Subgroups — C₃₇×#28379 #22649632

Order 9472.

944 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#479	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#478	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#463	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2861	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#124×C₃₇	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×#2015	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#2012	C₂	1	1	yes	maximal, characteristic
11	C₃₇×#1973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#1973	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₇×#1972	C₂	1	1	yes	maximal, characteristic
14	C₃₇×#1971	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
20	C₂×#125×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×Q₈×C₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
25	C₃₇×#479	—	2	4	no	—
26	C₃₇×#478	—	2	4	no	—
27	C₃₇×#464	—	2	4	no	—
28	C₃₇×#463	—	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×#106×C₃₇	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×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×#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	C₃₇×#391	C₂²	1	1	yes	characteristic
46	C₃₇×#391	C₂²	1	1	yes	characteristic
47	C₃₇×#391	C₂²	1	1	yes	characteristic
48	C₃₇×#390	C₂²	1	1	yes	characteristic
49	C₃₇×#390	C₂²	1	1	yes	characteristic
50	C₃₇×#390	C₂²	1	1	yes	characteristic
51	C₃₇×#388	—	2	2	no	—
52	C₃₇×#388	—	2	2	no	—
53	C₃₇×#388	—	2	2	no	—
54	C₃₇×#382	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊C₄×C₃₇	—	2	2	no	—
56	C₄³×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	C₂³	1	1	yes	characteristic
60	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₃₇	—	2	1	no	—
64	C₂×Q₁₆×C₃₇	—	2	2	no	—
65	C₂×Q₁₆×C₃₇	—	2	2	no	—
66	C₂×Q₁₆×C₃₇	—	4	1	no	—
67	C₂×SD₁₆×C₃₇	—	2	2	no	—
68	C₂×SD₁₆×C₃₇	—	2	2	no	—
69	C₂×SD₁₆×C₃₇	—	2	2	no	—
70	C₂×SD₁₆×C₃₇	—	2	2	no	—
71	C₂×SD₁₆×C₃₇	—	4	1	no	—
72	C₂×SD₁₆×C₃₇	—	4	1	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	#125×C₃₇	—	2	2	no	—
81	#125×C₃₇	—	2	2	no	—
82	#124×C₃₇	—	2	2	no	—
83	#124×C₃₇	—	2	2	no	—
84	#124×C₃₇	—	2	2	no	—
85	#124×C₃₇	—	2	2	no	—
86	C₄×Q₈×C₃₇	—	2	2	no	—
87	C₄×Q₈×C₃₇	—	2	2	no	—
88	C₄×D₄×C₃₇	—	2	2	no	—
89	C₄×D₄×C₃₇	—	2	2	no	—
90	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
91	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
92	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
93	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₃₇	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
103	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
104	C₂×C₄²×C₃₇	—	2	1	no	—
105	C₂×C₄²×C₃₇	D₄	1	2	yes	—
106	C₂×C₄²×C₃₇	D₄	1	2	yes	—
107	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
110	#107×C₃₇	—	2	2	no	—
111	#107×C₃₇	—	2	2	no	—
