Subgroups — C₃₇×#28474 #22649727

Order 9472.

1200 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#495	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₇×#459	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₇×#440	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2548	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2544	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, complemented
11	C₃₇×#2012	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#2011	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₇×#1973	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#1970	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₇×#1771	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×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
22	C₂²×D₈×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×#127×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×#496	—	2	4	no	—
34	C₃₇×#496	—	2	4	no	—
35	C₃₇×#495	—	2	4	no	—
36	C₃₇×#464	—	2	4	no	—
37	C₃₇×#459	—	2	4	no	—
38	C₃₇×#440	—	2	4	no	—
39	C₂×#107×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×#102×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×#97×C₃₇	C₂²	1	1	yes	characteristic
48	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
50	C₃₇×#394	—	2	2	no	—
51	C₃₇×#394	—	2	2	no	—
52	C₃₇×#391	C₂²	1	1	yes	characteristic
53	C₃₇×#390	—	2	2	no	—
54	C₃₇×#390	C₂²	1	1	yes	characteristic
55	C₃₇×#390	C₂²	1	1	yes	characteristic
56	C₃₇×#390	C₂²	1	1	yes	characteristic
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×D₄×C₃₇	—	2	1	no	—
64	C₂²×D₄×C₃₇	—	2	2	no	—
65	C₂²×D₄×C₃₇	—	2	1	no	—
66	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₃₇	—	2	1	no	—
71	C₂×Q₁₆×C₃₇	—	2	2	no	—
72	C₂×Q₁₆×C₃₇	—	2	2	no	—
73	C₂×Q₁₆×C₃₇	—	4	1	no	—
74	C₂×SD₁₆×C₃₇	—	2	2	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	—	4	1	no	—
83	C₂×SD₁₆×C₃₇	—	4	1	no	—
84	C₂×SD₁₆×C₃₇	—	4	1	no	—
85	C₂×SD₁₆×C₃₇	D₄	1	4	yes	complemented
86	C₂×D₈×C₃₇	—	2	2	no	—
87	C₂×D₈×C₃₇	—	2	2	no	—
88	C₂×D₈×C₃₇	—	2	2	no	—
89	C₂×D₈×C₃₇	—	2	2	no	—
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	—	2	2	no	—
94	C₂×D₈×C₃₇	—	4	1	no	—
95	C₂×D₈×C₃₇	—	4	1	no	—
96	C₂×D₈×C₃₇	—	4	1	no	—
97	C₂×D₈×C₃₇	—	4	1	no	—
98	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
102	#127×C₃₇	—	2	2	no	—
103	#127×C₃₇	—	2	2	no	—
104	#127×C₃₇	—	2	2	no	—
105	#127×C₃₇	—	4	1	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	—	2	2	no	—
111	#124×C₃₇	—	4	1	no	—
112	#124×C₃₇	—	4	1	no	—
113	#124×C₃₇	—	4	1	no	—
114	C₄×Q₈×C₃₇	—	2	2	no	—
115	C₄×Q₈×C₃₇	—	2	2	no	—
116	C₄×D₄×C₃₇	—	2	2	no	—
117	C₄×D₄×C₃₇	—	2	2	no	—
118	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
119	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
120	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
124	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
