Subgroups — C₃₇×#28545 #22649798

Order 9472.

906 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#477	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#478	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₇×#440	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2565	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2542	C₂	1	1	yes	maximal, characteristic
7	C₃₇×#2096	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2095	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#2093	C₂	1	1	yes	maximal, characteristic
10	C₃₇×#2092	C₂	1	1	yes	maximal, characteristic
11	C₃₇×#1973	C₂	1	1	yes	maximal, characteristic
12	C₃₇×#1968	C₂	1	1	yes	maximal, characteristic
13	C₃₇×#1847	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#1845	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₇×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₃₇	—	2	2	no	—
20	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
22	C₃₇×#501	—	2	4	no	—
23	C₃₇×#478	—	2	4	no	—
24	C₃₇×#477	—	2	4	no	—
25	C₃₇×#440	—	2	4	no	—
26	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
27	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
28	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
29	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
32	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
33	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
34	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
36	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
37	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
38	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
39	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
40	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
41	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
42	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
43	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
45	C₃₇×#399	—	2	2	no	—
46	C₃₇×#398	—	2	2	no	—
47	C₃₇×#391	C₂²	1	1	yes	characteristic
48	C₃₇×#391	C₂²	1	1	yes	characteristic
49	C₃₇×#390	C₂²	1	1	yes	characteristic
50	C₃₇×#390	C₂²	1	1	yes	characteristic
51	C₃₇×#387	—	2	2	no	—
52	C₃₇×#384	C₂²	1	1	yes	characteristic
53	C₃₇×#384	C₂²	1	1	yes	characteristic
54	C₃₇×#384	C₂²	1	1	yes	characteristic
55	C₃₇×#382	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
57	C₃₇×#336	C₂²	1	1	yes	characteristic
58	C₃₇×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₃₇	—	2	1	no	—
60	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₃₇	—	2	1	no	—
63	C₂×SD₁₆×C₃₇	—	2	2	no	—
64	C₂×SD₁₆×C₃₇	—	2	2	no	—
65	C₂×SD₁₆×C₃₇	Q₈	1	4	yes	complemented
66	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
70	C₄⋊Q₈×C₃₇	—	2	2	no	—
71	C₄⋊Q₈×C₃₇	—	2	2	no	—
72	#125×C₃₇	—	2	2	no	—
73	#125×C₃₇	—	2	2	no	—
74	C₂²⋊Q₈×C₃₇	—	4	8	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	2	no	—
80	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
81	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
82	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
85	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
86	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
87	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
96	C₂×C₄²×C₃₇	—	2	1	no	—
97	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
