Subgroups — C₃₇×#28716 #22649969

Order 9472.

1018 conjugacy classes of subgroups.

The subgroup lattice has 386 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	2	yes	maximal
2	C₃₇×#2868	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#127×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2071	C₂	1	4	yes	maximal, complemented
5	C₃₇×#1990	C₂	1	2	yes	maximal, complemented
6	C₃₇×#1802	C₂	1	4	yes	maximal, complemented
7	C₄×C₄⋊C₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄⋊Q₈×C₃₇	—	2	1	no	—
9	C₂×C₄⋊Q₈×C₃₇	—	2	1	no	—
10	C₂×C₄⋊Q₈×C₃₇	C₂²	1	2	yes	—
11	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₃₇	—	2	1	no	—
13	C₂×C₄×D₄×C₃₇	—	2	1	no	—
14	C₂×C₄×D₄×C₃₇	C₂²	1	2	yes	—
15	C₃₇×#486	—	2	8	no	—
16	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
17	C₂×#102×C₃₇	C₂²	1	8	yes	—
18	C₂×C₄×C₈×C₃₇	C₂²	1	2	yes	—
19	C₃₇×#390	—	2	1	no	—
20	C₃₇×#390	—	2	1	no	—
21	C₃₇×#390	C₂²	1	2	yes	—
22	C₃₇×#384	—	2	1	no	—
23	C₃₇×#384	—	2	1	no	—
24	C₃₇×#384	C₂²	1	2	yes	—
25	C₃₇×#384	C₂²	1	2	yes	—
26	C₃₇×#384	C₂²	1	1	yes	characteristic
27	C₄³×C₃₇	C₂²	1	1	yes	characteristic
28	C₃₇×#340	C₂²	1	8	yes	—
29	C₃₇×#336	C₂²	1	2	yes	—
30	C₂²×Q₈×C₃₇	—	2	2	no	—
31	C₂²×D₄×C₃₇	—	2	1	no	—
32	C₂²×D₄×C₃₇	—	2	1	no	—
33	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
34	C₂³×C₄×C₃₇	—	2	2	no	—
35	C₂²×C₈×C₃₇	C₂³	1	4	yes	—
36	C₄⋊Q₈×C₃₇	—	2	4	no	—
37	C₄⋊Q₈×C₃₇	—	2	4	no	—
38	C₄⋊Q₈×C₃₇	—	4	4	no	—
39	C₄⋊Q₈×C₃₇	—	4	4	no	—
40	#127×C₃₇	—	2	2	no	—
41	#127×C₃₇	D₄	1	4	yes	—
42	C₄×D₄×C₃₇	—	2	8	no	—
43	C₄×D₄×C₃₇	—	4	4	no	—
44	C₄×D₄×C₃₇	—	4	4	no	—
45	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
48	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
51	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
52	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
53	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
54	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
57	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
64	C₄⋊C₈×C₃₇	—	2	4	no	—
65	#102×C₃₇	—	2	16	no	—
66	C₄×C₈×C₃₇	—	2	4	no	—
67	C₂⁴×C₃₇	—	2	2	no	—
68	C₂×Q₈×C₃₇	—	4	4	no	—
69	C₂×Q₈×C₃₇	—	4	4	no	—
70	C₂×Q₈×C₃₇	—	4	4	no	—
71	C₂×D₄×C₃₇	—	2	4	no	—
72	C₂×D₄×C₃₇	—	2	4	no	—
73	C₂×D₄×C₃₇	—	2	4	no	—
74	C₂×D₄×C₃₇	—	2	2	no	—
75	C₂×D₄×C₃₇	—	2	4	no	—
76	C₂×D₄×C₃₇	—	4	2	no	—
77	C₂×D₄×C₃₇	—	4	2	no	—
78	C₂×D₄×C₃₇	—	4	2	no	—
79	C₂×D₄×C₃₇	—	4	2	no	—
80	C₂×D₄×C₃₇	C₂×D₄	1	4	yes	—
81	C₂²×C₄×C₃₇	—	2	2	no	—
82	C₂²×C₄×C₃₇	—	2	4	no	—
83	C₂²×C₄×C₃₇	—	4	4	no	—
84	C₂²×C₄×C₃₇	—	4	4	no	—
85	C₂²×C₄×C₃₇	—	4	4	no	—
86	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
93	C₂×C₈×C₃₇	—	2	4	no	—
94	C₂×C₈×C₃₇	—	2	4	no	—
95	C₂×C₈×C₃₇	—	2	4	no	—
96	C₄⋊C₄×C₃₇	—	2	4	no	—
97	C₄⋊C₄×C₃₇	—	2	4	no	—
98	C₄⋊C₄×C₃₇	—	2	4	no	—
99	C₄⋊C₄×C₃₇	—	4	4	no	—