125	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
126	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
129	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
130	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
131	C₂×C₄²×C₃₇	—	2	1	no	—
132	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
135	#107×C₃₇	—	2	2	no	—
136	C₄⋊C₈×C₃₇	D₄	1	4	yes	complemented
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	#102×C₃₇	—	2	2	no	—
143	#97×C₃₇	—	2	2	no	—
144	#97×C₃₇	D₄	1	4	yes	complemented
145	C₄×C₈×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	C₂⁴×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	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
168	C₂×D₄×C₃₇	—	2	1	no	—
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	—	2	1	no	—
187	C₂×D₄×C₃₇	—	4	4	no	—
188	C₂×D₄×C₃₇	—	4	4	no	—
189	C₂×D₄×C₃₇	—	4	4	no	—
190	C₂×D₄×C₃₇	—	4	2	no	—
191	C₂×D₄×C₃₇	—	4	2	no	—
192	C₂×D₄×C₃₇	—	8	2	no	—
193	C₂×D₄×C₃₇	—	8	2	no	—
194	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
195	C₂²×C₄×C₃₇	—	2	1	no	—
196	C₂²×C₄×C₃₇	—	2	1	no	—
197	C₂²×C₄×C₃₇	—	2	1	no	—
198	C₂²×C₄×C₃₇	—	2	1	no	—
199	C₂²×C₄×C₃₇	—	4	2	no	—
200	C₂²×C₄×C₃₇	—	8	2	no	—
201	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
203	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
206	Q₁₆×C₃₇	—	4	4	no	—
207	SD₁₆×C₃₇	—	2	8	no	—
208	SD₁₆×C₃₇	—	4	4	no	—
209	SD₁₆×C₃₇	—	4	4	no	—
210	SD₁₆×C₃₇	—	4	4	no	—
211	D₈×C₃₇	—	4	4	no	—
212	D₈×C₃₇	—	4	4	no	—
213	D₈×C₃₇	—	4	4	no	—
214	D₈×C₃₇	—	4	4	no	—
215	C₂×C₈×C₃₇	—	2	1	no	—
216	C₂×C₈×C₃₇	—	2	1	no	—
217	C₂×C₈×C₃₇	—	2	1	no	—
218	C₂×C₈×C₃₇	—	2	1	no	—
219	C₂×C₈×C₃₇	—	2	1	no	—
220	C₂×C₈×C₃₇	—	2	1	no	—
221	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
222	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
223	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
224	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
225	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
226	C₂×C₈×C₃₇	#41	1	2	yes	—
227	C₄⋊C₄×C₃₇	—	2	1	no	—
228	C₄⋊C₄×C₃₇	—	2	1	no	—
229	C₄⋊C₄×C₃₇	—	2	1	no	—
230	C₄⋊C₄×C₃₇	—	2	1	no	—
231	C₄⋊C₄×C₃₇	—	4	2	no	—
232	C₄⋊C₄×C₃₇	—	4	2	no	—
233	C₂²⋊C₄×C₃₇	—	4	4	no	—
234	C₂²⋊C₄×C₃₇	—	4	4	no	—
235	C₂²⋊C₄×C₃₇	—	4	4	no	—
236	C₂²⋊C₄×C₃₇	—	4	2	no	—
237	C₂²⋊C₄×C₃₇	—	4	2	no	—
238	C₂²⋊C₄×C₃₇	—	4	2	no	—
239	C₂²⋊C₄×C₃₇	—	8	2	no	—
240	C₂²⋊C₄×C₃₇	—	8	2	no	—
241	C₂²⋊C₄×C₃₇	—	8	2	no	—
242	C₄²×C₃₇	—	2	1	no	—
243	C₄²×C₃₇	—	2	1	no	—
244	C₄²×C₃₇	—	2	1	no	—
245	C₄²×C₃₇	—	2	1	no	—
246	C₄²×C₃₇	—	4	2	no	—
247	C₄²×C₃₇	C₂×D₄	1	2	yes	—
248	C₄²×C₃₇	C₂×D₄	1	2	yes	—
249	C₂³×C₃₇	—	2	2	no	—
250	C₂³×C₃₇	—	4	1	no	—
251	C₂³×C₃₇	—	4	1	no	—
252	C₂³×C₃₇	—	4	2	no	—
253	C₂³×C₃₇	—	4	2	no	—
254	C₂³×C₃₇	—	4	1	no	—
255	C₂³×C₃₇	—	4	1	no	—
256	C₂³×C₃₇	—	4	1	no	—
257	C₂³×C₃₇	—	4	1	no	—
258	C₂³×C₃₇	—	4	1	no	—
259	C₂³×C₃₇	—	4	1	no	—
260	C₂³×C₃₇	—	4	1	no	—
