Subgroups — C₃₇×#28366 #22649619

Order 9472.

1112 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#481	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#468	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#452	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#417	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2503	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2431	C₂	1	1	yes	maximal, characteristic
7	C₃₇×#2097	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2092	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#2015	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#2014	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1971	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#1968	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×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×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×C₂²⋊Q₈×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×#481	—	2	4	no	—
27	C₃₇×#468	—	2	4	no	—
28	C₃₇×#452	—	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×#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×#103×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×#400	—	2	2	no	—
47	C₃₇×#392	—	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×#390	C₂²	1	1	yes	characteristic
52	C₃₇×#386	—	2	2	no	—
53	C₃₇×#382	C₂²	1	1	yes	characteristic
54	C₃₇×#382	C₂²	1	1	yes	characteristic
55	C₃₇×#381	—	2	2	no	—
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×Q₈×C₃₇	C₂³	1	1	yes	characteristic
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	C₂³×C₄×C₃₇	—	2	1	no	—
73	C₂³×C₄×C₃₇	—	2	1	no	—
74	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
75	C₂×Q₁₆×C₃₇	—	2	2	no	—
76	C₂×Q₁₆×C₃₇	—	2	2	no	—
77	C₂×Q₁₆×C₃₇	—	4	1	no	—
78	C₂×SD₁₆×C₃₇	—	2	2	no	—
79	C₂×SD₁₆×C₃₇	—	2	2	no	—
80	C₂×SD₁₆×C₃₇	—	2	2	no	—
81	C₂×SD₁₆×C₃₇	—	4	1	no	—
82	C₂×SD₁₆×C₃₇	—	4	1	no	—
83	C₂×SD₁₆×C₃₇	—	4	1	no	—
84	C₂×M₁₆×C₃₇	—	4	1	no	—
85	C₂×M₁₆×C₃₇	—	4	1	no	—
86	C₂×M₁₆×C₃₇	D₄	1	4	yes	complemented
87	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
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	#127×C₃₇	—	2	2	no	—
92	#127×C₃₇	—	4	1	no	—
93	#124×C₃₇	—	2	2	no	—
94	#124×C₃₇	—	4	1	no	—
95	C₂²⋊Q₈×C₃₇	—	2	2	no	—
96	C₂²⋊Q₈×C₃₇	—	2	2	no	—
97	#121×C₃₇	—	2	2	no	—
98	#121×C₃₇	—	2	2	no	—
99	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
100	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
101	C₂×C₄⋊C₄×C₃₇	—	2	1	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	D₄	1	2	yes	—
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	#102×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	C₂²⋊C₈×C₃₇	D₄	1	4	yes	complemented
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	—	2	1	no	—
137	C₂⁴×C₃₇	—	2	1	no	—
138	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
139	#41×C₃₇	—	2	8	no	—
140	#41×C₃₇	—	4	4	no	—
141	#41×C₃₇	—	4	4	no	—
142	#41×C₃₇	—	4	4	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	#41	1	2	yes	—
