Subgroups — C₃₇×#28354 #22649607

Order 9472.

1154 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#469	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#449	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#417	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2504	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2431	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2097	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2092	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#2012	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#2011	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#1970	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₇×#1961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#1958	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₇×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₃₇	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
21	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×#121×C₃₇	C₂²	1	1	yes	characteristic
24	C₂×#121×C₃₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
26	C₃₇×#480	—	2	4	no	—
27	C₃₇×#469	—	2	4	no	—
28	C₃₇×#449	—	2	4	no	—
29	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
32	C₃₇×#417	—	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×#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×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×#392	—	2	2	no	—
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×#390	C₂²	1	1	yes	characteristic
52	C₃₇×#386	—	2	2	no	—
53	C₃₇×#386	—	2	2	no	—
54	C₃₇×#382	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	C₂×#41×C₃₇	—	2	2	no	—
60	C₂×#41×C₃₇	—	2	2	no	—
61	C₂×#41×C₃₇	—	2	2	no	—
62	C₂×#41×C₃₇	—	2	2	no	—
63	C₂×#41×C₃₇	—	4	1	no	—
64	C₂×#41×C₃₇	—	4	1	no	—
65	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₃₇	—	2	1	no	—
67	C₂²×D₄×C₃₇	—	2	1	no	—
68	C₂²×D₄×C₃₇	—	2	1	no	—
69	C₂²×D₄×C₃₇	—	2	2	no	—
70	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₃₇	—	2	1	no	—
74	C₂³×C₄×C₃₇	—	2	1	no	—
75	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
76	C₂×SD₁₆×C₃₇	—	2	2	no	—
77	C₂×SD₁₆×C₃₇	—	2	2	no	—
78	C₂×SD₁₆×C₃₇	—	4	1	no	—
79	C₂×D₈×C₃₇	—	2	2	no	—
80	C₂×D₈×C₃₇	—	2	2	no	—
81	C₂×D₈×C₃₇	—	2	2	no	—
82	C₂×D₈×C₃₇	—	4	1	no	—
83	C₂×D₈×C₃₇	—	4	1	no	—
84	C₂×D₈×C₃₇	—	4	1	no	—
85	C₂×M₁₆×C₃₇	—	4	1	no	—
86	C₂×M₁₆×C₃₇	—	4	1	no	—
87	C₂×M₁₆×C₃₇	D₄	1	4	yes	complemented
88	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
92	#127×C₃₇	—	2	2	no	—
93	#127×C₃₇	—	4	1	no	—
94	#124×C₃₇	—	2	2	no	—
95	#124×C₃₇	—	4	1	no	—
96	#121×C₃₇	—	2	2	no	—
97	#121×C₃₇	—	2	2	no	—
98	#121×C₃₇	—	2	2	no	—
99	#121×C₃₇	—	2	2	no	—
100	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
101	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
102	C₂×C₄⋊C₄×C₃₇	—	2	1	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	2	no	—
110	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