112	#106×C₃₇	—	2	2	no	—
113	#106×C₃₇	—	2	2	no	—
114	C₄⋊C₈×C₃₇	D₄	1	4	yes	—
115	C₄⋊C₈×C₃₇	D₄	1	4	yes	—
116	#103×C₃₇	—	2	2	no	—
117	#103×C₃₇	—	2	2	no	—
118	#103×C₃₇	—	2	2	no	—
119	#103×C₃₇	—	2	2	no	—
120	#102×C₃₇	—	2	2	no	—
121	#102×C₃₇	—	2	2	no	—
122	#102×C₃₇	—	2	2	no	—
123	#102×C₃₇	—	2	2	no	—
124	#97×C₃₇	—	4	1	no	—
125	#97×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	—	2	2	no	—
130	C₂⁴×C₃₇	—	2	1	no	—
131	C₂⁴×C₃₇	—	2	1	no	—
132	C₂×Q₈×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	—	2	1	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	#41	1	2	yes	—
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	#41	1	2	yes	—
156	C₂²×C₄×C₃₇	—	2	1	no	—
157	C₂²×C₄×C₃₇	—	2	1	no	—
158	C₂²×C₄×C₃₇	—	2	1	no	—
159	C₂²×C₄×C₃₇	—	2	1	no	—
160	C₂²×C₄×C₃₇	—	2	1	no	—
161	C₂²×C₄×C₃₇	—	2	1	no	—
162	C₂²×C₄×C₃₇	—	4	4	no	—
163	C₂²×C₄×C₃₇	—	4	2	no	—
164	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
169	Q₁₆×C₃₇	—	4	4	no	—
170	SD₁₆×C₃₇	—	4	4	no	—
171	SD₁₆×C₃₇	—	4	4	no	—
172	D₈×C₃₇	—	4	4	no	—
173	C₂×C₈×C₃₇	—	2	1	no	—
174	C₂×C₈×C₃₇	—	2	1	no	—
175	C₂×C₈×C₃₇	—	2	1	no	—
176	C₂×C₈×C₃₇	—	2	1	no	—
177	C₂×C₈×C₃₇	—	2	1	no	—
178	C₂×C₈×C₃₇	—	2	1	no	—
179	C₂×C₈×C₃₇	—	2	1	no	—
180	C₂×C₈×C₃₇	—	2	1	no	—
181	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
182	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
183	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
184	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
185	C₄⋊C₄×C₃₇	—	2	1	no	—
186	C₄⋊C₄×C₃₇	—	2	1	no	—
187	C₄⋊C₄×C₃₇	—	2	1	no	—
188	C₄⋊C₄×C₃₇	—	2	1	no	—
189	C₄⋊C₄×C₃₇	—	2	1	no	—
190	C₄⋊C₄×C₃₇	—	2	1	no	—
191	C₄⋊C₄×C₃₇	—	2	1	no	—
192	C₄⋊C₄×C₃₇	—	2	1	no	—
193	C₄⋊C₄×C₃₇	—	4	2	no	—
194	C₄⋊C₄×C₃₇	—	4	2	no	—
195	C₄⋊C₄×C₃₇	—	4	2	no	—
196	C₂²⋊C₄×C₃₇	—	2	8	no	—
197	C₂²⋊C₄×C₃₇	—	4	4	no	—
198	C₂²⋊C₄×C₃₇	—	4	4	no	—
199	C₂²⋊C₄×C₃₇	—	4	4	no	—
200	C₂²⋊C₄×C₃₇	—	4	2	no	—
201	C₂²⋊C₄×C₃₇	—	4	2	no	—
202	C₂²⋊C₄×C₃₇	—	4	2	no	—
203	C₄²×C₃₇	—	2	1	no	—
204	C₄²×C₃₇	—	2	1	no	—
205	C₄²×C₃₇	—	2	1	no	—
206	C₄²×C₃₇	—	2	1	no	—
207	C₄²×C₃₇	—	4	2	no	—
208	C₄²×C₃₇	—	4	2	no	—
209	C₄²×C₃₇	—	4	2	no	—
210	C₄²×C₃₇	C₂×D₄	1	2	yes	—
211	C₄²×C₃₇	C₂×D₄	1	2	yes	—
212	C₂³×C₃₇	—	2	2	no	—
213	C₂³×C₃₇	—	4	1	no	—
214	C₂³×C₃₇	—	4	1	no	—
215	C₂³×C₃₇	—	4	2	no	—
216	C₂³×C₃₇	—	4	2	no	—
217	C₂³×C₃₇	—	4	1	no	—
218	C₂³×C₃₇	—	4	1	no	—
219	C₂³×C₃₇	—	4	1	no	—
220	C₂³×C₃₇	—	4	2	no	—
221	C₂³×C₃₇	—	4	2	no	—
222	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
223	Q₈×C₃₇	—	2	2	no	—
224	Q₈×C₃₇	—	2	2	no	—
225	Q₈×C₃₇	—	4	1	no	—
226	Q₈×C₃₇	—	4	1	no	—
227	Q₈×C₃₇	—	4	1	no	—
228	Q₈×C₃₇	—	4	1	no	—
229	Q₈×C₃₇	—	4	1	no	—
230	Q₈×C₃₇	—	4	1	no	—
231	D₄×C₃₇	—	2	2	no	—
232	D₄×C₃₇	—	2	2	no	—
233	D₄×C₃₇	—	4	1	no	—
234	D₄×C₃₇	—	4	1	no	—
235	D₄×C₃₇	—	4	1	no	—
236	D₄×C₃₇	—	4	1	no	—
237	D₄×C₃₇	—	4	1	no	—
238	D₄×C₃₇	—	4	1	no	—
239	C₂×C₄×C₃₇	—	2	2	no	—
