Subgroups — C₃₇×#28471 #22649724

Order 9472.

1082 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#497	C₂	1	2	yes	maximal
2	C₂×C₃₇×#494	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#461	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×SD₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₃₇×#2547	C₂	1	1	yes	maximal, characteristic
7	C₃₇×#2546	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2016	C₂	1	2	yes	maximal, complemented
9	C₃₇×#2015	C₂	1	2	yes	maximal
10	C₃₇×#1971	C₂	1	2	yes	maximal, complemented
11	C₃₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₃₇	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₃₇	C₂²	1	2	yes	—
14	C₂²×Q₁₆×C₃₇	C₂²	1	2	yes	—
15	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
16	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₃₇	C₂²	1	2	yes	—
20	C₂×#124×C₃₇	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
23	C₃₇×#497	—	2	8	no	—
24	C₃₇×#494	—	2	4	no	—
25	C₃₇×#462	—	2	4	no	—
26	C₃₇×#461	—	2	4	no	—
27	C₄×SD₁₆×C₃₇	—	2	4	no	—
28	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×#103×C₃₇	C₂²	1	2	yes	—
32	C₂×#103×C₃₇	C₂²	1	2	yes	—
33	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
34	C₂×#97×C₃₇	C₂²	1	2	yes	—
35	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
36	C₃₇×#398	—	2	2	no	—
37	C₃₇×#397	—	2	2	no	—
38	C₃₇×#391	C₂²	1	2	yes	—
39	C₃₇×#391	C₂²	1	2	yes	—
40	C₃₇×#389	—	2	2	no	—
41	C₃₇×#380	—	2	2	no	—
42	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
43	C₃₇×#336	C₂²	1	2	yes	—
44	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
45	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
46	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₃₇	—	2	1	no	—
49	C₂×Q₁₆×C₃₇	—	2	4	no	—
50	C₂×Q₁₆×C₃₇	—	2	4	no	—
51	C₂×Q₁₆×C₃₇	—	2	4	no	—
52	C₂×Q₁₆×C₃₇	—	2	4	no	—
53	C₂×Q₁₆×C₃₇	—	2	4	no	—
54	C₂×Q₁₆×C₃₇	—	2	4	no	—
55	C₂×Q₁₆×C₃₇	—	4	2	no	—
56	C₂×Q₁₆×C₃₇	—	4	2	no	—
57	C₂×Q₁₆×C₃₇	—	4	2	no	—
58	C₂×SD₁₆×C₃₇	—	2	4	no	—
59	C₂×SD₁₆×C₃₇	—	2	2	no	—
60	C₂×SD₁₆×C₃₇	—	2	4	no	—
61	C₂×SD₁₆×C₃₇	—	2	2	no	—
62	C₂×SD₁₆×C₃₇	—	4	2	no	—
63	C₂×SD₁₆×C₃₇	D₄	1	4	yes	—
64	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
65	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
67	C₄⋊Q₈×C₃₇	—	2	4	no	—
68	C₄⋊Q₈×C₃₇	—	2	2	no	—
69	C₄⋊Q₈×C₃₇	—	2	2	no	—
70	C₄⋊Q₈×C₃₇	—	2	2	no	—
71	C₄⋊Q₈×C₃₇	—	2	2	no	—
72	C₄⋊Q₈×C₃₇	—	4	2	no	—
73	#124×C₃₇	—	2	4	no	—
74	#124×C₃₇	—	4	2	no	—
75	C₄×Q₈×C₃₇	—	2	2	no	—
76	C₄×Q₈×C₃₇	—	2	2	no	—
77	C₄×D₄×C₃₇	—	2	2	no	—
78	C₄×D₄×C₃₇	—	2	2	no	—
79	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
81	C₂×C₄⋊C₄×C₃₇	—	2	4	no	—
82	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
85	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
86	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