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	—	4	2	no	—
167	C₂×D₄×C₃₇	—	4	4	no	—
168	C₂×D₄×C₃₇	—	4	4	no	—
169	C₂×D₄×C₃₇	—	4	2	no	—
170	C₂×D₄×C₃₇	—	4	2	no	—
171	C₂×D₄×C₃₇	—	4	2	no	—
172	C₂×D₄×C₃₇	—	8	2	no	—
173	C₂×D₄×C₃₇	—	8	2	no	—
174	C₂×D₄×C₃₇	#41	1	2	yes	—
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	—	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	—	4	2	no	—
186	C₂²×C₄×C₃₇	—	4	2	no	—
187	C₂²×C₄×C₃₇	—	4	2	no	—
188	C₂²×C₄×C₃₇	—	4	4	no	—
189	C₂²×C₄×C₃₇	—	4	2	no	—
190	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
192	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
194	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
195	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
196	Q₁₆×C₃₇	—	4	4	no	—
197	SD₁₆×C₃₇	—	4	4	no	—
198	SD₁₆×C₃₇	—	4	4	no	—
199	M₁₆×C₃₇	—	4	4	no	—
200	C₂×C₈×C₃₇	—	2	1	no	—
201	C₂×C₈×C₃₇	—	2	1	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	C₂×D₄	1	2	yes	—
209	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
210	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
211	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
212	C₄⋊C₄×C₃₇	—	2	1	no	—
213	C₄⋊C₄×C₃₇	—	2	1	no	—
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	—	4	2	no	—
221	C₄⋊C₄×C₃₇	—	4	2	no	—
222	C₂²⋊C₄×C₃₇	—	4	2	no	—
223	C₂²⋊C₄×C₃₇	—	4	4	no	—
224	C₂²⋊C₄×C₃₇	—	4	2	no	—
225	C₂²⋊C₄×C₃₇	—	4	2	no	—
226	C₂²⋊C₄×C₃₇	—	8	2	no	—
227	C₄²×C₃₇	—	2	1	no	—
228	C₄²×C₃₇	—	2	1	no	—
229	C₄²×C₃₇	—	2	1	no	—
230	C₄²×C₃₇	—	2	1	no	—
231	C₂³×C₃₇	—	2	1	no	—
232	C₂³×C₃₇	—	2	1	no	—
233	C₂³×C₃₇	—	2	2	no	—
234	C₂³×C₃₇	—	2	2	no	—
235	C₂³×C₃₇	—	2	2	no	—
236	C₂³×C₃₇	—	4	1	no	—
237	C₂³×C₃₇	—	4	1	no	—
238	C₂³×C₃₇	—	4	2	no	—
239	C₂³×C₃₇	—	4	2	no	—
240	C₂³×C₃₇	—	4	1	no	—
241	C₂³×C₃₇	—	4	1	no	—
242	C₂³×C₃₇	—	4	1	no	—
243	C₂³×C₃₇	—	4	2	no	—
244	C₂³×C₃₇	—	4	2	no	—
245	C₂³×C₃₇	#127	1	2	yes	—
246	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
247	Q₈×C₃₇	—	2	2	no	—
248	Q₈×C₃₇	—	2	2	no	—
249	Q₈×C₃₇	—	4	1	no	—
250	Q₈×C₃₇	—	4	1	no	—
251	Q₈×C₃₇	—	4	1	no	—
252	Q₈×C₃₇	—	4	1	no	—
253	Q₈×C₃₇	—	4	1	no	—
254	Q₈×C₃₇	—	4	1	no	—
255	D₄×C₃₇	—	2	2	no	—
256	D₄×C₃₇	—	2	2	no	—
257	D₄×C₃₇	—	4	8	no	—
258	D₄×C₃₇	—	4	1	no	—
259	D₄×C₃₇	—	4	1	no	—
260	D₄×C₃₇	—	4	1	no	—
261	D₄×C₃₇	—	4	1	no	—
262	D₄×C₃₇	—	4	1	no	—
263	D₄×C₃₇	—	4	1	no	—
264	D₄×C₃₇	—	8	8	no	—
265	D₄×C₃₇	—	8	4	no	—
266	C₂×C₄×C₃₇	—	2	1	no	—
267	C₂×C₄×C₃₇	—	2	1	no	—
268	C₂×C₄×C₃₇	—	2	2	no	—
269	C₂×C₄×C₃₇	—	2	2	no	—
270	C₂×C₄×C₃₇	—	2	2	no	—
271	C₂×C₄×C₃₇	—	2	2	no	—
272	C₂×C₄×C₃₇	—	2	2	no	—
273	C₂×C₄×C₃₇	—	2	2	no	—
274	C₂×C₄×C₃₇	—	2	2	no	—
275	C₂×C₄×C₃₇	—	2	2	no	—
276	C₂×C₄×C₃₇	—	2	2	no	—
277	C₂×C₄×C₃₇	—	2	2	no	—
278	C₂×C₄×C₃₇	—	2	2	no	—
279	C₂×C₄×C₃₇	—	4	8	no	—
280	C₂×C₄×C₃₇	—	4	1	no	—
281	C₂×C₄×C₃₇	—	4	1	no	—
282	C₂×C₄×C₃₇	—	4	1	no	—
283	C₂×C₄×C₃₇	—	4	1	no	—
284	C₂×C₄×C₃₇	—	4	1	no	—
285	C₂×C₄×C₃₇	—	4	1	no	—
286	C₂×C₄×C₃₇	—	4	1	no	—
287	C₂×C₄×C₃₇	—	4	1	no	—
288	C₂×C₄×C₃₇	—	4	1	no	—
289	C₂×C₄×C₃₇	—	4	2	no	—
