Subgroups — C₃₇×#28464 #22649717

Order 9472.

1162 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#495	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#492	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₇×#463	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×SD₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2545	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2544	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#2016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#2015	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#2012	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#2011	C₂	1	1	yes	maximal, characteristic
13	C₃₇×#1968	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#1968	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₄⋊C₄×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×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×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
22	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
23	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
24	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
26	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
27	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
28	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
29	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
33	C₃₇×#495	—	2	4	no	—
34	C₃₇×#495	—	2	4	no	—
35	C₃₇×#492	—	2	4	no	—
36	C₃₇×#464	—	2	4	no	—
37	C₃₇×#463	—	2	4	no	—
38	C₄×SD₁₆×C₃₇	—	2	4	no	—
39	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₈×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×#103×C₃₇	C₂²	1	1	yes	characteristic
44	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
45	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
46	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
50	C₃₇×#396	—	2	2	no	—
51	C₃₇×#394	—	2	2	no	—
52	C₃₇×#391	C₂²	1	1	yes	characteristic
53	C₃₇×#391	C₂²	1	1	yes	characteristic
54	C₃₇×#390	C₂²	1	1	yes	characteristic
55	C₃₇×#390	C₂²	1	1	yes	characteristic
56	C₃₇×#388	—	2	2	no	—
57	C₃₇×#386	—	2	2	no	—
58	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
59	C₃₇×#336	C₂²	1	1	yes	characteristic
60	C₃₇×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₃₇	—	2	2	no	—
65	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₃₇	—	2	1	no	—
69	C₂×Q₁₆×C₃₇	—	2	2	no	—
70	C₂×Q₁₆×C₃₇	—	2	2	no	—
71	C₂×Q₁₆×C₃₇	—	2	2	no	—
72	C₂×Q₁₆×C₃₇	—	4	1	no	—
73	C₂×Q₁₆×C₃₇	—	4	1	no	—
74	C₂×Q₁₆×C₃₇	—	4	1	no	—
75	C₂×SD₁₆×C₃₇	—	2	2	no	—
76	C₂×SD₁₆×C₃₇	—	2	2	no	—