261	C₂³×C₃₇	—	4	1	no	—
262	C₂³×C₃₇	—	4	1	no	—
263	C₂³×C₃₇	—	4	2	no	—
264	C₂³×C₃₇	—	4	2	no	—
265	C₂³×C₃₇	—	4	2	no	—
266	C₂³×C₃₇	—	4	2	no	—
267	C₂³×C₃₇	—	4	2	no	—
268	C₂³×C₃₇	—	4	2	no	—
269	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
270	Q₈×C₃₇	—	2	2	no	—
271	Q₈×C₃₇	—	2	2	no	—
272	Q₈×C₃₇	—	4	1	no	—
273	Q₈×C₃₇	—	4	1	no	—
274	Q₈×C₃₇	—	4	1	no	—
275	Q₈×C₃₇	—	4	1	no	—
276	Q₈×C₃₇	—	4	1	no	—
277	Q₈×C₃₇	—	4	1	no	—
278	D₄×C₃₇	—	2	2	no	—
279	D₄×C₃₇	—	2	2	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	—	4	1	no	—
287	D₄×C₃₇	—	4	1	no	—
288	D₄×C₃₇	—	4	1	no	—
289	D₄×C₃₇	—	4	1	no	—
290	D₄×C₃₇	—	4	1	no	—
291	D₄×C₃₇	—	4	1	no	—
292	D₄×C₃₇	—	4	1	no	—
293	D₄×C₃₇	—	4	1	no	—
294	D₄×C₃₇	—	8	4	no	—
295	D₄×C₃₇	—	8	4	no	—
296	D₄×C₃₇	—	8	8	no	—
297	C₂×C₄×C₃₇	—	2	2	no	—
298	C₂×C₄×C₃₇	—	2	2	no	—
299	C₂×C₄×C₃₇	—	2	2	no	—
300	C₂×C₄×C₃₇	—	2	2	no	—
301	C₂×C₄×C₃₇	—	2	2	no	—
302	C₂×C₄×C₃₇	—	2	2	no	—
303	C₂×C₄×C₃₇	—	2	2	no	—
304	C₂×C₄×C₃₇	—	2	2	no	—
305	C₂×C₄×C₃₇	—	2	2	no	—
306	C₂×C₄×C₃₇	—	4	1	no	—
307	C₂×C₄×C₃₇	—	4	1	no	—
308	C₂×C₄×C₃₇	—	4	1	no	—
309	C₂×C₄×C₃₇	—	4	1	no	—
310	C₂×C₄×C₃₇	—	4	1	no	—
311	C₂×C₄×C₃₇	—	4	1	no	—
312	C₂×C₄×C₃₇	—	4	1	no	—
313	C₂×C₄×C₃₇	—	4	2	no	—
314	C₂×C₄×C₃₇	—	4	2	no	—
315	C₂×C₄×C₃₇	—	8	4	no	—
316	C₂×C₄×C₃₇	#127	1	2	yes	—
317	C₂×C₄×C₃₇	#127	1	2	yes	—
318	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
322	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
323	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
324	C₈×C₃₇	—	2	2	no	—
325	C₈×C₃₇	—	2	2	no	—
326	C₈×C₃₇	—	2	2	no	—
327	C₈×C₃₇	#121	1	4	yes	—
328	#28474	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂²×C₃₇	—	4	4	no	—
330	C₂²×C₃₇	—	4	2	no	—
331	C₂²×C₃₇	—	8	2	no	—
332	C₂²×C₃₇	—	8	1	no	—
333	C₂²×C₃₇	—	8	1	no	—
334	C₂²×C₃₇	—	8	2	no	—
335	C₂²×C₃₇	—	8	2	no	—
336	C₂²×C₃₇	—	8	2	no	—
337	C₂²×C₃₇	—	8	1	no	—
338	C₂²×C₃₇	—	8	1	no	—
339	C₂²×C₃₇	—	8	1	no	—
340	C₂²×C₃₇	—	8	1	no	—
341	C₂²×C₃₇	—	8	1	no	—
342	C₂²×C₃₇	—	8	1	no	—
343	C₂²×C₃₇	—	8	2	no	—
344	C₂²×C₃₇	—	8	2	no	—
345	C₂²×C₃₇	—	8	2	no	—
346	C₂²×C₃₇	—	8	1	no	—
347	C₂²×C₃₇	—	8	1	no	—
348	C₂²×C₃₇	—	8	1	no	—
349	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
350	C₂²×C₃₇	D₄²	1	1	yes	characteristic
351	C₂²×C₃₇	#550	1	1	yes	characteristic
352	C₂²×C₃₇	#575	1	2	yes	—
353	C₂²×C₃₇	#576	1	2	yes	—
354	C₄×C₃₇	—	2	2	no	—
355	C₄×C₃₇	—	2	2	no	—
356	C₄×C₃₇	—	4	2	no	—
357	C₄×C₃₇	—	4	2	no	—
358	C₄×C₃₇	—	4	2	no	—
359	C₄×C₃₇	—	8	1	no	—
360	C₄×C₃₇	—	8	1	no	—
361	C₄×C₃₇	—	8	1	no	—
362	C₄×C₃₇	C₂×#121	1	1	yes	characteristic
363	C₄×C₃₇	#535	1	1	yes	characteristic
364	C₄×C₃₇	D₄²	1	1	yes	characteristic
365	C₄×C₃₇	#550	1	1	yes	characteristic
366	C₂×#496	C₂×C₃₇	1	1	yes	characteristic, complemented
367	C₂×#496	C₂×C₃₇	1	1	yes	characteristic, complemented
368	C₂×#495	C₂×C₃₇	1	1	yes	characteristic, complemented