100	#107×C₃₇	—	2	2	no	—
101	#107×C₃₇	—	2	2	no	—
102	#107×C₃₇	—	2	2	no	—
103	#107×C₃₇	—	2	2	no	—
104	#107×C₃₇	—	2	2	no	—
105	#107×C₃₇	—	2	2	no	—
106	#106×C₃₇	—	2	2	no	—
107	#106×C₃₇	—	2	2	no	—
108	#106×C₃₇	—	2	2	no	—
109	C₄⋊C₈×C₃₇	D₄	1	4	yes	—
110	#103×C₃₇	—	2	2	no	—
111	#103×C₃₇	—	2	2	no	—
112	#103×C₃₇	—	2	2	no	—
113	#102×C₃₇	—	2	2	no	—
114	#102×C₃₇	—	2	2	no	—
115	#102×C₃₇	—	2	2	no	—
116	#97×C₃₇	—	2	2	no	—
117	#97×C₃₇	D₄	1	4	yes	—
118	C₄×C₈×C₃₇	—	2	2	no	—
119	#95×C₃₇	—	2	2	no	—
120	#95×C₃₇	—	2	2	no	—
121	#95×C₃₇	—	2	2	no	—
122	#95×C₃₇	D₄	1	2	yes	—
123	C₂⁴×C₃₇	—	2	1	no	—
124	C₂×Q₈×C₃₇	—	2	1	no	—
125	C₂×Q₈×C₃₇	—	2	1	no	—
126	C₂×Q₈×C₃₇	—	2	1	no	—
127	C₂×Q₈×C₃₇	—	2	1	no	—
128	C₂×Q₈×C₃₇	—	2	1	no	—
129	C₂×Q₈×C₃₇	—	4	4	no	—
130	C₂×Q₈×C₃₇	—	4	2	no	—
131	C₂×Q₈×C₃₇	C₂×Q₈	1	2	yes	—
132	C₂×D₄×C₃₇	—	2	1	no	—
133	C₂×D₄×C₃₇	—	2	1	no	—
134	C₂×D₄×C₃₇	—	2	1	no	—
135	C₂×D₄×C₃₇	—	2	1	no	—
136	C₂×D₄×C₃₇	—	2	1	no	—
137	C₂×D₄×C₃₇	C₂×Q₈	1	2	yes	—
138	C₂²×C₄×C₃₇	—	2	1	no	—
139	C₂²×C₄×C₃₇	—	2	1	no	—
140	C₂²×C₄×C₃₇	—	2	1	no	—
141	C₂²×C₄×C₃₇	—	2	1	no	—
142	C₂²×C₄×C₃₇	—	2	1	no	—
143	C₂²×C₄×C₃₇	—	2	1	no	—
144	C₂²×C₄×C₃₇	—	2	1	no	—
145	C₂²×C₄×C₃₇	—	4	4	no	—
146	C₂²×C₄×C₃₇	—	4	2	no	—
147	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
152	SD₁₆×C₃₇	—	2	8	no	—
153	C₂×C₈×C₃₇	—	2	1	no	—
154	C₂×C₈×C₃₇	—	2	1	no	—
155	C₂×C₈×C₃₇	—	2	1	no	—
156	C₂×C₈×C₃₇	—	2	1	no	—
157	C₂×C₈×C₃₇	—	2	1	no	—
158	C₂×C₈×C₃₇	—	2	1	no	—
159	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
160	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
161	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
162	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
163	C₂×C₈×C₃₇	C₂×Q₈	1	2	yes	—
164	C₂×C₈×C₃₇	#41	1	2	yes	—
165	C₄⋊C₄×C₃₇	—	2	4	no	—
166	C₄⋊C₄×C₃₇	—	2	1	no	—
167	C₄⋊C₄×C₃₇	—	2	1	no	—
168	C₄⋊C₄×C₃₇	—	2	1	no	—
169	C₄⋊C₄×C₃₇	—	2	1	no	—
170	C₄⋊C₄×C₃₇	—	2	1	no	—
171	C₄⋊C₄×C₃₇	—	2	1	no	—
172	C₄⋊C₄×C₃₇	—	2	1	no	—
173	C₄⋊C₄×C₃₇	—	2	1	no	—
174	C₄⋊C₄×C₃₇	—	2	1	no	—
175	C₄⋊C₄×C₃₇	—	2	1	no	—
176	C₄⋊C₄×C₃₇	—	2	1	no	—
177	C₄⋊C₄×C₃₇	—	2	1	no	—
178	C₄⋊C₄×C₃₇	—	4	4	no	—
179	C₄⋊C₄×C₃₇	—	4	2	no	—
180	C₄⋊C₄×C₃₇	—	4	2	no	—
181	C₄⋊C₄×C₃₇	—	4	2	no	—
182	C₄⋊C₄×C₃₇	—	4	2	no	—
183	C₄⋊C₄×C₃₇	—	4	4	no	—
184	C₄⋊C₄×C₃₇	—	4	4	no	—
185	C₂²⋊C₄×C₃₇	—	4	4	no	—
186	C₂²⋊C₄×C₃₇	—	4	2	no	—
187	C₂²⋊C₄×C₃₇	—	4	4	no	—
188	C₄²×C₃₇	—	2	1	no	—
189	C₄²×C₃₇	—	2	1	no	—
190	C₄²×C₃₇	—	2	1	no	—
191	C₄²×C₃₇	—	2	1	no	—
192	C₄²×C₃₇	—	4	2	no	—
193	C₄²×C₃₇	C₂×D₄	1	2	yes	—
194	C₄²×C₃₇	C₂×D₄	1	2	yes	—
195	C₂³×C₃₇	—	2	2	no	—
196	C₂³×C₃₇	—	4	1	no	—
197	C₂³×C₃₇	—	4	1	no	—
198	C₂³×C₃₇	—	4	2	no	—
199	C₂³×C₃₇	—	4	2	no	—
200	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
201	Q₈×C₃₇	—	2	2	no	—
202	Q₈×C₃₇	—	2	2	no	—
203	Q₈×C₃₇	—	4	1	no	—
204	Q₈×C₃₇	—	4	1	no	—
205	Q₈×C₃₇	—	8	4	no	—
206	D₄×C₃₇	—	2	2	no	—
207	D₄×C₃₇	—	2	2	no	—
208	D₄×C₃₇	—	4	1	no	—
209	D₄×C₃₇	—	4	1	no	—
210	C₂×C₄×C₃₇	—	2	2	no	—
211	C₂×C₄×C₃₇	—	2	2	no	—
212	C₂×C₄×C₃₇	—	2	2	no	—
213	C₂×C₄×C₃₇	—	2	2	no	—
214	C₂×C₄×C₃₇	—	2	2	no	—
215	C₂×C₄×C₃₇	—	2	2	no	—
216	C₂×C₄×C₃₇	—	2	2	no	—
217	C₂×C₄×C₃₇	—	2	2	no	—
218	C₂×C₄×C₃₇	—	4	1	no	—
219	C₂×C₄×C₃₇	—	4	1	no	—
220	C₂×C₄×C₃₇	—	4	1	no	—
221	C₂×C₄×C₃₇	—	4	1	no	—
222	C₂×C₄×C₃₇	—	4	1	no	—
223	C₂×C₄×C₃₇	—	4	1	no	—
224	C₂×C₄×C₃₇	—	4	1	no	—
225	C₂×C₄×C₃₇	—	4	1	no	—
226	C₂×C₄×C₃₇	—	4	2	no	—