77	C₂×SD₁₆×C₃₇	—	2	2	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	—	2	2	no	—
82	C₂×SD₁₆×C₃₇	—	2	2	no	—
83	C₂×SD₁₆×C₃₇	—	2	2	no	—
84	C₂×SD₁₆×C₃₇	—	2	2	no	—
85	C₂×SD₁₆×C₃₇	—	2	2	no	—
86	C₂×SD₁₆×C₃₇	—	2	2	no	—
87	C₂×SD₁₆×C₃₇	—	4	1	no	—
88	C₂×SD₁₆×C₃₇	—	4	1	no	—
89	C₂×SD₁₆×C₃₇	D₄	1	4	yes	—
90	C₂×D₈×C₃₇	—	2	2	no	—
91	C₂×D₈×C₃₇	—	2	2	no	—
92	C₂×D₈×C₃₇	—	2	2	no	—
93	C₂×D₈×C₃₇	—	4	1	no	—
94	C₂×D₈×C₃₇	—	4	1	no	—
95	C₂×D₈×C₃₇	—	4	1	no	—
96	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₃₇	—	2	2	no	—
101	C₄⋊Q₈×C₃₇	—	4	1	no	—
102	#127×C₃₇	—	2	2	no	—
103	#127×C₃₇	—	4	1	no	—
104	#124×C₃₇	—	2	2	no	—
105	#124×C₃₇	—	2	2	no	—
106	#124×C₃₇	—	2	2	no	—
107	#124×C₃₇	—	2	2	no	—
108	#124×C₃₇	—	2	2	no	—
109	#124×C₃₇	—	2	2	no	—
110	#124×C₃₇	—	4	1	no	—
111	#124×C₃₇	—	4	1	no	—
112	C₄×Q₈×C₃₇	—	2	2	no	—
113	C₄×Q₈×C₃₇	—	2	2	no	—
114	C₄×D₄×C₃₇	—	2	2	no	—
115	C₄×D₄×C₃₇	—	2	2	no	—
116	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
117	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
118	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
119	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
123	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
125	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
128	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
130	C₂×C₄²×C₃₇	—	2	1	no	—
131	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
134	#106×C₃₇	—	2	2	no	—
135	C₄⋊C₈×C₃₇	D₄	1	4	yes	complemented
136	#103×C₃₇	—	2	2	no	—
137	#103×C₃₇	—	2	2	no	—
138	#103×C₃₇	—	2	2	no	—
139	#102×C₃₇	—	2	2	no	—
140	#102×C₃₇	—	2	2	no	—
141	#102×C₃₇	—	2	2	no	—
142	C₄×C₈×C₃₇	—	2	2	no	—
143	C₄×C₈×C₃₇	—	2	2	no	—
144	C₄×C₈×C₃₇	D₄	1	4	yes	complemented
145	#95×C₃₇	—	2	2	no	—
146	#95×C₃₇	—	2	2	no	—
147	#95×C₃₇	D₄	1	2	yes	—
148	C₂⁴×C₃₇	—	2	1	no	—
149	C₂⁴×C₃₇	—	2	1	no	—
150	C₂⁴×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	—	2	1	no	—
161	C₂×Q₈×C₃₇	—	2	1	no	—
162	C₂×Q₈×C₃₇	—	2	1	no	—
163	C₂×Q₈×C₃₇	—	2	1	no	—
164	C₂×Q₈×C₃₇	—	2	1	no	—
165	C₂×Q₈×C₃₇	—	2	1	no	—
166	C₂×Q₈×C₃₇	—	2	1	no	—
167	C₂×Q₈×C₃₇	—	2	1	no	—
168	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
169	C₂×D₄×C₃₇	—	2	1	no	—
170	C₂×D₄×C₃₇	—	2	1	no	—
171	C₂×D₄×C₃₇	—	2	1	no	—
172	C₂×D₄×C₃₇	—	2	1	no	—
173	C₂×D₄×C₃₇	—	2	1	no	—
174	C₂×D₄×C₃₇	—	2	1	no	—
175	C₂×D₄×C₃₇	—	2	1	no	—
176	C₂×D₄×C₃₇	—	2	1	no	—
177	C₂×D₄×C₃₇	—	2	1	no	—
178	C₂×D₄×C₃₇	—	2	1	no	—
179	C₂×D₄×C₃₇	—	2	1	no	—
180	C₂×D₄×C₃₇	—	2	1	no	—
181	C₂×D₄×C₃₇	—	2	1	no	—
182	C₂×D₄×C₃₇	—	2	1	no	—
183	C₂×D₄×C₃₇	—	2	1	no	—
184	C₂×D₄×C₃₇	—	2	1	no	—
185	C₂×D₄×C₃₇	—	2	1	no	—
186	C₂×D₄×C₃₇	—	4	4	no	—
