Subgroups — C₃₇×#28525 #22649778

Order 9472.

910 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#478	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#478	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#474	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2660	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2328	C₂	1	1	yes	maximal, characteristic
7	C₃₇×#2094	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2093	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#2092	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#2092	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1961	C₂	1	1	yes	maximal, characteristic
12	C₃₇×#1957	C₂	1	1	yes	maximal, characteristic
13	C₃₇×#1847	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#1846	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
21	C₃₇×#478	—	2	4	no	—
22	C₃₇×#478	—	2	4	no	—
23	C₃₇×#476	—	2	4	no	—
24	C₃₇×#474	—	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×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
35	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
36	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
37	C₂×#102×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×#102×C₃₇	C₂²	1	1	yes	characteristic
42	C₂×#102×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×#398	—	2	2	no	—
46	C₃₇×#395	—	2	2	no	—
47	C₃₇×#390	C₂²	1	1	yes	characteristic
48	C₃₇×#390	C₂²	1	1	yes	characteristic
49	C₃₇×#386	—	2	2	no	—
50	C₃₇×#386	—	2	2	no	—
51	C₃₇×#384	C₂²	1	1	yes	characteristic
52	C₃₇×#384	C₂²	1	1	yes	characteristic
53	C₃₇×#382	C₂²	1	1	yes	characteristic
54	C₃₇×#382	C₂²	1	1	yes	characteristic
55	C₃₇×#382	C₂²	1	1	yes	characteristic
56	C₃₇×#376	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×D₄×C₃₇	—	2	2	no	—
61	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₃₇	—	2	1	no	—
64	C₂³×C₄×C₃₇	—	2	1	no	—
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	C₄⋊Q₈×C₃₇	—	2	2	no	—
70	C₄⋊Q₈×C₃₇	—	2	2	no	—
71	#127×C₃₇	—	2	2	no	—
72	#127×C₃₇	Q₈	1	4	yes	complemented
73	#125×C₃₇	—	2	2	no	—
74	#125×C₃₇	—	2	2	no	—
75	C₄×D₄×C₃₇	—	2	2	no	—
76	C₄×D₄×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	1	no	—
82	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
83	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
84	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₃₇	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
94	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
97	#107×C₃₇	—	2	2	no	—
98	#107×C₃₇	—	2	2	no	—
99	#107×C₃₇	—	2	2	no	—
100	#107×C₃₇	—	2	2	no	—
101	#106×C₃₇	—	2	2	no	—
102	#106×C₃₇	—	2	2	no	—
103	#106×C₃₇	—	2	2	no	—
104	#106×C₃₇	—	2	2	no	—
105	C₄⋊C₈×C₃₇	D₄	1	4	yes	complemented
106	C₄⋊C₈×C₃₇	D₄	1	4	yes	complemented
107	#102×C₃₇	—	2	2	no	—
108	#102×C₃₇	—	2	2	no	—
109	#102×C₃₇	—	2	2	no	—
110	#102×C₃₇	—	2	2	no	—
111	#102×C₃₇	—	2	2	no	—
112	#102×C₃₇	—	2	2	no	—
113	#102×C₃₇	—	2	2	no	—
114	#102×C₃₇	—	2	2	no	—
115	#97×C₃₇	—	2	2	no	—
116	C₄×C₈×C₃₇	—	2	2	no	—
117	#95×C₃₇	—	2	2	no	—
118	#95×C₃₇	—	2	2	no	—
119	#95×C₃₇	—	2	2	no	—
120	#95×C₃₇	D₄	1	2	yes	—
