Subgroups — C₃₇×#28749 #22650002

Order 9472.

1194 conjugacy classes of subgroups.

The subgroup lattice has 406 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, complemented
2	C₃₇×#2867	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2041	C₂	1	4	yes	maximal, complemented
5	C₃₇×#1982	C₂	1	4	yes	maximal, complemented
6	C₃₇×#1957	C₂	1	2	yes	maximal, complemented
7	C₄×C₄⋊C₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
9	C₂×#127×C₃₇	—	2	1	no	—
10	C₂×#127×C₃₇	—	2	1	no	—
11	C₂×#127×C₃₇	—	2	1	no	—
12	C₂×#127×C₃₇	—	2	1	no	—
13	C₂×#127×C₃₇	C₂²	1	2	yes	—
14	C₂×#127×C₃₇	C₂²	1	2	yes	—
15	C₂×#127×C₃₇	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₃₇	—	2	1	no	—
17	C₃₇×#486	—	2	8	no	—
18	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
19	C₂×#102×C₃₇	C₂²	1	8	yes	—
20	C₂×#102×C₃₇	C₂²	1	8	yes	—
21	C₂×C₄×C₈×C₃₇	C₂²	1	2	yes	—
22	C₃₇×#391	—	2	1	no	—
23	C₃₇×#389	—	2	1	no	—
24	C₃₇×#389	C₂²	1	2	yes	—
25	C₃₇×#384	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₃₇	—	2	1	no	—
27	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
28	C₄³×C₃₇	C₂²	1	1	yes	characteristic
29	C₃₇×#336	C₂²	1	2	yes	—
30	C₂²×Q₈×C₃₇	—	2	1	no	—
31	C₂²×D₄×C₃₇	—	2	2	no	—
32	C₂²×D₄×C₃₇	—	2	2	no	—
33	C₂²×D₄×C₃₇	—	2	2	no	—
34	C₂²×D₄×C₃₇	—	2	2	no	—
35	C₂²×D₄×C₃₇	—	2	2	no	—
36	C₂²×D₄×C₃₇	—	2	2	no	—
37	C₂²×D₄×C₃₇	C₂³	1	4	yes	—
38	C₂²×C₈×C₃₇	C₂³	1	4	yes	—
39	C₄⋊Q₈×C₃₇	—	2	2	no	—
40	C₄⋊Q₈×C₃₇	D₄	1	4	yes	complemented
41	#127×C₃₇	—	2	4	no	—
42	#127×C₃₇	—	2	4	no	—
43	#127×C₃₇	—	2	8	no	—
44	#127×C₃₇	—	4	4	no	—
45	#127×C₃₇	—	4	4	no	—
46	#127×C₃₇	—	4	4	no	—
47	#127×C₃₇	—	4	4	no	—
48	#127×C₃₇	—	4	4	no	—
49	C₄×Q₈×C₃₇	—	4	4	no	—
50	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
51	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
52	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
56	C₂×C₄²×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	#102×C₃₇	—	4	8	no	—
67	C₄×C₈×C₃₇	—	2	4	no	—
68	#95×C₃₇	—	2	2	no	—
69	#95×C₃₇	—	2	2	no	—
70	C₂⁴×C₃₇	—	2	4	no	—
71	C₂×Q₈×C₃₇	—	2	4	no	—
72	C₂×Q₈×C₃₇	—	4	2	no	—
73	C₂×Q₈×C₃₇	—	4	2	no	—
74	C₂×D₄×C₃₇	—	2	4	no	—
75	C₂×D₄×C₃₇	—	2	8	no	—
76	C₂×D₄×C₃₇	—	2	4	no	—
77	C₂×D₄×C₃₇	—	2	8	no	—
78	C₂×D₄×C₃₇	—	4	4	no	—
79	C₂×D₄×C₃₇	—	4	4	no	—
80	C₂×D₄×C₃₇	—	4	4	no	—
81	C₂×D₄×C₃₇	—	4	4	no	—
82	C₂×D₄×C₃₇	—	4	4	no	—