89	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
90	C₂×C₄²×C₃₇	—	2	1	no	—
91	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
92	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
93	#106×C₃₇	—	2	2	no	—
94	C₄⋊C₈×C₃₇	D₄	1	4	yes	—
95	#103×C₃₇	—	2	2	no	—
96	#103×C₃₇	—	2	4	no	—
97	#103×C₃₇	—	2	4	no	—
98	#102×C₃₇	—	2	2	no	—
99	#97×C₃₇	—	2	4	no	—
100	C₄×C₈×C₃₇	D₄	1	4	yes	—
101	#95×C₃₇	—	2	4	no	—
102	#95×C₃₇	—	2	4	no	—
103	#95×C₃₇	D₄	1	2	yes	—
104	C₂⁴×C₃₇	—	2	1	no	—
105	C₂×Q₈×C₃₇	—	2	1	no	—
106	C₂×Q₈×C₃₇	—	2	1	no	—
107	C₂×Q₈×C₃₇	—	2	1	no	—
108	C₂×Q₈×C₃₇	—	2	2	no	—
109	C₂×Q₈×C₃₇	—	2	2	no	—
110	C₂×Q₈×C₃₇	—	2	2	no	—
111	C₂×Q₈×C₃₇	—	2	2	no	—
112	C₂×Q₈×C₃₇	—	2	2	no	—
113	C₂×Q₈×C₃₇	—	2	2	no	—
114	C₂×Q₈×C₃₇	—	2	1	no	—
115	C₂×Q₈×C₃₇	—	2	2	no	—
116	C₂×Q₈×C₃₇	—	2	2	no	—
117	C₂×Q₈×C₃₇	—	2	1	no	—
118	C₂×Q₈×C₃₇	—	2	2	no	—
119	C₂×Q₈×C₃₇	—	2	2	no	—
120	C₂×Q₈×C₃₇	—	2	2	no	—
121	C₂×Q₈×C₃₇	—	2	2	no	—
122	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
123	C₂×D₄×C₃₇	—	2	1	no	—
124	C₂×D₄×C₃₇	—	2	1	no	—
125	C₂×D₄×C₃₇	—	2	1	no	—
126	C₂×D₄×C₃₇	—	2	1	no	—
127	C₂×D₄×C₃₇	—	2	1	no	—
128	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₃₇	—	2	1	no	—
130	C₂²×C₄×C₃₇	—	2	1	no	—
131	C₂²×C₄×C₃₇	—	2	1	no	—
132	C₂²×C₄×C₃₇	—	2	2	no	—
133	C₂²×C₄×C₃₇	—	2	2	no	—
134	C₂²×C₄×C₃₇	—	4	2	no	—
135	C₂²×C₄×C₃₇	—	4	4	no	—
136	C₂²×C₄×C₃₇	C₂×D₄	1	4	yes	—
137	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
140	Q₁₆×C₃₇	—	4	8	no	—
141	Q₁₆×C₃₇	—	4	8	no	—
142	Q₁₆×C₃₇	—	4	8	no	—
143	SD₁₆×C₃₇	—	2	8	no	—
144	SD₁₆×C₃₇	—	4	8	no	—
145	C₂×C₈×C₃₇	—	2	2	no	—
146	C₂×C₈×C₃₇	—	2	2	no	—
147	C₂×C₈×C₃₇	—	2	1	no	—
148	C₂×C₈×C₃₇	—	2	1	no	—
149	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
151	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₃₇	#41	1	2	yes	—
154	C₄⋊C₄×C₃₇	—	2	4	no	—
155	C₄⋊C₄×C₃₇	—	2	1	no	—
156	C₄⋊C₄×C₃₇	—	2	1	no	—
157	C₄⋊C₄×C₃₇	—	2	1	no	—
158	C₄⋊C₄×C₃₇	—	2	1	no	—
159	C₄⋊C₄×C₃₇	—	4	8	no	—
160	C₄⋊C₄×C₃₇	—	4	2	no	—
161	C₄⋊C₄×C₃₇	—	4	2	no	—
162	C₄⋊C₄×C₃₇	—	4	2	no	—
163	C₄⋊C₄×C₃₇	—	4	2	no	—
164	C₄⋊C₄×C₃₇	—	4	2	no	—
165	C₂²⋊C₄×C₃₇	—	4	8	no	—
166	C₂²⋊C₄×C₃₇	—	4	2	no	—
167	C₄²×C₃₇	—	2	2	no	—
168	C₄²×C₃₇	—	2	2	no	—
169	C₄²×C₃₇	—	4	2	no	—
170	C₄²×C₃₇	C₂×D₄	1	2	yes	—
171	C₄²×C₃₇	C₂×D₄	1	2	yes	—
172	C₂³×C₃₇	—	2	2	no	—
173	C₂³×C₃₇	—	4	1	no	—
174	C₂³×C₃₇	—	4	1	no	—
175	C₂³×C₃₇	—	4	2	no	—
176	C₂³×C₃₇	—	4	2	no	—
177	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
178	Q₈×C₃₇	—	2	2	no	—
179	Q₈×C₃₇	—	2	2	no	—
180	Q₈×C₃₇	—	4	1	no	—
181	Q₈×C₃₇	—	4	1	no	—
182	Q₈×C₃₇	—	4	2	no	—
183	Q₈×C₃₇	—	4	2	no	—
184	Q₈×C₃₇	—	4	2	no	—
185	Q₈×C₃₇	—	4	2	no	—
186	Q₈×C₃₇	—	4	2	no	—
187	Q₈×C₃₇	—	4	2	no	—
188	Q₈×C₃₇	—	4	2	no	—
189	Q₈×C₃₇	—	4	2	no	—
190	D₄×C₃₇	—	2	2	no	—
191	D₄×C₃₇	—	2	2	no	—
192	D₄×C₃₇	—	4	1	no	—