121	#95×C₃₇	D₄	1	2	yes	—
122	C₂⁴×C₃₇	—	2	1	no	—
123	C₂⁴×C₃₇	—	2	1	no	—
124	C₂×Q₈×C₃₇	—	4	2	no	—
125	C₂×Q₈×C₃₇	—	8	2	no	—
126	C₂×D₄×C₃₇	—	2	8	no	—
127	C₂×D₄×C₃₇	—	2	1	no	—
128	C₂×D₄×C₃₇	—	2	1	no	—
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	—	2	1	no	—
135	C₂×D₄×C₃₇	—	2	1	no	—
136	C₂×D₄×C₃₇	—	2	1	no	—
137	C₂×D₄×C₃₇	—	8	2	no	—
138	C₂×D₄×C₃₇	—	8	2	no	—
139	C₂×D₄×C₃₇	C₂×Q₈	1	2	yes	—
140	C₂×D₄×C₃₇	C₂×Q₈	1	2	yes	—
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	—	2	1	no	—
146	C₂²×C₄×C₃₇	—	2	1	no	—
147	C₂²×C₄×C₃₇	—	4	2	no	—
148	C₂²×C₄×C₃₇	—	4	2	no	—
149	C₂²×C₄×C₃₇	—	8	2	no	—
150	C₂²×C₄×C₃₇	—	8	2	no	—
151	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
160	C₂×C₈×C₃₇	—	2	1	no	—
161	C₂×C₈×C₃₇	—	2	1	no	—
162	C₂×C₈×C₃₇	—	2	1	no	—
163	C₂×C₈×C₃₇	—	2	1	no	—
164	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
165	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
166	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
167	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
179	C₄⋊C₄×C₃₇	—	2	1	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	—	8	2	no	—
184	C₄⋊C₄×C₃₇	—	8	2	no	—
185	C₂²⋊C₄×C₃₇	—	4	2	no	—
186	C₂²⋊C₄×C₃₇	—	4	2	no	—
187	C₂²⋊C₄×C₃₇	—	8	2	no	—
188	C₂²⋊C₄×C₃₇	—	8	2	no	—
189	C₄²×C₃₇	—	2	1	no	—
190	C₄²×C₃₇	—	2	1	no	—
191	C₄²×C₃₇	C₂×D₄	1	2	yes	—
192	C₄²×C₃₇	C₂×D₄	1	2	yes	—
193	C₄²×C₃₇	C₂×Q₈	1	2	yes	—
194	C₄²×C₃₇	#41	1	2	yes	—
195	C₂³×C₃₇	—	2	2	no	—
196	C₂³×C₃₇	—	2	2	no	—
197	C₂³×C₃₇	—	4	1	no	—
198	C₂³×C₃₇	—	4	1	no	—
199	C₂³×C₃₇	—	4	1	no	—
200	C₂³×C₃₇	—	4	1	no	—
201	C₂³×C₃₇	—	4	2	no	—
202	C₂³×C₃₇	—	4	2	no	—
203	C₂³×C₃₇	—	4	2	no	—
204	C₂³×C₃₇	—	4	2	no	—
205	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
206	Q₈×C₃₇	—	8	4	no	—
207	D₄×C₃₇	—	2	2	no	—
208	D₄×C₃₇	—	2	2	no	—
209	D₄×C₃₇	—	2	2	no	—
210	D₄×C₃₇	—	2	2	no	—
211	D₄×C₃₇	—	4	1	no	—
212	D₄×C₃₇	—	4	1	no	—
213	D₄×C₃₇	—	4	1	no	—
214	D₄×C₃₇	—	4	1	no	—
215	D₄×C₃₇	—	8	8	no	—
216	C₂×C₄×C₃₇	—	2	2	no	—
217	C₂×C₄×C₃₇	—	2	2	no	—
218	C₂×C₄×C₃₇	—	2	2	no	—
219	C₂×C₄×C₃₇	—	2	2	no	—
220	C₂×C₄×C₃₇	—	2	2	no	—
221	C₂×C₄×C₃₇	—	2	2	no	—
222	C₂×C₄×C₃₇	—	2	2	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	1	no	—
227	C₂×C₄×C₃₇	—	4	1	no	—
228	C₂×C₄×C₃₇	—	4	1	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	—	4	2	no	—
233	C₂×C₄×C₃₇	—	4	2	no	—
234	C₂×C₄×C₃₇	—	4	2	no	—
235	C₂×C₄×C₃₇	—	8	4	no	—
236	C₂×C₄×C₃₇	—	8	4	no	—
237	C₂×C₄×C₃₇	C₂²⋊Q₈	1	4	yes	—
238	C₂×C₄×C₃₇	#127	1	2	yes	—
239	C₂×C₄×C₃₇	#127	1	2	yes	—
240	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
243	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
245	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
246	C₈×C₃₇	—	2	2	no	—
247	C₈×C₃₇	—	2	2	no	—
248	C₈×C₃₇	—	2	2	no	—
249	C₈×C₃₇	—	2	2	no	—
250	#28525	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
251	C₂²×C₃₇	—	4	4	no	—
252	C₂²×C₃₇	—	4	4	no	—
253	C₂²×C₃₇	—	4	2	no	—
254	C₂²×C₃₇	—	4	2	no	—
255	C₂²×C₃₇	—	8	1	no	—
256	C₂²×C₃₇	—	8	1	no	—
257	C₂²×C₃₇	—	8	1	no	—
258	C₂²×C₃₇	—	8	1	no	—
259	C₂²×C₃₇	—	8	2	no	—
260	C₂²×C₃₇	—	8	2	no	—
261	C₂²×C₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
