Subgroups — C₃₇×#28355 #22649608

Order 9472.

1022 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#485	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₇×#470	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₇×#451	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₇×#419	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2499	C₂	1	1	yes	maximal, characteristic
6	C₃₇×#2434	C₂	1	1	yes	maximal, characteristic
7	C₃₇×#2097	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2096	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#2016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#2016	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1971	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#1969	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₇×#1960	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#1956	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₇×#1753	C₂	1	1	yes	maximal, characteristic
16	C₂³×Q₈×C₃₇	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×#117×C₃₇	C₂²	1	1	yes	characteristic
26	C₃₇×#485	—	2	4	no	—
27	C₃₇×#470	—	2	4	no	—
28	C₃₇×#451	—	2	4	no	—
29	C₂×#107×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	C₃₇×#419	—	2	4	no	—
33	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
34	C₂×#103×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×#103×C₃₇	C₂²	1	1	yes	characteristic
39	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
40	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
41	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
42	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
44	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
46	C₃₇×#397	—	2	2	no	—
47	C₃₇×#395	—	2	2	no	—
48	C₃₇×#391	C₂²	1	1	yes	characteristic
49	C₃₇×#391	C₂²	1	1	yes	characteristic
50	C₃₇×#391	C₂²	1	1	yes	characteristic
51	C₃₇×#391	C₂²	1	1	yes	characteristic
52	C₃₇×#387	—	2	2	no	—
53	C₃₇×#385	—	2	2	no	—
54	C₃₇×#384	C₂²	1	1	yes	characteristic
55	C₃₇×#382	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊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	—	2	2	no	—
61	C₂²×Q₈×C₃₇	—	2	2	no	—
62	C₂²×Q₈×C₃₇	—	2	2	no	—
63	C₂²×Q₈×C₃₇	—	2	2	no	—
64	C₂²×Q₈×C₃₇	—	4	1	no	—
65	C₂²×Q₈×C₃₇	—	4	1	no	—
66	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₃₇	—	2	1	no	—
71	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
72	C₂×Q₁₆×C₃₇	—	2	2	no	—
73	C₂×Q₁₆×C₃₇	—	2	2	no	—
74	C₂×Q₁₆×C₃₇	—	2	2	no	—
75	C₂×Q₁₆×C₃₇	—	2	2	no	—
76	C₂×Q₁₆×C₃₇	—	2	2	no	—
77	C₂×Q₁₆×C₃₇	—	4	1	no	—
78	C₂×Q₁₆×C₃₇	—	4	1	no	—
79	C₂×Q₁₆×C₃₇	—	4	1	no	—
80	C₂×Q₁₆×C₃₇	—	4	1	no	—
81	C₂×M₁₆×C₃₇	—	4	1	no	—
82	C₂×M₁₆×C₃₇	—	4	1	no	—
83	C₂×M₁₆×C₃₇	D₄	1	4	yes	—
84	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
88	C₄⋊Q₈×C₃₇	—	2	2	no	—
89	C₄⋊Q₈×C₃₇	—	2	2	no	—
90	C₄⋊Q₈×C₃₇	—	4	1	no	—
91	C₄⋊Q₈×C₃₇	—	4	1	no	—
92	C₂²⋊Q₈×C₃₇	—	2	2	no	—
93	C₂²⋊Q₈×C₃₇	—	2	2	no	—
94	C₂²⋊Q₈×C₃₇	—	2	2	no	—
95	C₂²⋊Q₈×C₃₇	—	2	2	no	—
96	#117×C₃₇	—	2	2	no	—
97	#117×C₃₇	—	2	2	no	—