193	D₄×C₃₇	—	4	1	no	—
194	C₂×C₄×C₃₇	—	2	2	no	—
195	C₂×C₄×C₃₇	—	2	4	no	—
196	C₂×C₄×C₃₇	—	2	2	no	—
197	C₂×C₄×C₃₇	—	2	4	no	—
198	C₂×C₄×C₃₇	—	2	4	no	—
199	C₂×C₄×C₃₇	—	4	1	no	—
200	C₂×C₄×C₃₇	—	4	1	no	—
201	C₂×C₄×C₃₇	—	4	1	no	—
202	C₂×C₄×C₃₇	—	4	1	no	—
203	C₂×C₄×C₃₇	—	4	2	no	—
204	C₂×C₄×C₃₇	—	4	2	no	—
205	C₂×C₄×C₃₇	—	4	2	no	—
206	C₂×C₄×C₃₇	—	4	2	no	—
207	C₂×C₄×C₃₇	—	4	2	no	—
208	C₂×C₄×C₃₇	—	4	2	no	—
209	C₂×C₄×C₃₇	—	4	2	no	—
210	C₂×C₄×C₃₇	—	4	2	no	—
211	C₂×C₄×C₃₇	—	8	4	no	—
212	C₂×C₄×C₃₇	#127	1	2	yes	—
213	C₂×C₄×C₃₇	#127	1	2	yes	—
214	C₂×C₄×C₃₇	#137	1	4	yes	—
215	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
220	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
221	C₈×C₃₇	—	2	2	no	—
222	C₈×C₃₇	—	2	4	no	—
223	C₈×C₃₇	#121	1	4	yes	—
224	#28471	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂²×C₃₇	—	4	4	no	—
226	C₂²×C₃₇	—	4	2	no	—
227	C₂²×C₃₇	—	8	2	no	—
228	C₂²×C₃₇	—	8	1	no	—
229	C₂²×C₃₇	—	8	1	no	—
230	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
231	C₂²×C₃₇	D₄²	1	1	yes	characteristic
232	C₂²×C₃₇	#550	1	1	yes	characteristic
233	C₂²×C₃₇	C₂×#137	1	2	yes	—
234	C₂²×C₃₇	#578	1	2	yes	—
235	C₄×C₃₇	—	2	2	no	—
236	C₄×C₃₇	—	4	4	no	—
237	C₄×C₃₇	—	4	2	no	—
238	C₄×C₃₇	—	8	1	no	—
239	C₄×C₃₇	—	8	1	no	—
240	C₄×C₃₇	—	8	2	no	—
241	C₄×C₃₇	—	8	2	no	—
242	C₄×C₃₇	#497	1	4	yes	complemented
243	C₄×C₃₇	C₂×#121	1	1	yes	characteristic
244	C₄×C₃₇	#535	1	1	yes	characteristic
245	C₄×C₃₇	D₄²	1	1	yes	characteristic
246	C₄×C₃₇	#550	1	1	yes	characteristic
247	C₂×#497	C₂×C₃₇	1	2	yes	—
248	C₂×#494	C₂×C₃₇	1	1	yes	characteristic, complemented
249	C₂×#462	C₂×C₃₇	1	1	yes	characteristic, complemented
250	C₂×#461	C₂×C₃₇	1	1	yes	characteristic
251	C₂×C₄×SD₁₆	C₂×C₃₇	1	1	yes	characteristic
252	#2547	C₂×C₃₇	1	1	yes	characteristic
253	#2546	C₂×C₃₇	1	1	yes	characteristic, complemented
254	#2016	C₂×C₃₇	1	2	yes	complemented
255	#2015	C₂×C₃₇	1	2	yes	—
256	#1971	C₂×C₃₇	1	2	yes	complemented
257	#1770	C₂×C₃₇	1	1	yes	characteristic, complemented
258	C₂×C₃₇	—	8	2	no	—
259	C₂×C₃₇	#2541	1	1	yes	characteristic
260	C₂×C₃₇	C₂×#497	1	1	yes	characteristic
261	C₂×C₃₇	#3156	1	1	yes	characteristic
262	C₂×C₃₇	#3276	1	2	yes	—
263	C₂×C₃₇	#3398	1	2	yes	—
264	C₂²×Q₁₆	C₂²×C₃₇	1	2	yes	—
265	C₂²×Q₁₆	C₂²×C₃₇	1	2	yes	—
266	C₂²×Q₁₆	C₂²×C₃₇	1	2	yes	—
267	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
268	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
269	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
270	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
271	C₂×C₄⋊Q₈	C₂²×C₃₇	1	2	yes	—
272	C₂×#124	C₂²×C₃₇	1	2	yes	—
273	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
274	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
275	#497	—	2	8	no	—
276	#494	—	2	4	no	—
277	#462	—	2	4	no	—
278	#461	—	2	4	no	—
