Subgroups — C₃₇×#28321 #22649574

Order 9472.

1200 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#485	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#450	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#447	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2620	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2309	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2094	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2093	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#2012	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#2012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#1972	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₇×#1970	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#1968	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₇×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×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	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
21	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×#121×C₃₇	C₂²	1	1	yes	characteristic
24	C₂×#117×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×#117×C₃₇	C₂²	1	1	yes	characteristic
26	C₃₇×#485	—	2	4	no	—
27	C₃₇×#482	—	2	4	no	—
28	C₃₇×#450	—	2	4	no	—
29	C₃₇×#447	—	2	4	no	—
30	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic, complemented
31	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic, complemented
32	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic, complemented
33	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic, complemented
34	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic, complemented
35	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic, complemented
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, complemented
41	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₂²⋊C₈×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, complemented
45	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
46	C₃₇×#396	—	2	2	no	—
47	C₃₇×#394	—	2	2	no	—
48	C₃₇×#391	C₂²	1	1	yes	characteristic, complemented
49	C₃₇×#390	—	2	2	no	—
50	C₃₇×#390	C₂²	1	1	yes	characteristic
51	C₃₇×#390	C₂²	1	1	yes	characteristic
52	C₃₇×#390	C₂²	1	1	yes	characteristic
53	C₃₇×#390	C₂²	1	1	yes	characteristic
54	C₃₇×#390	C₂²	1	1	yes	characteristic, complemented
55	C₃₇×#384	C₂²	1	1	yes	characteristic, complemented
56	C₃₇×#379	—	2	2	no	—
57	C₃₇×#336	C₂²	1	1	yes	characteristic, complemented
58	C₃₇×#336	C₂²	1	1	yes	characteristic, complemented
59	C₂⁵×C₃₇	—	2	1	no	—
60	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₃₇	—	2	2	no	—
62	C₂²×D₄×C₃₇	—	2	2	no	—
63	C₂²×D₄×C₃₇	—	2	1	no	—
64	C₂²×D₄×C₃₇	—	2	1	no	—
65	C₂²×D₄×C₃₇	—	2	2	no	—
66	C₂²×D₄×C₃₇	—	2	2	no	—
67	C₂²×D₄×C₃₇	—	4	1	no	—
68	C₂²×D₄×C₃₇	—	4	1	no	—
69	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
73	C₂×SD₁₆×C₃₇	—	2	2	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	—	4	1	no	—
78	C₂×SD₁₆×C₃₇	—	4	1	no	—
79	C₂×D₈×C₃₇	—	2	2	no	—
80	C₂×D₈×C₃₇	—	2	2	no	—
81	C₂×D₈×C₃₇	—	2	2	no	—
