Subgroups — C₃₇×#29801 #22651054

Order 9472.

918 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#464	C₂	1	2	yes	maximal, complemented
2	C₃₇×#2858	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2043	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2042	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2041	C₂	1	1	yes	maximal, characteristic
7	C₃₇×#2016	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2015	C₂	1	2	yes	maximal, complemented
9	C₃₇×#2014	C₂	1	1	yes	maximal, characteristic
10	C₃₇×#1983	C₂	1	2	yes	maximal, complemented
11	C₃₇×#1831	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₃₇	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
16	C₂×#124×C₃₇	C₂²	1	2	yes	—
17	C₂×#124×C₃₇	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
19	C₃₇×#464	—	2	8	no	—
20	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
21	C₂×#103×C₃₇	C₂²	1	2	yes	—
22	C₂×#103×C₃₇	C₂²	1	2	yes	—
23	C₂×#103×C₃₇	C₂²	1	2	yes	—
24	C₂×#102×C₃₇	C₂²	1	2	yes	—
25	C₂×#102×C₃₇	C₂²	1	2	yes	—
26	C₂×#102×C₃₇	C₂²	1	2	yes	—
27	C₃₇×#391	C₂²	1	1	yes	characteristic
28	C₃₇×#391	C₂²	1	1	yes	characteristic
29	C₃₇×#390	—	2	1	no	—
30	C₃₇×#390	—	2	1	no	—
31	C₃₇×#390	—	2	1	no	—
32	C₃₇×#390	—	2	1	no	—
33	C₃₇×#389	C₂²	1	1	yes	characteristic
34	C₃₇×#389	C₂²	1	1	yes	characteristic
35	C₃₇×#387	—	2	1	no	—
36	C₃₇×#387	—	2	1	no	—
37	C₄×C₄⋊C₄×C₃₇	—	2	1	no	—
38	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
39	C₃₇×#376	—	2	1	no	—
40	C₄³×C₃₇	C₂²	1	1	yes	characteristic
41	C₃₇×#336	C₂²	1	1	yes	characteristic
42	C₃₇×#336	C₂²	1	2	yes	—
43	C₃₇×#336	C₂²	1	1	yes	characteristic
44	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
45	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₃₇	—	2	1	no	—
47	C₂²×D₄×C₃₇	—	2	1	no	—
48	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
49	C₂×Q₁₆×C₃₇	—	2	4	no	—
50	C₂×Q₁₆×C₃₇	—	4	2	no	—
51	C₂×Q₁₆×C₃₇	—	4	2	no	—
52	C₂×SD₁₆×C₃₇	—	2	4	no	—
53	C₂×SD₁₆×C₃₇	—	4	2	no	—
54	C₂×SD₁₆×C₃₇	—	4	2	no	—
55	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
56	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₃₇	—	4	2	no	—
58	#127×C₃₇	—	4	2	no	—
59	#124×C₃₇	—	2	4	no	—
60	#124×C₃₇	—	2	4	no	—
61	#124×C₃₇	—	4	2	no	—
62	#124×C₃₇	—	4	2	no	—
63	C₄×Q₈×C₃₇	—	2	2	no	—
64	C₄×Q₈×C₃₇	D₄	1	4	yes	complemented
65	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
68	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
77	C₂×C₄²×C₃₇	—	2	1	no	—
78	C₂×C₄²×C₃₇	—	2	1	no	—
79	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₃₇	—	2	4	no	—
87	#103×C₃₇	—	2	4	no	—
88	#103×C₃₇	—	4	2	no	—
89	#103×C₃₇	—	4	2	no	—
90	#102×C₃₇	—	2	4	no	—
91	#102×C₃₇	—	4	2	no	—
92	#102×C₃₇	—	4	2	no	—
93	#95×C₃₇	—	2	1	no	—