111	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
112	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
113	C₂×C₂²⋊C₄×C₃₇	D₄	1	2	yes	—
114	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
116	#107×C₃₇	—	2	2	no	—
117	#107×C₃₇	—	2	2	no	—
118	#106×C₃₇	—	2	2	no	—
119	#103×C₃₇	—	2	2	no	—
120	#103×C₃₇	—	2	2	no	—
121	#103×C₃₇	—	2	2	no	—
122	#102×C₃₇	—	2	2	no	—
123	#102×C₃₇	—	2	2	no	—
124	#102×C₃₇	—	2	2	no	—
125	#102×C₃₇	—	2	2	no	—
126	#102×C₃₇	—	2	2	no	—
127	#102×C₃₇	—	2	2	no	—
128	#102×C₃₇	—	2	2	no	—
129	C₂²⋊C₈×C₃₇	D₄	1	4	yes	complemented
130	#97×C₃₇	—	4	1	no	—
131	C₄×C₈×C₃₇	—	4	1	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	—	2	1	no	—
137	C₂⁴×C₃₇	—	2	1	no	—
138	C₂⁴×C₃₇	—	2	1	no	—
139	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
140	#41×C₃₇	—	2	8	no	—
141	#41×C₃₇	—	4	4	no	—
142	#41×C₃₇	—	4	4	no	—
143	#41×C₃₇	—	4	4	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	#41	1	2	yes	—
150	C₂×D₄×C₃₇	—	2	1	no	—
151	C₂×D₄×C₃₇	—	2	1	no	—
152	C₂×D₄×C₃₇	—	2	1	no	—
153	C₂×D₄×C₃₇	—	2	1	no	—
154	C₂×D₄×C₃₇	—	2	1	no	—
155	C₂×D₄×C₃₇	—	2	1	no	—
156	C₂×D₄×C₃₇	—	2	1	no	—
157	C₂×D₄×C₃₇	—	2	1	no	—
158	C₂×D₄×C₃₇	—	2	1	no	—
159	C₂×D₄×C₃₇	—	2	1	no	—
160	C₂×D₄×C₃₇	—	2	1	no	—
161	C₂×D₄×C₃₇	—	2	1	no	—
162	C₂×D₄×C₃₇	—	2	1	no	—
163	C₂×D₄×C₃₇	—	2	1	no	—
164	C₂×D₄×C₃₇	—	2	1	no	—
165	C₂×D₄×C₃₇	—	2	1	no	—
166	C₂×D₄×C₃₇	—	2	1	no	—
167	C₂×D₄×C₃₇	—	4	2	no	—
168	C₂×D₄×C₃₇	—	4	4	no	—
169	C₂×D₄×C₃₇	—	4	4	no	—
170	C₂×D₄×C₃₇	—	4	2	no	—
171	C₂×D₄×C₃₇	—	4	2	no	—
172	C₂×D₄×C₃₇	—	4	4	no	—
173	C₂×D₄×C₃₇	—	4	2	no	—
174	C₂×D₄×C₃₇	—	4	2	no	—
175	C₂×D₄×C₃₇	—	8	2	no	—
176	C₂×D₄×C₃₇	—	8	2	no	—
177	C₂×D₄×C₃₇	#41	1	2	yes	—
178	C₂²×C₄×C₃₇	—	2	1	no	—
179	C₂²×C₄×C₃₇	—	2	1	no	—
180	C₂²×C₄×C₃₇	—	2	1	no	—
181	C₂²×C₄×C₃₇	—	2	1	no	—
182	C₂²×C₄×C₃₇	—	2	1	no	—
183	C₂²×C₄×C₃₇	—	2	1	no	—
184	C₂²×C₄×C₃₇	—	2	1	no	—
185	C₂²×C₄×C₃₇	—	2	1	no	—
186	C₂²×C₄×C₃₇	—	2	1	no	—
187	C₂²×C₄×C₃₇	—	4	2	no	—
188	C₂²×C₄×C₃₇	—	4	2	no	—
189	C₂²×C₄×C₃₇	—	4	2	no	—
190	C₂²×C₄×C₃₇	—	4	2	no	—
191	C₂²×C₄×C₃₇	—	8	2	no	—
192	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
193	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
194	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
196	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
197	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
198	SD₁₆×C₃₇	—	4	4	no	—
199	D₈×C₃₇	—	4	4	no	—
200	D₈×C₃₇	—	4	4	no	—
201	M₁₆×C₃₇	—	4	4	no	—
202	C₂×C₈×C₃₇	—	2	1	no	—
203	C₂×C₈×C₃₇	—	2	1	no	—
204	C₂×C₈×C₃₇	—	2	1	no	—
205	C₂×C₈×C₃₇	—	2	1	no	—
206	C₂×C₈×C₃₇	—	2	1	no	—
207	C₂×C₈×C₃₇	—	2	1	no	—
208	C₂×C₈×C₃₇	—	2	1	no	—
209	C₂×C₈×C₃₇	—	2	1	no	—
210	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
211	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
212	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
213	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