240	C₂×C₄×C₃₇	—	2	2	no	—
241	C₂×C₄×C₃₇	—	2	2	no	—
242	C₂×C₄×C₃₇	—	2	2	no	—
243	C₂×C₄×C₃₇	—	2	2	no	—
244	C₂×C₄×C₃₇	—	2	2	no	—
245	C₂×C₄×C₃₇	—	2	2	no	—
246	C₂×C₄×C₃₇	—	2	2	no	—
247	C₂×C₄×C₃₇	—	2	2	no	—
248	C₂×C₄×C₃₇	—	4	1	no	—
249	C₂×C₄×C₃₇	—	4	1	no	—
250	C₂×C₄×C₃₇	—	4	1	no	—
251	C₂×C₄×C₃₇	—	4	1	no	—
252	C₂×C₄×C₃₇	—	4	1	no	—
253	C₂×C₄×C₃₇	—	4	1	no	—
254	C₂×C₄×C₃₇	—	4	1	no	—
255	C₂×C₄×C₃₇	—	4	1	no	—
256	C₂×C₄×C₃₇	—	4	1	no	—
257	C₂×C₄×C₃₇	—	4	2	no	—
258	C₂×C₄×C₃₇	—	4	2	no	—
259	C₂×C₄×C₃₇	—	4	2	no	—
260	C₂×C₄×C₃₇	—	4	2	no	—
261	C₂×C₄×C₃₇	—	8	4	no	—
262	C₂×C₄×C₃₇	#127	1	2	yes	—
263	C₂×C₄×C₃₇	#127	1	2	yes	—
264	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
267	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
268	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
269	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
270	C₈×C₃₇	—	2	2	no	—
271	C₈×C₃₇	—	2	2	no	—
272	C₈×C₃₇	—	2	2	no	—
273	C₈×C₃₇	—	2	2	no	—
274	#28379	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
275	C₂²×C₃₇	—	4	4	no	—
276	C₂²×C₃₇	—	4	2	no	—
277	C₂²×C₃₇	—	8	1	no	—
278	C₂²×C₃₇	—	8	1	no	—
279	C₂²×C₃₇	—	8	2	no	—
280	C₂²×C₃₇	—	8	2	no	—
281	C₂²×C₃₇	—	8	1	no	—
282	C₂²×C₃₇	—	8	1	no	—
283	C₂²×C₃₇	—	8	2	no	—
284	C₂²×C₃₇	—	8	1	no	—
285	C₂²×C₃₇	#525	1	1	yes	characteristic
286	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
287	C₂²×C₃₇	#537	1	1	yes	characteristic
288	C₂²×C₃₇	#575	1	2	yes	—
289	C₂²×C₃₇	#575	1	2	yes	—
290	C₄×C₃₇	—	2	2	no	—
291	C₄×C₃₇	—	2	2	no	—
292	C₄×C₃₇	—	4	2	no	—
293	C₄×C₃₇	—	4	2	no	—
294	C₄×C₃₇	—	4	2	no	—
295	C₄×C₃₇	—	8	1	no	—
296	C₄×C₃₇	—	8	1	no	—
297	C₄×C₃₇	—	8	1	no	—
298	C₄×C₃₇	—	8	1	no	—
299	C₄×C₃₇	—	8	1	no	—
300	C₄×C₃₇	#546	1	1	yes	characteristic
301	C₄×C₃₇	#546	1	1	yes	characteristic
302	C₄×C₃₇	#548	1	1	yes	characteristic
303	C₄×C₃₇	#548	1	1	yes	characteristic
304	C₂×#479	C₂×C₃₇	1	1	yes	characteristic, complemented
305	C₂×#478	C₂×C₃₇	1	1	yes	characteristic, complemented
306	C₂×#464	C₂×C₃₇	1	1	yes	characteristic, complemented
307	C₂×#463	C₂×C₃₇	1	1	yes	characteristic
308	#2861	C₂×C₃₇	1	1	yes	characteristic, complemented
309	C₄×#124	C₂×C₃₇	1	1	yes	characteristic, complemented
310	#2097	C₂×C₃₇	1	1	yes	characteristic, complemented
311	#2092	C₂×C₃₇	1	1	yes	characteristic, complemented
312	#2015	C₂×C₃₇	1	1	yes	characteristic, complemented
313	#2012	C₂×C₃₇	1	1	yes	characteristic
314	#1973	C₂×C₃₇	1	1	yes	characteristic, complemented
315	#1973	C₂×C₃₇	1	1	yes	characteristic, complemented
316	#1972	C₂×C₃₇	1	1	yes	characteristic
317	#1971	C₂×C₃₇	1	1	yes	characteristic, complemented
318	#1767	C₂×C₃₇	1	1	yes	characteristic, complemented
319	C₂×C₃₇	—	8	2	no	—
320	C₂×C₃₇	—	16	1	no	—
321	C₂×C₃₇	#2540	1	1	yes	characteristic
322	C₂×C₃₇	#3111	1	2	yes	—
323	C₂×C₃₇	#3150	1	1	yes	characteristic
324	C₂×C₃₇	#3153	1	1	yes	characteristic