83	C₂×D₄×C₃₇	—	4	4	no	—
84	C₂×D₄×C₃₇	—	4	4	no	—
85	C₂×D₄×C₃₇	—	4	4	no	—
86	C₂×D₄×C₃₇	—	4	4	no	—
87	C₂×D₄×C₃₇	—	4	4	no	—
88	C₂×D₄×C₃₇	—	4	4	no	—
89	C₂×D₄×C₃₇	—	4	4	no	—
90	C₂×D₄×C₃₇	—	4	4	no	—
91	C₂×D₄×C₃₇	—	4	4	no	—
92	C₂×D₄×C₃₇	—	4	4	no	—
93	C₂×D₄×C₃₇	—	4	4	no	—
94	C₂×D₄×C₃₇	—	4	4	no	—
95	C₂×D₄×C₃₇	—	4	4	no	—
96	C₂²×C₄×C₃₇	—	2	2	no	—
97	C₂²×C₄×C₃₇	—	2	2	no	—
98	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
105	C₂×C₈×C₃₇	—	2	4	no	—
106	C₂×C₈×C₃₇	—	2	4	no	—
107	C₂×C₈×C₃₇	—	2	4	no	—
108	C₄⋊C₄×C₃₇	—	2	4	no	—
109	C₄⋊C₄×C₃₇	—	2	2	no	—
110	C₄⋊C₄×C₃₇	—	2	4	no	—
111	C₄⋊C₄×C₃₇	—	4	4	no	—
112	C₄⋊C₄×C₃₇	—	4	2	no	—
113	C₄⋊C₄×C₃₇	—	4	2	no	—
114	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
115	C₄²×C₃₇	—	2	2	no	—
116	C₄²×C₃₇	—	2	2	no	—
117	C₄²×C₃₇	—	2	2	no	—
118	C₄²×C₃₇	—	4	4	no	—
119	C₄²×C₃₇	D₈	1	4	yes	—
120	C₄²×C₃₇	SD₁₆	1	4	yes	—
121	C₄²×C₃₇	C₂×D₄	1	2	yes	—
122	C₄²×C₃₇	#41	1	2	yes	—
123	C₄²×C₃₇	#41	1	4	yes	—
124	C₂³×C₃₇	—	4	4	no	—
125	C₂³×C₃₇	—	4	4	no	—
126	C₂³×C₃₇	—	4	4	no	—
127	C₂³×C₃₇	—	4	4	no	—
128	C₂³×C₃₇	—	4	4	no	—
129	C₂³×C₃₇	—	4	4	no	—
130	C₂³×C₃₇	—	4	4	no	—
131	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
132	Q₈×C₃₇	—	4	8	no	—
133	D₄×C₃₇	—	4	8	no	—
134	D₄×C₃₇	—	4	8	no	—
135	D₄×C₃₇	—	8	8	no	—
136	D₄×C₃₇	—	8	8	no	—
137	D₄×C₃₇	—	8	8	no	—
138	D₄×C₃₇	—	8	8	no	—
139	D₄×C₃₇	—	8	8	no	—
140	D₄×C₃₇	—	8	8	no	—
141	C₂×C₄×C₃₇	—	2	1	no	—
142	C₂×C₄×C₃₇	—	2	1	no	—
143	C₂×C₄×C₃₇	—	2	1	no	—
144	C₂×C₄×C₃₇	—	2	1	no	—
145	C₂×C₄×C₃₇	—	2	1	no	—
146	C₂×C₄×C₃₇	—	2	1	no	—
147	C₂×C₄×C₃₇	—	2	4	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	—	4	2	no	—
152	C₂×C₄×C₃₇	—	4	2	no	—
153	C₂×C₄×C₃₇	#121	1	2	yes	—
154	C₂×C₄×C₃₇	#121	1	2	yes	—
155	C₂×C₄×C₃₇	#124	1	2	yes	—
156	C₂×C₄×C₃₇	#124	1	2	yes	—
157	C₂×C₄×C₃₇	C₂×D₈	1	2	yes	—
158	C₂×C₄×C₃₇	C₂×D₈	1	2	yes	—
159	C₂×C₄×C₃₇	C₂×D₈	1	2	yes	—
160	C₂×C₄×C₃₇	C₂×SD₁₆	1	2	yes	—
161	C₂×C₄×C₃₇	C₂×SD₁₆	1	2	yes	—
162	C₂×C₄×C₃₇	C₂×SD₁₆	1	2	yes	—
163	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
164	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
165	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
167	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
169	C₈×C₃₇	—	4	4	no	—
170	#28749	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂²×C₃₇	—	8	4	no	—