262	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
263	C₂²×C₃₇	#536	1	1	yes	characteristic
264	C₂²×C₃₇	#576	1	2	yes	—
265	C₂²×C₃₇	#577	1	2	yes	—
266	C₄×C₃₇	—	2	4	no	—
267	C₄×C₃₇	—	2	2	no	—
268	C₄×C₃₇	—	2	2	no	—
269	C₄×C₃₇	—	4	2	no	—
270	C₄×C₃₇	—	8	1	no	—
271	C₄×C₃₇	—	8	1	no	—
272	C₄×C₃₇	—	8	1	no	—
273	C₄×C₃₇	—	8	1	no	—
274	C₄×C₃₇	—	8	1	no	—
275	C₄×C₃₇	—	8	1	no	—
276	C₄×C₃₇	#547	1	1	yes	characteristic
277	C₄×C₃₇	#547	1	1	yes	characteristic
278	C₄×C₃₇	D₄×Q₈	1	1	yes	characteristic
279	C₄×C₃₇	D₄×Q₈	1	1	yes	characteristic
280	C₂×#478	C₂×C₃₇	1	1	yes	characteristic, complemented
281	C₂×#478	C₂×C₃₇	1	1	yes	characteristic, complemented
282	C₂×#476	C₂×C₃₇	1	1	yes	characteristic, complemented
283	C₂×#474	C₂×C₃₇	1	1	yes	characteristic, complemented
284	#2660	C₂×C₃₇	1	1	yes	characteristic, complemented
285	#2328	C₂×C₃₇	1	1	yes	characteristic
286	#2094	C₂×C₃₇	1	1	yes	characteristic, complemented
287	#2093	C₂×C₃₇	1	1	yes	characteristic, complemented
288	#2092	C₂×C₃₇	1	1	yes	characteristic, complemented
289	#2092	C₂×C₃₇	1	1	yes	characteristic, complemented
290	#1961	C₂×C₃₇	1	1	yes	characteristic
291	#1957	C₂×C₃₇	1	1	yes	characteristic
292	#1847	C₂×C₃₇	1	1	yes	characteristic, complemented
293	#1846	C₂×C₃₇	1	1	yes	characteristic, complemented
294	#1768	C₂×C₃₇	1	1	yes	characteristic, complemented
295	C₂×C₃₇	—	8	2	no	—
296	C₂×C₃₇	—	8	2	no	—
297	C₂×C₃₇	#2542	1	1	yes	characteristic
298	C₂×C₃₇	#3081	1	2	yes	—
299	C₂×C₃₇	#3154	1	1	yes	characteristic
300	C₂×C₃₇	#3155	1	1	yes	characteristic
301	C₂×C₃₇	#3241	1	2	yes	—
302	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
303	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
304	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
305	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
306	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
307	#478	—	2	4	no	—
308	#478	—	2	4	no	—
309	#476	—	2	4	no	—
310	#474	—	2	4	no	—
311	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
312	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
313	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
314	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
315	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
316	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
317	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
318	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
319	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
320	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
321	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
322	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
323	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
324	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
325	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
326	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
327	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
328	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
329	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