290	C₂×C₄×C₃₇	—	4	2	no	—
291	C₂×C₄×C₃₇	—	4	2	no	—
292	C₂×C₄×C₃₇	—	4	2	no	—
293	C₂×C₄×C₃₇	—	8	4	no	—
294	C₂×C₄×C₃₇	#127	1	2	yes	—
295	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
299	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
300	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
301	C₈×C₃₇	—	2	2	no	—
302	C₈×C₃₇	—	2	2	no	—
303	C₈×C₃₇	—	2	2	no	—
304	C₈×C₃₇	—	2	2	no	—
305	#28366	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
306	C₂²×C₃₇	—	2	2	no	—
307	C₂²×C₃₇	—	2	2	no	—
308	C₂²×C₃₇	—	2	2	no	—
309	C₂²×C₃₇	—	4	2	no	—
310	C₂²×C₃₇	—	4	2	no	—
311	C₂²×C₃₇	—	4	2	no	—
312	C₂²×C₃₇	—	4	4	no	—
313	C₂²×C₃₇	—	8	1	no	—
314	C₂²×C₃₇	—	8	1	no	—
315	C₂²×C₃₇	—	8	2	no	—
316	C₂²×C₃₇	—	8	1	no	—
317	C₂²×C₃₇	—	8	1	no	—
318	C₂²×C₃₇	—	8	1	no	—
319	C₂²×C₃₇	—	8	2	no	—
320	C₂²×C₃₇	—	8	2	no	—
321	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
322	C₂²×C₃₇	#546	1	1	yes	characteristic
323	C₂²×C₃₇	#546	1	1	yes	characteristic
324	C₂²×C₃₇	#575	1	2	yes	—
325	C₂²×C₃₇	#577	1	2	yes	—
326	C₄×C₃₇	—	2	2	no	—
327	C₄×C₃₇	—	4	2	no	—
328	C₄×C₃₇	—	4	2	no	—
329	C₄×C₃₇	—	4	2	no	—
330	C₄×C₃₇	—	8	1	no	—
331	C₄×C₃₇	—	8	1	no	—
332	C₄×C₃₇	—	8	1	no	—
333	C₄×C₃₇	—	8	1	no	—
334	C₄×C₃₇	—	8	1	no	—
335	C₄×C₃₇	#525	1	1	yes	characteristic
336	C₄×C₃₇	#534	1	1	yes	characteristic
337	C₄×C₃₇	#546	1	1	yes	characteristic
338	C₄×C₃₇	#546	1	1	yes	characteristic
339	C₂×#481	C₂×C₃₇	1	1	yes	characteristic, complemented
340	C₂×#468	C₂×C₃₇	1	1	yes	characteristic, complemented
341	C₂×#452	C₂×C₃₇	1	1	yes	characteristic, complemented
342	C₂×#417	C₂×C₃₇	1	1	yes	characteristic, complemented
343	#2503	C₂×C₃₇	1	1	yes	characteristic, complemented
344	#2431	C₂×C₃₇	1	1	yes	characteristic
345	#2097	C₂×C₃₇	1	1	yes	characteristic, complemented
346	#2092	C₂×C₃₇	1	1	yes	characteristic, complemented
347	#2015	C₂×C₃₇	1	1	yes	characteristic, complemented
348	#2014	C₂×C₃₇	1	1	yes	characteristic, complemented
349	#1971	C₂×C₃₇	1	1	yes	characteristic, complemented
350	#1968	C₂×C₃₇	1	1	yes	characteristic, complemented
351	#1961	C₂×C₃₇	1	1	yes	characteristic, complemented
352	#1958	C₂×C₃₇	1	1	yes	characteristic, complemented
353	#1753	C₂×C₃₇	1	1	yes	characteristic, complemented
354	C₂×C₃₇	—	4	2	no	—
355	C₂×C₃₇	—	8	2	no	—
356	C₂×C₃₇	—	16	1	no	—
357	C₂×C₃₇	#2539	1	1	yes	characteristic
358	C₂×C₃₇	#3153	1	1	yes	characteristic
359	C₂×C₃₇	#3154	1	1	yes	characteristic
360	C₂×C₃₇	#3317	1	2	yes	—
361	C₂×C₃₇	#3323	1	2	yes	—
362	C₂²×#41	C₂²×C₃₇	1	1	yes	characteristic
363	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
364	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
365	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
366	C₂²×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
367	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
368	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
369	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
370	C₂×#121	C₂²×C₃₇	1	1	yes	characteristic