94	#95×C₃₇	—	2	1	no	—
95	#95×C₃₇	—	2	1	no	—
96	#95×C₃₇	—	2	1	no	—
97	#95×C₃₇	—	2	1	no	—
98	#95×C₃₇	—	2	1	no	—
99	#95×C₃₇	—	2	1	no	—
100	C₂⁴×C₃₇	—	2	2	no	—
101	C₂×Q₈×C₃₇	—	2	1	no	—
102	C₂×Q₈×C₃₇	—	2	2	no	—
103	C₂×Q₈×C₃₇	—	2	2	no	—
104	C₂×Q₈×C₃₇	—	2	2	no	—
105	C₂×Q₈×C₃₇	—	2	2	no	—
106	C₂×Q₈×C₃₇	—	2	2	no	—
107	C₂×Q₈×C₃₇	—	2	2	no	—
108	C₂×Q₈×C₃₇	—	2	2	no	—
109	C₂×Q₈×C₃₇	—	2	2	no	—
110	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
111	C₂×D₄×C₃₇	—	2	2	no	—
112	C₂×D₄×C₃₇	—	2	2	no	—
113	C₂×D₄×C₃₇	—	2	2	no	—
114	C₂×D₄×C₃₇	—	2	2	no	—
115	C₂×D₄×C₃₇	—	2	2	no	—
116	C₂×D₄×C₃₇	—	2	2	no	—
117	C₂×D₄×C₃₇	—	4	2	no	—
118	C₂×D₄×C₃₇	—	4	2	no	—
119	C₂×D₄×C₃₇	—	4	2	no	—
120	C₂×D₄×C₃₇	—	4	2	no	—
121	C₂×D₄×C₃₇	—	4	2	no	—
122	C₂×D₄×C₃₇	—	4	2	no	—
123	C₂²×C₄×C₃₇	—	2	1	no	—
124	C₂²×C₄×C₃₇	—	2	1	no	—
125	C₂²×C₄×C₃₇	—	2	1	no	—
126	C₂²×C₄×C₃₇	—	2	1	no	—
127	C₂²×C₄×C₃₇	—	2	2	no	—
128	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
135	Q₁₆×C₃₇	—	4	8	no	—
136	SD₁₆×C₃₇	—	4	8	no	—
137	C₂×C₈×C₃₇	—	2	2	no	—
138	C₂×C₈×C₃₇	—	2	2	no	—
139	C₂×C₈×C₃₇	—	2	2	no	—
140	C₂×C₈×C₃₇	—	2	2	no	—
141	C₂×C₈×C₃₇	—	2	2	no	—
142	C₂×C₈×C₃₇	—	2	2	no	—
143	C₄⋊C₄×C₃₇	—	2	4	no	—
144	C₄⋊C₄×C₃₇	—	2	1	no	—
145	C₄⋊C₄×C₃₇	—	2	2	no	—
146	C₄⋊C₄×C₃₇	—	2	2	no	—
147	C₄⋊C₄×C₃₇	—	4	2	no	—
148	C₄⋊C₄×C₃₇	—	4	2	no	—
149	C₄⋊C₄×C₃₇	—	4	2	no	—
150	C₄⋊C₄×C₃₇	—	4	2	no	—
151	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
152	C₂²⋊C₄×C₃₇	—	4	4	no	—
153	C₂²⋊C₄×C₃₇	—	4	4	no	—
154	C₂²⋊C₄×C₃₇	—	4	4	no	—
155	C₂²⋊C₄×C₃₇	—	4	4	no	—
156	C₄²×C₃₇	—	2	4	no	—
157	C₄²×C₃₇	—	2	2	no	—
158	C₄²×C₃₇	—	2	2	no	—
159	C₄²×C₃₇	—	2	2	no	—
160	C₄²×C₃₇	—	2	2	no	—
161	C₄²×C₃₇	—	4	1	no	—
162	C₄²×C₃₇	—	4	1	no	—
163	C₄²×C₃₇	—	4	2	no	—
164	C₄²×C₃₇	C₂×D₄	1	2	yes	—
165	C₄²×C₃₇	#41	1	2	yes	—
166	C₂³×C₃₇	—	4	2	no	—
167	C₂³×C₃₇	—	4	2	no	—
168	C₂³×C₃₇	—	4	2	no	—
169	C₂³×C₃₇	—	4	2	no	—
170	C₂³×C₃₇	—	4	2	no	—
171	C₂³×C₃₇	—	4	2	no	—
172	C₂³×C₃₇	—	4	2	no	—
173	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
174	Q₈×C₃₇	—	2	4	no	—
175	Q₈×C₃₇	—	4	2	no	—
176	Q₈×C₃₇	—	4	2	no	—
177	Q₈×C₃₇	—	4	2	no	—
178	Q₈×C₃₇	—	4	2	no	—
179	Q₈×C₃₇	—	4	2	no	—
180	D₄×C₃₇	—	4	2	no	—
181	D₄×C₃₇	—	4	2	no	—
182	D₄×C₃₇	—	4	2	no	—
183	D₄×C₃₇	—	4	2	no	—
184	D₄×C₃₇	—	8	4	no	—
185	D₄×C₃₇	—	8	4	no	—
186	C₂×C₄×C₃₇	—	2	1	no	—
187	C₂×C₄×C₃₇	—	2	1	no	—
188	C₂×C₄×C₃₇	—	2	1	no	—
189	C₂×C₄×C₃₇	—	2	1	no	—
190	C₂×C₄×C₃₇	—	2	1	no	—
191	C₂×C₄×C₃₇	—	2	1	no	—
192	C₂×C₄×C₃₇	—	2	1	no	—
193	C₂×C₄×C₃₇	—	2	1	no	—
194	C₂×C₄×C₃₇	—	2	2	no	—
195	C₂×C₄×C₃₇	—	2	2	no	—
196	C₂×C₄×C₃₇	—	2	1	no	—
197	C₂×C₄×C₃₇	—	2	1	no	—
198	C₂×C₄×C₃₇	—	2	1	no	—
199	C₂×C₄×C₃₇	—	2	1	no	—
200	C₂×C₄×C₃₇	—	2	1	no	—
201	C₂×C₄×C₃₇	—	2	1	no	—