100	C₄⋊C₄×C₃₇	—	4	4	no	—
101	C₄⋊C₄×C₃₇	—	4	4	no	—
102	C₄⋊C₄×C₃₇	—	4	2	no	—
103	C₄⋊C₄×C₃₇	—	4	4	no	—
104	C₄⋊C₄×C₃₇	—	4	4	no	—
105	C₄⋊C₄×C₃₇	—	4	2	no	—
106	C₂²⋊C₄×C₃₇	—	4	4	no	—
107	C₂²⋊C₄×C₃₇	—	4	4	no	—
108	C₂²⋊C₄×C₃₇	—	4	4	no	—
109	C₄²×C₃₇	—	2	2	no	—
110	C₄²×C₃₇	—	2	2	no	—
111	C₄²×C₃₇	—	2	2	no	—
112	C₄²×C₃₇	D₈	1	4	yes	—
113	C₄²×C₃₇	SD₁₆	1	4	yes	—
114	C₄²×C₃₇	C₂×D₄	1	2	yes	—
115	C₄²×C₃₇	#41	1	2	yes	—
116	C₄²×C₃₇	#41	1	4	yes	—
117	C₂³×C₃₇	—	2	4	no	—
118	C₂³×C₃₇	—	4	2	no	—
119	C₂³×C₃₇	—	4	2	no	—
120	C₂³×C₃₇	—	4	2	no	—
121	C₂³×C₃₇	—	4	2	no	—
122	C₂³×C₃₇	—	4	2	no	—
123	C₂³×C₃₇	—	4	2	no	—
124	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
125	Q₈×C₃₇	—	8	8	no	—
126	D₄×C₃₇	—	2	8	no	—
127	D₄×C₃₇	—	4	4	no	—
128	D₄×C₃₇	—	4	8	no	—
129	D₄×C₃₇	—	4	8	no	—
130	C₂×C₄×C₃₇	—	2	1	no	—
131	C₂×C₄×C₃₇	—	2	1	no	—
132	C₂×C₄×C₃₇	—	2	1	no	—
133	C₂×C₄×C₃₇	—	2	1	no	—
134	C₂×C₄×C₃₇	—	2	1	no	—
135	C₂×C₄×C₃₇	—	2	1	no	—
136	C₂×C₄×C₃₇	—	4	4	no	—
137	C₂×C₄×C₃₇	—	4	2	no	—
138	C₂×C₄×C₃₇	—	4	2	no	—
139	C₂×C₄×C₃₇	—	4	4	no	—
140	C₂×C₄×C₃₇	—	4	2	no	—
141	C₂×C₄×C₃₇	—	4	4	no	—
142	C₂×C₄×C₃₇	—	8	8	no	—
143	C₂×C₄×C₃₇	#121	1	2	yes	—
144	C₂×C₄×C₃₇	#121	1	2	yes	—
145	C₂×C₄×C₃₇	#124	1	2	yes	—
146	C₂×C₄×C₃₇	#124	1	2	yes	—
147	C₂×C₄×C₃₇	C₂×D₈	1	2	yes	—
148	C₂×C₄×C₃₇	C₂×D₈	1	2	yes	—
149	C₂×C₄×C₃₇	C₂×D₈	1	2	yes	—
150	C₂×C₄×C₃₇	C₂×SD₁₆	1	2	yes	—
151	C₂×C₄×C₃₇	C₂×SD₁₆	1	2	yes	—
152	C₂×C₄×C₃₇	C₂×SD₁₆	1	2	yes	—
153	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
154	C₂×C₄×C₃₇	#137	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	—	4	4	no	—
160	#28716	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂²×C₃₇	—	4	4	no	—
162	C₂²×C₃₇	—	4	4	no	—
163	C₂²×C₃₇	—	4	4	no	—
164	C₂²×C₃₇	—	8	2	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	C₂×#124	1	1	yes	characteristic
170	C₂²×C₃₇	#536	1	1	yes	characteristic
171	C₂²×C₃₇	C₂²×D₈	1	1	yes	characteristic
172	C₂²×C₃₇	C₂²×SD₁₆	1	1	yes	characteristic
173	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
174	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
175	C₄×C₃₇	—	2	2	no	—
176	C₄×C₃₇	—	2	2	no	—
177	C₄×C₃₇	—	2	2	no	—
178	C₄×C₃₇	—	8	2	no	—
179	C₄×C₃₇	—	8	4	no	—
180	C₄×C₃₇	#459	1	4	yes	—
181	C₄×C₃₇	#461	1	4	yes	—
182	C₄×C₃₇	#486	1	4	yes	complemented
183	C₄×C₃₇	#547	1	2	yes	—
184	C₄×C₃₇	#556	1	2	yes	—
185	C₂×#486	C₂×C₃₇	1	2	yes	—
186	#2868	C₂×C₃₇	1	1	yes	characteristic, complemented
187	C₄×#127	C₂×C₃₇	1	1	yes	characteristic
188	#2071	C₂×C₃₇	1	4	yes	complemented
189	#1990	C₂×C₃₇	1	2	yes	complemented
190	#1802	C₂×C₃₇	1	4	yes	complemented
191	C₄×C₄⋊C₈	C₂×C₃₇	1	1	yes	characteristic, complemented
192	C₂×C₃₇	—	8	4	no	—
193	C₂×C₃₇	#2547	1	1	yes	characteristic
194	C₂×C₃₇	C₂×#459	1	1	yes	characteristic
195	C₂×C₃₇	C₂×#461	1	1	yes	characteristic
