Subgroups — C₃₇×#28422 #22649675

Order 9472.

1008 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#489	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#474	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#463	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#442	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2563	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2544	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
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×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
20	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
21	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
25	C₃₇×#489	—	2	4	no	—
26	C₃₇×#474	—	2	4	no	—
27	C₃₇×#463	—	2	4	no	—
28	C₃₇×#442	—	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	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
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×#97×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×#394	—	2	2	no	—
47	C₃₇×#393	—	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×#382	C₂²	1	1	yes	characteristic
54	C₃₇×#382	C₂²	1	1	yes	characteristic
55	C₃₇×#380	—	2	2	no	—
56	C₄×C₄⋊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	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₃₇	—	2	2	no	—
62	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₃₇	—	2	1	no	—
66	C₂³×C₄×C₃₇	—	2	1	no	—
67	C₂×SD₁₆×C₃₇	—	2	2	no	—
68	C₂×SD₁₆×C₃₇	—	2	2	no	—
69	C₂×SD₁₆×C₃₇	—	4	1	no	—
70	C₂×D₈×C₃₇	—	2	2	no	—
71	C₂×D₈×C₃₇	—	2	2	no	—
72	C₂×D₈×C₃₇	—	2	2	no	—
73	C₂×D₈×C₃₇	—	2	2	no	—
74	C₂×D₈×C₃₇	—	2	2	no	—
75	C₂×D₈×C₃₇	—	4	1	no	—
76	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
80	C₄⋊Q₈×C₃₇	—	2	2	no	—
81	C₄⋊Q₈×C₃₇	—	2	2	no	—
82	#127×C₃₇	—	2	2	no	—
83	#127×C₃₇	—	4	1	no	—
84	#124×C₃₇	—	2	2	no	—
85	#124×C₃₇	—	2	2	no	—
86	#124×C₃₇	—	2	2	no	—
87	#124×C₃₇	—	4	1	no	—
88	C₄×D₄×C₃₇	—	2	2	no	—
89	C₄×D₄×C₃₇	—	2	2	no	—
90	C₄×D₄×C₃₇	—	2	2	no	—
91	C₄×D₄×C₃₇	—	2	2	no	—
92	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
93	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
94	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
104	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
105	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
106	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
109	#107×C₃₇	—	2	2	no	—
110	#107×C₃₇	—	2	2	no	—
111	#106×C₃₇	—	2	2	no	—
112	C₄⋊C₈×C₃₇	D₄	1	4	yes	complemented
113	#103×C₃₇	—	2	2	no	—
114	#103×C₃₇	—	2	2	no	—
115	#103×C₃₇	—	2	2	no	—
116	#102×C₃₇	—	2	2	no	—
117	#102×C₃₇	—	2	2	no	—
118	#102×C₃₇	—	2	2	no	—
119	#102×C₃₇	—	2	2	no	—
120	#102×C₃₇	—	2	2	no	—
121	#102×C₃₇	—	2	2	no	—
122	#102×C₃₇	—	2	2	no	—
123	#97×C₃₇	—	4	1	no	—
124	#97×C₃₇	D₄	1	4	yes	complemented
125	C₄×C₈×C₃₇	—	4	1	no	—
126	#95×C₃₇	—	2	2	no	—
127	#95×C₃₇	—	2	2	no	—
128	#95×C₃₇	—	2	2	no	—
129	#95×C₃₇	D₄	1	2	yes	—
130	C₂⁴×C₃₇	—	2	1	no	—
131	C₂⁴×C₃₇	—	2	1	no	—