82	C₂×D₈×C₃₇	—	2	2	no	—
83	C₂×D₈×C₃₇	—	4	1	no	—
84	C₂×D₈×C₃₇	—	4	1	no	—
85	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
89	#124×C₃₇	—	4	1	no	—
90	#124×C₃₇	—	4	1	no	—
91	C₂²⋊Q₈×C₃₇	—	2	2	no	—
92	C₂²⋊Q₈×C₃₇	—	2	2	no	—
93	#121×C₃₇	—	2	2	no	—
94	#121×C₃₇	—	2	2	no	—
95	#117×C₃₇	—	2	2	no	—
96	#117×C₃₇	—	2	2	no	—
97	#117×C₃₇	—	4	1	no	—
98	#117×C₃₇	—	4	1	no	—
99	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
100	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
101	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
102	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₃₇	—	2	1	no	—
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	—	2	2	no	—
112	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
113	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
114	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
115	C₂×C₂²⋊C₄×C₃₇	D₄	1	2	yes	—
116	C₂×C₄²×C₃₇	—	2	1	no	—
117	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
119	#107×C₃₇	—	2	2	no	—
120	#107×C₃₇	—	2	2	no	—
121	#106×C₃₇	—	2	2	no	—
122	#106×C₃₇	—	2	2	no	—
123	#103×C₃₇	—	2	2	no	—
124	#103×C₃₇	—	2	2	no	—
125	#102×C₃₇	—	2	2	no	—
126	#102×C₃₇	—	2	2	no	—
127	#102×C₃₇	—	2	2	no	—
128	#102×C₃₇	—	2	2	no	—
129	#102×C₃₇	—	2	2	no	—
130	#102×C₃₇	—	2	2	no	—
131	C₂²⋊C₈×C₃₇	D₄	1	4	yes	—
132	C₂²⋊C₈×C₃₇	D₄	1	4	yes	—
133	#97×C₃₇	—	4	1	no	—
134	C₄×C₈×C₃₇	—	4	1	no	—
135	#95×C₃₇	—	2	2	no	—
136	C₂⁴×C₃₇	—	2	4	no	—
137	C₂⁴×C₃₇	—	2	1	no	—
138	C₂⁴×C₃₇	—	2	1	no	—
139	C₂⁴×C₃₇	—	2	1	no	—
140	C₂⁴×C₃₇	—	4	2	no	—
141	C₂⁴×C₃₇	—	4	2	no	—
142	C₂⁴×C₃₇	—	8	2	no	—
143	C₂⁴×C₃₇	—	8	2	no	—
144	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
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×D₄×C₃₇	—	2	4	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	—	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	—	2	1	no	—
167	C₂×D₄×C₃₇	—	2	1	no	—
168	C₂×D₄×C₃₇	—	4	4	no	—
169	C₂×D₄×C₃₇	—	4	4	no	—
170	C₂×D₄×C₃₇	—	4	4	no	—
171	C₂×D₄×C₃₇	—	4	4	no	—
172	C₂×D₄×C₃₇	—	4	2	no	—
173	C₂×D₄×C₃₇	—	4	2	no	—
174	C₂×D₄×C₃₇	—	4	2	no	—
175	C₂×D₄×C₃₇	—	8	2	no	—
176	C₂×D₄×C₃₇	#41	1	2	yes	—
177	C₂×D₄×C₃₇	#41	1	2	yes	—
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	—	2	1	no	—
186	C₂²×C₄×C₃₇	—	2	1	no	—
187	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
189	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
192	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
193	SD₁₆×C₃₇	—	4	4	no	—
194	SD₁₆×C₃₇	—	4	4	no	—
195	D₈×C₃₇	—	4	4	no	—
196	D₈×C₃₇	—	4	4	no	—
197	C₂×C₈×C₃₇	—	2	1	no	—
198	C₂×C₈×C₃₇	—	2	1	no	—
199	C₂×C₈×C₃₇	—	2	1	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	C₂×D₄	1	2	yes	—
206	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
207	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
208	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
209	C₄⋊C₄×C₃₇	—	2	1	no	—
210	C₄⋊C₄×C₃₇	—	2	1	no	—
211	C₄⋊C₄×C₃₇	—	2	1	no	—
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	—	4	2	no	—
218	C₄⋊C₄×C₃₇	—	4	2	no	—
219	C₄⋊C₄×C₃₇	—	8	2	no	—
220	C₂²⋊C₄×C₃₇	—	4	2	no	—
