Subgroups — C₃₇×#28533 #22649786

Order 9472.

854 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#479	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#478	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×SD₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2566	C₂	1	1	yes	maximal, characteristic
6	C₃₇×#2565	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2097	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×#1968	C₂	1	1	yes	maximal, characteristic
12	C₃₇×#1968	C₂	1	1	yes	maximal, characteristic
13	C₃₇×#1846	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#1844	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₄⋊C₄×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
21	C₃₇×#499	—	2	4	no	—
22	C₃₇×#479	—	2	4	no	—
23	C₃₇×#478	—	2	4	no	—
24	C₄×SD₁₆×C₃₇	—	2	4	no	—
25	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
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×#106×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×#106×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×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
35	C₂×#103×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×#102×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×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
44	C₃₇×#398	—	2	2	no	—
45	C₃₇×#396	—	2	2	no	—
46	C₃₇×#391	C₂²	1	1	yes	characteristic
47	C₃₇×#391	C₂²	1	1	yes	characteristic
48	C₃₇×#390	C₂²	1	1	yes	characteristic
49	C₃₇×#390	C₂²	1	1	yes	characteristic
50	C₃₇×#387	—	2	2	no	—
51	C₃₇×#385	—	2	2	no	—
52	C₃₇×#384	C₂²	1	1	yes	characteristic
53	C₃₇×#384	C₂²	1	1	yes	characteristic
54	C₃₇×#382	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	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₃₇	—	2	1	no	—
62	C₂×SD₁₆×C₃₇	—	2	2	no	—
63	C₂×SD₁₆×C₃₇	—	2	2	no	—
64	C₂×SD₁₆×C₃₇	Q₈	1	4	yes	—
65	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
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	#125×C₃₇	—	2	2	no	—
70	#125×C₃₇	—	2	2	no	—
71	#125×C₃₇	—	2	2	no	—
72	#125×C₃₇	—	2	2	no	—
73	C₄×Q₈×C₃₇	—	2	2	no	—
74	C₄×Q₈×C₃₇	—	2	2	no	—
75	C₄×D₄×C₃₇	—	2	2	no	—
76	C₄×D₄×C₃₇	—	2	2	no	—
77	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
78	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
79	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
81	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
82	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
84	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
85	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₃₇	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
94	C₂×C₄²×C₃₇	—	2	1	no	—
95	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
98	#107×C₃₇	—	2	2	no	—
99	#107×C₃₇	—	2	2	no	—
100	#107×C₃₇	—	2	2	no	—
101	#107×C₃₇	—	2	2	no	—
102	#106×C₃₇	—	2	2	no	—
103	#106×C₃₇	—	2	2	no	—
104	#106×C₃₇	—	2	2	no	—
105	#106×C₃₇	—	2	2	no	—
106	#106×C₃₇	—	2	2	no	—
107	C₄⋊C₈×C₃₇	D₄	1	4	yes	—
108	#103×C₃₇	—	2	2	no	—
109	#103×C₃₇	—	2	2	no	—