371	C₂²×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
372	#481	—	2	4	no	—
373	#468	—	2	4	no	—
374	#452	—	2	4	no	—
375	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
376	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
377	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
378	#417	—	2	4	no	—
379	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
380	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
381	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
382	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
383	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
384	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
385	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
386	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
387	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
388	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
389	C₂×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
390	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
391	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
392	#400	—	2	2	no	—
393	#392	—	2	2	no	—
394	#391	C₂²×C₃₇	1	1	yes	characteristic
395	#391	C₂²×C₃₇	1	1	yes	characteristic
396	#391	C₂²×C₃₇	1	1	yes	characteristic
397	#390	C₂²×C₃₇	1	1	yes	characteristic
398	#386	—	2	2	no	—
399	#382	C₂²×C₃₇	1	1	yes	characteristic
400	#382	C₂²×C₃₇	1	1	yes	characteristic
401	#381	—	2	2	no	—
402	C₄×C₂²⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
403	#336	C₂²×C₃₇	1	1	yes	characteristic
404	#336	C₂²×C₃₇	1	1	yes	characteristic
405	C₃₇	#28366	1	1	yes	characteristic, direct product factor, Sylow
406	C₂×#41	—	2	2	no	—
407	C₂×#41	—	2	2	no	—
408	C₂×#41	—	2	2	no	—
409	C₂×#41	—	2	2	no	—
410	C₂×#41	—	4	1	no	—
411	C₂×#41	—	4	1	no	—
412	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
413	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
414	C₂²×D₄	—	2	1	no	—
415	C₂²×D₄	—	2	1	no	—
416	C₂²×D₄	—	2	2	no	—
417	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
418	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
419	C₂³×C₄	—	2	1	no	—
420	C₂³×C₄	—	2	1	no	—
421	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
422	C₂×Q₁₆	—	2	2	no	—
423	C₂×Q₁₆	—	2	2	no	—
424	C₂×Q₁₆	—	4	1	no	—
425	C₂×SD₁₆	—	2	2	no	—
426	C₂×SD₁₆	—	2	2	no	—
427	C₂×SD₁₆	—	2	2	no	—
428	C₂×SD₁₆	—	4	1	no	—
429	C₂×SD₁₆	—	4	1	no	—
430	C₂×SD₁₆	—	4	1	no	—
431	C₂×M₁₆	—	4	1	no	—
432	C₂×M₁₆	—	4	1	no	—
433	C₂×M₁₆	D₄×C₃₇	1	4	yes	complemented
434	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
435	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
436	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
437	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
438	#127	—	2	2	no	—
439	#127	—	4	1	no	—
440	#124	—	2	2	no	—
441	#124	—	4	1	no	—
442	C₂²⋊Q₈	—	2	2	no	—
443	C₂²⋊Q₈	—	2	2	no	—
444	#121	—	2	2	no	—
445	#121	—	2	2	no	—
446	C₂×C₄⋊C₄	—	2	2	no	—
447	C₂×C₄⋊C₄	—	2	2	no	—
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	—	2	1	no	—