132	C₂⁴×C₃₇	—	2	1	no	—
133	C₂×Q₈×C₃₇	—	2	1	no	—
134	C₂×Q₈×C₃₇	—	2	1	no	—
135	C₂×Q₈×C₃₇	—	2	1	no	—
136	C₂×Q₈×C₃₇	—	2	1	no	—
137	C₂×Q₈×C₃₇	—	2	1	no	—
138	C₂×Q₈×C₃₇	—	2	1	no	—
139	C₂×Q₈×C₃₇	—	4	2	no	—
140	C₂×Q₈×C₃₇	—	8	2	no	—
141	C₂×D₄×C₃₇	—	2	1	no	—
142	C₂×D₄×C₃₇	—	2	1	no	—
143	C₂×D₄×C₃₇	—	2	1	no	—
144	C₂×D₄×C₃₇	—	2	1	no	—
145	C₂×D₄×C₃₇	—	2	1	no	—
146	C₂×D₄×C₃₇	—	2	1	no	—
147	C₂×D₄×C₃₇	—	2	1	no	—
148	C₂×D₄×C₃₇	—	2	1	no	—
149	C₂×D₄×C₃₇	—	2	1	no	—
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	—	4	4	no	—
158	C₂×D₄×C₃₇	—	4	4	no	—
159	C₂×D₄×C₃₇	—	8	2	no	—
160	C₂×D₄×C₃₇	#41	1	2	yes	—
161	C₂×D₄×C₃₇	#41	1	2	yes	—
162	C₂²×C₄×C₃₇	—	2	1	no	—
163	C₂²×C₄×C₃₇	—	2	1	no	—
164	C₂²×C₄×C₃₇	—	2	1	no	—
165	C₂²×C₄×C₃₇	—	2	1	no	—
166	C₂²×C₄×C₃₇	—	2	1	no	—
167	C₂²×C₄×C₃₇	—	4	4	no	—
168	C₂²×C₄×C₃₇	—	4	2	no	—
169	C₂²×C₄×C₃₇	—	4	2	no	—
170	C₂²×C₄×C₃₇	—	8	2	no	—
171	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
176	SD₁₆×C₃₇	—	4	4	no	—
177	D₈×C₃₇	—	2	8	no	—
178	D₈×C₃₇	—	4	4	no	—
179	C₂×C₈×C₃₇	—	2	1	no	—
180	C₂×C₈×C₃₇	—	2	1	no	—
181	C₂×C₈×C₃₇	—	2	1	no	—
182	C₂×C₈×C₃₇	—	2	1	no	—
183	C₂×C₈×C₃₇	—	2	1	no	—
184	C₂×C₈×C₃₇	—	2	1	no	—
185	C₂×C₈×C₃₇	—	2	1	no	—
186	C₂×C₈×C₃₇	—	2	1	no	—
187	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
188	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
189	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
190	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
191	C₄⋊C₄×C₃₇	—	2	1	no	—
192	C₄⋊C₄×C₃₇	—	2	1	no	—
193	C₄⋊C₄×C₃₇	—	2	1	no	—
194	C₄⋊C₄×C₃₇	—	2	1	no	—
195	C₄⋊C₄×C₃₇	—	2	1	no	—
196	C₄⋊C₄×C₃₇	—	2	1	no	—
197	C₄⋊C₄×C₃₇	—	2	1	no	—
198	C₄⋊C₄×C₃₇	—	2	1	no	—
199	C₄⋊C₄×C₃₇	—	4	2	no	—
200	C₄⋊C₄×C₃₇	—	4	2	no	—
201	C₂²⋊C₄×C₃₇	—	4	4	no	—
202	C₂²⋊C₄×C₃₇	—	4	2	no	—
203	C₂²⋊C₄×C₃₇	—	4	2	no	—
204	C₂²⋊C₄×C₃₇	—	4	2	no	—
205	C₂²⋊C₄×C₃₇	—	4	2	no	—
206	C₂²⋊C₄×C₃₇	—	8	2	no	—
207	C₂²⋊C₄×C₃₇	—	8	2	no	—
208	C₂²⋊C₄×C₃₇	—	8	2	no	—
209	C₄²×C₃₇	—	2	1	no	—
210	C₄²×C₃₇	—	2	1	no	—
211	C₄²×C₃₇	—	2	1	no	—
212	C₄²×C₃₇	—	2	1	no	—
213	C₄²×C₃₇	C₂×D₄	1	2	yes	—
214	C₄²×C₃₇	C₂×D₄	1	2	yes	—
215	C₂³×C₃₇	—	2	2	no	—
216	C₂³×C₃₇	—	2	2	no	—
217	C₂³×C₃₇	—	4	1	no	—
218	C₂³×C₃₇	—	4	1	no	—
219	C₂³×C₃₇	—	4	1	no	—
220	C₂³×C₃₇	—	4	1	no	—
221	C₂³×C₃₇	—	4	2	no	—
222	C₂³×C₃₇	—	4	2	no	—
223	C₂³×C₃₇	—	4	2	no	—
224	C₂³×C₃₇	—	4	2	no	—
225	C₂³×C₃₇	—	4	1	no	—
226	C₂³×C₃₇	—	4	1	no	—
227	C₂³×C₃₇	—	4	1	no	—
228	C₂³×C₃₇	—	4	2	no	—
229	C₂³×C₃₇	—	4	2	no	—
230	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
231	Q₈×C₃₇	—	4	1	no	—
232	Q₈×C₃₇	—	4	1	no	—
233	Q₈×C₃₇	—	4	1	no	—
234	Q₈×C₃₇	—	4	1	no	—
235	Q₈×C₃₇	—	8	4	no	—
236	D₄×C₃₇	—	2	2	no	—
237	D₄×C₃₇	—	2	2	no	—
238	D₄×C₃₇	—	2	2	no	—
239	D₄×C₃₇	—	2	2	no	—
240	D₄×C₃₇	—	4	1	no	—
241	D₄×C₃₇	—	4	1	no	—
242	D₄×C₃₇	—	4	1	no	—
243	D₄×C₃₇	—	4	1	no	—
244	D₄×C₃₇	—	4	1	no	—
245	D₄×C₃₇	—	4	1	no	—
246	D₄×C₃₇	—	4	1	no	—
247	D₄×C₃₇	—	4	1	no	—
248	D₄×C₃₇	—	8	8	no	—
249	C₂×C₄×C₃₇	—	2	2	no	—
250	C₂×C₄×C₃₇	—	2	2	no	—