110	#103×C₃₇	—	2	2	no	—
111	#102×C₃₇	—	2	2	no	—
112	#102×C₃₇	—	2	2	no	—
113	#102×C₃₇	—	2	2	no	—
114	C₄×C₈×C₃₇	—	2	2	no	—
115	C₄×C₈×C₃₇	—	2	2	no	—
116	C₄×C₈×C₃₇	D₄	1	4	yes	—
117	#95×C₃₇	—	2	2	no	—
118	#95×C₃₇	—	2	2	no	—
119	#95×C₃₇	—	2	2	no	—
120	#95×C₃₇	—	2	2	no	—
121	#95×C₃₇	D₄	1	2	yes	—
122	C₂⁴×C₃₇	—	2	1	no	—
123	C₂×Q₈×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	C₂×Q₈	1	2	yes	—
129	C₂×D₄×C₃₇	—	2	1	no	—
130	C₂×D₄×C₃₇	—	2	1	no	—
131	C₂×D₄×C₃₇	—	2	1	no	—
132	C₂×D₄×C₃₇	—	2	1	no	—
133	C₂×D₄×C₃₇	—	2	1	no	—
134	C₂×D₄×C₃₇	C₂×Q₈	1	2	yes	—
135	C₂²×C₄×C₃₇	—	2	1	no	—
136	C₂²×C₄×C₃₇	—	2	1	no	—
137	C₂²×C₄×C₃₇	—	2	1	no	—
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	—	4	2	no	—
143	C₂²×C₄×C₃₇	—	8	2	no	—
144	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
149	SD₁₆×C₃₇	—	2	8	no	—
150	C₂×C₈×C₃₇	—	2	1	no	—
151	C₂×C₈×C₃₇	—	2	1	no	—
152	C₂×C₈×C₃₇	—	2	1	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	C₂×D₄	1	2	yes	—
157	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
158	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
159	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
160	C₂×C₈×C₃₇	C₂×Q₈	1	2	yes	—
161	C₂×C₈×C₃₇	#41	1	2	yes	—
162	C₄⋊C₄×C₃₇	—	2	4	no	—
163	C₄⋊C₄×C₃₇	—	2	1	no	—
164	C₄⋊C₄×C₃₇	—	2	1	no	—
165	C₄⋊C₄×C₃₇	—	2	1	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	—	4	2	no	—
176	C₄⋊C₄×C₃₇	—	4	2	no	—
177	C₄⋊C₄×C₃₇	—	4	2	no	—
178	C₄⋊C₄×C₃₇	—	4	2	no	—
179	C₄⋊C₄×C₃₇	—	4	2	no	—
180	C₄⋊C₄×C₃₇	—	4	4	no	—
181	C₄⋊C₄×C₃₇	—	8	2	no	—
182	C₂²⋊C₄×C₃₇	—	4	2	no	—
183	C₂²⋊C₄×C₃₇	—	4	4	no	—
184	C₂²⋊C₄×C₃₇	—	8	2	no	—
185	C₄²×C₃₇	—	2	1	no	—
186	C₄²×C₃₇	—	2	1	no	—
187	C₄²×C₃₇	—	2	1	no	—
188	C₄²×C₃₇	—	2	1	no	—
189	C₄²×C₃₇	—	4	2	no	—
190	C₄²×C₃₇	C₂×D₄	1	2	yes	—
191	C₄²×C₃₇	C₂×D₄	1	2	yes	—
192	C₂³×C₃₇	—	2	2	no	—
193	C₂³×C₃₇	—	4	1	no	—
194	C₂³×C₃₇	—	4	1	no	—
195	C₂³×C₃₇	—	4	2	no	—
196	C₂³×C₃₇	—	4	2	no	—
197	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
198	Q₈×C₃₇	—	2	2	no	—
199	Q₈×C₃₇	—	2	2	no	—
200	Q₈×C₃₇	—	4	1	no	—
201	Q₈×C₃₇	—	4	1	no	—
202	D₄×C₃₇	—	2	2	no	—
203	D₄×C₃₇	—	2	2	no	—
204	D₄×C₃₇	—	4	1	no	—
205	D₄×C₃₇	—	4	1	no	—
206	C₂×C₄×C₃₇	—	2	2	no	—
207	C₂×C₄×C₃₇	—	2	2	no	—
208	C₂×C₄×C₃₇	—	2	2	no	—
209	C₂×C₄×C₃₇	—	2	2	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	—	4	1	no	—
215	C₂×C₄×C₃₇	—	4	1	no	—
216	C₂×C₄×C₃₇	—	4	1	no	—
217	C₂×C₄×C₃₇	—	4	1	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	2	no	—
223	C₂×C₄×C₃₇	—	4	2	no	—
224	C₂×C₄×C₃₇	—	4	2	no	—
225	C₂×C₄×C₃₇	—	4	2	no	—
226	C₂×C₄×C₃₇	—	4	2	no	—
227	C₂×C₄×C₃₇	—	4	2	no	—
228	C₂×C₄×C₃₇	—	8	4	no	—
229	C₂×C₄×C₃₇	#127	1	2	yes	—
230	C₂×C₄×C₃₇	#127	1	2	yes	—
231	C₂×C₄×C₃₇	#135	1	4	yes	—
232	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
235	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
237	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
238	C₈×C₃₇	—	2	2	no	—
239	C₈×C₃₇	—	2	2	no	—
240	C₈×C₃₇	—	2	2	no	—
241	C₈×C₃₇	C₂²⋊Q₈	1	4	yes	—
242	#28533	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂²×C₃₇	—	4	4	no	—