221	C₂²⋊C₄×C₃₇	—	4	4	no	—
222	C₂²⋊C₄×C₃₇	—	4	2	no	—
223	C₂²⋊C₄×C₃₇	—	4	2	no	—
224	C₂²⋊C₄×C₃₇	—	4	2	no	—
225	C₂²⋊C₄×C₃₇	—	8	2	no	—
226	C₂²⋊C₄×C₃₇	—	8	2	no	—
227	C₂²⋊C₄×C₃₇	—	8	2	no	—
228	C₂²⋊C₄×C₃₇	—	8	2	no	—
229	C₂²⋊C₄×C₃₇	—	8	2	no	—
230	C₄²×C₃₇	—	2	1	no	—
231	C₄²×C₃₇	—	2	1	no	—
232	C₄²×C₃₇	—	2	1	no	—
233	C₄²×C₃₇	—	2	1	no	—
234	C₄²×C₃₇	—	4	2	no	—
235	C₂³×C₃₇	—	2	1	no	—
236	C₂³×C₃₇	—	2	1	no	—
237	C₂³×C₃₇	—	2	2	no	—
238	C₂³×C₃₇	—	2	2	no	—
239	C₂³×C₃₇	—	2	2	no	—
240	C₂³×C₃₇	—	2	2	no	—
241	C₂³×C₃₇	—	4	8	no	—
242	C₂³×C₃₇	—	4	1	no	—
243	C₂³×C₃₇	—	4	1	no	—
244	C₂³×C₃₇	—	4	1	no	—
245	C₂³×C₃₇	—	4	1	no	—
246	C₂³×C₃₇	—	4	2	no	—
247	C₂³×C₃₇	—	4	2	no	—
248	C₂³×C₃₇	—	4	2	no	—
249	C₂³×C₃₇	—	4	2	no	—
250	C₂³×C₃₇	—	4	1	no	—
251	C₂³×C₃₇	—	4	1	no	—
252	C₂³×C₃₇	—	4	1	no	—
253	C₂³×C₃₇	—	4	2	no	—
254	C₂³×C₃₇	—	4	2	no	—
255	C₂³×C₃₇	—	8	4	no	—
256	C₂³×C₃₇	—	8	4	no	—
257	C₂³×C₃₇	—	8	8	no	—
258	C₂³×C₃₇	—	8	8	no	—
259	C₂³×C₃₇	#127	1	2	yes	—
260	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
261	Q₈×C₃₇	—	4	1	no	—
262	Q₈×C₃₇	—	4	1	no	—
263	Q₈×C₃₇	—	4	1	no	—
264	Q₈×C₃₇	—	4	1	no	—
265	D₄×C₃₇	—	2	2	no	—
266	D₄×C₃₇	—	2	2	no	—
267	D₄×C₃₇	—	2	2	no	—
268	D₄×C₃₇	—	2	2	no	—
269	D₄×C₃₇	—	4	8	no	—
270	D₄×C₃₇	—	4	1	no	—
271	D₄×C₃₇	—	4	1	no	—
272	D₄×C₃₇	—	4	1	no	—
273	D₄×C₃₇	—	4	1	no	—
274	D₄×C₃₇	—	4	1	no	—
275	D₄×C₃₇	—	4	1	no	—
276	D₄×C₃₇	—	4	1	no	—
277	D₄×C₃₇	—	4	1	no	—
278	D₄×C₃₇	—	8	4	no	—
279	C₂×C₄×C₃₇	—	2	1	no	—
280	C₂×C₄×C₃₇	—	2	1	no	—
281	C₂×C₄×C₃₇	—	2	2	no	—
282	C₂×C₄×C₃₇	—	2	2	no	—
283	C₂×C₄×C₃₇	—	2	2	no	—
284	C₂×C₄×C₃₇	—	2	2	no	—
285	C₂×C₄×C₃₇	—	2	2	no	—
286	C₂×C₄×C₃₇	—	2	2	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	—	4	1	no	—
292	C₂×C₄×C₃₇	—	4	1	no	—
293	C₂×C₄×C₃₇	—	4	1	no	—
294	C₂×C₄×C₃₇	—	4	1	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	2	no	—
299	C₂×C₄×C₃₇	—	4	2	no	—
300	C₂×C₄×C₃₇	—	4	2	no	—
301	C₂×C₄×C₃₇	—	4	2	no	—
302	C₂×C₄×C₃₇	#127	1	2	yes	—
303	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
306	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
307	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
308	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
309	C₈×C₃₇	—	2	2	no	—
310	C₈×C₃₇	—	2	2	no	—
311	C₈×C₃₇	—	2	2	no	—
312	C₈×C₃₇	—	2	2	no	—
313	#28321	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
314	C₂²×C₃₇	—	2	2	no	—
315	C₂²×C₃₇	—	2	2	no	—
316	C₂²×C₃₇	—	2	2	no	—
317	C₂²×C₃₇	—	4	2	no	—
318	C₂²×C₃₇	—	4	2	no	—
319	C₂²×C₃₇	—	4	4	no	—
320	C₂²×C₃₇	—	4	4	no	—
321	C₂²×C₃₇	—	4	2	no	—
322	C₂²×C₃₇	—	4	2	no	—
323	C₂²×C₃₇	—	8	16	no	—
324	C₂²×C₃₇	—	8	1	no	—
325	C₂²×C₃₇	—	8	1	no	—
326	C₂²×C₃₇	—	8	1	no	—
327	C₂²×C₃₇	—	8	1	no	—
328	C₂²×C₃₇	—	8	2	no	—
329	C₂²×C₃₇	—	8	2	no	—
330	C₂²×C₃₇	—	8	2	no	—
331	C₂²×C₃₇	—	8	1	no	—
332	C₂²×C₃₇	—	8	1	no	—
333	C₂²×C₃₇	—	8	2	no	—
334	C₂²×C₃₇	—	8	1	no	—
335	C₂²×C₃₇	#525	1	1	yes	characteristic
336	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
337	C₂²×C₃₇	#534	1	1	yes	characteristic
338	C₂²×C₃₇	#576	1	2	yes	—
339	C₂²×C₃₇	#577	1	2	yes	—
340	C₄×C₃₇	—	2	2	no	—
341	C₄×C₃₇	—	4	2	no	—