227	C₂×C₄×C₃₇	—	4	2	no	—
228	C₂×C₄×C₃₇	—	4	2	no	—
229	C₂×C₄×C₃₇	—	4	2	no	—
230	C₂×C₄×C₃₇	—	4	2	no	—
231	C₂×C₄×C₃₇	—	4	2	no	—
232	C₂×C₄×C₃₇	—	8	4	no	—
233	C₂×C₄×C₃₇	#127	1	2	yes	—
234	C₂×C₄×C₃₇	#127	1	2	yes	—
235	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	4	yes	—
236	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
239	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
241	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
242	C₈×C₃₇	—	2	2	no	—
243	C₈×C₃₇	—	2	2	no	—
244	C₈×C₃₇	—	2	2	no	—
245	C₈×C₃₇	C₂²⋊Q₈	1	4	yes	complemented
246	#28545	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₂²×C₃₇	—	4	4	no	—
248	C₂²×C₃₇	—	4	2	no	—
249	C₂²×C₃₇	—	8	2	no	—
250	C₂²×C₃₇	—	8	1	no	—
251	C₂²×C₃₇	—	8	1	no	—
252	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
253	C₂²×C₃₇	#547	1	1	yes	characteristic
254	C₂²×C₃₇	D₄×Q₈	1	1	yes	characteristic
255	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
256	C₂²×C₃₇	#578	1	2	yes	—
257	C₄×C₃₇	—	2	4	no	—
258	C₄×C₃₇	—	2	2	no	—
259	C₄×C₃₇	—	2	2	no	—
260	C₄×C₃₇	—	4	2	no	—
261	C₄×C₃₇	—	4	2	no	—
262	C₄×C₃₇	—	8	1	no	—
263	C₄×C₃₇	—	8	1	no	—
264	C₄×C₃₇	—	8	1	no	—
265	C₄×C₃₇	—	8	1	no	—
266	C₄×C₃₇	—	8	1	no	—
267	C₄×C₃₇	—	8	1	no	—
268	C₄×C₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
269	C₄×C₃₇	#536	1	1	yes	characteristic
270	C₄×C₃₇	#547	1	1	yes	characteristic
271	C₄×C₃₇	D₄×Q₈	1	1	yes	characteristic
272	C₂×#501	C₂×C₃₇	1	1	yes	characteristic, complemented
273	C₂×#477	C₂×C₃₇	1	1	yes	characteristic, complemented
274	C₂×#478	C₂×C₃₇	1	1	yes	characteristic
275	C₂×#440	C₂×C₃₇	1	1	yes	characteristic
276	#2565	C₂×C₃₇	1	1	yes	characteristic, complemented
277	#2542	C₂×C₃₇	1	1	yes	characteristic
278	#2096	C₂×C₃₇	1	1	yes	characteristic, complemented
279	#2095	C₂×C₃₇	1	1	yes	characteristic, complemented
280	#2093	C₂×C₃₇	1	1	yes	characteristic
281	#2092	C₂×C₃₇	1	1	yes	characteristic
282	#1973	C₂×C₃₇	1	1	yes	characteristic
283	#1968	C₂×C₃₇	1	1	yes	characteristic
284	#1847	C₂×C₃₇	1	1	yes	characteristic, complemented
285	#1845	C₂×C₃₇	1	1	yes	characteristic, complemented
286	#1771	C₂×C₃₇	1	1	yes	characteristic, complemented
287	C₂×C₃₇	—	8	2	no	—
288	C₂×C₃₇	#2542	1	1	yes	characteristic
289	C₂×C₃₇	#3151	1	1	yes	characteristic
290	C₂×C₃₇	#3156	1	1	yes	characteristic
291	C₂×C₃₇	#3343	1	2	yes	—
292	C₂×C₃₇	#3386	1	2	yes	—
293	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
294	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
295	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
296	C₂×C₂²⋊Q₈	—	2	2	no	—
297	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
298	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
299	#501	—	2	4	no	—
300	#478	—	2	4	no	—
301	#477	—	2	4	no	—
302	#440	—	2	4	no	—
303	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
304	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
305	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
306	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
307	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
308	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
309	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
310	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
311	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
312	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