279	C₄×SD₁₆	—	2	4	no	—
280	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
282	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
283	C₂×#103	C₂²×C₃₇	1	2	yes	—
284	C₂×#103	C₂²×C₃₇	1	2	yes	—
285	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
286	C₂×#97	C₂²×C₃₇	1	2	yes	—
287	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
288	#398	—	2	2	no	—
289	#397	—	2	2	no	—
290	#391	C₂²×C₃₇	1	2	yes	—
291	#391	C₂²×C₃₇	1	2	yes	—
292	#389	—	2	2	no	—
293	#380	—	2	2	no	—
294	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
295	#336	C₂²×C₃₇	1	2	yes	—
296	C₃₇	#28471	1	1	yes	characteristic, direct product factor, Sylow
297	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
298	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
299	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
300	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
301	C₂³×C₄	—	2	1	no	—
302	C₂×Q₁₆	—	2	4	no	—
303	C₂×Q₁₆	—	2	4	no	—
304	C₂×Q₁₆	—	2	4	no	—
305	C₂×Q₁₆	—	2	4	no	—
306	C₂×Q₁₆	—	2	4	no	—
307	C₂×Q₁₆	—	2	4	no	—
308	C₂×Q₁₆	—	4	2	no	—
309	C₂×Q₁₆	—	4	2	no	—
310	C₂×Q₁₆	—	4	2	no	—
311	C₂×SD₁₆	—	2	4	no	—
312	C₂×SD₁₆	—	2	2	no	—
313	C₂×SD₁₆	—	2	4	no	—
314	C₂×SD₁₆	—	2	2	no	—
315	C₂×SD₁₆	—	4	2	no	—
316	C₂×SD₁₆	D₄×C₃₇	1	4	yes	—
317	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
318	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
320	C₄⋊Q₈	—	2	4	no	—
321	C₄⋊Q₈	—	2	2	no	—
322	C₄⋊Q₈	—	2	2	no	—
323	C₄⋊Q₈	—	2	2	no	—
324	C₄⋊Q₈	—	2	2	no	—
325	C₄⋊Q₈	—	4	2	no	—
326	#124	—	2	4	no	—
327	#124	—	4	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	4	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
339	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₂²⋊C₄	—	2	4	no	—
343	C₂×C₄²	—	2	1	no	—
344	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
345	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
346	#106	—	2	2	no	—
347	C₄⋊C₈	D₄×C₃₇	1	4	yes	—
348	#103	—	2	2	no	—
349	#103	—	2	4	no	—
350	#103	—	2	4	no	—
351	#102	—	2	2	no	—
352	#97	—	2	4	no	—
353	C₄×C₈	D₄×C₃₇	1	4	yes	—
354	#95	—	2	4	no	—
355	#95	—	2	4	no	—
356	#95	D₄×C₃₇	1	2	yes	—
357	C₂⁴	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	4	4	no	—
389	C₂²×C₄	C₂×D₄×C₃₇	1	4	yes	—
390	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
392	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
393	Q₁₆	—	4	8	no	—
394	Q₁₆	—	4	8	no	—
395	Q₁₆	—	4	8	no	—
396	SD₁₆	—	2	8	no	—
397	SD₁₆	—	4	8	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
403	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
404	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
405	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
406	C₂×C₈	#41×C₃₇	1	2	yes	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	4	8	no	—
413	C₄⋊C₄	—	4	2	no	—