214	C₄⋊C₄×C₃₇	—	2	1	no	—
215	C₄⋊C₄×C₃₇	—	2	1	no	—
216	C₄⋊C₄×C₃₇	—	2	1	no	—
217	C₄⋊C₄×C₃₇	—	2	1	no	—
218	C₄⋊C₄×C₃₇	—	2	1	no	—
219	C₄⋊C₄×C₃₇	—	2	1	no	—
220	C₄⋊C₄×C₃₇	—	2	1	no	—
221	C₄⋊C₄×C₃₇	—	2	1	no	—
222	C₄⋊C₄×C₃₇	—	4	2	no	—
223	C₂²⋊C₄×C₃₇	—	4	2	no	—
224	C₂²⋊C₄×C₃₇	—	4	4	no	—
225	C₂²⋊C₄×C₃₇	—	4	2	no	—
226	C₂²⋊C₄×C₃₇	—	4	2	no	—
227	C₂²⋊C₄×C₃₇	—	8	2	no	—
228	C₂²⋊C₄×C₃₇	—	8	2	no	—
229	C₂²⋊C₄×C₃₇	—	8	2	no	—
230	C₄²×C₃₇	—	2	1	no	—
231	C₄²×C₃₇	—	2	1	no	—
232	C₄²×C₃₇	—	2	1	no	—
233	C₄²×C₃₇	—	2	1	no	—
234	C₂³×C₃₇	—	2	1	no	—
235	C₂³×C₃₇	—	2	1	no	—
236	C₂³×C₃₇	—	2	2	no	—
237	C₂³×C₃₇	—	2	2	no	—
238	C₂³×C₃₇	—	2	2	no	—
239	C₂³×C₃₇	—	4	1	no	—
240	C₂³×C₃₇	—	4	1	no	—
241	C₂³×C₃₇	—	4	2	no	—
242	C₂³×C₃₇	—	4	2	no	—
243	C₂³×C₃₇	—	4	1	no	—
244	C₂³×C₃₇	—	4	1	no	—
245	C₂³×C₃₇	—	4	1	no	—
246	C₂³×C₃₇	—	4	1	no	—
247	C₂³×C₃₇	—	4	1	no	—
248	C₂³×C₃₇	—	4	1	no	—
249	C₂³×C₃₇	—	4	2	no	—
250	C₂³×C₃₇	—	4	2	no	—
251	C₂³×C₃₇	—	4	2	no	—
252	C₂³×C₃₇	—	4	2	no	—
253	C₂³×C₃₇	#127	1	2	yes	—
254	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
255	Q₈×C₃₇	—	2	2	no	—
256	Q₈×C₃₇	—	2	2	no	—
257	Q₈×C₃₇	—	4	1	no	—
258	Q₈×C₃₇	—	4	1	no	—
259	D₄×C₃₇	—	2	2	no	—
260	D₄×C₃₇	—	2	2	no	—
261	D₄×C₃₇	—	4	8	no	—
262	D₄×C₃₇	—	4	1	no	—
263	D₄×C₃₇	—	4	1	no	—
264	D₄×C₃₇	—	4	1	no	—
265	D₄×C₃₇	—	4	1	no	—
266	D₄×C₃₇	—	4	1	no	—
267	D₄×C₃₇	—	4	1	no	—
268	D₄×C₃₇	—	4	1	no	—
269	D₄×C₃₇	—	4	1	no	—
270	D₄×C₃₇	—	4	1	no	—
271	D₄×C₃₇	—	4	1	no	—
272	D₄×C₃₇	—	8	8	no	—
273	D₄×C₃₇	—	8	4	no	—
274	D₄×C₃₇	—	8	4	no	—
275	C₂×C₄×C₃₇	—	2	1	no	—
276	C₂×C₄×C₃₇	—	2	1	no	—
277	C₂×C₄×C₃₇	—	2	2	no	—
278	C₂×C₄×C₃₇	—	2	2	no	—
279	C₂×C₄×C₃₇	—	2	2	no	—
280	C₂×C₄×C₃₇	—	2	2	no	—
281	C₂×C₄×C₃₇	—	2	2	no	—
282	C₂×C₄×C₃₇	—	2	2	no	—
283	C₂×C₄×C₃₇	—	2	2	no	—
284	C₂×C₄×C₃₇	—	2	2	no	—
285	C₂×C₄×C₃₇	—	2	2	no	—
286	C₂×C₄×C₃₇	—	2	2	no	—
287	C₂×C₄×C₃₇	—	2	2	no	—
288	C₂×C₄×C₃₇	—	4	8	no	—
289	C₂×C₄×C₃₇	—	4	1	no	—
290	C₂×C₄×C₃₇	—	4	1	no	—
291	C₂×C₄×C₃₇	—	4	1	no	—
292	C₂×C₄×C₃₇	—	4	1	no	—
293	C₂×C₄×C₃₇	—	4	1	no	—
294	C₂×C₄×C₃₇	—	4	1	no	—
295	C₂×C₄×C₃₇	—	4	2	no	—
296	C₂×C₄×C₃₇	—	4	2	no	—
297	C₂×C₄×C₃₇	—	4	2	no	—
298	C₂×C₄×C₃₇	—	4	2	no	—
299	C₂×C₄×C₃₇	—	8	4	no	—
300	C₂×C₄×C₃₇	#127	1	2	yes	—
301	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
304	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
305	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
306	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
307	C₈×C₃₇	—	2	2	no	—
308	C₈×C₃₇	—	2	2	no	—
309	C₈×C₃₇	—	2	2	no	—
310	C₈×C₃₇	—	2	2	no	—
311	#28354	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
312	C₂²×C₃₇	—	2	2	no	—
313	C₂²×C₃₇	—	2	2	no	—
314	C₂²×C₃₇	—	2	2	no	—
315	C₂²×C₃₇	—	4	2	no	—
316	C₂²×C₃₇	—	4	2	no	—
317	C₂²×C₃₇	—	4	2	no	—
318	C₂²×C₃₇	—	4	4	no	—
319	C₂²×C₃₇	—	8	1	no	—
320	C₂²×C₃₇	—	8	1	no	—
321	C₂²×C₃₇	—	8	2	no	—
322	C₂²×C₃₇	—	8	1	no	—
323	C₂²×C₃₇	—	8	1	no	—
324	C₂²×C₃₇	—	8	1	no	—
325	C₂²×C₃₇	—	8	1	no	—
326	C₂²×C₃₇	—	8	1	no	—