172	C₂²×C₃₇	—	8	4	no	—
173	C₂²×C₃₇	—	8	4	no	—
174	C₂²×C₃₇	—	8	4	no	—
175	C₂²×C₃₇	—	8	4	no	—
176	C₂²×C₃₇	—	8	4	no	—
177	C₂²×C₃₇	—	8	4	no	—
178	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
179	C₂²×C₃₇	C₂×#124	1	1	yes	characteristic
180	C₂²×C₃₇	#535	1	1	yes	characteristic
181	C₂²×C₃₇	C₂²×D₈	1	1	yes	characteristic
182	C₂²×C₃₇	C₂²×SD₁₆	1	1	yes	characteristic
183	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₄×C₃₇	—	2	2	no	—
186	C₄×C₃₇	—	2	2	no	—
187	C₄×C₃₇	—	2	2	no	—
188	C₄×C₃₇	—	4	4	no	—
189	C₄×C₃₇	—	8	2	no	—
190	C₄×C₃₇	#459	1	4	yes	—
191	C₄×C₃₇	#460	1	4	yes	—
192	C₄×C₃₇	#486	1	4	yes	complemented
193	C₄×C₃₇	#550	1	2	yes	—
194	C₄×C₃₇	#559	1	2	yes	—
195	C₂×#486	C₂×C₃₇	1	2	yes	complemented
196	#2867	C₂×C₃₇	1	1	yes	characteristic
197	C₄×C₄⋊Q₈	C₂×C₃₇	1	1	yes	characteristic, complemented
198	#2041	C₂×C₃₇	1	4	yes	complemented
199	#1982	C₂×C₃₇	1	4	yes	complemented
200	#1957	C₂×C₃₇	1	2	yes	complemented
201	C₄×C₄⋊C₈	C₂×C₃₇	1	1	yes	characteristic, complemented
202	C₂×C₃₇	—	16	4	no	—
203	C₂×C₃₇	#2548	1	1	yes	characteristic
204	C₂×C₃₇	C₂×#459	1	1	yes	characteristic
205	C₂×C₃₇	C₂×#460	1	1	yes	characteristic
206	C₂×C₃₇	C₂×#486	1	1	yes	characteristic
207	C₂×C₃₇	#3138	1	1	yes	characteristic
208	C₂×C₃₇	#3205	1	1	yes	characteristic
209	C₂×C₃₇	#3208	1	1	yes	characteristic
210	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
211	C₂×#127	—	2	1	no	—
212	C₂×#127	—	2	1	no	—
213	C₂×#127	—	2	1	no	—
214	C₂×#127	—	2	1	no	—
215	C₂×#127	C₂²×C₃₇	1	2	yes	—
216	C₂×#127	C₂²×C₃₇	1	2	yes	—
217	C₂×#127	C₂²×C₃₇	1	2	yes	—
218	C₂×C₄×Q₈	—	2	1	no	—
219	#486	—	2	8	no	—
220	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
221	C₂×#102	C₂²×C₃₇	1	8	yes	—
222	C₂×#102	C₂²×C₃₇	1	8	yes	—
223	C₂×C₄×C₈	C₂²×C₃₇	1	2	yes	—
224	#391	—	2	1	no	—
225	#389	—	2	1	no	—
226	#389	C₂²×C₃₇	1	2	yes	—
227	#384	C₂²×C₃₇	1	1	yes	characteristic
228	C₄×C₄⋊C₄	—	2	1	no	—
229	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
230	C₄³	C₂²×C₃₇	1	1	yes	characteristic
231	#336	C₂²×C₃₇	1	2	yes	—
232	C₃₇	#28749	1	1	yes	characteristic, direct product factor, Sylow
233	C₂²×Q₈	—	2	1	no	—
234	C₂²×D₄	—	2	2	no	—
235	C₂²×D₄	—	2	2	no	—
236	C₂²×D₄	—	2	2	no	—
237	C₂²×D₄	—	2	2	no	—
238	C₂²×D₄	—	2	2	no	—
239	C₂²×D₄	—	2	2	no	—
240	C₂²×D₄	C₂³×C₃₇	1	4	yes	—
241	C₂²×C₈	C₂³×C₃₇	1	4	yes	—