202	C₂×C₄×C₃₇	—	4	1	no	—
203	C₂×C₄×C₃₇	—	4	1	no	—
204	C₂×C₄×C₃₇	—	4	1	no	—
205	C₂×C₄×C₃₇	—	4	1	no	—
206	C₂×C₄×C₃₇	—	4	2	no	—
207	C₂×C₄×C₃₇	—	4	2	no	—
208	C₂×C₄×C₃₇	—	4	1	no	—
209	C₂×C₄×C₃₇	—	4	1	no	—
210	C₂×C₄×C₃₇	—	4	2	no	—
211	C₂×C₄×C₃₇	—	4	1	no	—
212	C₂×C₄×C₃₇	—	4	1	no	—
213	C₂×C₄×C₃₇	—	4	1	no	—
214	C₂×C₄×C₃₇	—	4	1	no	—
215	C₂×C₄×C₃₇	#121	1	2	yes	—
216	C₂×C₄×C₃₇	#121	1	2	yes	—
217	C₂×C₄×C₃₇	#135	1	2	yes	—
218	C₂×C₄×C₃₇	#137	1	2	yes	—
219	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
222	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
223	C₈×C₃₇	—	4	2	no	—
224	C₈×C₃₇	—	4	2	no	—
225	#29801	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₂²×C₃₇	—	8	2	no	—
227	C₂²×C₃₇	—	8	2	no	—
228	C₂²×C₃₇	—	8	2	no	—
229	C₂²×C₃₇	—	8	2	no	—
230	C₂²×C₃₇	—	8	2	no	—
231	C₂²×C₃₇	—	8	2	no	—
232	C₂²×C₃₇	—	8	2	no	—
233	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
234	C₂²×C₃₇	#535	1	1	yes	characteristic
235	C₂²×C₃₇	#535	1	1	yes	characteristic
236	C₂²×C₃₇	C₂×#135	1	1	yes	characteristic
237	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
238	C₂²×C₃₇	#575	1	1	yes	characteristic
239	C₂²×C₃₇	#575	1	1	yes	characteristic
240	C₄×C₃₇	—	2	2	no	—
241	C₄×C₃₇	—	2	2	no	—
242	C₄×C₃₇	—	2	2	no	—
243	C₄×C₃₇	—	2	2	no	—
244	C₄×C₃₇	—	4	2	no	—
245	C₄×C₃₇	—	4	1	no	—
246	C₄×C₃₇	—	4	1	no	—
247	C₄×C₃₇	—	4	2	no	—
248	C₄×C₃₇	—	8	2	no	—
249	C₄×C₃₇	—	8	1	no	—
250	C₄×C₃₇	—	8	1	no	—
251	C₄×C₃₇	#535	1	2	yes	—
252	C₄×C₃₇	#540	1	2	yes	—
253	C₂×#464	C₂×C₃₇	1	2	yes	complemented
254	#2858	C₂×C₃₇	1	1	yes	characteristic
255	#2295	C₂×C₃₇	1	1	yes	characteristic, complemented
256	#2043	C₂×C₃₇	1	1	yes	characteristic, complemented
257	#2042	C₂×C₃₇	1	2	yes	complemented
258	#2041	C₂×C₃₇	1	1	yes	characteristic
259	#2016	C₂×C₃₇	1	1	yes	characteristic, complemented
260	#2015	C₂×C₃₇	1	2	yes	complemented
261	#2014	C₂×C₃₇	1	1	yes	characteristic
262	#1983	C₂×C₃₇	1	2	yes	complemented
263	#1831	C₂×C₃₇	1	1	yes	characteristic, complemented
264	C₂×C₃₇	—	16	2	no	—
265	C₂×C₃₇	#2619	1	1	yes	characteristic
266	C₂×C₃₇	#3035	1	1	yes	characteristic
267	C₂×C₃₇	#3037	1	1	yes	characteristic
268	C₂×C₃₇	#3210	1	1	yes	characteristic
269	C₂×C₃₇	#3211	1	1	yes	characteristic
270	C₂×C₃₇	#3215	1	1	yes	characteristic
271	C₂×C₃₇	#3219	1	1	yes	characteristic
272	C₂²×Q₁₆	C₂²×C₃₇	1	2	yes	—
273	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
274	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
275	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
276	C₂×#124	C₂²×C₃₇	1	2	yes	—
277	C₂×#124	C₂²×C₃₇	1	2	yes	—
278	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
279	#464	—	2	8	no	—
280	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