251	C₂×C₄×C₃₇	—	2	2	no	—
252	C₂×C₄×C₃₇	—	2	2	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	—	4	1	no	—
258	C₂×C₄×C₃₇	—	4	1	no	—
259	C₂×C₄×C₃₇	—	4	1	no	—
260	C₂×C₄×C₃₇	—	4	1	no	—
261	C₂×C₄×C₃₇	—	4	1	no	—
262	C₂×C₄×C₃₇	—	4	1	no	—
263	C₂×C₄×C₃₇	—	4	1	no	—
264	C₂×C₄×C₃₇	—	4	2	no	—
265	C₂×C₄×C₃₇	—	4	2	no	—
266	C₂×C₄×C₃₇	—	4	2	no	—
267	C₂×C₄×C₃₇	—	4	2	no	—
268	C₂×C₄×C₃₇	—	8	4	no	—
269	C₂×C₄×C₃₇	—	8	4	no	—
270	C₂×C₄×C₃₇	#127	1	2	yes	—
271	C₂×C₄×C₃₇	#127	1	2	yes	—
272	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
275	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
277	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
278	C₈×C₃₇	—	2	2	no	—
279	C₈×C₃₇	—	2	2	no	—
280	C₈×C₃₇	—	2	2	no	—
281	C₈×C₃₇	—	2	2	no	—
282	#28422	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
283	C₂²×C₃₇	—	4	4	no	—
284	C₂²×C₃₇	—	4	2	no	—
285	C₂²×C₃₇	—	4	2	no	—
286	C₂²×C₃₇	—	4	4	no	—
287	C₂²×C₃₇	—	8	2	no	—
288	C₂²×C₃₇	—	8	1	no	—
289	C₂²×C₃₇	—	8	1	no	—
290	C₂²×C₃₇	—	8	1	no	—
291	C₂²×C₃₇	—	8	1	no	—
292	C₂²×C₃₇	—	8	2	no	—
293	C₂²×C₃₇	—	8	2	no	—
294	C₂²×C₃₇	—	8	1	no	—
295	C₂²×C₃₇	—	8	1	no	—
296	C₂²×C₃₇	—	8	1	no	—
297	C₂²×C₃₇	—	8	2	no	—
298	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
299	C₂²×C₃₇	#546	1	1	yes	characteristic
300	C₂²×C₃₇	#548	1	1	yes	characteristic
301	C₂²×C₃₇	#575	1	2	yes	—
302	C₂²×C₃₇	#576	1	2	yes	—
303	C₄×C₃₇	—	2	2	no	—
304	C₄×C₃₇	—	2	2	no	—
305	C₄×C₃₇	—	4	2	no	—
306	C₄×C₃₇	—	4	2	no	—
307	C₄×C₃₇	—	8	1	no	—
308	C₄×C₃₇	—	8	1	no	—
309	C₄×C₃₇	—	8	1	no	—
310	C₄×C₃₇	—	8	1	no	—
311	C₄×C₃₇	—	8	1	no	—
312	C₄×C₃₇	#525	1	1	yes	characteristic
313	C₄×C₃₇	#537	1	1	yes	characteristic
314	C₄×C₃₇	#546	1	1	yes	characteristic
315	C₄×C₃₇	#548	1	1	yes	characteristic
316	C₂×#489	C₂×C₃₇	1	1	yes	characteristic, complemented
317	C₂×#474	C₂×C₃₇	1	1	yes	characteristic, complemented
318	C₂×#463	C₂×C₃₇	1	1	yes	characteristic, complemented
319	C₂×#442	C₂×C₃₇	1	1	yes	characteristic, complemented
320	#2563	C₂×C₃₇	1	1	yes	characteristic, complemented
321	#2544	C₂×C₃₇	1	1	yes	characteristic, complemented
322	#2097	C₂×C₃₇	1	1	yes	characteristic, complemented
323	#2092	C₂×C₃₇	1	1	yes	characteristic, complemented
324	#2012	C₂×C₃₇	1	1	yes	characteristic, complemented
325	#2011	C₂×C₃₇	1	1	yes	characteristic
326	#1973	C₂×C₃₇	1	1	yes	characteristic, complemented
327	#1970	C₂×C₃₇	1	1	yes	characteristic, complemented
328	#1961	C₂×C₃₇	1	1	yes	characteristic, complemented
329	#1958	C₂×C₃₇	1	1	yes	characteristic, complemented
330	#1771	C₂×C₃₇	1	1	yes	characteristic, complemented
331	C₂×C₃₇	—	8	2	no	—
332	C₂×C₃₇	—	8	2	no	—
333	C₂×C₃₇	—	16	1	no	—
334	C₂×C₃₇	#2540	1	1	yes	characteristic
335	C₂×C₃₇	#3153	1	1	yes	characteristic
336	C₂×C₃₇	#3155	1	1	yes	characteristic
337	C₂×C₃₇	#3319	1	2	yes	—
338	C₂×C₃₇	#3370	1	2	yes	—
339	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
340	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