342	C₄×C₃₇	—	4	2	no	—
343	C₄×C₃₇	—	8	1	no	—
344	C₄×C₃₇	—	8	1	no	—
345	C₄×C₃₇	—	8	1	no	—
346	C₄×C₃₇	—	8	1	no	—
347	C₄×C₃₇	—	8	1	no	—
348	C₄×C₃₇	#546	1	1	yes	characteristic
349	C₄×C₃₇	#546	1	1	yes	characteristic
350	C₄×C₃₇	#546	1	1	yes	characteristic
351	C₄×C₃₇	#546	1	1	yes	characteristic
352	C₂×#485	C₂×C₃₇	1	1	yes	characteristic, complemented
353	C₂×#482	C₂×C₃₇	1	1	yes	characteristic, complemented
354	C₂×#450	C₂×C₃₇	1	1	yes	characteristic, complemented
355	C₂×#447	C₂×C₃₇	1	1	yes	characteristic
356	#2620	C₂×C₃₇	1	1	yes	characteristic, complemented
357	#2309	C₂×C₃₇	1	1	yes	characteristic, complemented
358	#2094	C₂×C₃₇	1	1	yes	characteristic, complemented
359	#2093	C₂×C₃₇	1	1	yes	characteristic, complemented
360	#2012	C₂×C₃₇	1	1	yes	characteristic, complemented
361	#2012	C₂×C₃₇	1	1	yes	characteristic, complemented
362	#1973	C₂×C₃₇	1	1	yes	characteristic, complemented
363	#1972	C₂×C₃₇	1	1	yes	characteristic, complemented
364	#1970	C₂×C₃₇	1	1	yes	characteristic, complemented
365	#1968	C₂×C₃₇	1	1	yes	characteristic, complemented
366	#1750	C₂×C₃₇	1	1	yes	characteristic, complemented
367	C₂×C₃₇	—	4	2	no	—
368	C₂×C₃₇	—	8	2	no	—
369	C₂×C₃₇	—	8	2	no	—
370	C₂×C₃₇	—	16	1	no	—
371	C₂×C₃₇	#2539	1	1	yes	characteristic
372	C₂×C₃₇	#3118	1	2	yes	—
373	C₂×C₃₇	#3154	1	1	yes	characteristic
374	C₂×C₃₇	#3155	1	1	yes	characteristic
375	C₂×C₃₇	#3198	1	2	yes	—
376	C₂³×D₄	C₂²×C₃₇	1	1	yes	characteristic
377	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
378	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
379	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
380	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
381	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic, complemented
382	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
383	C₂×#121	C₂²×C₃₇	1	1	yes	characteristic
384	C₂×#117	C₂²×C₃₇	1	1	yes	characteristic
385	C₂×#117	C₂²×C₃₇	1	1	yes	characteristic
386	#485	—	2	4	no	—
387	#482	—	2	4	no	—
388	#450	—	2	4	no	—
389	#447	—	2	4	no	—
390	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic, complemented
391	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic, complemented
392	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic, complemented
393	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic, complemented
394	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic, complemented
395	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic, complemented
396	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
397	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
398	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
399	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
400	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic, complemented
401	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic, complemented
402	C₂×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
403	C₂×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
404	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic, complemented
