
200	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
201	C₂×#124	—	2	1	no	—
202	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
203	#486	—	2	4	no	—
204	#446	—	2	4	no	—
205	C₂×#106	C₂²×C₃₇	1	2	yes	—
206	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
207	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
208	C₂×#102	C₂²×C₃₇	1	2	yes	—
209	C₂×#102	C₂²×C₃₇	1	4	yes	—
210	C₂×#102	C₂²×C₃₇	1	2	yes	—
211	C₂×#97	C₂²×C₃₇	1	2	yes	—
212	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
213	#398	—	2	2	no	—
214	#394	—	2	2	no	—
215	#391	—	2	1	no	—
216	#390	—	2	1	no	—
217	#390	C₂²×C₃₇	1	4	yes	—
218	#389	C₂²×C₃₇	1	4	yes	—
219	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
220	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
221	#340	C₂²×C₃₇	1	4	yes	—
222	#340	C₂²×C₃₇	1	2	yes	—
223	C₃₇	#28648	1	1	yes	characteristic, direct product factor, Sylow
224	C₂²×Q₈	—	2	1	no	—
225	C₂²×Q₈	D₄×C₃₇	1	1	yes	characteristic
226	C₂²×D₄	—	2	1	no	—
227	C₂²×D₄	—	2	1	no	—
228	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
229	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
230	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
232	C₄⋊Q₈	—	2	2	no	—
233	C₄⋊Q₈	—	2	2	no	—
234	C₄⋊Q₈	—	4	4	no	—
235	#127	—	2	2	no	—
236	#127	—	2	2	no	—
237	#124	—	4	4	no	—
238	C₄×Q₈	—	2	2	no	—
239	C₄×Q₈	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	4	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
243	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
244	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
245	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
246	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
247	C₂×C₂²⋊C₄	—	2	4	no	—
248	C₂×C₂²⋊C₄	—	2	4	no	—
249	C₂×C₄²	—	2	1	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
252	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
253	#106	—	2	4	no	—
254	C₄⋊C₈	—	2	4	no	—
255	C₄⋊C₈	—	2	2	no	—
256	#102	—	2	4	no	—
257	#102	—	2	4	no	—
258	#102	—	2	8	no	—
259	#97	—	2	4	no	—
260	C₄×C₈	D₄×C₃₇	1	4	yes	—
261	#95	—	2	1	no	—
262	#95	—	2	1	no	—
263	#95	—	2	4	no	—
264	C₂⁴	—	2	2	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	4	2	no	—
269	C₂×Q₈	—	4	2	no	—
270	C₂×Q₈	—	4	2	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	4	2	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	8	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
284	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
285	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
287	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	4	no	—
292	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
293	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	4	8	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄⋊C₄	#41×C₃₇	1	4	yes	—
304	C₂²⋊C₄	—	4	8	no	—
305	C₂²⋊C₄	—	8	4	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	4	2	no	—
309	C₄²	—	4	2	no	—
310	C₄²	C₂×D₄×C₃₇	1	2	yes	—
311	C₄²	#41×C₃₇	1	2	yes	—
312	C₂³	—	4	2	no	—
313	C₂³	—	4	4	no	—
314	C₂³	—	4	2	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	4	4	no	—
317	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
318	Q₈	—	4	4	no	—
319	Q₈	—	8	4	no	—
320	D₄	—	4	2	no	—
321	D₄	—	4	2	no	—
322	D₄	—	4	4	no	—
323	D₄	—	8	4	no	—
324	D₄	—	8	4	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	#121×C₃₇	1	2	yes	—
341	C₂×C₄	#121×C₃₇	1	2	yes	—
342	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
343	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
344	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
345	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
346	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
347	C₂×C₄	2₋¹⁺⁴×C₃₇	1	2	yes	—
348	C₈	—	2	2	no	—
349	C₈	—	2	2	no	—
350	C₈	—	4	2	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	8	2	no	—
353	C₂²	—	8	2	no	—
354	C₂²	—	8	4	no	—
355	C₂²	—	8	4	no	—
356	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
357	C₂²	C₃₇×#548	1	2	yes	—
358	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
359	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
360	C₂²	C₃₇×#577	1	2	yes	—
361	C₄	—	2	2	no	—
362	C₄	—	4	2	no	—
363	C₄	—	4	2	no	—
364	C₄	—	4	4	no	—
365	C₄	—	8	2	no	—
366	C₄	—	8	2	no	—
367	C₄	C₃₇×#469	1	4	yes	—
368	C₄	C₃₇×#532	1	1	yes	characteristic
369	C₄	C₃₇×#536	1	1	yes	characteristic
370	C₄	C₃₇×#556	1	2	yes	—
371	C₂	—	16	2	no	—
372	C₂	C₃₇×#2545	1	1	yes	characteristic
373	C₂	C₂×C₃₇×#469	1	1	yes	characteristic
374	C₂	C₃₇×#3057	1	1	yes	characteristic
375	C₂	C₃₇×#3368	1	2	yes	—
376	C₂	C₃₇×#3373	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×#127×C₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂×C₄×Q₈×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₇×#446	C₂	semidirect
4. C₃₇×#2546	C₂	semidirect
5. C₃₇×#2065	C₂	semidirect
6. C₃₇×#1988	C₂	semidirect
8. C₃₇×#1936	C₂	semidirect
9. C₄×#106×C₃₇	C₂	semidirect
162. #28648	C₃₇	direct (N × H)
184. C₂×#446	C₂×C₃₇	semidirect
186. #2546	C₂×C₃₇	semidirect
187. #2065	C₂×C₃₇	semidirect
188. #1988	C₂×C₃₇	semidirect
190. #1936	C₂×C₃₇	semidirect
191. C₄×#106	C₂×C₃₇	semidirect
223. C₃₇	#28648	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#486	2
C₂×C₃₇×#446	2
C₃₇×#2548	2
C₃₇×#2546	2
C₃₇×#2065	2
C₃₇×#1988	2
C₃₇×#1982	2
C₃₇×#1936	2
C₄×#106×C₃₇	2
#28648	37

Subgroups — C37×#28648 #22649901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28648 #22649901