242	C₄⋊Q₈	—	2	2	no	—
243	C₄⋊Q₈	D₄×C₃₇	1	4	yes	complemented
244	#127	—	2	4	no	—
245	#127	—	2	4	no	—
246	#127	—	2	8	no	—
247	#127	—	4	4	no	—
248	#127	—	4	4	no	—
249	#127	—	4	4	no	—
250	#127	—	4	4	no	—
251	#127	—	4	4	no	—
252	C₄×Q₈	—	4	4	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
259	C₂×C₄²	—	2	2	no	—
260	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
261	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
262	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
263	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
267	C₄⋊C₈	—	2	4	no	—
268	#102	—	2	16	no	—
269	#102	—	4	8	no	—
270	C₄×C₈	—	2	4	no	—
271	#95	—	2	2	no	—
272	#95	—	2	2	no	—
273	C₂⁴	—	2	4	no	—
274	C₂×Q₈	—	2	4	no	—
275	C₂×Q₈	—	4	2	no	—
276	C₂×Q₈	—	4	2	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	8	no	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	—	2	8	no	—
281	C₂×D₄	—	4	4	no	—
282	C₂×D₄	—	4	4	no	—
283	C₂×D₄	—	4	4	no	—
284	C₂×D₄	—	4	4	no	—
285	C₂×D₄	—	4	4	no	—
286	C₂×D₄	—	4	4	no	—
287	C₂×D₄	—	4	4	no	—
288	C₂×D₄	—	4	4	no	—
289	C₂×D₄	—	4	4	no	—
290	C₂×D₄	—	4	4	no	—
291	C₂×D₄	—	4	4	no	—
292	C₂×D₄	—	4	4	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂×D₄	—	4	4	no	—
295	C₂×D₄	—	4	4	no	—
296	C₂×D₄	—	4	4	no	—
297	C₂×D₄	—	4	4	no	—
298	C₂×D₄	—	4	4	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
307	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	4	4	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	4	4	no	—
322	C₄²	D₈×C₃₇	1	4	yes	—
323	C₄²	SD₁₆×C₃₇	1	4	yes	—
324	C₄²	C₂×D₄×C₃₇	1	2	yes	—
325	C₄²	#41×C₃₇	1	2	yes	—
326	C₄²	#41×C₃₇	1	4	yes	—
327	C₂³	—	4	4	no	—
328	C₂³	—	4	4	no	—
329	C₂³	—	4	4	no	—
330	C₂³	—	4	4	no	—
331	C₂³	—	4	4	no	—
332	C₂³	—	4	4	no	—
333	C₂³	—	4	4	no	—
334	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
335	Q₈	—	4	8	no	—
336	D₄	—	4	8	no	—
337	D₄	—	4	8	no	—
338	D₄	—	8	8	no	—
339	D₄	—	8	8	no	—
340	D₄	—	8	8	no	—
341	D₄	—	8	8	no	—
342	D₄	—	8	8	no	—
343	D₄	—	8	8	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	#121×C₃₇	1	2	yes	—
357	C₂×C₄	#121×C₃₇	1	2	yes	—
358	C₂×C₄	#124×C₃₇	1	2	yes	—
359	C₂×C₄	#124×C₃₇	1	2	yes	—
360	C₂×C₄	C₂×D₈×C₃₇	1	2	yes	—
361	C₂×C₄	C₂×D₈×C₃₇	1	2	yes	—
362	C₂×C₄	C₂×D₈×C₃₇	1	2	yes	—
363	C₂×C₄	C₂×SD₁₆×C₃₇	1	2	yes	—
364	C₂×C₄	C₂×SD₁₆×C₃₇	1	2	yes	—