369	C₂×#464	C₂×C₃₇	1	1	yes	characteristic, complemented
370	C₂×#459	C₂×C₃₇	1	1	yes	characteristic, complemented
371	C₂×#440	C₂×C₃₇	1	1	yes	characteristic, complemented
372	#2548	C₂×C₃₇	1	1	yes	characteristic, complemented
373	#2544	C₂×C₃₇	1	1	yes	characteristic, complemented
374	#2015	C₂×C₃₇	1	1	yes	characteristic, complemented
375	#2012	C₂×C₃₇	1	1	yes	characteristic, complemented
376	#2012	C₂×C₃₇	1	1	yes	characteristic, complemented
377	#2011	C₂×C₃₇	1	1	yes	characteristic, complemented
378	#1973	C₂×C₃₇	1	1	yes	characteristic, complemented
379	#1970	C₂×C₃₇	1	1	yes	characteristic, complemented
380	#1771	C₂×C₃₇	1	1	yes	characteristic, complemented
381	C₂×C₃₇	—	8	2	no	—
382	C₂×C₃₇	—	16	1	no	—
383	C₂×C₃₇	—	16	1	no	—
384	C₂×C₃₇	—	16	1	no	—
385	C₂×C₃₇	#2541	1	1	yes	characteristic
386	C₂×C₃₇	#3153	1	1	yes	characteristic
387	C₂×C₃₇	#3155	1	1	yes	characteristic
388	C₂×C₃₇	#3268	1	2	yes	—
389	C₂×C₃₇	#3403	1	2	yes	—
390	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
391	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
392	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
393	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
394	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
395	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
396	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
397	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
398	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
399	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
400	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
401	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
402	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
403	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
404	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
405	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
406	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
407	#496	—	2	4	no	—
408	#496	—	2	4	no	—
409	#495	—	2	4	no	—
410	#464	—	2	4	no	—
411	#459	—	2	4	no	—
412	#440	—	2	4	no	—
413	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
414	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
415	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
416	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
417	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
418	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
419	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
420	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
421	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
422	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
423	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
424	#394	—	2	2	no	—
425	#394	—	2	2	no	—
426	#391	C₂²×C₃₇	1	1	yes	characteristic
427	#390	—	2	2	no	—
428	#390	C₂²×C₃₇	1	1	yes	characteristic