327	C₂²×C₃₇	—	8	1	no	—
328	C₂²×C₃₇	—	8	2	no	—
329	C₂²×C₃₇	—	8	2	no	—
330	C₂²×C₃₇	—	8	2	no	—
331	C₂²×C₃₇	—	8	2	no	—
332	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
333	C₂²×C₃₇	#546	1	1	yes	characteristic
334	C₂²×C₃₇	#546	1	1	yes	characteristic
335	C₂²×C₃₇	#575	1	2	yes	—
336	C₂²×C₃₇	#576	1	2	yes	—
337	C₄×C₃₇	—	2	2	no	—
338	C₄×C₃₇	—	4	2	no	—
339	C₄×C₃₇	—	4	2	no	—
340	C₄×C₃₇	—	4	2	no	—
341	C₄×C₃₇	—	8	1	no	—
342	C₄×C₃₇	—	8	1	no	—
343	C₄×C₃₇	—	8	1	no	—
344	C₄×C₃₇	—	8	1	no	—
345	C₄×C₃₇	#525	1	1	yes	characteristic
346	C₄×C₃₇	#534	1	1	yes	characteristic
347	C₄×C₃₇	#546	1	1	yes	characteristic
348	C₄×C₃₇	#546	1	1	yes	characteristic
349	C₂×#480	C₂×C₃₇	1	1	yes	characteristic, complemented
350	C₂×#469	C₂×C₃₇	1	1	yes	characteristic, complemented
351	C₂×#449	C₂×C₃₇	1	1	yes	characteristic, complemented
352	C₂×#417	C₂×C₃₇	1	1	yes	characteristic, complemented
353	#2504	C₂×C₃₇	1	1	yes	characteristic, complemented
354	#2431	C₂×C₃₇	1	1	yes	characteristic, complemented
355	#2097	C₂×C₃₇	1	1	yes	characteristic, complemented
356	#2092	C₂×C₃₇	1	1	yes	characteristic, complemented
357	#2012	C₂×C₃₇	1	1	yes	characteristic, complemented
358	#2011	C₂×C₃₇	1	1	yes	characteristic, complemented
359	#1973	C₂×C₃₇	1	1	yes	characteristic, complemented
360	#1970	C₂×C₃₇	1	1	yes	characteristic, complemented
361	#1961	C₂×C₃₇	1	1	yes	characteristic, complemented
362	#1958	C₂×C₃₇	1	1	yes	characteristic, complemented
363	#1753	C₂×C₃₇	1	1	yes	characteristic, complemented
364	C₂×C₃₇	—	4	2	no	—
365	C₂×C₃₇	—	8	2	no	—
366	C₂×C₃₇	—	16	1	no	—
367	C₂×C₃₇	—	16	1	no	—
368	C₂×C₃₇	#2539	1	1	yes	characteristic
369	C₂×C₃₇	#3153	1	1	yes	characteristic
370	C₂×C₃₇	#3155	1	1	yes	characteristic
371	C₂×C₃₇	#3309	1	2	yes	—
372	C₂×C₃₇	#3322	1	2	yes	—
373	C₂²×#41	C₂²×C₃₇	1	1	yes	characteristic
374	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
375	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
376	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
377	C₂²×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
378	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
379	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
380	C₂×#121	C₂²×C₃₇	1	1	yes	characteristic
381	C₂×#121	C₂²×C₃₇	1	1	yes	characteristic
382	C₂²×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
383	#480	—	2	4	no	—
384	#469	—	2	4	no	—
385	#449	—	2	4	no	—
386	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
387	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
388	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
389	#417	—	2	4	no	—
390	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
391	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
392	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
393	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
394	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