365	C₂×C₄	C₂×SD₁₆×C₃₇	1	2	yes	—
366	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
367	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
368	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
369	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
370	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
371	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
372	C₈	—	4	4	no	—
373	C₂²	—	8	4	no	—
374	C₂²	—	8	4	no	—
375	C₂²	—	8	4	no	—
376	C₂²	—	8	4	no	—
377	C₂²	—	8	4	no	—
378	C₂²	—	8	4	no	—
379	C₂²	—	8	4	no	—
380	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
381	C₂²	C₂×#124×C₃₇	1	1	yes	characteristic
382	C₂²	C₃₇×#535	1	1	yes	characteristic
383	C₂²	C₂²×D₈×C₃₇	1	1	yes	characteristic
384	C₂²	C₂²×SD₁₆×C₃₇	1	1	yes	characteristic
385	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
386	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
387	C₄	—	2	2	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	4	4	no	—
391	C₄	—	8	2	no	—
392	C₄	C₃₇×#459	1	4	yes	—
393	C₄	C₃₇×#460	1	4	yes	—
394	C₄	C₃₇×#486	1	4	yes	complemented
395	C₄	C₃₇×#550	1	2	yes	—
396	C₄	C₃₇×#559	1	2	yes	—
397	C₂	—	16	4	no	—
398	C₂	C₃₇×#2548	1	1	yes	characteristic
399	C₂	C₂×C₃₇×#459	1	1	yes	characteristic
400	C₂	C₂×C₃₇×#460	1	1	yes	characteristic
401	C₂	C₂×C₃₇×#486	1	1	yes	characteristic
402	C₂	C₃₇×#3138	1	1	yes	characteristic
403	C₂	C₃₇×#3205	1	1	yes	characteristic
404	C₂	C₃₇×#3208	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#2867	C₂
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
1. C₂×C₃₇×#486	C₂	semidirect
3. C₄×C₄⋊Q₈×C₃₇	C₂	semidirect
4. C₃₇×#2041	C₂	semidirect
5. C₃₇×#1982	C₂	semidirect
6. C₃₇×#1957	C₂	semidirect
7. C₄×C₄⋊C₈×C₃₇	C₂	semidirect
40. C₄⋊Q₈×C₃₇	D₄	semidirect
170. #28749	C₃₇	direct (N × H)
192. C₄×C₃₇	#486	semidirect
195. C₂×#486	C₂×C₃₇	semidirect
197. C₄×C₄⋊Q₈	C₂×C₃₇	semidirect
198. #2041	C₂×C₃₇	semidirect
199. #1982	C₂×C₃₇	semidirect
200. #1957	C₂×C₃₇	semidirect
201. C₄×C₄⋊C₈	C₂×C₃₇	semidirect
232. C₃₇	#28749	direct (N × H)
243. C₄⋊Q₈	D₄×C₃₇	semidirect
394. 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×#2867	2
C₄×C₄⋊Q₈×C₃₇	2
C₃₇×#2041	2
C₃₇×#1982	2
C₃₇×#1957	2
C₄×C₄⋊C₈×C₃₇	2
#28749	37

Subgroups — C37×#28749 #22650002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28749 #22650002