429	#390	C₂²×C₃₇	1	1	yes	characteristic
430	#390	C₂²×C₃₇	1	1	yes	characteristic
431	#386	—	2	2	no	—
432	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
433	#336	C₂²×C₃₇	1	1	yes	characteristic
434	#336	C₂²×C₃₇	1	1	yes	characteristic
435	C₃₇	#28474	1	1	yes	characteristic, direct product factor, Sylow
436	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
437	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
438	C₂²×D₄	—	2	1	no	—
439	C₂²×D₄	—	2	2	no	—
440	C₂²×D₄	—	2	1	no	—
441	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
442	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
443	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
444	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
445	C₂³×C₄	—	2	1	no	—
446	C₂×Q₁₆	—	2	2	no	—
447	C₂×Q₁₆	—	2	2	no	—
448	C₂×Q₁₆	—	4	1	no	—
449	C₂×SD₁₆	—	2	2	no	—
450	C₂×SD₁₆	—	2	2	no	—
451	C₂×SD₁₆	—	2	2	no	—
452	C₂×SD₁₆	—	2	2	no	—
453	C₂×SD₁₆	—	2	2	no	—
454	C₂×SD₁₆	—	2	2	no	—
455	C₂×SD₁₆	—	2	2	no	—
456	C₂×SD₁₆	—	2	2	no	—
457	C₂×SD₁₆	—	4	1	no	—
458	C₂×SD₁₆	—	4	1	no	—
459	C₂×SD₁₆	—	4	1	no	—
460	C₂×SD₁₆	D₄×C₃₇	1	4	yes	complemented
461	C₂×D₈	—	2	2	no	—
462	C₂×D₈	—	2	2	no	—
463	C₂×D₈	—	2	2	no	—
464	C₂×D₈	—	2	2	no	—
465	C₂×D₈	—	2	2	no	—
466	C₂×D₈	—	2	2	no	—
467	C₂×D₈	—	2	2	no	—
468	C₂×D₈	—	2	2	no	—
469	C₂×D₈	—	4	1	no	—
470	C₂×D₈	—	4	1	no	—
471	C₂×D₈	—	4	1	no	—
472	C₂×D₈	—	4	1	no	—
473	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
475	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
476	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
477	#127	—	2	2	no	—
478	#127	—	2	2	no	—
479	#127	—	2	2	no	—
480	#127	—	4	1	no	—
481	#124	—	2	2	no	—
482	#124	—	2	2	no	—
483	#124	—	2	2	no	—
484	#124	—	2	2	no	—
485	#124	—	2	2	no	—
486	#124	—	4	1	no	—
487	#124	—	4	1	no	—
488	#124	—	4	1	no	—
489	C₄×Q₈	—	2	2	no	—
490	C₄×Q₈	—	2	2	no	—
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	—	2	2	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	2	no	—
500	C₂×C₂²⋊C₄	—	2	2	no	—
501	C₂×C₂²⋊C₄	—	2	2	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	—	2	2	no	—
504	C₂×C₂²⋊C₄	—	2	2	no	—
505	C₂×C₂²⋊C₄	—	2	2	no	—
506	C₂×C₄²	—	2	1	no	—
507	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
510	#107	—	2	2	no	—
511	C₄⋊C₈	D₄×C₃₇	1	4	yes	complemented
512	#103	—	2	2	no	—
513	#103	—	2	2	no	—
514	#102	—	2	2	no	—
515	#102	—	2	2	no	—
516	#102	—	2	2	no	—
517	#102	—	2	2	no	—
518	#97	—	2	2	no	—
519	#97	D₄×C₃₇	1	4	yes	complemented
520	C₄×C₈	—	2	2	no	—
521	#95	—	2	2	no	—
522	#95	D₄×C₃₇	1	2	yes	—
523	C₂⁴	—	2	1	no	—
524	C₂⁴	—	2	1	no	—
525	C₂⁴	—	2	1	no	—
526	C₂⁴	—	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	—	2	1	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	2	1	no	—
534	C₂×Q₈	—	2	1	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
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	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	4	4	no	—