341	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
342	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
343	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
344	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
345	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
346	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
347	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
348	#489	—	2	4	no	—
349	#474	—	2	4	no	—
350	#463	—	2	4	no	—
351	#442	—	2	4	no	—
352	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
353	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
354	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
355	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
356	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
357	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
358	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
359	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
360	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
361	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
362	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
363	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
364	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
365	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
366	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
367	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
368	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
369	#394	—	2	2	no	—
370	#393	—	2	2	no	—
371	#391	C₂²×C₃₇	1	1	yes	characteristic
372	#390	C₂²×C₃₇	1	1	yes	characteristic
373	#390	C₂²×C₃₇	1	1	yes	characteristic
374	#390	C₂²×C₃₇	1	1	yes	characteristic
375	#386	—	2	2	no	—
376	#382	C₂²×C₃₇	1	1	yes	characteristic
377	#382	C₂²×C₃₇	1	1	yes	characteristic
378	#380	—	2	2	no	—
379	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
380	#336	C₂²×C₃₇	1	1	yes	characteristic
381	#336	C₂²×C₃₇	1	1	yes	characteristic
382	C₃₇	#28422	1	1	yes	characteristic, direct product factor, Sylow
383	C₂²×Q₈	—	2	1	no	—
384	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
385	C₂²×D₄	—	2	2	no	—
386	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
387	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
388	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
389	C₂³×C₄	—	2	1	no	—
390	C₂³×C₄	—	2	1	no	—
391	C₂×SD₁₆	—	2	2	no	—
392	C₂×SD₁₆	—	2	2	no	—
393	C₂×SD₁₆	—	4	1	no	—
394	C₂×D₈	—	2	2	no	—
395	C₂×D₈	—	2	2	no	—
396	C₂×D₈	—	2	2	no	—
397	C₂×D₈	—	2	2	no	—
398	C₂×D₈	—	2	2	no	—
399	C₂×D₈	—	4	1	no	—
400	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
401	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
402	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
403	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
404	C₄⋊Q₈	—	2	2	no	—
405	C₄⋊Q₈	—	2	2	no	—
406	#127	—	2	2	no	—
407	#127	—	4	1	no	—
408	#124	—	2	2	no	—
409	#124	—	2	2	no	—
410	#124	—	2	2	no	—