98	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
99	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
100	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
101	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
102	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
103	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₃₇	D₄	1	2	yes	—
111	C₂×C₄²×C₃₇	—	2	1	no	—
112	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
114	#107×C₃₇	—	2	2	no	—
115	#106×C₃₇	—	2	2	no	—
116	#106×C₃₇	—	2	2	no	—
117	#103×C₃₇	—	2	2	no	—
118	#103×C₃₇	—	2	2	no	—
119	#103×C₃₇	—	2	2	no	—
120	#103×C₃₇	—	2	2	no	—
121	#103×C₃₇	—	2	2	no	—
122	#103×C₃₇	—	2	2	no	—
123	#103×C₃₇	—	2	2	no	—
124	#103×C₃₇	—	2	2	no	—
125	#103×C₃₇	—	2	2	no	—
126	#103×C₃₇	—	2	2	no	—
127	C₂²⋊C₈×C₃₇	D₄	1	4	yes	—
128	#97×C₃₇	—	4	1	no	—
129	C₄×C₈×C₃₇	—	4	1	no	—
130	#95×C₃₇	—	2	2	no	—
131	#95×C₃₇	—	2	2	no	—
132	#95×C₃₇	—	2	2	no	—
133	#95×C₃₇	—	2	2	no	—
134	#95×C₃₇	—	2	2	no	—
135	#95×C₃₇	D₄	1	2	yes	—
136	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
137	C₂×Q₈×C₃₇	—	2	1	no	—
138	C₂×Q₈×C₃₇	—	2	1	no	—
139	C₂×Q₈×C₃₇	—	2	8	no	—
140	C₂×Q₈×C₃₇	—	2	1	no	—
141	C₂×Q₈×C₃₇	—	2	1	no	—
142	C₂×Q₈×C₃₇	—	2	1	no	—
143	C₂×Q₈×C₃₇	—	2	1	no	—
144	C₂×Q₈×C₃₇	—	2	1	no	—
145	C₂×Q₈×C₃₇	—	2	1	no	—
146	C₂×Q₈×C₃₇	—	2	1	no	—
147	C₂×Q₈×C₃₇	—	2	1	no	—
148	C₂×Q₈×C₃₇	—	2	1	no	—
149	C₂×Q₈×C₃₇	—	2	1	no	—
150	C₂×Q₈×C₃₇	—	2	1	no	—
151	C₂×Q₈×C₃₇	—	2	1	no	—
152	C₂×Q₈×C₃₇	—	2	1	no	—
153	C₂×Q₈×C₃₇	—	2	1	no	—
154	C₂×Q₈×C₃₇	—	2	1	no	—
155	C₂×Q₈×C₃₇	—	2	1	no	—
156	C₂×Q₈×C₃₇	—	2	1	no	—
157	C₂×Q₈×C₃₇	—	2	1	no	—
158	C₂×Q₈×C₃₇	—	2	1	no	—
159	C₂×Q₈×C₃₇	—	2	1	no	—
160	C₂×Q₈×C₃₇	—	4	2	no	—
161	C₂×Q₈×C₃₇	—	4	2	no	—
162	C₂×Q₈×C₃₇	—	4	4	no	—
163	C₂×Q₈×C₃₇	—	4	4	no	—
164	C₂×Q₈×C₃₇	—	4	4	no	—
165	C₂×Q₈×C₃₇	—	4	2	no	—
166	C₂×Q₈×C₃₇	#41	1	2	yes	—
167	C₂×Q₈×C₃₇	#41	1	2	yes	—
168	C₂²×C₄×C₃₇	—	2	1	no	—
169	C₂²×C₄×C₃₇	—	2	1	no	—
170	C₂²×C₄×C₃₇	—	2	1	no	—
171	C₂²×C₄×C₃₇	—	2	1	no	—
172	C₂²×C₄×C₃₇	—	2	1	no	—
173	C₂²×C₄×C₃₇	—	2	1	no	—
174	C₂²×C₄×C₃₇	—	2	1	no	—
175	C₂²×C₄×C₃₇	—	2	1	no	—
176	C₂²×C₄×C₃₇	—	2	1	no	—
177	C₂²×C₄×C₃₇	—	2	1	no	—
178	C₂²×C₄×C₃₇	—	2	1	no	—
179	C₂²×C₄×C₃₇	—	2	1	no	—
180	C₂²×C₄×C₃₇	—	4	2	no	—
181	C₂²×C₄×C₃₇	—	4	2	no	—
182	C₂²×C₄×C₃₇	—	4	2	no	—
183	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
186	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
189	Q₁₆×C₃₇	—	4	4	no	—
190	Q₁₆×C₃₇	—	4	4	no	—
191	Q₁₆×C₃₇	—	4	4	no	—
192	M₁₆×C₃₇	—	4	4	no	—
193	C₂×C₈×C₃₇	—	2	1	no	—
194	C₂×C₈×C₃₇	—	2	1	no	—
195	C₂×C₈×C₃₇	—	2	1	no	—
196	C₂×C₈×C₃₇	—	2	1	no	—
197	C₂×C₈×C₃₇	—	2	1	no	—
198	C₂×C₈×C₃₇	—	2	1	no	—
199	C₂×C₈×C₃₇	—	2	1	no	—
200	C₂×C₈×C₃₇	—	2	1	no	—
201	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
202	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
203	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
204	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
205	C₄⋊C₄×C₃₇	—	2	1	no	—
206	C₄⋊C₄×C₃₇	—	2	1	no	—
207	C₄⋊C₄×C₃₇	—	2	1	no	—
208	C₄⋊C₄×C₃₇	—	2	1	no	—