330	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
331	#398	—	2	2	no	—
332	#395	—	2	2	no	—
333	#390	C₂²×C₃₇	1	1	yes	characteristic
334	#390	C₂²×C₃₇	1	1	yes	characteristic
335	#386	—	2	2	no	—
336	#386	—	2	2	no	—
337	#384	C₂²×C₃₇	1	1	yes	characteristic
338	#384	C₂²×C₃₇	1	1	yes	characteristic
339	#382	C₂²×C₃₇	1	1	yes	characteristic
340	#382	C₂²×C₃₇	1	1	yes	characteristic
341	#382	C₂²×C₃₇	1	1	yes	characteristic
342	#376	C₂²×C₃₇	1	1	yes	characteristic
343	#336	C₂²×C₃₇	1	1	yes	characteristic
344	#336	C₂²×C₃₇	1	1	yes	characteristic
345	C₃₇	#28525	1	1	yes	characteristic, direct product factor, Sylow
346	C₂²×Q₈	—	2	1	no	—
347	C₂²×D₄	—	2	2	no	—
348	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
349	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
350	C₂³×C₄	—	2	1	no	—
351	C₂³×C₄	—	2	1	no	—
352	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
355	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
356	C₄⋊Q₈	—	2	2	no	—
357	C₄⋊Q₈	—	2	2	no	—
358	#127	—	2	2	no	—
359	#127	Q₈×C₃₇	1	4	yes	complemented
360	#125	—	2	2	no	—
361	#125	—	2	2	no	—
362	C₄×D₄	—	2	2	no	—
363	C₄×D₄	—	2	2	no	—
364	C₄×D₄	—	2	2	no	—
365	C₄×D₄	—	2	2	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	2	no	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
384	#107	—	2	2	no	—
385	#107	—	2	2	no	—
386	#107	—	2	2	no	—
387	#107	—	2	2	no	—
388	#106	—	2	2	no	—
389	#106	—	2	2	no	—
390	#106	—	2	2	no	—
391	#106	—	2	2	no	—
392	C₄⋊C₈	D₄×C₃₇	1	4	yes	complemented
393	C₄⋊C₈	D₄×C₃₇	1	4	yes	complemented
394	#102	—	2	2	no	—
395	#102	—	2	2	no	—
396	#102	—	2	2	no	—
397	#102	—	2	2	no	—
398	#102	—	2	2	no	—
399	#102	—	2	2	no	—
400	#102	—	2	2	no	—
401	#102	—	2	2	no	—
402	#97	—	2	2	no	—
403	C₄×C₈	—	2	2	no	—
404	#95	—	2	2	no	—
405	#95	—	2	2	no	—
406	#95	—	2	2	no	—
407	#95	D₄×C₃₇	1	2	yes	—
408	#95	D₄×C₃₇	1	2	yes	—
409	C₂⁴	—	2	1	no	—
410	C₂⁴	—	2	1	no	—
411	C₂×Q₈	—	4	2	no	—
412	C₂×Q₈	—	8	2	no	—
413	C₂×D₄	—	2	8	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	8	2	no	—
425	C₂×D₄	—	8	2	no	—
426	C₂×D₄	C₂×Q₈×C₃₇	1	2	yes	—
427	C₂×D₄	C₂×Q₈×C₃₇	1	2	yes	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	4	2	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	—	8	2	no	—
437	C₂²×C₄	—	8	2	no	—
438	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
439	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
440	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
442	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
452	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
453	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
454	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	4	2	no	—
468	C₄⋊C₄	—	4	2	no	—
469	C₄⋊C₄	—	4	2	no	—
470	C₄⋊C₄	—	8	2	no	—
471	C₄⋊C₄	—	8	2	no	—
472	C₂²⋊C₄	—	4	2	no	—
473	C₂²⋊C₄	—	4	2	no	—
474	C₂²⋊C₄	—	8	2	no	—
475	C₂²⋊C₄	—	8	2	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	C₂×D₄×C₃₇	1	2	yes	—
479	C₄²	C₂×D₄×C₃₇	1	2	yes	—
480	C₄²	C₂×Q₈×C₃₇	1	2	yes	—
481	C₄²	#41×C₃₇	1	2	yes	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	1	no	—
488	C₂³	—	4	2	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