395	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
396	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
397	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
398	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
399	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
400	C₂×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
401	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
402	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
403	#397	—	2	2	no	—
404	#392	—	2	2	no	—
405	#391	C₂²×C₃₇	1	1	yes	characteristic
406	#390	C₂²×C₃₇	1	1	yes	characteristic
407	#390	C₂²×C₃₇	1	1	yes	characteristic
408	#390	C₂²×C₃₇	1	1	yes	characteristic
409	#386	—	2	2	no	—
410	#386	—	2	2	no	—
411	#382	C₂²×C₃₇	1	1	yes	characteristic
412	#382	C₂²×C₃₇	1	1	yes	characteristic
413	C₄×C₂²⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
414	#336	C₂²×C₃₇	1	1	yes	characteristic
415	#336	C₂²×C₃₇	1	1	yes	characteristic
416	C₃₇	#28354	1	1	yes	characteristic, direct product factor, Sylow
417	C₂×#41	—	2	2	no	—
418	C₂×#41	—	2	2	no	—
419	C₂×#41	—	2	2	no	—
420	C₂×#41	—	2	2	no	—
421	C₂×#41	—	4	1	no	—
422	C₂×#41	—	4	1	no	—
423	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
424	C₂²×D₄	—	2	1	no	—
425	C₂²×D₄	—	2	1	no	—
426	C₂²×D₄	—	2	1	no	—
427	C₂²×D₄	—	2	2	no	—
428	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
429	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
430	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
431	C₂³×C₄	—	2	1	no	—
432	C₂³×C₄	—	2	1	no	—
433	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
434	C₂×SD₁₆	—	2	2	no	—
435	C₂×SD₁₆	—	2	2	no	—
436	C₂×SD₁₆	—	4	1	no	—
437	C₂×D₈	—	2	2	no	—
438	C₂×D₈	—	2	2	no	—
439	C₂×D₈	—	2	2	no	—
440	C₂×D₈	—	4	1	no	—
441	C₂×D₈	—	4	1	no	—
442	C₂×D₈	—	4	1	no	—
443	C₂×M₁₆	—	4	1	no	—
444	C₂×M₁₆	—	4	1	no	—
445	C₂×M₁₆	D₄×C₃₇	1	4	yes	complemented
446	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
447	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
448	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
449	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
450	#127	—	2	2	no	—
451	#127	—	4	1	no	—
452	#124	—	2	2	no	—
453	#124	—	4	1	no	—
454	#121	—	2	2	no	—
455	#121	—	2	2	no	—
456	#121	—	2	2	no	—
457	#121	—	2	2	no	—
458	C₂×C₄⋊C₄	—	2	2	no	—
459	C₂×C₄⋊C₄	—	2	2	no	—
460	C₂×C₄⋊C₄	—	2	1	no	—
461	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	1	no	—
467	C₂×C₂²⋊C₄	—	2	2	no	—
468	C₂×C₂²⋊C₄	—	2	2	no	—
469	C₂×C₂²⋊C₄	—	2	2	no	—
470	C₂×C₂²⋊C₄	—	2	2	no	—
471	C₂×C₂²⋊C₄	D₄×C₃₇	1	2	yes	—
472	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
473	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
474	#107	—	2	2	no	—
475	#107	—	2	2	no	—
476	#106	—	2	2	no	—
477	#103	—	2	2	no	—
478	#103	—	2	2	no	—
479	#103	—	2	2	no	—
480	#102	—	2	2	no	—
481	#102	—	2	2	no	—
482	#102	—	2	2	no	—
483	#102	—	2	2	no	—
484	#102	—	2	2	no	—
485	#102	—	2	2	no	—