563	C₂×D₄	—	4	4	no	—
564	C₂×D₄	—	4	4	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	4	2	no	—
567	C₂×D₄	—	8	2	no	—
568	C₂×D₄	—	8	2	no	—
569	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	4	2	no	—
575	C₂²×C₄	—	8	2	no	—
576	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
577	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
578	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
579	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
581	Q₁₆	—	4	4	no	—
582	SD₁₆	—	2	8	no	—
583	SD₁₆	—	4	4	no	—
584	SD₁₆	—	4	4	no	—
585	SD₁₆	—	4	4	no	—
586	D₈	—	4	4	no	—
587	D₈	—	4	4	no	—
588	D₈	—	4	4	no	—
589	D₈	—	4	4	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
597	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
598	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
599	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
600	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
601	C₂×C₈	#41×C₃₇	1	2	yes	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	4	2	no	—
607	C₄⋊C₄	—	4	2	no	—
608	C₂²⋊C₄	—	4	4	no	—
609	C₂²⋊C₄	—	4	4	no	—
610	C₂²⋊C₄	—	4	4	no	—
611	C₂²⋊C₄	—	4	2	no	—
612	C₂²⋊C₄	—	4	2	no	—
613	C₂²⋊C₄	—	4	2	no	—
614	C₂²⋊C₄	—	8	2	no	—
615	C₂²⋊C₄	—	8	2	no	—
616	C₂²⋊C₄	—	8	2	no	—
617	C₄²	—	2	1	no	—
618	C₄²	—	2	1	no	—
619	C₄²	—	2	1	no	—
620	C₄²	—	2	1	no	—
621	C₄²	—	4	2	no	—
622	C₄²	C₂×D₄×C₃₇	1	2	yes	—
623	C₄²	C₂×D₄×C₃₇	1	2	yes	—
624	C₂³	—	2	2	no	—
625	C₂³	—	4	1	no	—
626	C₂³	—	4	1	no	—
627	C₂³	—	4	2	no	—
628	C₂³	—	4	2	no	—
629	C₂³	—	4	1	no	—
630	C₂³	—	4	1	no	—
631	C₂³	—	4	1	no	—
632	C₂³	—	4	1	no	—
633	C₂³	—	4	1	no	—
634	C₂³	—	4	1	no	—
635	C₂³	—	4	1	no	—
636	C₂³	—	4	1	no	—
637	C₂³	—	4	1	no	—
638	C₂³	—	4	2	no	—
639	C₂³	—	4	2	no	—
640	C₂³	—	4	2	no	—
641	C₂³	—	4	2	no	—
642	C₂³	—	4	2	no	—
643	C₂³	—	4	2	no	—
644	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
645	Q₈	—	2	2	no	—
646	Q₈	—	2	2	no	—
647	Q₈	—	4	1	no	—
648	Q₈	—	4	1	no	—
649	Q₈	—	4	1	no	—
650	Q₈	—	4	1	no	—
651	Q₈	—	4	1	no	—
652	Q₈	—	4	1	no	—
653	D₄	—	2	2	no	—
654	D₄	—	2	2	no	—
655	D₄	—	4	1	no	—
656	D₄	—	4	1	no	—
657	D₄	—	4	1	no	—
658	D₄	—	4	1	no	—
659	D₄	—	4	1	no	—
660	D₄	—	4	1	no	—
661	D₄	—	4	1	no	—
662	D₄	—	4	1	no	—
663	D₄	—	4	1	no	—
664	D₄	—	4	1	no	—
665	D₄	—	4	1	no	—
666	D₄	—	4	1	no	—
667	D₄	—	4	1	no	—
668	D₄	—	4	1	no	—
669	D₄	—	8	4	no	—
670	D₄	—	8	4	no	—
671	D₄	—	8	8	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	2	no	—
689	C₂×C₄	—	4	2	no	—
690	C₂×C₄	—	8	4	no	—
691	C₂×C₄	#127×C₃₇	1	2	yes	—
692	C₂×C₄	#127×C₃₇	1	2	yes	—
693	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
694	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
695	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
696	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
697	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