196	C₂×C₃₇	C₂×#486	1	1	yes	characteristic
197	C₂×C₃₇	#3141	1	1	yes	characteristic
198	C₂×C₃₇	#3226	1	1	yes	characteristic
199	C₂×C₃₇	#3227	1	1	yes	characteristic
200	C₂×C₄⋊Q₈	—	2	1	no	—
201	C₂×C₄⋊Q₈	—	2	1	no	—
202	C₂×C₄⋊Q₈	C₂²×C₃₇	1	2	yes	—
203	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
204	C₂×C₄×D₄	—	2	1	no	—
205	C₂×C₄×D₄	—	2	1	no	—
206	C₂×C₄×D₄	C₂²×C₃₇	1	2	yes	—
207	#486	—	2	8	no	—
208	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
209	C₂×#102	C₂²×C₃₇	1	8	yes	—
210	C₂×C₄×C₈	C₂²×C₃₇	1	2	yes	—
211	#390	—	2	1	no	—
212	#390	—	2	1	no	—
213	#390	C₂²×C₃₇	1	2	yes	—
214	#384	—	2	1	no	—
215	#384	—	2	1	no	—
216	#384	C₂²×C₃₇	1	1	yes	characteristic
217	#384	C₂²×C₃₇	1	2	yes	—
218	#384	C₂²×C₃₇	1	2	yes	—
219	C₄³	C₂²×C₃₇	1	1	yes	characteristic
220	#340	C₂²×C₃₇	1	8	yes	—
221	#336	C₂²×C₃₇	1	2	yes	—
222	C₃₇	#28716	1	1	yes	characteristic, direct product factor, Sylow
223	C₂²×Q₈	—	2	2	no	—
224	C₂²×D₄	—	2	1	no	—
225	C₂²×D₄	—	2	1	no	—
226	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
227	C₂³×C₄	—	2	2	no	—
228	C₂²×C₈	C₂³×C₃₇	1	4	yes	—
229	C₄⋊Q₈	—	2	4	no	—
230	C₄⋊Q₈	—	2	4	no	—
231	C₄⋊Q₈	—	4	4	no	—
232	C₄⋊Q₈	—	4	4	no	—
233	#127	—	2	2	no	—
234	#127	D₄×C₃₇	1	4	yes	—
235	C₄×D₄	—	2	8	no	—
236	C₄×D₄	—	4	4	no	—
237	C₄×D₄	—	4	4	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
246	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
251	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
252	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
253	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
254	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
257	C₄⋊C₈	—	2	4	no	—
258	#102	—	2	16	no	—
259	C₄×C₈	—	2	4	no	—
260	C₂⁴	—	2	2	no	—
261	C₂×Q₈	—	4	4	no	—
262	C₂×Q₈	—	4	4	no	—
263	C₂×Q₈	—	4	4	no	—
264	C₂×D₄	—	2	4	no	—
265	C₂×D₄	—	2	4	no	—
266	C₂×D₄	—	2	4	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	4	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	—	4	2	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂×D₄	—	4	2	no	—
273	C₂×D₄	C₂×D₄×C₃₇	1	4	yes	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	—	4	4	no	—
279	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
281	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
285	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	4	4	no	—
293	C₄⋊C₄	—	4	4	no	—
294	C₄⋊C₄	—	4	4	no	—
295	C₄⋊C₄	—	4	2	no	—
296	C₄⋊C₄	—	4	4	no	—
297	C₄⋊C₄	—	4	4	no	—
298	C₄⋊C₄	—	4	2	no	—
299	C₂²⋊C₄	—	4	4	no	—
300	C₂²⋊C₄	—	4	4	no	—
301	C₂²⋊C₄	—	4	4	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	D₈×C₃₇	1	4	yes	—
306	C₄²	SD₁₆×C₃₇	1	4	yes	—
307	C₄²	C₂×D₄×C₃₇	1	2	yes	—
308	C₄²	#41×C₃₇	1	2	yes	—
309	C₄²	#41×C₃₇	1	4	yes	—
310	C₂³	—	2	4	no	—
311	C₂³	—	4	2	no	—
312	C₂³	—	4	2	no	—