405	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic, complemented
406	#396	—	2	2	no	—
407	#394	—	2	2	no	—
408	#391	C₂²×C₃₇	1	1	yes	characteristic, complemented
409	#390	—	2	2	no	—
410	#390	C₂²×C₃₇	1	1	yes	characteristic
411	#390	C₂²×C₃₇	1	1	yes	characteristic
412	#390	C₂²×C₃₇	1	1	yes	characteristic
413	#390	C₂²×C₃₇	1	1	yes	characteristic
414	#390	C₂²×C₃₇	1	1	yes	characteristic, complemented
415	#384	C₂²×C₃₇	1	1	yes	characteristic, complemented
416	#379	—	2	2	no	—
417	#336	C₂²×C₃₇	1	1	yes	characteristic, complemented
418	#336	C₂²×C₃₇	1	1	yes	characteristic, complemented
419	C₃₇	#28321	1	1	yes	characteristic, direct product factor, Sylow
420	C₂⁵	—	2	1	no	—
421	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
422	C₂²×D₄	—	2	2	no	—
423	C₂²×D₄	—	2	2	no	—
424	C₂²×D₄	—	2	1	no	—
425	C₂²×D₄	—	2	1	no	—
426	C₂²×D₄	—	2	2	no	—
427	C₂²×D₄	—	2	2	no	—
428	C₂²×D₄	—	4	1	no	—
429	C₂²×D₄	—	4	1	no	—
430	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
431	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
432	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
433	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
434	C₂×SD₁₆	—	2	2	no	—
435	C₂×SD₁₆	—	2	2	no	—
436	C₂×SD₁₆	—	2	2	no	—
437	C₂×SD₁₆	—	2	2	no	—
438	C₂×SD₁₆	—	4	1	no	—
439	C₂×SD₁₆	—	4	1	no	—
440	C₂×D₈	—	2	2	no	—
441	C₂×D₈	—	2	2	no	—
442	C₂×D₈	—	2	2	no	—
443	C₂×D₈	—	2	2	no	—
444	C₂×D₈	—	4	1	no	—
445	C₂×D₈	—	4	1	no	—
446	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
447	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
448	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
449	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
450	#124	—	4	1	no	—
451	#124	—	4	1	no	—
452	C₂²⋊Q₈	—	2	2	no	—
453	C₂²⋊Q₈	—	2	2	no	—
454	#121	—	2	2	no	—
455	#121	—	2	2	no	—
456	#117	—	2	2	no	—
457	#117	—	2	2	no	—
458	#117	—	4	1	no	—
459	#117	—	4	1	no	—
460	C₂×C₄⋊C₄	—	2	1	no	—
461	C₂×C₄⋊C₄	—	2	2	no	—
462	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₂²⋊C₄	—	2	1	no	—
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₂²⋊C₄	—	2	2	no	—
471	C₂×C₂²⋊C₄	—	2	2	no	—
472	C₂×C₂²⋊C₄	—	2	2	no	—
473	C₂×C₂²⋊C₄	—	2	2	no	—
474	C₂×C₂²⋊C₄	—	2	2	no	—
475	C₂×C₂²⋊C₄	—	2	2	no	—
476	C₂×C₂²⋊C₄	D₄×C₃₇	1	2	yes	—
477	C₂×C₄²	—	2	1	no	—
478	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
479	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
480	#107	—	2	2	no	—
481	#107	—	2	2	no	—
482	#106	—	2	2	no	—
483	#106	—	2	2	no	—
484	#103	—	2	2	no	—
485	#103	—	2	2	no	—
486	#102	—	2	2	no	—
487	#102	—	2	2	no	—
488	#102	—	2	2	no	—
489	#102	—	2	2	no	—
490	#102	—	2	2	no	—
491	#102	—	2	2	no	—
492	C₂²⋊C₈	D₄×C₃₇	1	4	yes	—
493	C₂²⋊C₈	D₄×C₃₇	1	4	yes	—
494	#97	—	4	1	no	—
495	C₄×C₈	—	4	1	no	—
496	#95	—	2	2	no	—
497	C₂⁴	—	2	4	no	—
498	C₂⁴	—	2	1	no	—
499	C₂⁴	—	2	1	no	—
500	C₂⁴	—	2	1	no	—
501	C₂⁴	—	4	2	no	—
502	C₂⁴	—	4	2	no	—
503	C₂⁴	—	8	2	no	—
504	C₂⁴	—	8	2	no	—
505	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	2	1	no	—
527	C₂×D₄	—	2	1	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	4	4	no	—