486	#102	—	2	2	no	—
487	C₂²⋊C₈	D₄×C₃₇	1	4	yes	complemented
488	#97	—	4	1	no	—
489	C₄×C₈	—	4	1	no	—
490	#95	—	2	2	no	—
491	#95	—	2	2	no	—
492	#95	—	2	2	no	—
493	#95	D₄×C₃₇	1	2	yes	—
494	C₂⁴	—	2	1	no	—
495	C₂⁴	—	2	1	no	—
496	C₂⁴	—	2	1	no	—
497	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
498	#41	—	2	8	no	—
499	#41	—	4	4	no	—
500	#41	—	4	4	no	—
501	#41	—	4	4	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	#41×C₃₇	1	2	yes	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	4	2	no	—
526	C₂×D₄	—	4	4	no	—
527	C₂×D₄	—	4	4	no	—
528	C₂×D₄	—	4	2	no	—
529	C₂×D₄	—	4	2	no	—
530	C₂×D₄	—	4	4	no	—
531	C₂×D₄	—	4	2	no	—
532	C₂×D₄	—	4	2	no	—
533	C₂×D₄	—	8	2	no	—
534	C₂×D₄	—	8	2	no	—
535	C₂×D₄	#41×C₃₇	1	2	yes	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	4	2	no	—
546	C₂²×C₄	—	4	2	no	—
547	C₂²×C₄	—	4	2	no	—
548	C₂²×C₄	—	4	2	no	—
549	C₂²×C₄	—	8	2	no	—
550	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
551	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
552	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
553	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
554	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
555	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
556	SD₁₆	—	4	4	no	—
557	D₈	—	4	4	no	—
558	D₈	—	4	4	no	—
559	M₁₆	—	4	4	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
569	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
570	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
571	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	4	2	no	—
581	C₂²⋊C₄	—	4	2	no	—
582	C₂²⋊C₄	—	4	4	no	—
583	C₂²⋊C₄	—	4	2	no	—
584	C₂²⋊C₄	—	4	2	no	—
585	C₂²⋊C₄	—	8	2	no	—
586	C₂²⋊C₄	—	8	2	no	—
587	C₂²⋊C₄	—	8	2	no	—
588	C₄²	—	2	1	no	—
589	C₄²	—	2	1	no	—
590	C₄²	—	2	1	no	—
591	C₄²	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	2	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	2	no	—
600	C₂³	—	4	2	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	2	no	—
608	C₂³	—	4	2	no	—
609	C₂³	—	4	2	no	—
610	C₂³	—	4	2	no	—
611	C₂³	#127×C₃₇	1	2	yes	—
612	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
613	Q₈	—	2	2	no	—
614	Q₈	—	2	2	no	—
615	Q₈	—	4	1	no	—
616	Q₈	—	4	1	no	—
617	D₄	—	2	2	no	—
618	D₄	—	2	2	no	—
619	D₄	—	4	8	no	—
620	D₄	—	4	1	no	—
621	D₄	—	4	1	no	—
622	D₄	—	4	1	no	—
623	D₄	—	4	1	no	—
624	D₄	—	4	1	no	—
625	D₄	—	4	1	no	—
626	D₄	—	4	1	no	—
627	D₄	—	4	1	no	—
628	D₄	—	4	1	no	—
629	D₄	—	4	1	no	—
630	D₄	—	8	8	no	—
631	D₄	—	8	4	no	—
632	D₄	—	8	4	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	4	8	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	2	no	—
654	C₂×C₄	—	4	2	no	—
655	C₂×C₄	—	4	2	no	—
656	C₂×C₄	—	4	2	no	—
657	C₂×C₄	—	8	4	no	—
658	C₂×C₄	#127×C₃₇	1	2	yes	—
659	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
660	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
661	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