209	C₄⋊C₄×C₃₇	—	2	1	no	—
210	C₄⋊C₄×C₃₇	—	2	1	no	—
211	C₄⋊C₄×C₃₇	—	2	1	no	—
212	C₄⋊C₄×C₃₇	—	2	1	no	—
213	C₄⋊C₄×C₃₇	—	4	4	no	—
214	C₄⋊C₄×C₃₇	—	4	4	no	—
215	C₄⋊C₄×C₃₇	—	4	2	no	—
216	C₄⋊C₄×C₃₇	—	4	2	no	—
217	C₄⋊C₄×C₃₇	—	4	4	no	—
218	C₂²⋊C₄×C₃₇	—	2	4	no	—
219	C₂²⋊C₄×C₃₇	—	4	2	no	—
220	C₂²⋊C₄×C₃₇	—	4	2	no	—
221	C₂²⋊C₄×C₃₇	—	4	2	no	—
222	C₄²×C₃₇	—	2	1	no	—
223	C₄²×C₃₇	—	2	1	no	—
224	C₄²×C₃₇	—	2	1	no	—
225	C₄²×C₃₇	—	2	1	no	—
226	C₄²×C₃₇	—	4	2	no	—
227	C₂³×C₃₇	—	2	1	no	—
228	C₂³×C₃₇	—	2	1	no	—
229	C₂³×C₃₇	—	2	2	no	—
230	C₂³×C₃₇	—	2	2	no	—
231	C₂³×C₃₇	#127	1	2	yes	—
232	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
233	Q₈×C₃₇	—	2	2	no	—
234	Q₈×C₃₇	—	2	2	no	—
235	Q₈×C₃₇	—	2	2	no	—
236	Q₈×C₃₇	—	2	2	no	—
237	Q₈×C₃₇	—	4	8	no	—
238	Q₈×C₃₇	—	4	1	no	—
239	Q₈×C₃₇	—	4	1	no	—
240	Q₈×C₃₇	—	4	1	no	—
241	Q₈×C₃₇	—	4	1	no	—
242	Q₈×C₃₇	—	4	1	no	—
243	Q₈×C₃₇	—	4	1	no	—
244	Q₈×C₃₇	—	4	1	no	—
245	Q₈×C₃₇	—	4	1	no	—
246	Q₈×C₃₇	—	4	1	no	—
247	Q₈×C₃₇	—	4	1	no	—
248	Q₈×C₃₇	—	4	1	no	—
249	Q₈×C₃₇	—	4	1	no	—
250	C₂×C₄×C₃₇	—	2	2	no	—
251	C₂×C₄×C₃₇	—	2	1	no	—
252	C₂×C₄×C₃₇	—	2	1	no	—
253	C₂×C₄×C₃₇	—	2	2	no	—
254	C₂×C₄×C₃₇	—	2	2	no	—
255	C₂×C₄×C₃₇	—	2	2	no	—
256	C₂×C₄×C₃₇	—	2	2	no	—
257	C₂×C₄×C₃₇	—	2	2	no	—
258	C₂×C₄×C₃₇	—	2	2	no	—
259	C₂×C₄×C₃₇	—	2	2	no	—
260	C₂×C₄×C₃₇	—	2	2	no	—
261	C₂×C₄×C₃₇	—	2	2	no	—
262	C₂×C₄×C₃₇	—	2	2	no	—
263	C₂×C₄×C₃₇	—	4	8	no	—
264	C₂×C₄×C₃₇	—	4	1	no	—
265	C₂×C₄×C₃₇	—	4	1	no	—
266	C₂×C₄×C₃₇	—	4	1	no	—
267	C₂×C₄×C₃₇	—	4	1	no	—
268	C₂×C₄×C₃₇	—	4	1	no	—
269	C₂×C₄×C₃₇	—	4	1	no	—
270	C₂×C₄×C₃₇	—	4	1	no	—
271	C₂×C₄×C₃₇	—	4	1	no	—
272	C₂×C₄×C₃₇	—	4	1	no	—
273	C₂×C₄×C₃₇	—	4	1	no	—
274	C₂×C₄×C₃₇	—	4	1	no	—
275	C₂×C₄×C₃₇	—	4	1	no	—
276	C₂×C₄×C₃₇	—	4	1	no	—
277	C₂×C₄×C₃₇	—	4	1	no	—
278	C₂×C₄×C₃₇	—	4	2	no	—
279	C₂×C₄×C₃₇	—	4	2	no	—
280	C₂×C₄×C₃₇	—	4	2	no	—
281	C₂×C₄×C₃₇	—	4	2	no	—
282	C₂×C₄×C₃₇	#127	1	2	yes	—
283	C₂×C₄×C₃₇	#137	1	4	yes	—
284	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
287	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
289	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
290	C₈×C₃₇	—	2	2	no	—
291	C₈×C₃₇	—	2	2	no	—
292	C₈×C₃₇	—	2	2	no	—
293	C₈×C₃₇	—	2	2	no	—
294	#28355	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₂²×C₃₇	—	2	2	no	—
296	C₂²×C₃₇	—	2	2	no	—
297	C₂²×C₃₇	—	2	2	no	—
298	C₂²×C₃₇	—	4	2	no	—
299	C₂²×C₃₇	—	4	2	no	—
300	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
301	C₂²×C₃₇	#546	1	1	yes	characteristic
302	C₂²×C₃₇	#546	1	1	yes	characteristic
303	C₂²×C₃₇	C₂×#137	1	2	yes	—
304	C₂²×C₃₇	#578	1	2	yes	—
305	C₄×C₃₇	—	2	2	no	—
306	C₄×C₃₇	—	2	4	no	—
307	C₄×C₃₇	—	4	2	no	—
308	C₄×C₃₇	—	4	2	no	—
309	C₄×C₃₇	—	4	2	no	—
310	C₄×C₃₇	—	8	1	no	—
311	C₄×C₃₇	—	8	1	no	—
312	C₄×C₃₇	—	8	1	no	—
313	C₄×C₃₇	—	8	1	no	—
314	C₄×C₃₇	—	8	1	no	—
315	C₄×C₃₇	—	8	1	no	—
316	C₄×C₃₇	#525	1	1	yes	characteristic
317	C₄×C₃₇	#534	1	1	yes	characteristic
318	C₄×C₃₇	#546	1	1	yes	characteristic
319	C₄×C₃₇	#546	1	1	yes	characteristic
320	C₂×#485	C₂×C₃₇	1	1	yes	characteristic