530	C₂×D₄	—	4	4	no	—
531	C₂×D₄	—	4	4	no	—
532	C₂×D₄	—	4	4	no	—
533	C₂×D₄	—	4	2	no	—
534	C₂×D₄	—	4	2	no	—
535	C₂×D₄	—	4	2	no	—
536	C₂×D₄	—	8	2	no	—
537	C₂×D₄	#41×C₃₇	1	2	yes	—
538	C₂×D₄	#41×C₃₇	1	2	yes	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
549	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
550	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
551	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
552	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
554	SD₁₆	—	4	4	no	—
555	SD₁₆	—	4	4	no	—
556	D₈	—	4	4	no	—
557	D₈	—	4	4	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
567	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
568	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
569	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	4	2	no	—
579	C₄⋊C₄	—	4	2	no	—
580	C₄⋊C₄	—	8	2	no	—
581	C₂²⋊C₄	—	4	2	no	—
582	C₂²⋊C₄	—	4	4	no	—
583	C₂²⋊C₄	—	4	2	no	—
584	C₂²⋊C₄	—	4	2	no	—
585	C₂²⋊C₄	—	4	2	no	—
586	C₂²⋊C₄	—	8	2	no	—
587	C₂²⋊C₄	—	8	2	no	—
588	C₂²⋊C₄	—	8	2	no	—
589	C₂²⋊C₄	—	8	2	no	—
590	C₂²⋊C₄	—	8	2	no	—
591	C₄²	—	2	1	no	—
592	C₄²	—	2	1	no	—
593	C₄²	—	2	1	no	—
594	C₄²	—	2	1	no	—
595	C₄²	—	4	2	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	4	8	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	2	no	—
608	C₂³	—	4	2	no	—
609	C₂³	—	4	2	no	—
610	C₂³	—	4	2	no	—
611	C₂³	—	4	1	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	2	no	—
615	C₂³	—	4	2	no	—
616	C₂³	—	8	4	no	—
617	C₂³	—	8	4	no	—
618	C₂³	—	8	8	no	—
619	C₂³	—	8	8	no	—
620	C₂³	#127×C₃₇	1	2	yes	—
621	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
622	Q₈	—	4	1	no	—
623	Q₈	—	4	1	no	—
624	Q₈	—	4	1	no	—
625	Q₈	—	4	1	no	—
626	D₄	—	2	2	no	—
627	D₄	—	2	2	no	—
628	D₄	—	2	2	no	—
629	D₄	—	2	2	no	—
630	D₄	—	4	8	no	—
631	D₄	—	4	1	no	—
632	D₄	—	4	1	no	—
633	D₄	—	4	1	no	—
634	D₄	—	4	1	no	—
635	D₄	—	4	1	no	—
636	D₄	—	4	1	no	—
637	D₄	—	4	1	no	—
638	D₄	—	4	1	no	—
639	D₄	—	8	4	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	2	no	—
660	C₂×C₄	—	4	2	no	—
661	C₂×C₄	—	4	2	no	—
662	C₂×C₄	—	4	2	no	—
663	C₂×C₄	#127×C₃₇	1	2	yes	—
664	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
665	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
666	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
667	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
668	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
669	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
670	C₈	—	2	2	no	—
671	C₈	—	2	2	no	—
672	C₈	—	2	2	no	—
673	C₈	—	2	2	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	4	2	no	—
678	C₂²	—	4	2	no	—
679	C₂²	—	4	4	no	—
680	C₂²	—	4	4	no	—
681	C₂²	—	4	2	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	8	16	no	—
684	C₂²	—	8	1	no	—
685	C₂²	—	8	1	no	—
686	C₂²	—	8	1	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	8	2	no	—
689	C₂²	—	8	2	no	—
690	C₂²	—	8	2	no	—
691	C₂²	—	8	1	no	—
692	C₂²	—	8	1	no	—
693	C₂²	—	8	2	no	—
694	C₂²	—	8	1	no	—
695	C₂²	C₃₇×#525	1	1	yes	characteristic
696	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