187	C₂×D₄×C₃₇	—	4	4	no	—
188	C₂×D₄×C₃₇	—	8	2	no	—
189	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
190	C₂²×C₄×C₃₇	—	2	1	no	—
191	C₂²×C₄×C₃₇	—	2	1	no	—
192	C₂²×C₄×C₃₇	—	2	1	no	—
193	C₂²×C₄×C₃₇	—	2	1	no	—
194	C₂²×C₄×C₃₇	—	2	1	no	—
195	C₂²×C₄×C₃₇	—	4	2	no	—
196	C₂²×C₄×C₃₇	—	8	2	no	—
197	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
201	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
202	Q₁₆×C₃₇	—	4	4	no	—
203	Q₁₆×C₃₇	—	4	4	no	—
204	SD₁₆×C₃₇	—	2	8	no	—
205	SD₁₆×C₃₇	—	4	4	no	—
206	SD₁₆×C₃₇	—	4	4	no	—
207	SD₁₆×C₃₇	—	4	4	no	—
208	SD₁₆×C₃₇	—	4	4	no	—
209	D₈×C₃₇	—	4	4	no	—
210	D₈×C₃₇	—	4	4	no	—
211	C₂×C₈×C₃₇	—	2	1	no	—
212	C₂×C₈×C₃₇	—	2	1	no	—
213	C₂×C₈×C₃₇	—	2	1	no	—
214	C₂×C₈×C₃₇	—	2	1	no	—
215	C₂×C₈×C₃₇	—	2	1	no	—
216	C₂×C₈×C₃₇	—	2	1	no	—
217	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
218	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
219	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
220	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
221	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
222	C₂×C₈×C₃₇	#41	1	2	yes	—
223	C₄⋊C₄×C₃₇	—	2	4	no	—
224	C₄⋊C₄×C₃₇	—	2	1	no	—
225	C₄⋊C₄×C₃₇	—	2	1	no	—
226	C₄⋊C₄×C₃₇	—	2	1	no	—
227	C₄⋊C₄×C₃₇	—	2	1	no	—
228	C₄⋊C₄×C₃₇	—	4	4	no	—
229	C₄⋊C₄×C₃₇	—	4	2	no	—
230	C₂²⋊C₄×C₃₇	—	4	4	no	—
231	C₂²⋊C₄×C₃₇	—	4	4	no	—
232	C₂²⋊C₄×C₃₇	—	4	2	no	—
233	C₂²⋊C₄×C₃₇	—	4	2	no	—
234	C₂²⋊C₄×C₃₇	—	4	2	no	—
235	C₂²⋊C₄×C₃₇	—	4	2	no	—
236	C₂²⋊C₄×C₃₇	—	4	2	no	—
237	C₂²⋊C₄×C₃₇	—	4	4	no	—
238	C₂²⋊C₄×C₃₇	—	8	2	no	—
239	C₄²×C₃₇	—	2	1	no	—
240	C₄²×C₃₇	—	2	1	no	—
241	C₄²×C₃₇	—	2	1	no	—
242	C₄²×C₃₇	—	2	1	no	—
243	C₄²×C₃₇	—	4	2	no	—
244	C₄²×C₃₇	C₂×D₄	1	2	yes	—
245	C₄²×C₃₇	C₂×D₄	1	2	yes	—
246	C₂³×C₃₇	—	2	2	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	1	no	—
252	C₂³×C₃₇	—	4	1	no	—
253	C₂³×C₃₇	—	4	1	no	—
254	C₂³×C₃₇	—	4	1	no	—
255	C₂³×C₃₇	—	4	1	no	—
256	C₂³×C₃₇	—	4	1	no	—
257	C₂³×C₃₇	—	4	2	no	—
258	C₂³×C₃₇	—	4	2	no	—
259	C₂³×C₃₇	—	4	2	no	—
260	C₂³×C₃₇	—	4	2	no	—
261	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
262	Q₈×C₃₇	—	2	2	no	—
263	Q₈×C₃₇	—	2	2	no	—
264	Q₈×C₃₇	—	4	1	no	—
265	Q₈×C₃₇	—	4	1	no	—
266	Q₈×C₃₇	—	4	1	no	—
267	Q₈×C₃₇	—	4	1	no	—
268	Q₈×C₃₇	—	4	1	no	—
269	Q₈×C₃₇	—	4	1	no	—
270	Q₈×C₃₇	—	4	1	no	—
271	Q₈×C₃₇	—	4	1	no	—
272	Q₈×C₃₇	—	4	1	no	—
273	Q₈×C₃₇	—	4	1	no	—
274	D₄×C₃₇	—	2	2	no	—
275	D₄×C₃₇	—	2	2	no	—
276	D₄×C₃₇	—	4	1	no	—
277	D₄×C₃₇	—	4	1	no	—
278	D₄×C₃₇	—	4	1	no	—
279	D₄×C₃₇	—	4	1	no	—
280	D₄×C₃₇	—	4	1	no	—
281	D₄×C₃₇	—	4	1	no	—
282	D₄×C₃₇	—	4	1	no	—
283	D₄×C₃₇	—	4	1	no	—
284	D₄×C₃₇	—	4	1	no	—