321	C₂×#470	C₂×C₃₇	1	1	yes	characteristic
322	C₂×#451	C₂×C₃₇	1	1	yes	characteristic
323	C₂×#419	C₂×C₃₇	1	1	yes	characteristic
324	#2499	C₂×C₃₇	1	1	yes	characteristic
325	#2434	C₂×C₃₇	1	1	yes	characteristic
326	#2097	C₂×C₃₇	1	1	yes	characteristic, complemented
327	#2096	C₂×C₃₇	1	1	yes	characteristic, complemented
328	#2016	C₂×C₃₇	1	1	yes	characteristic, complemented
329	#2016	C₂×C₃₇	1	1	yes	characteristic, complemented
330	#1971	C₂×C₃₇	1	1	yes	characteristic, complemented
331	#1969	C₂×C₃₇	1	1	yes	characteristic, complemented
332	#1960	C₂×C₃₇	1	1	yes	characteristic, complemented
333	#1956	C₂×C₃₇	1	1	yes	characteristic, complemented
334	#1753	C₂×C₃₇	1	1	yes	characteristic
335	C₂×C₃₇	—	4	2	no	—
336	C₂×C₃₇	#2539	1	1	yes	characteristic
337	C₂×C₃₇	#3152	1	1	yes	characteristic
338	C₂×C₃₇	#3156	1	1	yes	characteristic
339	C₂×C₃₇	#3312	1	2	yes	—
340	C₂×C₃₇	#3328	1	2	yes	—
341	C₂³×Q₈	C₂²×C₃₇	1	1	yes	characteristic
342	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
343	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
344	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
345	C₂²×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
346	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
347	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
348	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
349	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
350	C₂×#117	C₂²×C₃₇	1	1	yes	characteristic
351	#485	—	2	4	no	—
352	#470	—	2	4	no	—
353	#451	—	2	4	no	—
354	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
355	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
356	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
357	#419	—	2	4	no	—
358	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
359	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
360	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
361	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
362	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
363	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
364	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
365	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
366	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
367	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
368	C₂×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
369	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
370	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
371	#397	—	2	2	no	—
372	#395	—	2	2	no	—
373	#391	C₂²×C₃₇	1	1	yes	characteristic
374	#391	C₂²×C₃₇	1	1	yes	characteristic
375	#391	C₂²×C₃₇	1	1	yes	characteristic
376	#391	C₂²×C₃₇	1	1	yes	characteristic
377	#387	—	2	2	no	—
378	#385	—	2	2	no	—
379	#384	C₂²×C₃₇	1	1	yes	characteristic
380	#382	C₂²×C₃₇	1	1	yes	characteristic
381	C₄×C₂²⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
382	#336	C₂²×C₃₇	1	1	yes	characteristic
383	#336	C₂²×C₃₇	1	1	yes	characteristic