493	Q₈	—	8	4	no	—
494	D₄	—	2	2	no	—
495	D₄	—	2	2	no	—
496	D₄	—	2	2	no	—
497	D₄	—	2	2	no	—
498	D₄	—	4	1	no	—
499	D₄	—	4	1	no	—
500	D₄	—	4	1	no	—
501	D₄	—	4	1	no	—
502	D₄	—	8	8	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	8	4	no	—
523	C₂×C₄	—	8	4	no	—
524	C₂×C₄	C₂²⋊Q₈×C₃₇	1	4	yes	—
525	C₂×C₄	#127×C₃₇	1	2	yes	—
526	C₂×C₄	#127×C₃₇	1	2	yes	—
527	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
529	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
530	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
531	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
532	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
533	C₈	—	2	2	no	—
534	C₈	—	2	2	no	—
535	C₈	—	2	2	no	—
536	C₈	—	2	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	4	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	8	1	no	—
542	C₂²	—	8	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	2	no	—
546	C₂²	—	8	2	no	—
547	C₂²	C₂×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
548	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
549	C₂²	C₃₇×#536	1	1	yes	characteristic
550	C₂²	C₃₇×#576	1	2	yes	—
551	C₂²	C₃₇×#577	1	2	yes	—
552	C₄	—	2	2	no	—
553	C₄	—	2	2	no	—
554	C₄	—	2	4	no	—
555	C₄	—	4	2	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	1	no	—
558	C₄	—	8	1	no	—
559	C₄	—	8	1	no	—
560	C₄	—	8	1	no	—
561	C₄	—	8	1	no	—
562	C₄	C₃₇×#547	1	1	yes	characteristic
563	C₄	C₃₇×#547	1	1	yes	characteristic
564	C₄	D₄×Q₈×C₃₇	1	1	yes	characteristic
565	C₄	D₄×Q₈×C₃₇	1	1	yes	characteristic
566	C₂	—	8	2	no	—
567	C₂	—	8	2	no	—
568	C₂	C₃₇×#2542	1	1	yes	characteristic
569	C₂	C₃₇×#3081	1	2	yes	—
570	C₂	C₃₇×#3154	1	1	yes	characteristic
571	C₂	C₃₇×#3155	1	1	yes	characteristic
572	C₂	C₃₇×#3241	1	2	yes	—

	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 ◁ C₃₇×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#478	C₂	semidirect
2. C₂×C₃₇×#478	C₂	semidirect
3. C₂×C₃₇×#476	C₂	semidirect
4. C₂×C₃₇×#474	C₂	semidirect
5. C₃₇×#2660	C₂	semidirect
7. C₃₇×#2094	C₂	semidirect
8. C₃₇×#2093	C₂	semidirect
9. C₃₇×#2092	C₂	semidirect
10. C₃₇×#2092	C₂	semidirect
13. C₃₇×#1847	C₂	semidirect
14. C₃₇×#1846	C₂	semidirect
15. C₃₇×#1768	C₂	semidirect
72. #127×C₃₇	Q₈	semidirect
105. C₄⋊C₈×C₃₇	D₄	semidirect
106. C₄⋊C₈×C₃₇	D₄	semidirect
250. #28525	C₃₇	direct (N × H)
280. C₂×#478	C₂×C₃₇	semidirect
281. C₂×#478	C₂×C₃₇	semidirect
282. C₂×#476	C₂×C₃₇	semidirect
283. C₂×#474	C₂×C₃₇	semidirect
284. #2660	C₂×C₃₇	semidirect
286. #2094	C₂×C₃₇	semidirect
287. #2093	C₂×C₃₇	semidirect
288. #2092	C₂×C₃₇	semidirect
289. #2092	C₂×C₃₇	semidirect
292. #1847	C₂×C₃₇	semidirect
293. #1846	C₂×C₃₇	semidirect
294. #1768	C₂×C₃₇	semidirect
345. C₃₇	#28525	direct (N × H)
359. #127	Q₈×C₃₇	semidirect
392. C₄⋊C₈	D₄×C₃₇	semidirect
393. C₄⋊C₈	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×#478	2
C₂×C₃₇×#476	2
C₂×C₃₇×#474	2
C₃₇×#2660	2
C₃₇×#2328	2
C₃₇×#2094	2
C₃₇×#2093	2
C₃₇×#2092	2
C₃₇×#1961	2
C₃₇×#1957	2
C₃₇×#1847	2
C₃₇×#1846	2
C₃₇×#1768	2
#28525	37

Subgroups — C37×#28525 #22649778

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28525 #22649778