285	D₄×C₃₇	—	4	1	no	—
286	D₄×C₃₇	—	8	8	no	—
287	C₂×C₄×C₃₇	—	2	2	no	—
288	C₂×C₄×C₃₇	—	2	2	no	—
289	C₂×C₄×C₃₇	—	2	2	no	—
290	C₂×C₄×C₃₇	—	2	2	no	—
291	C₂×C₄×C₃₇	—	2	2	no	—
292	C₂×C₄×C₃₇	—	2	2	no	—
293	C₂×C₄×C₃₇	—	2	2	no	—
294	C₂×C₄×C₃₇	—	2	2	no	—
295	C₂×C₄×C₃₇	—	4	1	no	—
296	C₂×C₄×C₃₇	—	4	1	no	—
297	C₂×C₄×C₃₇	—	4	1	no	—
298	C₂×C₄×C₃₇	—	4	1	no	—
299	C₂×C₄×C₃₇	—	4	1	no	—
300	C₂×C₄×C₃₇	—	4	1	no	—
301	C₂×C₄×C₃₇	—	4	1	no	—
302	C₂×C₄×C₃₇	—	4	1	no	—
303	C₂×C₄×C₃₇	—	4	1	no	—
304	C₂×C₄×C₃₇	—	4	1	no	—
305	C₂×C₄×C₃₇	—	4	2	no	—
306	C₂×C₄×C₃₇	—	4	2	no	—
307	C₂×C₄×C₃₇	—	8	4	no	—
308	C₂×C₄×C₃₇	#127	1	2	yes	—
309	C₂×C₄×C₃₇	#127	1	2	yes	—
310	C₂×C₄×C₃₇	#135	1	4	yes	—
311	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
315	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
316	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
317	C₈×C₃₇	—	2	2	no	—
318	C₈×C₃₇	—	2	2	no	—
319	C₈×C₃₇	—	2	2	no	—
320	C₈×C₃₇	#121	1	4	yes	—
321	#28464	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂²×C₃₇	—	4	4	no	—
323	C₂²×C₃₇	—	4	2	no	—
324	C₂²×C₃₇	—	8	2	no	—
325	C₂²×C₃₇	—	8	1	no	—
326	C₂²×C₃₇	—	8	1	no	—
327	C₂²×C₃₇	—	8	2	no	—
328	C₂²×C₃₇	—	8	2	no	—
329	C₂²×C₃₇	—	8	1	no	—
330	C₂²×C₃₇	—	8	1	no	—
331	C₂²×C₃₇	—	8	1	no	—
332	C₂²×C₃₇	—	8	1	no	—
333	C₂²×C₃₇	—	8	2	no	—
334	C₂²×C₃₇	—	8	2	no	—
335	C₂²×C₃₇	—	8	1	no	—
336	C₂²×C₃₇	—	8	1	no	—
337	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
338	C₂²×C₃₇	D₄²	1	1	yes	characteristic
339	C₂²×C₃₇	#550	1	1	yes	characteristic
340	C₂²×C₃₇	C₂×#135	1	2	yes	—
341	C₂²×C₃₇	#577	1	2	yes	—
342	C₄×C₃₇	—	2	2	no	—
343	C₄×C₃₇	—	2	2	no	—
344	C₄×C₃₇	—	2	4	no	—
345	C₄×C₃₇	—	4	2	no	—
346	C₄×C₃₇	—	4	2	no	—
347	C₄×C₃₇	—	8	1	no	—
348	C₄×C₃₇	—	8	1	no	—
349	C₄×C₃₇	—	8	1	no	—
350	C₄×C₃₇	—	8	1	no	—
351	C₄×C₃₇	C₂×#121	1	1	yes	characteristic
352	C₄×C₃₇	#535	1	1	yes	characteristic
353	C₄×C₃₇	D₄²	1	1	yes	characteristic
354	C₄×C₃₇	#550	1	1	yes	characteristic
355	C₂×#495	C₂×C₃₇	1	1	yes	characteristic, complemented
356	C₂×#495	C₂×C₃₇	1	1	yes	characteristic, complemented
357	C₂×#492	C₂×C₃₇	1	1	yes	characteristic, complemented
358	C₂×#464	C₂×C₃₇	1	1	yes	characteristic, complemented
359	C₂×#463	C₂×C₃₇	1	1	yes	characteristic, complemented
360	C₂×C₄×SD₁₆	C₂×C₃₇	1	1	yes	characteristic, complemented
361	#2545	C₂×C₃₇	1	1	yes	characteristic, complemented
362	#2544	C₂×C₃₇	1	1	yes	characteristic, complemented
363	#2016	C₂×C₃₇	1	1	yes	characteristic, complemented
364	#2015	C₂×C₃₇	1	1	yes	characteristic, complemented
365	#2012	C₂×C₃₇	1	1	yes	characteristic, complemented
366	#2011	C₂×C₃₇	1	1	yes	characteristic