313	C₂³	—	4	2	no	—
314	C₂³	—	4	2	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	4	2	no	—
317	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
318	Q₈	—	8	8	no	—
319	D₄	—	2	8	no	—
320	D₄	—	4	4	no	—
321	D₄	—	4	8	no	—
322	D₄	—	4	8	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	8	8	no	—
336	C₂×C₄	#121×C₃₇	1	2	yes	—
337	C₂×C₄	#121×C₃₇	1	2	yes	—
338	C₂×C₄	#124×C₃₇	1	2	yes	—
339	C₂×C₄	#124×C₃₇	1	2	yes	—
340	C₂×C₄	C₂×D₈×C₃₇	1	2	yes	—
341	C₂×C₄	C₂×D₈×C₃₇	1	2	yes	—
342	C₂×C₄	C₂×D₈×C₃₇	1	2	yes	—
343	C₂×C₄	C₂×SD₁₆×C₃₇	1	2	yes	—
344	C₂×C₄	C₂×SD₁₆×C₃₇	1	2	yes	—
345	C₂×C₄	C₂×SD₁₆×C₃₇	1	2	yes	—
346	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
347	C₂×C₄	#137×C₃₇	1	2	yes	—
348	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
349	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
350	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
351	C₂×C₄	2₋¹⁺⁴×C₃₇	1	2	yes	—
352	C₈	—	4	4	no	—
353	C₂²	—	4	4	no	—
354	C₂²	—	4	4	no	—
355	C₂²	—	4	4	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	8	2	no	—
359	C₂²	—	8	2	no	—
360	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
361	C₂²	C₂×#124×C₃₇	1	1	yes	characteristic
362	C₂²	C₃₇×#536	1	1	yes	characteristic
363	C₂²	C₂²×D₈×C₃₇	1	1	yes	characteristic
364	C₂²	C₂²×SD₁₆×C₃₇	1	1	yes	characteristic
365	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
366	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
367	C₄	—	2	2	no	—
368	C₄	—	2	2	no	—
369	C₄	—	2	2	no	—
370	C₄	—	8	2	no	—
371	C₄	—	8	4	no	—
372	C₄	C₃₇×#459	1	4	yes	—
373	C₄	C₃₇×#461	1	4	yes	—
374	C₄	C₃₇×#486	1	4	yes	complemented
375	C₄	C₃₇×#547	1	2	yes	—
376	C₄	C₃₇×#556	1	2	yes	—
377	C₂	—	8	4	no	—
378	C₂	C₃₇×#2547	1	1	yes	characteristic
379	C₂	C₂×C₃₇×#459	1	1	yes	characteristic
380	C₂	C₂×C₃₇×#461	1	1	yes	characteristic
381	C₂	C₂×C₃₇×#486	1	1	yes	characteristic
382	C₂	C₃₇×#3141	1	1	yes	characteristic
383	C₂	C₃₇×#3226	1	1	yes	characteristic
384	C₂	C₃₇×#3227	1	1	yes	characteristic

	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 ◁ C₄³×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₇×#2868	C₂	semidirect
4. C₃₇×#2071	C₂	semidirect
5. C₃₇×#1990	C₂	semidirect
6. C₃₇×#1802	C₂	semidirect
7. C₄×C₄⋊C₈×C₃₇	C₂	semidirect
160. #28716	C₃₇	direct (N × H)
182. C₄×C₃₇	#486	semidirect
186. #2868	C₂×C₃₇	semidirect
188. #2071	C₂×C₃₇	semidirect
189. #1990	C₂×C₃₇	semidirect
190. #1802	C₂×C₃₇	semidirect
191. C₄×C₄⋊C₈	C₂×C₃₇	semidirect
222. C₃₇	#28716	direct (N × H)
374. C₄	C₃₇×#486	semidirect

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
C₃₇×#2868	2
C₄×#127×C₃₇	2
C₃₇×#2071	2
C₃₇×#1990	2
C₃₇×#1802	2
C₄×C₄⋊C₈×C₃₇	2
#28716	37

Subgroups — C37×#28716 #22649969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28716 #22649969