450	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	2	2	no	—
457	C₂×C₂²⋊C₄	—	2	2	no	—
458	C₂×C₂²⋊C₄	D₄×C₃₇	1	2	yes	—
459	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
460	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
461	#107	—	2	2	no	—
462	#106	—	2	2	no	—
463	#106	—	2	2	no	—
464	#103	—	2	2	no	—
465	#103	—	2	2	no	—
466	#103	—	2	2	no	—
467	#103	—	2	2	no	—
468	#102	—	2	2	no	—
469	#102	—	2	2	no	—
470	#102	—	2	2	no	—
471	#102	—	2	2	no	—
472	#102	—	2	2	no	—
473	#102	—	2	2	no	—
474	C₂²⋊C₈	D₄×C₃₇	1	4	yes	complemented
475	#97	—	4	1	no	—
476	C₄×C₈	—	4	1	no	—
477	#95	—	2	2	no	—
478	#95	—	2	2	no	—
479	#95	—	2	2	no	—
480	#95	—	2	2	no	—
481	#95	—	2	2	no	—
482	#95	D₄×C₃₇	1	2	yes	—
483	C₂⁴	—	2	1	no	—
484	C₂⁴	—	2	1	no	—
485	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
486	#41	—	2	8	no	—
487	#41	—	4	4	no	—
488	#41	—	4	4	no	—
489	#41	—	4	4	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	#41×C₃₇	1	2	yes	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
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	—	4	2	no	—
514	C₂×D₄	—	4	4	no	—
515	C₂×D₄	—	4	4	no	—
516	C₂×D₄	—	4	2	no	—
517	C₂×D₄	—	4	2	no	—
518	C₂×D₄	—	4	2	no	—
519	C₂×D₄	—	8	2	no	—
520	C₂×D₄	—	8	2	no	—
521	C₂×D₄	#41×C₃₇	1	2	yes	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	4	2	no	—
533	C₂²×C₄	—	4	2	no	—
534	C₂²×C₄	—	4	2	no	—
535	C₂²×C₄	—	4	4	no	—
536	C₂²×C₄	—	4	2	no	—
537	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
538	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
539	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
540	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
541	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
543	Q₁₆	—	4	4	no	—
544	SD₁₆	—	4	4	no	—
545	SD₁₆	—	4	4	no	—
546	M₁₆	—	4	4	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
556	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
557	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
558	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	4	2	no	—
568	C₄⋊C₄	—	4	2	no	—
569	C₂²⋊C₄	—	4	2	no	—
570	C₂²⋊C₄	—	4	4	no	—
571	C₂²⋊C₄	—	4	2	no	—
572	C₂²⋊C₄	—	4	2	no	—
573	C₂²⋊C₄	—	8	2	no	—
574	C₄²	—	2	1	no	—
575	C₄²	—	2	1	no	—
576	C₄²	—	2	1	no	—
577	C₄²	—	2	1	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	4	1	no	—
585	C₂³	—	4	2	no	—
586	C₂³	—	4	2	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	4	1	no	—
590	C₂³	—	4	2	no	—
591	C₂³	—	4	2	no	—
592	C₂³	#127×C₃₇	1	2	yes	—
593	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
594	Q₈	—	2	2	no	—
595	Q₈	—	2	2	no	—
596	Q₈	—	4	1	no	—
597	Q₈	—	4	1	no	—
598	Q₈	—	4	1	no	—
599	Q₈	—	4	1	no	—
600	Q₈	—	4	1	no	—
601	Q₈	—	4	1	no	—
602	D₄	—	2	2	no	—
603	D₄	—	2	2	no	—
604	D₄	—	4	8	no	—
605	D₄	—	4	1	no	—
606	D₄	—	4	1	no	—
607	D₄	—	4	1	no	—
608	D₄	—	4	1	no	—
609	D₄	—	4	1	no	—
610	D₄	—	4	1	no	—
611	D₄	—	8	8	no	—
612	D₄	—	8	4	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	4	8	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	4	2	no	—