281	C₂×#103	C₂²×C₃₇	1	2	yes	—
282	C₂×#103	C₂²×C₃₇	1	2	yes	—
283	C₂×#103	C₂²×C₃₇	1	2	yes	—
284	C₂×#102	C₂²×C₃₇	1	2	yes	—
285	C₂×#102	C₂²×C₃₇	1	2	yes	—
286	C₂×#102	C₂²×C₃₇	1	2	yes	—
287	#391	C₂²×C₃₇	1	1	yes	characteristic
288	#391	C₂²×C₃₇	1	1	yes	characteristic
289	#390	—	2	1	no	—
290	#390	—	2	1	no	—
291	#390	—	2	1	no	—
292	#390	—	2	1	no	—
293	#389	C₂²×C₃₇	1	1	yes	characteristic
294	#389	C₂²×C₃₇	1	1	yes	characteristic
295	#387	—	2	1	no	—
296	#387	—	2	1	no	—
297	C₄×C₄⋊C₄	—	2	1	no	—
298	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
299	#376	—	2	1	no	—
300	C₄³	C₂²×C₃₇	1	1	yes	characteristic
301	#336	C₂²×C₃₇	1	1	yes	characteristic
302	#336	C₂²×C₃₇	1	2	yes	—
303	#336	C₂²×C₃₇	1	1	yes	characteristic
304	C₃₇	#29801	1	1	yes	characteristic, direct product factor, Sylow
305	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
306	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
307	C₂²×D₄	—	2	1	no	—
308	C₂²×D₄	—	2	1	no	—
309	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
310	C₂×Q₁₆	—	2	4	no	—
311	C₂×Q₁₆	—	4	2	no	—
312	C₂×Q₁₆	—	4	2	no	—
313	C₂×SD₁₆	—	2	4	no	—
314	C₂×SD₁₆	—	4	2	no	—
315	C₂×SD₁₆	—	4	2	no	—
316	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
317	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
318	C₄⋊Q₈	—	4	2	no	—
319	#127	—	4	2	no	—
320	#124	—	2	4	no	—
321	#124	—	2	4	no	—
322	#124	—	4	2	no	—
323	#124	—	4	2	no	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	D₄×C₃₇	1	4	yes	complemented
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₄²	—	2	1	no	—
339	C₂×C₄²	—	2	1	no	—
340	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
341	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
342	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
343	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
345	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
346	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
347	C₄⋊C₈	—	2	4	no	—
348	#103	—	2	4	no	—
349	#103	—	4	2	no	—
350	#103	—	4	2	no	—
351	#102	—	2	4	no	—
352	#102	—	4	2	no	—
353	#102	—	4	2	no	—
354	#95	—	2	1	no	—
355	#95	—	2	1	no	—
356	#95	—	2	1	no	—
357	#95	—	2	1	no	—
358	#95	—	2	1	no	—
359	#95	—	2	1	no	—
360	#95	—	2	1	no	—
361	C₂⁴	—	2	2	no	—
362	C₂×Q₈	—	2	1	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	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	4	2	no	—
379	C₂×D₄	—	4	2	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	4	2	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
396	Q₁₆	—	4	8	no	—
397	SD₁₆	—	4	8	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
413	C₂²⋊C₄	—	4	4	no	—
414	C₂²⋊C₄	—	4	4	no	—
415	C₂²⋊C₄	—	4	4	no	—
416	C₂²⋊C₄	—	4	4	no	—