367	#1968	C₂×C₃₇	1	1	yes	characteristic, complemented
368	#1968	C₂×C₃₇	1	1	yes	characteristic, complemented
369	C₈×C₄⋊C₄	C₂×C₃₇	1	1	yes	characteristic, complemented
370	C₂×C₃₇	—	8	2	no	—
371	C₂×C₃₇	—	16	1	no	—
372	C₂×C₃₇	—	16	1	no	—
373	C₂×C₃₇	#2541	1	1	yes	characteristic
374	C₂×C₃₇	#3147	1	1	yes	characteristic
375	C₂×C₃₇	#3154	1	1	yes	characteristic
376	C₂×C₃₇	#3282	1	2	yes	—
377	C₂×C₃₇	#3394	1	2	yes	—
378	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
379	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
380	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
381	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
382	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
383	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
384	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
385	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
386	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
387	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
388	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
389	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
390	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
391	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
392	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
393	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
394	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
395	#495	—	2	4	no	—
396	#495	—	2	4	no	—
397	#492	—	2	4	no	—
398	#464	—	2	4	no	—
399	#463	—	2	4	no	—
400	C₄×SD₁₆	—	2	4	no	—
401	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
402	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
403	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
404	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
405	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
406	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
407	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
408	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
409	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
410	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
411	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
412	#396	—	2	2	no	—
413	#394	—	2	2	no	—
414	#391	C₂²×C₃₇	1	1	yes	characteristic
415	#391	C₂²×C₃₇	1	1	yes	characteristic
416	#390	C₂²×C₃₇	1	1	yes	characteristic
417	#390	C₂²×C₃₇	1	1	yes	characteristic
418	#388	—	2	2	no	—
419	#386	—	2	2	no	—
420	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
421	#336	C₂²×C₃₇	1	1	yes	characteristic
422	#336	C₂²×C₃₇	1	1	yes	characteristic