384	C₃₇	#28355	1	1	yes	characteristic, direct product factor, Sylow
385	C₂²×Q₈	—	2	1	no	—
386	C₂²×Q₈	—	2	2	no	—
387	C₂²×Q₈	—	2	2	no	—
388	C₂²×Q₈	—	2	2	no	—
389	C₂²×Q₈	—	2	2	no	—
390	C₂²×Q₈	—	4	1	no	—
391	C₂²×Q₈	—	4	1	no	—
392	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
393	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
394	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
395	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
396	C₂³×C₄	—	2	1	no	—
397	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
398	C₂×Q₁₆	—	2	2	no	—
399	C₂×Q₁₆	—	2	2	no	—
400	C₂×Q₁₆	—	2	2	no	—
401	C₂×Q₁₆	—	2	2	no	—
402	C₂×Q₁₆	—	2	2	no	—
403	C₂×Q₁₆	—	4	1	no	—
404	C₂×Q₁₆	—	4	1	no	—
405	C₂×Q₁₆	—	4	1	no	—
406	C₂×Q₁₆	—	4	1	no	—
407	C₂×M₁₆	—	4	1	no	—
408	C₂×M₁₆	—	4	1	no	—
409	C₂×M₁₆	D₄×C₃₇	1	4	yes	—
410	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
412	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
413	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
414	C₄⋊Q₈	—	2	2	no	—
415	C₄⋊Q₈	—	2	2	no	—
416	C₄⋊Q₈	—	4	1	no	—
417	C₄⋊Q₈	—	4	1	no	—
418	C₂²⋊Q₈	—	2	2	no	—
419	C₂²⋊Q₈	—	2	2	no	—
420	C₂²⋊Q₈	—	2	2	no	—
421	C₂²⋊Q₈	—	2	2	no	—
422	#117	—	2	2	no	—
423	#117	—	2	2	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	2	no	—
427	C₂×C₄⋊C₄	—	2	2	no	—
428	C₂×C₄⋊C₄	—	2	2	no	—
429	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₂²⋊C₄	D₄×C₃₇	1	2	yes	—
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
439	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
440	#107	—	2	2	no	—
441	#106	—	2	2	no	—
442	#106	—	2	2	no	—
443	#103	—	2	2	no	—
444	#103	—	2	2	no	—
445	#103	—	2	2	no	—
446	#103	—	2	2	no	—
447	#103	—	2	2	no	—
448	#103	—	2	2	no	—
449	#103	—	2	2	no	—
450	#103	—	2	2	no	—
451	#103	—	2	2	no	—
452	#103	—	2	2	no	—
453	C₂²⋊C₈	D₄×C₃₇	1	4	yes	—
454	#97	—	4	1	no	—
455	C₄×C₈	—	4	1	no	—
456	#95	—	2	2	no	—
457	#95	—	2	2	no	—
458	#95	—	2	2	no	—
459	#95	—	2	2	no	—
460	#95	—	2	2	no	—
461	#95	D₄×C₃₇	1	2	yes	—
462	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	8	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	4	2	no	—
487	C₂×Q₈	—	4	2	no	—
488	C₂×Q₈	—	4	4	no	—
489	C₂×Q₈	—	4	4	no	—
490	C₂×Q₈	—	4	4	no	—
491	C₂×Q₈	—	4	2	no	—
492	C₂×Q₈	#41×C₃₇	1	2	yes	—
493	C₂×Q₈	#41×C₃₇	1	2	yes	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	4	2	no	—
507	C₂²×C₄	—	4	2	no	—
508	C₂²×C₄	—	4	2	no	—
509	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
510	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
512	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
513	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
514	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
515	Q₁₆	—	4	4	no	—
516	Q₁₆	—	4	4	no	—
517	Q₁₆	—	4	4	no	—
518	M₁₆	—	4	4	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
528	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
529	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
530	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	4	4	no	—
540	C₄⋊C₄	—	4	4	no	—