417	C₄²	—	2	4	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	4	1	no	—
423	C₄²	—	4	1	no	—
424	C₄²	—	4	2	no	—
425	C₄²	C₂×D₄×C₃₇	1	2	yes	—
426	C₄²	#41×C₃₇	1	2	yes	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
435	Q₈	—	2	4	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	D₄	—	4	2	no	—
442	D₄	—	4	2	no	—
443	D₄	—	4	2	no	—
444	D₄	—	4	2	no	—
445	D₄	—	8	4	no	—
446	D₄	—	8	4	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	#121×C₃₇	1	2	yes	—
477	C₂×C₄	#121×C₃₇	1	2	yes	—
478	C₂×C₄	#135×C₃₇	1	2	yes	—
479	C₂×C₄	#137×C₃₇	1	2	yes	—
480	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
481	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
482	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
483	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
484	C₈	—	4	2	no	—
485	C₈	—	4	2	no	—
486	C₂²	—	8	2	no	—
487	C₂²	—	8	2	no	—
488	C₂²	—	8	2	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	2	no	—
491	C₂²	—	8	2	no	—
492	C₂²	—	8	2	no	—
493	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
494	C₂²	C₃₇×#535	1	1	yes	characteristic
495	C₂²	C₃₇×#535	1	1	yes	characteristic
496	C₂²	C₂×#135×C₃₇	1	1	yes	characteristic
497	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
498	C₂²	C₃₇×#575	1	1	yes	characteristic
499	C₂²	C₃₇×#575	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	1	no	—
506	C₄	—	4	1	no	—
507	C₄	—	4	2	no	—
508	C₄	—	8	2	no	—
509	C₄	—	8	1	no	—
510	C₄	—	8	1	no	—
511	C₄	C₃₇×#535	1	2	yes	—
512	C₄	C₃₇×#540	1	2	yes	—
513	C₂	—	16	2	no	—
514	C₂	C₃₇×#2619	1	1	yes	characteristic
515	C₂	C₃₇×#3035	1	1	yes	characteristic
516	C₂	C₃₇×#3037	1	1	yes	characteristic
517	C₂	C₃₇×#3210	1	1	yes	characteristic
518	C₂	C₃₇×#3211	1	1	yes	characteristic
519	C₂	C₃₇×#3215	1	1	yes	characteristic
520	C₂	C₃₇×#3219	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
1. C₂×C₃₇×#464	C₂	semidirect
3. C₃₇×#2295	C₂	semidirect
4. C₃₇×#2043	C₂	semidirect
5. C₃₇×#2042	C₂	semidirect
7. C₃₇×#2016	C₂	semidirect
8. C₃₇×#2015	C₂	semidirect
10. C₃₇×#1983	C₂	semidirect
11. C₃₇×#1831	C₂	semidirect
64. C₄×Q₈×C₃₇	D₄	semidirect
225. #29801	C₃₇	direct (N × H)
253. C₂×#464	C₂×C₃₇	semidirect
255. #2295	C₂×C₃₇	semidirect
256. #2043	C₂×C₃₇	semidirect
257. #2042	C₂×C₃₇	semidirect
259. #2016	C₂×C₃₇	semidirect
260. #2015	C₂×C₃₇	semidirect
262. #1983	C₂×C₃₇	semidirect
263. #1831	C₂×C₃₇	semidirect
304. C₃₇	#29801	direct (N × H)
325. C₄×Q₈	D₄×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#464	2
C₃₇×#2858	2
C₃₇×#2295	2
C₃₇×#2043	2
C₃₇×#2042	2
C₃₇×#2041	2
C₃₇×#2016	2
C₃₇×#2015	2
C₃₇×#2014	2
C₃₇×#1983	2
C₃₇×#1831	2
#29801	37

Subgroups — C37×#29801 #22651054

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#29801 #22651054