698	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
699	C₈	—	2	2	no	—
700	C₈	—	2	2	no	—
701	C₈	—	2	2	no	—
702	C₈	#121×C₃₇	1	4	yes	—
703	C₂²	—	4	4	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	8	2	no	—
706	C₂²	—	8	1	no	—
707	C₂²	—	8	1	no	—
708	C₂²	—	8	2	no	—
709	C₂²	—	8	2	no	—
710	C₂²	—	8	2	no	—
711	C₂²	—	8	1	no	—
712	C₂²	—	8	1	no	—
713	C₂²	—	8	1	no	—
714	C₂²	—	8	1	no	—
715	C₂²	—	8	1	no	—
716	C₂²	—	8	1	no	—
717	C₂²	—	8	2	no	—
718	C₂²	—	8	2	no	—
719	C₂²	—	8	2	no	—
720	C₂²	—	8	1	no	—
721	C₂²	—	8	1	no	—
722	C₂²	—	8	1	no	—
723	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
724	C₂²	D₄²×C₃₇	1	1	yes	characteristic
725	C₂²	C₃₇×#550	1	1	yes	characteristic
726	C₂²	C₃₇×#575	1	2	yes	—
727	C₂²	C₃₇×#576	1	2	yes	—
728	C₄	—	2	2	no	—
729	C₄	—	2	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	8	1	no	—
734	C₄	—	8	1	no	—
735	C₄	—	8	1	no	—
736	C₄	C₂×#121×C₃₇	1	1	yes	characteristic
737	C₄	C₃₇×#535	1	1	yes	characteristic
738	C₄	D₄²×C₃₇	1	1	yes	characteristic
739	C₄	C₃₇×#550	1	1	yes	characteristic
740	C₂	—	8	2	no	—
741	C₂	—	16	1	no	—
742	C₂	—	16	1	no	—
743	C₂	—	16	1	no	—
744	C₂	C₃₇×#2541	1	1	yes	characteristic
745	C₂	C₃₇×#3153	1	1	yes	characteristic
746	C₂	C₃₇×#3155	1	1	yes	characteristic
747	C₂	C₃₇×#3268	1	2	yes	—
748	C₂	C₃₇×#3403	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×C₄⋊C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#496	C₂	semidirect
2. C₂×C₃₇×#496	C₂	semidirect
3. C₂×C₃₇×#495	C₂	semidirect
4. C₂×C₃₇×#464	C₂	semidirect
5. C₂×C₃₇×#459	C₂	semidirect
6. C₂×C₃₇×#440	C₂	semidirect
7. C₃₇×#2548	C₂	semidirect
8. C₃₇×#2544	C₂	semidirect
9. C₃₇×#2015	C₂	semidirect
10. C₃₇×#2012	C₂	semidirect
11. C₃₇×#2012	C₂	semidirect
12. C₃₇×#2011	C₂	semidirect
13. C₃₇×#1973	C₂	semidirect
14. C₃₇×#1970	C₂	semidirect
15. C₃₇×#1771	C₂	semidirect
85. C₂×SD₁₆×C₃₇	D₄	semidirect
136. C₄⋊C₈×C₃₇	D₄	semidirect
144. #97×C₃₇	D₄	semidirect
328. #28474	C₃₇	direct (N × H)
366. C₂×#496	C₂×C₃₇	semidirect
367. C₂×#496	C₂×C₃₇	semidirect
368. C₂×#495	C₂×C₃₇	semidirect
369. C₂×#464	C₂×C₃₇	semidirect
370. C₂×#459	C₂×C₃₇	semidirect
371. C₂×#440	C₂×C₃₇	semidirect
372. #2548	C₂×C₃₇	semidirect
373. #2544	C₂×C₃₇	semidirect
374. #2015	C₂×C₃₇	semidirect
375. #2012	C₂×C₃₇	semidirect
376. #2012	C₂×C₃₇	semidirect
377. #2011	C₂×C₃₇	semidirect
378. #1973	C₂×C₃₇	semidirect
379. #1970	C₂×C₃₇	semidirect
380. #1771	C₂×C₃₇	semidirect
435. C₃₇	#28474	direct (N × H)
460. C₂×SD₁₆	D₄×C₃₇	semidirect
511. C₄⋊C₈	D₄×C₃₇	semidirect
519. #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×#496	2
C₂×C₃₇×#495	2
C₂×C₃₇×#464	2
C₂×C₃₇×#459	2
C₂×C₃₇×#440	2
C₃₇×#2548	2
C₃₇×#2544	2
C₃₇×#2015	2
C₃₇×#2012	2
C₃₇×#2011	2
C₃₇×#1973	2
C₃₇×#1970	2
C₃₇×#1771	2
#28474	37

Subgroups — C37×#28474 #22649727

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28474 #22649727