541	C₄⋊C₄	—	4	2	no	—
542	C₄⋊C₄	—	4	2	no	—
543	C₄⋊C₄	—	4	4	no	—
544	C₂²⋊C₄	—	2	4	no	—
545	C₂²⋊C₄	—	4	2	no	—
546	C₂²⋊C₄	—	4	2	no	—
547	C₂²⋊C₄	—	4	2	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	4	2	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	2	no	—
557	C₂³	#127×C₃₇	1	2	yes	—
558	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
559	Q₈	—	2	2	no	—
560	Q₈	—	2	2	no	—
561	Q₈	—	2	2	no	—
562	Q₈	—	2	2	no	—
563	Q₈	—	4	8	no	—
564	Q₈	—	4	1	no	—
565	Q₈	—	4	1	no	—
566	Q₈	—	4	1	no	—
567	Q₈	—	4	1	no	—
568	Q₈	—	4	1	no	—
569	Q₈	—	4	1	no	—
570	Q₈	—	4	1	no	—
571	Q₈	—	4	1	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	4	1	no	—
574	Q₈	—	4	1	no	—
575	Q₈	—	4	1	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	4	8	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	#127×C₃₇	1	2	yes	—
609	C₂×C₄	#137×C₃₇	1	4	yes	—
610	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
611	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
612	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
613	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
614	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
615	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
616	C₈	—	2	2	no	—
617	C₈	—	2	2	no	—
618	C₈	—	2	2	no	—
619	C₈	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	4	2	no	—
625	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
626	C₂²	C₃₇×#546	1	1	yes	characteristic
627	C₂²	C₃₇×#546	1	1	yes	characteristic
628	C₂²	C₂×#137×C₃₇	1	2	yes	—
629	C₂²	C₃₇×#578	1	2	yes	—
630	C₄	—	2	2	no	—
631	C₄	—	2	4	no	—
632	C₄	—	4	2	no	—
633	C₄	—	4	2	no	—
634	C₄	—	4	2	no	—
635	C₄	—	8	1	no	—
636	C₄	—	8	1	no	—
637	C₄	—	8	1	no	—
638	C₄	—	8	1	no	—
639	C₄	—	8	1	no	—
640	C₄	—	8	1	no	—
641	C₄	C₃₇×#525	1	1	yes	characteristic
642	C₄	C₃₇×#534	1	1	yes	characteristic
643	C₄	C₃₇×#546	1	1	yes	characteristic
644	C₄	C₃₇×#546	1	1	yes	characteristic
645	C₂	—	4	2	no	—
646	C₂	C₃₇×#2539	1	1	yes	characteristic
647	C₂	C₃₇×#3152	1	1	yes	characteristic
648	C₂	C₃₇×#3156	1	1	yes	characteristic
649	C₂	C₃₇×#3312	1	2	yes	—
650	C₂	C₃₇×#3328	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
7. C₃₇×#2097	C₂	semidirect
8. C₃₇×#2096	C₂	semidirect
9. C₃₇×#2016	C₂	semidirect
10. C₃₇×#2016	C₂	semidirect
11. C₃₇×#1971	C₂	semidirect
12. C₃₇×#1969	C₂	semidirect
13. C₃₇×#1960	C₂	semidirect
14. C₃₇×#1956	C₂	semidirect
294. #28355	C₃₇	direct (N × H)
326. #2097	C₂×C₃₇	semidirect
327. #2096	C₂×C₃₇	semidirect
328. #2016	C₂×C₃₇	semidirect
329. #2016	C₂×C₃₇	semidirect
330. #1971	C₂×C₃₇	semidirect
331. #1969	C₂×C₃₇	semidirect
332. #1960	C₂×C₃₇	semidirect
333. #1956	C₂×C₃₇	semidirect
384. C₃₇	#28355	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×#485	2
C₂×C₃₇×#470	2
C₂×C₃₇×#451	2
C₂×C₃₇×#419	2
C₃₇×#2499	2
C₃₇×#2434	2
C₃₇×#2097	2
C₃₇×#2096	2
C₃₇×#2016	2
C₃₇×#1971	2
C₃₇×#1969	2
C₃₇×#1960	2
C₃₇×#1956	2
C₃₇×#1753	2
#28355	37

Subgroups — C37×#28355 #22649608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28355 #22649608