313	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
314	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
315	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
316	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
317	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
318	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
319	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
320	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
321	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
322	#399	—	2	2	no	—
323	#398	—	2	2	no	—
324	#391	C₂²×C₃₇	1	1	yes	characteristic
325	#391	C₂²×C₃₇	1	1	yes	characteristic
326	#390	C₂²×C₃₇	1	1	yes	characteristic
327	#390	C₂²×C₃₇	1	1	yes	characteristic
328	#387	—	2	2	no	—
329	#384	C₂²×C₃₇	1	1	yes	characteristic
330	#384	C₂²×C₃₇	1	1	yes	characteristic
331	#384	C₂²×C₃₇	1	1	yes	characteristic
332	#382	C₂²×C₃₇	1	1	yes	characteristic
333	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
334	#336	C₂²×C₃₇	1	1	yes	characteristic
335	#336	C₂²×C₃₇	1	1	yes	characteristic
336	C₃₇	#28545	1	1	yes	characteristic, direct product factor, Sylow
337	C₂²×Q₈	—	2	1	no	—
338	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
339	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
340	C₂³×C₄	—	2	1	no	—
341	C₂×SD₁₆	—	2	2	no	—
342	C₂×SD₁₆	—	2	2	no	—
343	C₂×SD₁₆	Q₈×C₃₇	1	4	yes	complemented
344	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
345	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
347	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
348	C₄⋊Q₈	—	2	2	no	—
349	C₄⋊Q₈	—	2	2	no	—
350	#125	—	2	2	no	—
351	#125	—	2	2	no	—
352	C₂²⋊Q₈	—	4	8	no	—
353	C₄×Q₈	—	2	2	no	—
354	C₄×Q₈	—	2	2	no	—
355	C₄×D₄	—	2	2	no	—
356	C₄×D₄	—	2	2	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	2	no	—
364	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	—	2	2	no	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
377	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
378	#107	—	2	2	no	—
379	#107	—	2	2	no	—
380	#107	—	2	2	no	—
381	#107	—	2	2	no	—
382	#107	—	2	2	no	—
383	#107	—	2	2	no	—
384	#106	—	2	2	no	—
385	#106	—	2	2	no	—
386	#106	—	2	2	no	—
387	C₄⋊C₈	D₄×C₃₇	1	4	yes	—
388	#103	—	2	2	no	—
389	#103	—	2	2	no	—
390	#103	—	2	2	no	—
391	#102	—	2	2	no	—
392	#102	—	2	2	no	—
393	#102	—	2	2	no	—
394	#97	—	2	2	no	—
395	#97	D₄×C₃₇	1	4	yes	—
396	C₄×C₈	—	2	2	no	—
397	#95	—	2	2	no	—
398	#95	—	2	2	no	—
399	#95	—	2	2	no	—
400	#95	D₄×C₃₇	1	2	yes	—
401	C₂⁴	—	2	1	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	2	1	no	—
404	C₂×Q₈	—	2	1	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	4	4	no	—
408	C₂×Q₈	—	4	2	no	—
409	C₂×Q₈	C₂×Q₈×C₃₇	1	2	yes	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	C₂×Q₈×C₃₇	1	2	yes	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	4	4	no	—
424	C₂²×C₄	—	4	2	no	—
425	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
426	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
429	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
430	SD₁₆	—	2	8	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
438	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
439	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
440	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