423	C₃₇	#28464	1	1	yes	characteristic, direct product factor, Sylow
424	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
425	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
426	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
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	C₂×Q₁₆	—	2	2	no	—
433	C₂×Q₁₆	—	2	2	no	—
434	C₂×Q₁₆	—	2	2	no	—
435	C₂×Q₁₆	—	4	1	no	—
436	C₂×Q₁₆	—	4	1	no	—
437	C₂×Q₁₆	—	4	1	no	—
438	C₂×SD₁₆	—	2	2	no	—
439	C₂×SD₁₆	—	2	2	no	—
440	C₂×SD₁₆	—	2	2	no	—
441	C₂×SD₁₆	—	2	2	no	—
442	C₂×SD₁₆	—	2	2	no	—
443	C₂×SD₁₆	—	2	2	no	—
444	C₂×SD₁₆	—	2	2	no	—
445	C₂×SD₁₆	—	2	2	no	—
446	C₂×SD₁₆	—	2	2	no	—
447	C₂×SD₁₆	—	2	2	no	—
448	C₂×SD₁₆	—	2	2	no	—
449	C₂×SD₁₆	—	2	2	no	—
450	C₂×SD₁₆	—	4	1	no	—
451	C₂×SD₁₆	—	4	1	no	—
452	C₂×SD₁₆	D₄×C₃₇	1	4	yes	—
453	C₂×D₈	—	2	2	no	—
454	C₂×D₈	—	2	2	no	—
455	C₂×D₈	—	2	2	no	—
456	C₂×D₈	—	4	1	no	—
457	C₂×D₈	—	4	1	no	—
458	C₂×D₈	—	4	1	no	—
459	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
460	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
461	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
462	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
463	C₄⋊Q₈	—	2	2	no	—
464	C₄⋊Q₈	—	4	1	no	—
465	#127	—	2	2	no	—
466	#127	—	4	1	no	—
467	#124	—	2	2	no	—
468	#124	—	2	2	no	—
469	#124	—	2	2	no	—
470	#124	—	2	2	no	—
471	#124	—	2	2	no	—
472	#124	—	2	2	no	—
473	#124	—	4	1	no	—
474	#124	—	4	1	no	—
475	C₄×Q₈	—	2	2	no	—
476	C₄×Q₈	—	2	2	no	—
477	C₄×D₄	—	2	2	no	—
478	C₄×D₄	—	2	2	no	—
479	C₂×C₄⋊C₄	—	2	1	no	—
480	C₂×C₄⋊C₄	—	2	2	no	—
481	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	—	2	1	no	—
485	C₂×C₂²⋊C₄	—	2	1	no	—
486	C₂×C₂²⋊C₄	—	2	2	no	—
487	C₂×C₂²⋊C₄	—	2	1	no	—
488	C₂×C₂²⋊C₄	—	2	2	no	—
489	C₂×C₂²⋊C₄	—	2	1	no	—
490	C₂×C₂²⋊C₄	—	2	1	no	—
491	C₂×C₂²⋊C₄	—	2	2	no	—
492	C₂×C₂²⋊C₄	—	2	2	no	—
493	C₂×C₄²	—	2	1	no	—
494	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
497	#106	—	2	2	no	—
498	C₄⋊C₈	D₄×C₃₇	1	4	yes	complemented
499	#103	—	2	2	no	—
500	#103	—	2	2	no	—
501	#103	—	2	2	no	—
502	#102	—	2	2	no	—
503	#102	—	2	2	no	—
504	#102	—	2	2	no	—
505	C₄×C₈	—	2	2	no	—
506	C₄×C₈	—	2	2	no	—
507	C₄×C₈	D₄×C₃₇	1	4	yes	complemented
508	#95	—	2	2	no	—
509	#95	—	2	2	no	—
510	#95	D₄×C₃₇	1	2	yes	—
511	C₂⁴	—	2	1	no	—
512	C₂⁴	—	2	1	no	—
513	C₂⁴	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
532	C₂×D₄	—	2	1	no	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	4	4	no	—
550	C₂×D₄	—	4	4	no	—
551	C₂×D₄	—	8	2	no	—
552	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	4	2	no	—
559	C₂²×C₄	—	8	2	no	—
560	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