244	C₂²×C₃₇	—	4	2	no	—
245	C₂²×C₃₇	—	8	2	no	—
246	C₂²×C₃₇	—	8	1	no	—
247	C₂²×C₃₇	—	8	1	no	—
248	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
249	C₂²×C₃₇	#547	1	1	yes	characteristic
250	C₂²×C₃₇	D₄×Q₈	1	1	yes	characteristic
251	C₂²×C₃₇	C₂×#135	1	2	yes	—
252	C₂²×C₃₇	#577	1	2	yes	—
253	C₄×C₃₇	—	2	4	no	—
254	C₄×C₃₇	—	2	2	no	—
255	C₄×C₃₇	—	2	2	no	—
256	C₄×C₃₇	—	4	2	no	—
257	C₄×C₃₇	—	4	2	no	—
258	C₄×C₃₇	—	8	1	no	—
259	C₄×C₃₇	—	8	1	no	—
260	C₄×C₃₇	—	8	1	no	—
261	C₄×C₃₇	—	8	1	no	—
262	C₄×C₃₇	—	8	1	no	—
263	C₄×C₃₇	—	8	1	no	—
264	C₄×C₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
265	C₄×C₃₇	#536	1	1	yes	characteristic
266	C₄×C₃₇	#547	1	1	yes	characteristic
267	C₄×C₃₇	D₄×Q₈	1	1	yes	characteristic
268	C₂×#499	C₂×C₃₇	1	1	yes	characteristic, complemented
269	C₂×#479	C₂×C₃₇	1	1	yes	characteristic, complemented
270	C₂×#478	C₂×C₃₇	1	1	yes	characteristic
271	C₂×C₄×SD₁₆	C₂×C₃₇	1	1	yes	characteristic
272	#2566	C₂×C₃₇	1	1	yes	characteristic
273	#2565	C₂×C₃₇	1	1	yes	characteristic, complemented
274	#2097	C₂×C₃₇	1	1	yes	characteristic, complemented
275	#2095	C₂×C₃₇	1	1	yes	characteristic, complemented
276	#2093	C₂×C₃₇	1	1	yes	characteristic
277	#2092	C₂×C₃₇	1	1	yes	characteristic
278	#1968	C₂×C₃₇	1	1	yes	characteristic
279	#1968	C₂×C₃₇	1	1	yes	characteristic
280	#1846	C₂×C₃₇	1	1	yes	characteristic, complemented
281	#1844	C₂×C₃₇	1	1	yes	characteristic, complemented
282	C₈×C₄⋊C₄	C₂×C₃₇	1	1	yes	characteristic, complemented
283	C₂×C₃₇	—	8	2	no	—
284	C₂×C₃₇	#2542	1	1	yes	characteristic
285	C₂×C₃₇	#3147	1	1	yes	characteristic
286	C₂×C₃₇	#3154	1	1	yes	characteristic
287	C₂×C₃₇	#3337	1	2	yes	—
288	C₂×C₃₇	#3381	1	2	yes	—
289	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
290	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
291	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
292	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
293	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
294	#499	—	2	4	no	—
295	#479	—	2	4	no	—
296	#478	—	2	4	no	—
297	C₄×SD₁₆	—	2	4	no	—
298	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
299	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
300	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
301	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
302	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
303	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
304	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
305	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
306	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
307	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
308	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
309	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
310	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
311	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
312	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
313	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