441	C₂×C₈	C₂×Q₈×C₃₇	1	2	yes	—
442	C₂×C₈	#41×C₃₇	1	2	yes	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	4	4	no	—
457	C₄⋊C₄	—	4	2	no	—
458	C₄⋊C₄	—	4	2	no	—
459	C₄⋊C₄	—	4	2	no	—
460	C₄⋊C₄	—	4	2	no	—
461	C₄⋊C₄	—	4	4	no	—
462	C₄⋊C₄	—	4	4	no	—
463	C₂²⋊C₄	—	4	4	no	—
464	C₂²⋊C₄	—	4	2	no	—
465	C₂²⋊C₄	—	4	4	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	4	2	no	—
471	C₄²	C₂×D₄×C₃₇	1	2	yes	—
472	C₄²	C₂×D₄×C₃₇	1	2	yes	—
473	C₂³	—	2	2	no	—
474	C₂³	—	4	1	no	—
475	C₂³	—	4	1	no	—
476	C₂³	—	4	2	no	—
477	C₂³	—	4	2	no	—
478	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
479	Q₈	—	2	2	no	—
480	Q₈	—	2	2	no	—
481	Q₈	—	4	1	no	—
482	Q₈	—	4	1	no	—
483	Q₈	—	8	4	no	—
484	D₄	—	2	2	no	—
485	D₄	—	2	2	no	—
486	D₄	—	4	1	no	—
487	D₄	—	4	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	8	4	no	—
511	C₂×C₄	#127×C₃₇	1	2	yes	—
512	C₂×C₄	#127×C₃₇	1	2	yes	—
513	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	4	yes	—
514	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
516	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
517	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
518	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
519	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
520	C₈	—	2	2	no	—
521	C₈	—	2	2	no	—
522	C₈	—	2	2	no	—
523	C₈	C₂²⋊Q₈×C₃₇	1	4	yes	complemented
524	C₂²	—	4	4	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	8	1	no	—
527	C₂²	—	8	1	no	—
528	C₂²	—	8	2	no	—
529	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
530	C₂²	C₃₇×#547	1	1	yes	characteristic
531	C₂²	D₄×Q₈×C₃₇	1	1	yes	characteristic
532	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	2	yes	—
533	C₂²	C₃₇×#578	1	2	yes	—
534	C₄	—	2	2	no	—
535	C₄	—	2	2	no	—
536	C₄	—	2	4	no	—
537	C₄	—	4	2	no	—
538	C₄	—	4	2	no	—
539	C₄	—	8	1	no	—
540	C₄	—	8	1	no	—
541	C₄	—	8	1	no	—
542	C₄	—	8	1	no	—
543	C₄	—	8	1	no	—
544	C₄	—	8	1	no	—
545	C₄	C₂×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
546	C₄	C₃₇×#536	1	1	yes	characteristic
547	C₄	C₃₇×#547	1	1	yes	characteristic
548	C₄	D₄×Q₈×C₃₇	1	1	yes	characteristic
549	C₂	—	8	2	no	—
550	C₂	C₃₇×#2542	1	1	yes	characteristic
551	C₂	C₃₇×#3151	1	1	yes	characteristic
552	C₂	C₃₇×#3156	1	1	yes	characteristic
553	C₂	C₃₇×#3343	1	2	yes	—
554	C₂	C₃₇×#3386	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
1. C₂×C₃₇×#501	C₂	semidirect
2. C₂×C₃₇×#477	C₂	semidirect
5. C₃₇×#2565	C₂	semidirect
7. C₃₇×#2096	C₂	semidirect
8. C₃₇×#2095	C₂	semidirect
13. C₃₇×#1847	C₂	semidirect
14. C₃₇×#1845	C₂	semidirect
15. C₃₇×#1771	C₂	semidirect
65. C₂×SD₁₆×C₃₇	Q₈	semidirect
245. C₈×C₃₇	C₂²⋊Q₈	semidirect
246. #28545	C₃₇	direct (N × H)
272. C₂×#501	C₂×C₃₇	semidirect
273. C₂×#477	C₂×C₃₇	semidirect
276. #2565	C₂×C₃₇	semidirect
278. #2096	C₂×C₃₇	semidirect
279. #2095	C₂×C₃₇	semidirect
284. #1847	C₂×C₃₇	semidirect
285. #1845	C₂×C₃₇	semidirect
286. #1771	C₂×C₃₇	semidirect
336. C₃₇	#28545	direct (N × H)
343. C₂×SD₁₆	Q₈×C₃₇	semidirect
523. C₈	C₂²⋊Q₈×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×#501	2
C₂×C₃₇×#477	2
C₂×C₃₇×#478	2
C₂×C₃₇×#440	2
C₃₇×#2565	2
C₃₇×#2542	2
C₃₇×#2096	2
C₃₇×#2095	2
C₃₇×#2093	2
C₃₇×#2092	2
C₃₇×#1973	2
C₃₇×#1968	2
C₃₇×#1847	2
C₃₇×#1845	2
C₃₇×#1771	2
#28545	37

Subgroups — C37×#28545 #22649798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28545 #22649798