697	C₂²	C₃₇×#534	1	1	yes	characteristic
698	C₂²	C₃₇×#576	1	2	yes	—
699	C₂²	C₃₇×#577	1	2	yes	—
700	C₄	—	2	2	no	—
701	C₄	—	4	2	no	—
702	C₄	—	4	2	no	—
703	C₄	—	8	1	no	—
704	C₄	—	8	1	no	—
705	C₄	—	8	1	no	—
706	C₄	—	8	1	no	—
707	C₄	—	8	1	no	—
708	C₄	C₃₇×#546	1	1	yes	characteristic
709	C₄	C₃₇×#546	1	1	yes	characteristic
710	C₄	C₃₇×#546	1	1	yes	characteristic
711	C₄	C₃₇×#546	1	1	yes	characteristic
712	C₂	—	4	2	no	—
713	C₂	—	8	2	no	—
714	C₂	—	8	2	no	—
715	C₂	—	16	1	no	—
716	C₂	C₃₇×#2539	1	1	yes	characteristic
717	C₂	C₃₇×#3118	1	2	yes	—
718	C₂	C₃₇×#3154	1	1	yes	characteristic
719	C₂	C₃₇×#3155	1	1	yes	characteristic
720	C₂	C₃₇×#3198	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×C₃₇×#447	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂×#117×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#485	C₂	semidirect
2. C₂×C₃₇×#482	C₂	semidirect
3. C₂×C₃₇×#450	C₂	semidirect
5. C₃₇×#2620	C₂	semidirect
6. C₃₇×#2309	C₂	semidirect
7. C₃₇×#2094	C₂	semidirect
8. C₃₇×#2093	C₂	semidirect
9. C₃₇×#2012	C₂	semidirect
10. C₃₇×#2012	C₂	semidirect
11. C₃₇×#1973	C₂	semidirect
12. C₃₇×#1972	C₂	semidirect
13. C₃₇×#1970	C₂	semidirect
14. C₃₇×#1968	C₂	semidirect
15. C₃₇×#1750	C₂	semidirect
21. C₂×#124×C₃₇	C₂²	semidirect
30. C₂×#107×C₃₇	C₂²	semidirect
31. C₂×#107×C₃₇	C₂²	semidirect
32. C₂×#106×C₃₇	C₂²	semidirect
33. C₂×#106×C₃₇	C₂²	semidirect
34. C₂×#103×C₃₇	C₂²	semidirect
35. C₂×#103×C₃₇	C₂²	semidirect
40. C₂×#102×C₃₇	C₂²	semidirect
41. C₂×#102×C₃₇	C₂²	semidirect
44. C₂×#97×C₃₇	C₂²	semidirect
45. C₂×C₄×C₈×C₃₇	C₂²	semidirect
48. C₃₇×#391	C₂²	semidirect
54. C₃₇×#390	C₂²	semidirect
55. C₃₇×#384	C₂²	semidirect
57. C₃₇×#336	C₂²	semidirect
58. C₃₇×#336	C₂²	semidirect
313. #28321	C₃₇	direct (N × H)
352. C₂×#485	C₂×C₃₇	semidirect
353. C₂×#482	C₂×C₃₇	semidirect
354. C₂×#450	C₂×C₃₇	semidirect
356. #2620	C₂×C₃₇	semidirect
357. #2309	C₂×C₃₇	semidirect
358. #2094	C₂×C₃₇	semidirect
359. #2093	C₂×C₃₇	semidirect
360. #2012	C₂×C₃₇	semidirect
361. #2012	C₂×C₃₇	semidirect
362. #1973	C₂×C₃₇	semidirect
363. #1972	C₂×C₃₇	semidirect
364. #1970	C₂×C₃₇	semidirect
365. #1968	C₂×C₃₇	semidirect
366. #1750	C₂×C₃₇	semidirect
381. C₂×#124	C₂²×C₃₇	semidirect
390. C₂×#107	C₂²×C₃₇	semidirect
391. C₂×#107	C₂²×C₃₇	semidirect
392. C₂×#106	C₂²×C₃₇	semidirect
393. C₂×#106	C₂²×C₃₇	semidirect
394. C₂×#103	C₂²×C₃₇	semidirect
395. C₂×#103	C₂²×C₃₇	semidirect
400. C₂×#102	C₂²×C₃₇	semidirect
401. C₂×#102	C₂²×C₃₇	semidirect
404. C₂×#97	C₂²×C₃₇	semidirect
405. C₂×C₄×C₈	C₂²×C₃₇	semidirect
408. #391	C₂²×C₃₇	semidirect
414. #390	C₂²×C₃₇	semidirect
415. #384	C₂²×C₃₇	semidirect
417. #336	C₂²×C₃₇	semidirect
418. #336	C₂²×C₃₇	semidirect
419. C₃₇	#28321	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×#485	2
C₂×C₃₇×#482	2
C₂×C₃₇×#450	2
C₂×C₃₇×#447	2
C₃₇×#2620	2
C₃₇×#2309	2
C₃₇×#2094	2
C₃₇×#2093	2
C₃₇×#2012	2
C₃₇×#1973	2
C₃₇×#1972	2
C₃₇×#1970	2
C₃₇×#1968	2
C₃₇×#1750	2
#28321	37

Subgroups — C37×#28321 #22649574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28321 #22649574