411	#124	—	4	1	no	—
412	C₄×D₄	—	2	2	no	—
413	C₄×D₄	—	2	2	no	—
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	—	2	2	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
418	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	2	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	2	no	—
428	C₂×C₂²⋊C₄	—	2	2	no	—
429	C₂×C₂²⋊C₄	—	2	2	no	—
430	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
433	#107	—	2	2	no	—
434	#107	—	2	2	no	—
435	#106	—	2	2	no	—
436	C₄⋊C₈	D₄×C₃₇	1	4	yes	complemented
437	#103	—	2	2	no	—
438	#103	—	2	2	no	—
439	#103	—	2	2	no	—
440	#102	—	2	2	no	—
441	#102	—	2	2	no	—
442	#102	—	2	2	no	—
443	#102	—	2	2	no	—
444	#102	—	2	2	no	—
445	#102	—	2	2	no	—
446	#102	—	2	2	no	—
447	#97	—	4	1	no	—
448	#97	D₄×C₃₇	1	4	yes	complemented
449	C₄×C₈	—	4	1	no	—
450	#95	—	2	2	no	—
451	#95	—	2	2	no	—
452	#95	—	2	2	no	—
453	#95	D₄×C₃₇	1	2	yes	—
454	C₂⁴	—	2	1	no	—
455	C₂⁴	—	2	1	no	—
456	C₂⁴	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	4	2	no	—
464	C₂×Q₈	—	8	2	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	4	4	no	—
482	C₂×D₄	—	4	4	no	—
483	C₂×D₄	—	8	2	no	—
484	C₂×D₄	#41×C₃₇	1	2	yes	—
485	C₂×D₄	#41×C₃₇	1	2	yes	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	4	4	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	—	4	2	no	—
494	C₂²×C₄	—	8	2	no	—
495	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
496	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
497	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
499	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
500	SD₁₆	—	4	4	no	—
501	D₈	—	2	8	no	—
502	D₈	—	4	4	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
512	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
513	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
514	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	4	2	no	—
524	C₄⋊C₄	—	4	2	no	—
525	C₂²⋊C₄	—	4	4	no	—
526	C₂²⋊C₄	—	4	2	no	—
527	C₂²⋊C₄	—	4	2	no	—
528	C₂²⋊C₄	—	4	2	no	—
529	C₂²⋊C₄	—	4	2	no	—
530	C₂²⋊C₄	—	8	2	no	—
531	C₂²⋊C₄	—	8	2	no	—
532	C₂²⋊C₄	—	8	2	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	1	no	—
537	C₄²	C₂×D₄×C₃₇	1	2	yes	—
538	C₄²	C₂×D₄×C₃₇	1	2	yes	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	4	1	no	—
542	C₂³	—	4	1	no	—
543	C₂³	—	4	1	no	—
544	C₂³	—	4	1	no	—
545	C₂³	—	4	2	no	—
546	C₂³	—	4	2	no	—
547	C₂³	—	4	2	no	—
548	C₂³	—	4	2	no	—
549	C₂³	—	4	1	no	—
550	C₂³	—	4	1	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	4	2	no	—
554	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
555	Q₈	—	4	1	no	—
556	Q₈	—	4	1	no	—
557	Q₈	—	4	1	no	—
558	Q₈	—	4	1	no	—
559	Q₈	—	8	4	no	—
560	D₄	—	2	2	no	—
561	D₄	—	2	2	no	—
562	D₄	—	2	2	no	—
563	D₄	—	2	2	no	—
564	D₄	—	4	1	no	—
565	D₄	—	4	1	no	—
566	D₄	—	4	1	no	—
567	D₄	—	4	1	no	—
568	D₄	—	4	1	no	—
569	D₄	—	4	1	no	—
570	D₄	—	4	1	no	—
571	D₄	—	4	1	no	—
572	D₄	—	8	8	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	8	4	no	—