325	C₂×C₃₇	#3256	1	2	yes	—
326	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
327	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
328	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
329	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
330	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
331	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
332	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
333	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
334	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
335	#479	—	2	4	no	—
336	#478	—	2	4	no	—
337	#464	—	2	4	no	—
338	#463	—	2	4	no	—
339	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
340	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
341	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
342	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
343	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
344	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
345	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
346	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
347	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
348	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
349	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
350	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
351	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
352	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
353	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
354	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
355	#391	C₂²×C₃₇	1	1	yes	characteristic
356	#391	C₂²×C₃₇	1	1	yes	characteristic
357	#391	C₂²×C₃₇	1	1	yes	characteristic
358	#390	C₂²×C₃₇	1	1	yes	characteristic
359	#390	C₂²×C₃₇	1	1	yes	characteristic
360	#390	C₂²×C₃₇	1	1	yes	characteristic
361	#388	—	2	2	no	—
362	#388	—	2	2	no	—
363	#388	—	2	2	no	—
364	#382	C₂²×C₃₇	1	1	yes	characteristic
365	C₄×C₂²⋊C₄	—	2	2	no	—
366	C₄³	C₂²×C₃₇	1	1	yes	characteristic
367	#336	C₂²×C₃₇	1	1	yes	characteristic
368	#336	C₂²×C₃₇	1	1	yes	characteristic
369	C₃₇	#28379	1	1	yes	characteristic, direct product factor, Sylow
370	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
371	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
372	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
373	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
374	C₂³×C₄	—	2	1	no	—
375	C₂×Q₁₆	—	2	2	no	—
376	C₂×Q₁₆	—	2	2	no	—
377	C₂×Q₁₆	—	4	1	no	—
378	C₂×SD₁₆	—	2	2	no	—
379	C₂×SD₁₆	—	2	2	no	—
380	C₂×SD₁₆	—	2	2	no	—
381	C₂×SD₁₆	—	2	2	no	—
382	C₂×SD₁₆	—	4	1	no	—
383	C₂×SD₁₆	—	4	1	no	—
384	C₂×D₈	—	2	2	no	—
385	C₂×D₈	—	2	2	no	—
386	C₂×D₈	—	4	1	no	—
387	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
388	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