414	C₄⋊C₄	—	4	2	no	—
415	C₄⋊C₄	—	4	2	no	—
416	C₄⋊C₄	—	4	2	no	—
417	C₄⋊C₄	—	4	2	no	—
418	C₂²⋊C₄	—	4	8	no	—
419	C₂²⋊C₄	—	4	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	4	2	no	—
423	C₄²	C₂×D₄×C₃₇	1	2	yes	—
424	C₄²	C₂×D₄×C₃₇	1	2	yes	—
425	C₂³	—	2	2	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
431	Q₈	—	2	2	no	—
432	Q₈	—	2	2	no	—
433	Q₈	—	4	1	no	—
434	Q₈	—	4	1	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	4	2	no	—
437	Q₈	—	4	2	no	—
438	Q₈	—	4	2	no	—
439	Q₈	—	4	2	no	—
440	Q₈	—	4	2	no	—
441	Q₈	—	4	2	no	—
442	Q₈	—	4	2	no	—
443	D₄	—	2	2	no	—
444	D₄	—	2	2	no	—
445	D₄	—	4	1	no	—
446	D₄	—	4	1	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	8	4	no	—
465	C₂×C₄	#127×C₃₇	1	2	yes	—
466	C₂×C₄	#127×C₃₇	1	2	yes	—
467	C₂×C₄	#137×C₃₇	1	4	yes	—
468	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
469	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
471	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
472	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
473	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	—	2	4	no	—
476	C₈	#121×C₃₇	1	4	yes	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	8	2	no	—
480	C₂²	—	8	1	no	—
481	C₂²	—	8	1	no	—
482	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
483	C₂²	D₄²×C₃₇	1	1	yes	characteristic
484	C₂²	C₃₇×#550	1	1	yes	characteristic
485	C₂²	C₂×#137×C₃₇	1	2	yes	—
486	C₂²	C₃₇×#578	1	2	yes	—
487	C₄	—	2	2	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	2	no	—
490	C₄	—	8	1	no	—
491	C₄	—	8	1	no	—
492	C₄	—	8	2	no	—
493	C₄	—	8	2	no	—
494	C₄	C₃₇×#497	1	4	yes	complemented
495	C₄	C₂×#121×C₃₇	1	1	yes	characteristic
496	C₄	C₃₇×#535	1	1	yes	characteristic
497	C₄	D₄²×C₃₇	1	1	yes	characteristic
498	C₄	C₃₇×#550	1	1	yes	characteristic
499	C₂	—	8	2	no	—
500	C₂	C₃₇×#2541	1	1	yes	characteristic
501	C₂	C₂×C₃₇×#497	1	1	yes	characteristic
502	C₂	C₃₇×#3156	1	1	yes	characteristic
503	C₂	C₃₇×#3276	1	2	yes	—
504	C₂	C₃₇×#3398	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₇×#494	C₂	semidirect
3. C₂×C₃₇×#462	C₂	semidirect
7. C₃₇×#2546	C₂	semidirect
8. C₃₇×#2016	C₂	semidirect
10. C₃₇×#1971	C₂	semidirect
11. C₃₇×#1770	C₂	semidirect
224. #28471	C₃₇	direct (N × H)
242. C₄×C₃₇	#497	semidirect
248. C₂×#494	C₂×C₃₇	semidirect
249. C₂×#462	C₂×C₃₇	semidirect
253. #2546	C₂×C₃₇	semidirect
254. #2016	C₂×C₃₇	semidirect
256. #1971	C₂×C₃₇	semidirect
257. #1770	C₂×C₃₇	semidirect
296. C₃₇	#28471	direct (N × H)
494. C₄	C₃₇×#497	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#497	2
C₂×C₃₇×#494	2
C₂×C₃₇×#462	2
C₂×C₃₇×#461	2
C₂×C₄×SD₁₆×C₃₇	2
C₃₇×#2547	2
C₃₇×#2546	2
C₃₇×#2016	2
C₃₇×#2015	2
C₃₇×#1971	2
C₃₇×#1770	2
#28471	37

Subgroups — C37×#28471 #22649724

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28471 #22649724