314	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
315	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
316	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
317	#398	—	2	2	no	—
318	#396	—	2	2	no	—
319	#391	C₂²×C₃₇	1	1	yes	characteristic
320	#391	C₂²×C₃₇	1	1	yes	characteristic
321	#390	C₂²×C₃₇	1	1	yes	characteristic
322	#390	C₂²×C₃₇	1	1	yes	characteristic
323	#387	—	2	2	no	—
324	#385	—	2	2	no	—
325	#384	C₂²×C₃₇	1	1	yes	characteristic
326	#384	C₂²×C₃₇	1	1	yes	characteristic
327	#382	C₂²×C₃₇	1	1	yes	characteristic
328	#382	C₂²×C₃₇	1	1	yes	characteristic
329	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
330	#336	C₂²×C₃₇	1	1	yes	characteristic
331	#336	C₂²×C₃₇	1	1	yes	characteristic
332	C₃₇	#28533	1	1	yes	characteristic, direct product factor, Sylow
333	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
334	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
335	C₂³×C₄	—	2	1	no	—
336	C₂×SD₁₆	—	2	2	no	—
337	C₂×SD₁₆	—	2	2	no	—
338	C₂×SD₁₆	Q₈×C₃₇	1	4	yes	—
339	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
342	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
343	#125	—	2	2	no	—
344	#125	—	2	2	no	—
345	#125	—	2	2	no	—
346	#125	—	2	2	no	—
347	C₄×Q₈	—	2	2	no	—
348	C₄×Q₈	—	2	2	no	—
349	C₄×D₄	—	2	2	no	—
350	C₄×D₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	2	no	—
357	C₂×C₄⋊C₄	—	2	2	no	—
358	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
359	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
370	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
371	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
372	#107	—	2	2	no	—
373	#107	—	2	2	no	—
374	#107	—	2	2	no	—
375	#107	—	2	2	no	—
376	#106	—	2	2	no	—
377	#106	—	2	2	no	—
378	#106	—	2	2	no	—
379	#106	—	2	2	no	—
380	#106	—	2	2	no	—
381	C₄⋊C₈	D₄×C₃₇	1	4	yes	—
382	#103	—	2	2	no	—
383	#103	—	2	2	no	—
384	#103	—	2	2	no	—
385	#102	—	2	2	no	—
386	#102	—	2	2	no	—
387	#102	—	2	2	no	—
388	C₄×C₈	—	2	2	no	—
389	C₄×C₈	—	2	2	no	—
390	C₄×C₈	D₄×C₃₇	1	4	yes	—
391	#95	—	2	2	no	—
392	#95	—	2	2	no	—
393	#95	—	2	2	no	—
394	#95	—	2	2	no	—
395	#95	D₄×C₃₇	1	2	yes	—
396	C₂⁴	—	2	1	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	C₂×Q₈×C₃₇	1	2	yes	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	C₂×Q₈×C₃₇	1	2	yes	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	4	2	no	—
417	C₂²×C₄	—	8	2	no	—
418	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
419	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
422	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
423	SD₁₆	—	2	8	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
431	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
432	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
433	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
434	C₂×C₈	C₂×Q₈×C₃₇	1	2	yes	—
435	C₂×C₈	#41×C₃₇	1	2	yes	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	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	—	4	2	no	—