389	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
390	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
391	#125	—	2	2	no	—
392	#125	—	2	2	no	—
393	#124	—	2	2	no	—
394	#124	—	2	2	no	—
395	#124	—	2	2	no	—
396	#124	—	2	2	no	—
397	C₄×Q₈	—	2	2	no	—
398	C₄×Q₈	—	2	2	no	—
399	C₄×D₄	—	2	2	no	—
400	C₄×D₄	—	2	2	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
408	C₂×C₂²⋊C₄	—	2	2	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	2	no	—
413	C₂×C₂²⋊C₄	—	2	2	no	—
414	C₂×C₂²⋊C₄	—	2	2	no	—
415	C₂×C₄²	—	2	1	no	—
416	C₂×C₄²	D₄×C₃₇	1	2	yes	—
417	C₂×C₄²	D₄×C₃₇	1	2	yes	—
418	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
419	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
420	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
421	#107	—	2	2	no	—
422	#107	—	2	2	no	—
423	#106	—	2	2	no	—
424	#106	—	2	2	no	—
425	C₄⋊C₈	D₄×C₃₇	1	4	yes	—
426	C₄⋊C₈	D₄×C₃₇	1	4	yes	—
427	#103	—	2	2	no	—
428	#103	—	2	2	no	—
429	#103	—	2	2	no	—
430	#103	—	2	2	no	—
431	#102	—	2	2	no	—
432	#102	—	2	2	no	—
433	#102	—	2	2	no	—
434	#102	—	2	2	no	—
435	#97	—	4	1	no	—
436	#97	—	4	1	no	—
437	#95	—	2	2	no	—
438	#95	—	2	2	no	—
439	#95	—	2	2	no	—
440	#95	—	2	2	no	—
441	C₂⁴	—	2	1	no	—
442	C₂⁴	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	#41×C₃₇	1	2	yes	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	#41×C₃₇	1	2	yes	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	4	4	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
476	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
477	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
479	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
480	Q₁₆	—	4	4	no	—
481	SD₁₆	—	4	4	no	—
482	SD₁₆	—	4	4	no	—
483	D₈	—	4	4	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
493	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
494	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
495	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	4	2	no	—
505	C₄⋊C₄	—	4	2	no	—
506	C₄⋊C₄	—	4	2	no	—
507	C₂²⋊C₄	—	2	8	no	—
508	C₂²⋊C₄	—	4	4	no	—
509	C₂²⋊C₄	—	4	4	no	—
510	C₂²⋊C₄	—	4	4	no	—
511	C₂²⋊C₄	—	4	2	no	—
512	C₂²⋊C₄	—	4	2	no	—
513	C₂²⋊C₄	—	4	2	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	4	2	no	—
519	C₄²	—	4	2	no	—
520	C₄²	—	4	2	no	—
521	C₄²	C₂×D₄×C₃₇	1	2	yes	—
522	C₄²	C₂×D₄×C₃₇	1	2	yes	—
523	C₂³	—	2	2	no	—
524	C₂³	—	4	1	no	—
525	C₂³	—	4	1	no	—
526	C₂³	—	4	2	no	—
527	C₂³	—	4	2	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	4	1	no	—
530	C₂³	—	4	1	no	—
531	C₂³	—	4	2	no	—
532	C₂³	—	4	2	no	—
533	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
534	Q₈	—	2	2	no	—
535	Q₈	—	2	2	no	—
536	Q₈	—	4	1	no	—
537	Q₈	—	4	1	no	—
538	Q₈	—	4	1	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	4	1	no	—
541	Q₈	—	4	1	no	—
542	D₄	—	2	2	no	—