593	C₂×C₄	—	8	4	no	—
594	C₂×C₄	#127×C₃₇	1	2	yes	—
595	C₂×C₄	#127×C₃₇	1	2	yes	—
596	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
597	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
598	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
599	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
600	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
601	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
602	C₈	—	2	2	no	—
603	C₈	—	2	2	no	—
604	C₈	—	2	2	no	—
605	C₈	—	2	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	4	no	—
609	C₂²	—	4	4	no	—
610	C₂²	—	8	1	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	8	1	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	2	no	—
615	C₂²	—	8	2	no	—
616	C₂²	—	8	1	no	—
617	C₂²	—	8	1	no	—
618	C₂²	—	8	1	no	—
619	C₂²	—	8	2	no	—
620	C₂²	—	8	2	no	—
621	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
622	C₂²	C₃₇×#546	1	1	yes	characteristic
623	C₂²	C₃₇×#548	1	1	yes	characteristic
624	C₂²	C₃₇×#575	1	2	yes	—
625	C₂²	C₃₇×#576	1	2	yes	—
626	C₄	—	2	2	no	—
627	C₄	—	2	2	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	2	no	—
630	C₄	—	8	1	no	—
631	C₄	—	8	1	no	—
632	C₄	—	8	1	no	—
633	C₄	—	8	1	no	—
634	C₄	—	8	1	no	—
635	C₄	C₃₇×#525	1	1	yes	characteristic
636	C₄	C₃₇×#537	1	1	yes	characteristic
637	C₄	C₃₇×#546	1	1	yes	characteristic
638	C₄	C₃₇×#548	1	1	yes	characteristic
639	C₂	—	8	2	no	—
640	C₂	—	8	2	no	—
641	C₂	—	16	1	no	—
642	C₂	C₃₇×#2540	1	1	yes	characteristic
643	C₂	C₃₇×#3153	1	1	yes	characteristic
644	C₂	C₃₇×#3155	1	1	yes	characteristic
645	C₂	C₃₇×#3319	1	2	yes	—
646	C₂	C₃₇×#3370	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×#489	C₂	semidirect
2. C₂×C₃₇×#474	C₂	semidirect
3. C₂×C₃₇×#463	C₂	semidirect
4. C₂×C₃₇×#442	C₂	semidirect
5. C₃₇×#2563	C₂	semidirect
6. C₃₇×#2544	C₂	semidirect
7. C₃₇×#2097	C₂	semidirect
8. C₃₇×#2092	C₂	semidirect
9. C₃₇×#2012	C₂	semidirect
11. C₃₇×#1973	C₂	semidirect
12. C₃₇×#1970	C₂	semidirect
13. C₃₇×#1961	C₂	semidirect
14. C₃₇×#1958	C₂	semidirect
15. C₃₇×#1771	C₂	semidirect
112. C₄⋊C₈×C₃₇	D₄	semidirect
124. #97×C₃₇	D₄	semidirect
282. #28422	C₃₇	direct (N × H)
316. C₂×#489	C₂×C₃₇	semidirect
317. C₂×#474	C₂×C₃₇	semidirect
318. C₂×#463	C₂×C₃₇	semidirect
319. C₂×#442	C₂×C₃₇	semidirect
320. #2563	C₂×C₃₇	semidirect
321. #2544	C₂×C₃₇	semidirect
322. #2097	C₂×C₃₇	semidirect
323. #2092	C₂×C₃₇	semidirect
324. #2012	C₂×C₃₇	semidirect
326. #1973	C₂×C₃₇	semidirect
327. #1970	C₂×C₃₇	semidirect
328. #1961	C₂×C₃₇	semidirect
329. #1958	C₂×C₃₇	semidirect
330. #1771	C₂×C₃₇	semidirect
382. C₃₇	#28422	direct (N × H)
436. C₄⋊C₈	D₄×C₃₇	semidirect
448. #97	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×#489	2
C₂×C₃₇×#474	2
C₂×C₃₇×#463	2
C₂×C₃₇×#442	2
C₃₇×#2563	2
C₃₇×#2544	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×#1771	2
#28422	37

Subgroups — C37×#28422 #22649675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28422 #22649675