561	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
562	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
564	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
565	Q₁₆	—	4	4	no	—
566	Q₁₆	—	4	4	no	—
567	SD₁₆	—	2	8	no	—
568	SD₁₆	—	4	4	no	—
569	SD₁₆	—	4	4	no	—
570	SD₁₆	—	4	4	no	—
571	SD₁₆	—	4	4	no	—
572	D₈	—	4	4	no	—
573	D₈	—	4	4	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
581	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
582	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
583	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
584	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
585	C₂×C₈	#41×C₃₇	1	2	yes	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	4	4	no	—
592	C₄⋊C₄	—	4	2	no	—
593	C₂²⋊C₄	—	4	4	no	—
594	C₂²⋊C₄	—	4	4	no	—
595	C₂²⋊C₄	—	4	2	no	—
596	C₂²⋊C₄	—	4	2	no	—
597	C₂²⋊C₄	—	4	2	no	—
598	C₂²⋊C₄	—	4	2	no	—
599	C₂²⋊C₄	—	4	2	no	—
600	C₂²⋊C₄	—	4	4	no	—
601	C₂²⋊C₄	—	8	2	no	—
602	C₄²	—	2	1	no	—
603	C₄²	—	2	1	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	2	1	no	—
606	C₄²	—	4	2	no	—
607	C₄²	C₂×D₄×C₃₇	1	2	yes	—
608	C₄²	C₂×D₄×C₃₇	1	2	yes	—
609	C₂³	—	2	2	no	—
610	C₂³	—	4	1	no	—
611	C₂³	—	4	1	no	—
612	C₂³	—	4	2	no	—
613	C₂³	—	4	2	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	4	1	no	—
617	C₂³	—	4	1	no	—
618	C₂³	—	4	1	no	—
619	C₂³	—	4	1	no	—
620	C₂³	—	4	2	no	—
621	C₂³	—	4	2	no	—
622	C₂³	—	4	2	no	—
623	C₂³	—	4	2	no	—
624	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
625	Q₈	—	2	2	no	—
626	Q₈	—	2	2	no	—
627	Q₈	—	4	1	no	—
628	Q₈	—	4	1	no	—
629	Q₈	—	4	1	no	—
630	Q₈	—	4	1	no	—
631	Q₈	—	4	1	no	—
632	Q₈	—	4	1	no	—
633	Q₈	—	4	1	no	—
634	Q₈	—	4	1	no	—
635	Q₈	—	4	1	no	—
636	Q₈	—	4	1	no	—
637	D₄	—	2	2	no	—
638	D₄	—	2	2	no	—
639	D₄	—	4	1	no	—
640	D₄	—	4	1	no	—
641	D₄	—	4	1	no	—
642	D₄	—	4	1	no	—
643	D₄	—	4	1	no	—
644	D₄	—	4	1	no	—
645	D₄	—	4	1	no	—
646	D₄	—	4	1	no	—
647	D₄	—	4	1	no	—
648	D₄	—	4	1	no	—
649	D₄	—	8	8	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	2	no	—
669	C₂×C₄	—	4	2	no	—
670	C₂×C₄	—	8	4	no	—
671	C₂×C₄	#127×C₃₇	1	2	yes	—
672	C₂×C₄	#127×C₃₇	1	2	yes	—
673	C₂×C₄	#135×C₃₇	1	4	yes	—
674	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
675	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
676	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
677	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
678	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
679	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
680	C₈	—	2	2	no	—
681	C₈	—	2	2	no	—
682	C₈	—	2	2	no	—