450	C₄⋊C₄	—	4	2	no	—
451	C₄⋊C₄	—	4	2	no	—
452	C₄⋊C₄	—	4	2	no	—
453	C₄⋊C₄	—	4	2	no	—
454	C₄⋊C₄	—	4	4	no	—
455	C₄⋊C₄	—	8	2	no	—
456	C₂²⋊C₄	—	4	2	no	—
457	C₂²⋊C₄	—	4	4	no	—
458	C₂²⋊C₄	—	8	2	no	—
459	C₄²	—	2	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₄²	—	2	1	no	—
463	C₄²	—	4	2	no	—
464	C₄²	C₂×D₄×C₃₇	1	2	yes	—
465	C₄²	C₂×D₄×C₃₇	1	2	yes	—
466	C₂³	—	2	2	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	4	2	no	—
471	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
472	Q₈	—	2	2	no	—
473	Q₈	—	2	2	no	—
474	Q₈	—	4	1	no	—
475	Q₈	—	4	1	no	—
476	D₄	—	2	2	no	—
477	D₄	—	2	2	no	—
478	D₄	—	4	1	no	—
479	D₄	—	4	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	8	4	no	—
503	C₂×C₄	#127×C₃₇	1	2	yes	—
504	C₂×C₄	#127×C₃₇	1	2	yes	—
505	C₂×C₄	#135×C₃₇	1	4	yes	—
506	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
508	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
509	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
510	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
511	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
512	C₈	—	2	2	no	—
513	C₈	—	2	2	no	—
514	C₈	—	2	2	no	—
515	C₈	C₂²⋊Q₈×C₃₇	1	4	yes	—
516	C₂²	—	4	4	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	8	1	no	—
519	C₂²	—	8	1	no	—
520	C₂²	—	8	2	no	—
521	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
522	C₂²	C₃₇×#547	1	1	yes	characteristic
523	C₂²	D₄×Q₈×C₃₇	1	1	yes	characteristic
524	C₂²	C₂×#135×C₃₇	1	2	yes	—
525	C₂²	C₃₇×#577	1	2	yes	—
526	C₄	—	2	2	no	—
527	C₄	—	2	2	no	—
528	C₄	—	2	4	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	2	no	—
531	C₄	—	8	1	no	—
532	C₄	—	8	1	no	—
533	C₄	—	8	1	no	—
534	C₄	—	8	1	no	—
535	C₄	—	8	1	no	—
536	C₄	—	8	1	no	—
537	C₄	C₂×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
538	C₄	C₃₇×#536	1	1	yes	characteristic
539	C₄	C₃₇×#547	1	1	yes	characteristic
540	C₄	D₄×Q₈×C₃₇	1	1	yes	characteristic
541	C₂	—	8	2	no	—
542	C₂	C₃₇×#2542	1	1	yes	characteristic
543	C₂	C₃₇×#3147	1	1	yes	characteristic
544	C₂	C₃₇×#3154	1	1	yes	characteristic
545	C₂	C₃₇×#3337	1	2	yes	—
546	C₂	C₃₇×#3381	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×#499	C₂	semidirect
2. C₂×C₃₇×#479	C₂	semidirect
6. C₃₇×#2565	C₂	semidirect
7. C₃₇×#2097	C₂	semidirect
8. C₃₇×#2095	C₂	semidirect
13. C₃₇×#1846	C₂	semidirect
14. C₃₇×#1844	C₂	semidirect
15. C₈×C₄⋊C₄×C₃₇	C₂	semidirect
242. #28533	C₃₇	direct (N × H)
268. C₂×#499	C₂×C₃₇	semidirect
269. C₂×#479	C₂×C₃₇	semidirect
273. #2565	C₂×C₃₇	semidirect
274. #2097	C₂×C₃₇	semidirect
275. #2095	C₂×C₃₇	semidirect
280. #1846	C₂×C₃₇	semidirect
281. #1844	C₂×C₃₇	semidirect
282. C₈×C₄⋊C₄	C₂×C₃₇	semidirect
332. C₃₇	#28533	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#499	2
C₂×C₃₇×#479	2
C₂×C₃₇×#478	2
C₂×C₄×SD₁₆×C₃₇	2
C₃₇×#2566	2
C₃₇×#2565	2
C₃₇×#2097	2
C₃₇×#2095	2
C₃₇×#2093	2
C₃₇×#2092	2
C₃₇×#1968	2
C₃₇×#1846	2
C₃₇×#1844	2
C₈×C₄⋊C₄×C₃₇	2
#28533	37

Subgroups — C37×#28533 #22649786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28533 #22649786