662	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
663	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
664	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
665	C₈	—	2	2	no	—
666	C₈	—	2	2	no	—
667	C₈	—	2	2	no	—
668	C₈	—	2	2	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	4	2	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	4	4	no	—
676	C₂²	—	8	1	no	—
677	C₂²	—	8	1	no	—
678	C₂²	—	8	2	no	—
679	C₂²	—	8	1	no	—
680	C₂²	—	8	1	no	—
681	C₂²	—	8	1	no	—
682	C₂²	—	8	1	no	—
683	C₂²	—	8	1	no	—
684	C₂²	—	8	1	no	—
685	C₂²	—	8	2	no	—
686	C₂²	—	8	2	no	—
687	C₂²	—	8	2	no	—
688	C₂²	—	8	2	no	—
689	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
690	C₂²	C₃₇×#546	1	1	yes	characteristic
691	C₂²	C₃₇×#546	1	1	yes	characteristic
692	C₂²	C₃₇×#575	1	2	yes	—
693	C₂²	C₃₇×#576	1	2	yes	—
694	C₄	—	2	2	no	—
695	C₄	—	4	2	no	—
696	C₄	—	4	2	no	—
697	C₄	—	4	2	no	—
698	C₄	—	8	1	no	—
699	C₄	—	8	1	no	—
700	C₄	—	8	1	no	—
701	C₄	—	8	1	no	—
702	C₄	C₃₇×#525	1	1	yes	characteristic
703	C₄	C₃₇×#534	1	1	yes	characteristic
704	C₄	C₃₇×#546	1	1	yes	characteristic
705	C₄	C₃₇×#546	1	1	yes	characteristic
706	C₂	—	4	2	no	—
707	C₂	—	8	2	no	—
708	C₂	—	16	1	no	—
709	C₂	—	16	1	no	—
710	C₂	C₃₇×#2539	1	1	yes	characteristic
711	C₂	C₃₇×#3153	1	1	yes	characteristic
712	C₂	C₃₇×#3155	1	1	yes	characteristic
713	C₂	C₃₇×#3309	1	2	yes	—
714	C₂	C₃₇×#3322	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
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
1. C₂×C₃₇×#480	C₂	semidirect
2. C₂×C₃₇×#469	C₂	semidirect
3. C₂×C₃₇×#449	C₂	semidirect
4. C₂×C₃₇×#417	C₂	semidirect
5. C₃₇×#2504	C₂	semidirect
6. C₃₇×#2431	C₂	semidirect
7. C₃₇×#2097	C₂	semidirect
8. C₃₇×#2092	C₂	semidirect
9. C₃₇×#2012	C₂	semidirect
10. C₃₇×#2011	C₂	semidirect
11. C₃₇×#1973	C₂	semidirect
12. C₃₇×#1970	C₂	semidirect
13. C₃₇×#1961	C₂	semidirect
14. C₃₇×#1958	C₂	semidirect
15. C₃₇×#1753	C₂	semidirect
87. C₂×M₁₆×C₃₇	D₄	semidirect
129. C₂²⋊C₈×C₃₇	D₄	semidirect
311. #28354	C₃₇	direct (N × H)
349. C₂×#480	C₂×C₃₇	semidirect
350. C₂×#469	C₂×C₃₇	semidirect
351. C₂×#449	C₂×C₃₇	semidirect
352. C₂×#417	C₂×C₃₇	semidirect
353. #2504	C₂×C₃₇	semidirect
354. #2431	C₂×C₃₇	semidirect
355. #2097	C₂×C₃₇	semidirect
356. #2092	C₂×C₃₇	semidirect
357. #2012	C₂×C₃₇	semidirect
358. #2011	C₂×C₃₇	semidirect
359. #1973	C₂×C₃₇	semidirect
360. #1970	C₂×C₃₇	semidirect
361. #1961	C₂×C₃₇	semidirect
362. #1958	C₂×C₃₇	semidirect
363. #1753	C₂×C₃₇	semidirect
416. C₃₇	#28354	direct (N × H)
445. C₂×M₁₆	D₄×C₃₇	semidirect
487. C₂²⋊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×#480	2
C₂×C₃₇×#469	2
C₂×C₃₇×#449	2
C₂×C₃₇×#417	2
C₃₇×#2504	2
C₃₇×#2431	2
C₃₇×#2097	2
C₃₇×#2092	2
C₃₇×#2012	2
C₃₇×#2011	2
C₃₇×#1973	2
C₃₇×#1970	2
C₃₇×#1961	2
C₃₇×#1958	2
C₃₇×#1753	2
#28354	37

Subgroups — C37×#28354 #22649607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28354 #22649607