683	C₈	#121×C₃₇	1	4	yes	—
684	C₂²	—	4	4	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	8	2	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	8	1	no	—
689	C₂²	—	8	2	no	—
690	C₂²	—	8	2	no	—
691	C₂²	—	8	1	no	—
692	C₂²	—	8	1	no	—
693	C₂²	—	8	1	no	—
694	C₂²	—	8	1	no	—
695	C₂²	—	8	2	no	—
696	C₂²	—	8	2	no	—
697	C₂²	—	8	1	no	—
698	C₂²	—	8	1	no	—
699	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
700	C₂²	D₄²×C₃₇	1	1	yes	characteristic
701	C₂²	C₃₇×#550	1	1	yes	characteristic
702	C₂²	C₂×#135×C₃₇	1	2	yes	—
703	C₂²	C₃₇×#577	1	2	yes	—
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	4	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	2	no	—
709	C₄	—	8	1	no	—
710	C₄	—	8	1	no	—
711	C₄	—	8	1	no	—
712	C₄	—	8	1	no	—
713	C₄	C₂×#121×C₃₇	1	1	yes	characteristic
714	C₄	C₃₇×#535	1	1	yes	characteristic
715	C₄	D₄²×C₃₇	1	1	yes	characteristic
716	C₄	C₃₇×#550	1	1	yes	characteristic
717	C₂	—	8	2	no	—
718	C₂	—	16	1	no	—
719	C₂	—	16	1	no	—
720	C₂	C₃₇×#2541	1	1	yes	characteristic
721	C₂	C₃₇×#3147	1	1	yes	characteristic
722	C₂	C₃₇×#3154	1	1	yes	characteristic
723	C₂	C₃₇×#3282	1	2	yes	—
724	C₂	C₃₇×#3394	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#2011	C₂
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×#495	C₂	semidirect
2. C₂×C₃₇×#495	C₂	semidirect
3. C₂×C₃₇×#492	C₂	semidirect
4. C₂×C₃₇×#464	C₂	semidirect
5. C₂×C₃₇×#463	C₂	semidirect
6. C₂×C₄×SD₁₆×C₃₇	C₂	semidirect
7. C₃₇×#2545	C₂	semidirect
8. C₃₇×#2544	C₂	semidirect
9. C₃₇×#2016	C₂	semidirect
10. C₃₇×#2015	C₂	semidirect
11. C₃₇×#2012	C₂	semidirect
13. C₃₇×#1968	C₂	semidirect
14. C₃₇×#1968	C₂	semidirect
15. C₈×C₄⋊C₄×C₃₇	C₂	semidirect
135. C₄⋊C₈×C₃₇	D₄	semidirect
144. C₄×C₈×C₃₇	D₄	semidirect
321. #28464	C₃₇	direct (N × H)
355. C₂×#495	C₂×C₃₇	semidirect
356. C₂×#495	C₂×C₃₇	semidirect
357. C₂×#492	C₂×C₃₇	semidirect
358. C₂×#464	C₂×C₃₇	semidirect
359. C₂×#463	C₂×C₃₇	semidirect
360. C₂×C₄×SD₁₆	C₂×C₃₇	semidirect
361. #2545	C₂×C₃₇	semidirect
362. #2544	C₂×C₃₇	semidirect
363. #2016	C₂×C₃₇	semidirect
364. #2015	C₂×C₃₇	semidirect
365. #2012	C₂×C₃₇	semidirect
367. #1968	C₂×C₃₇	semidirect
368. #1968	C₂×C₃₇	semidirect
369. C₈×C₄⋊C₄	C₂×C₃₇	semidirect
423. C₃₇	#28464	direct (N × H)
498. C₄⋊C₈	D₄×C₃₇	semidirect
507. 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×#495	2
C₂×C₃₇×#492	2
C₂×C₃₇×#464	2
C₂×C₃₇×#463	2
C₂×C₄×SD₁₆×C₃₇	2
C₃₇×#2545	2
C₃₇×#2544	2
C₃₇×#2016	2
C₃₇×#2015	2
C₃₇×#2012	2
C₃₇×#2011	2
C₃₇×#1968	2
C₈×C₄⋊C₄×C₃₇	2
#28464	37

Subgroups — C37×#28464 #22649717

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28464 #22649717