638	C₂×C₄	—	4	2	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	8	4	no	—
641	C₂×C₄	#127×C₃₇	1	2	yes	—
642	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
643	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
644	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
645	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
646	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
647	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
648	C₈	—	2	2	no	—
649	C₈	—	2	2	no	—
650	C₈	—	2	2	no	—
651	C₈	—	2	2	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	4	2	no	—
658	C₂²	—	4	4	no	—
659	C₂²	—	8	1	no	—
660	C₂²	—	8	1	no	—
661	C₂²	—	8	2	no	—
662	C₂²	—	8	1	no	—
663	C₂²	—	8	1	no	—
664	C₂²	—	8	1	no	—
665	C₂²	—	8	2	no	—
666	C₂²	—	8	2	no	—
667	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
668	C₂²	C₃₇×#546	1	1	yes	characteristic
669	C₂²	C₃₇×#546	1	1	yes	characteristic
670	C₂²	C₃₇×#575	1	2	yes	—
671	C₂²	C₃₇×#577	1	2	yes	—
672	C₄	—	2	2	no	—
673	C₄	—	4	2	no	—
674	C₄	—	4	2	no	—
675	C₄	—	4	2	no	—
676	C₄	—	8	1	no	—
677	C₄	—	8	1	no	—
678	C₄	—	8	1	no	—
679	C₄	—	8	1	no	—
680	C₄	—	8	1	no	—
681	C₄	C₃₇×#525	1	1	yes	characteristic
682	C₄	C₃₇×#534	1	1	yes	characteristic
683	C₄	C₃₇×#546	1	1	yes	characteristic
684	C₄	C₃₇×#546	1	1	yes	characteristic
685	C₂	—	4	2	no	—
686	C₂	—	8	2	no	—
687	C₂	—	16	1	no	—
688	C₂	C₃₇×#2539	1	1	yes	characteristic
689	C₂	C₃₇×#3153	1	1	yes	characteristic
690	C₂	C₃₇×#3154	1	1	yes	characteristic
691	C₂	C₃₇×#3317	1	2	yes	—
692	C₂	C₃₇×#3323	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#2431	C₂
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×#481	C₂	semidirect
2. C₂×C₃₇×#468	C₂	semidirect
3. C₂×C₃₇×#452	C₂	semidirect
4. C₂×C₃₇×#417	C₂	semidirect
5. C₃₇×#2503	C₂	semidirect
7. C₃₇×#2097	C₂	semidirect
8. C₃₇×#2092	C₂	semidirect
9. C₃₇×#2015	C₂	semidirect
10. C₃₇×#2014	C₂	semidirect
11. C₃₇×#1971	C₂	semidirect
12. C₃₇×#1968	C₂	semidirect
13. C₃₇×#1961	C₂	semidirect
14. C₃₇×#1958	C₂	semidirect
15. C₃₇×#1753	C₂	semidirect
86. C₂×M₁₆×C₃₇	D₄	semidirect
127. C₂²⋊C₈×C₃₇	D₄	semidirect
305. #28366	C₃₇	direct (N × H)
339. C₂×#481	C₂×C₃₇	semidirect
340. C₂×#468	C₂×C₃₇	semidirect
341. C₂×#452	C₂×C₃₇	semidirect
342. C₂×#417	C₂×C₃₇	semidirect
343. #2503	C₂×C₃₇	semidirect
345. #2097	C₂×C₃₇	semidirect
346. #2092	C₂×C₃₇	semidirect
347. #2015	C₂×C₃₇	semidirect
348. #2014	C₂×C₃₇	semidirect
349. #1971	C₂×C₃₇	semidirect
350. #1968	C₂×C₃₇	semidirect
351. #1961	C₂×C₃₇	semidirect
352. #1958	C₂×C₃₇	semidirect
353. #1753	C₂×C₃₇	semidirect
405. C₃₇	#28366	direct (N × H)
433. C₂×M₁₆	D₄×C₃₇	semidirect
474. 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×#481	2
C₂×C₃₇×#468	2
C₂×C₃₇×#452	2
C₂×C₃₇×#417	2
C₃₇×#2503	2
C₃₇×#2431	2
C₃₇×#2097	2
C₃₇×#2092	2
C₃₇×#2015	2
C₃₇×#2014	2
C₃₇×#1971	2
C₃₇×#1968	2
C₃₇×#1961	2
C₃₇×#1958	2
C₃₇×#1753	2
#28366	37

Subgroups — C37×#28366 #22649619

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28366 #22649619