543	D₄	—	2	2	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	1	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	8	4	no	—
573	C₂×C₄	#127×C₃₇	1	2	yes	—
574	C₂×C₄	#127×C₃₇	1	2	yes	—
575	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
576	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
577	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
578	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
579	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
580	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
581	C₈	—	2	2	no	—
582	C₈	—	2	2	no	—
583	C₈	—	2	2	no	—
584	C₈	—	2	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	4	no	—
587	C₂²	—	8	1	no	—
588	C₂²	—	8	1	no	—
589	C₂²	—	8	2	no	—
590	C₂²	—	8	1	no	—
591	C₂²	—	8	1	no	—
592	C₂²	—	8	2	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	2	no	—
595	C₂²	C₃₇×#525	1	1	yes	characteristic
596	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
597	C₂²	C₃₇×#537	1	1	yes	characteristic
598	C₂²	C₃₇×#575	1	2	yes	—
599	C₂²	C₃₇×#575	1	2	yes	—
600	C₄	—	2	2	no	—
601	C₄	—	2	2	no	—
602	C₄	—	4	2	no	—
603	C₄	—	4	2	no	—
604	C₄	—	4	2	no	—
605	C₄	—	8	1	no	—
606	C₄	—	8	1	no	—
607	C₄	—	8	1	no	—
608	C₄	—	8	1	no	—
609	C₄	—	8	1	no	—
610	C₄	C₃₇×#546	1	1	yes	characteristic
611	C₄	C₃₇×#546	1	1	yes	characteristic
612	C₄	C₃₇×#548	1	1	yes	characteristic
613	C₄	C₃₇×#548	1	1	yes	characteristic
614	C₂	—	8	2	no	—
615	C₂	—	16	1	no	—
616	C₂	C₃₇×#2540	1	1	yes	characteristic
617	C₂	C₃₇×#3111	1	2	yes	—
618	C₂	C₃₇×#3150	1	1	yes	characteristic
619	C₂	C₃₇×#3153	1	1	yes	characteristic
620	C₂	C₃₇×#3256	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂²×D₈×C₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₄³×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#479	C₂	semidirect
2. C₂×C₃₇×#478	C₂	semidirect
3. C₂×C₃₇×#464	C₂	semidirect
5. C₃₇×#2861	C₂	semidirect
6. C₄×#124×C₃₇	C₂	semidirect
7. C₃₇×#2097	C₂	semidirect
8. C₃₇×#2092	C₂	semidirect
9. C₃₇×#2015	C₂	semidirect
11. C₃₇×#1973	C₂	semidirect
12. C₃₇×#1973	C₂	semidirect
14. C₃₇×#1971	C₂	semidirect
15. C₃₇×#1767	C₂	semidirect
274. #28379	C₃₇	direct (N × H)
304. C₂×#479	C₂×C₃₇	semidirect
305. C₂×#478	C₂×C₃₇	semidirect
306. C₂×#464	C₂×C₃₇	semidirect
308. #2861	C₂×C₃₇	semidirect
309. C₄×#124	C₂×C₃₇	semidirect
310. #2097	C₂×C₃₇	semidirect
311. #2092	C₂×C₃₇	semidirect
312. #2015	C₂×C₃₇	semidirect
314. #1973	C₂×C₃₇	semidirect
315. #1973	C₂×C₃₇	semidirect
317. #1971	C₂×C₃₇	semidirect
318. #1767	C₂×C₃₇	semidirect
369. C₃₇	#28379	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×#479	2
C₂×C₃₇×#478	2
C₂×C₃₇×#464	2
C₂×C₃₇×#463	2
C₃₇×#2861	2
C₄×#124×C₃₇	2
C₃₇×#2097	2
C₃₇×#2092	2
C₃₇×#2015	2
C₃₇×#2012	2
C₃₇×#1973	2
C₃₇×#1972	2
C₃₇×#1971	2
C₃₇×#1767	2
#28379	37

Subgroups — C37×#28379 #22649632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28379 #22649632