Subgroups — C₃₇×#28529 #22649782

Order 9472.

870 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#477	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#474	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×SD₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2568	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2563	C₂	1	1	yes	maximal, characteristic
7	C₃₇×#2097	C₂	1	2	yes	maximal, complemented
8	C₃₇×#2092	C₂	1	2	yes	maximal
9	C₃₇×#1968	C₂	1	2	yes	maximal
10	C₃₇×#1846	C₂	1	2	yes	maximal, complemented
11	C₈×C₄⋊C₄×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
17	C₃₇×#498	—	2	4	no	—
18	C₃₇×#477	—	2	4	no	—
19	C₃₇×#474	—	2	4	no	—
20	C₄×SD₁₆×C₃₇	—	2	4	no	—
21	C₂×#107×C₃₇	C₂²	1	2	yes	—
22	C₂×#107×C₃₇	C₂²	1	2	yes	—
23	C₂×#106×C₃₇	C₂²	1	2	yes	—
24	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×#106×C₃₇	C₂²	1	2	yes	—
26	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
27	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
28	C₂×#103×C₃₇	C₂²	1	2	yes	—
29	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×#102×C₃₇	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₃₇	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
33	C₃₇×#400	—	2	2	no	—
34	C₃₇×#393	—	2	2	no	—
35	C₃₇×#391	—	2	2	no	—
36	C₃₇×#391	C₂²	1	2	yes	—
37	C₃₇×#390	C₂²	1	2	yes	—
38	C₃₇×#382	C₂²	1	2	yes	—
39	C₃₇×#382	C₂²	1	2	yes	—
40	C₃₇×#380	—	2	2	no	—
41	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
42	C₃₇×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₃₇	—	2	1	no	—
44	C₂²×Q₈×C₃₇	—	2	1	no	—
45	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₃₇	—	2	1	no	—
48	C₂×SD₁₆×C₃₇	—	2	2	no	—
49	C₂×SD₁₆×C₃₇	—	2	2	no	—
50	C₂×SD₁₆×C₃₇	Q₈	1	4	yes	complemented
51	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
53	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
54	C₄⋊Q₈×C₃₇	—	2	2	no	—
55	C₄⋊Q₈×C₃₇	—	2	2	no	—
56	C₄⋊Q₈×C₃₇	—	2	2	no	—
57	C₄⋊Q₈×C₃₇	—	2	2	no	—
58	C₄×Q₈×C₃₇	—	2	2	no	—
59	C₄×Q₈×C₃₇	—	2	2	no	—
60	C₄×D₄×C₃₇	—	2	2	no	—
61	C₄×D₄×C₃₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
72	C₂×C₄²×C₃₇	—	2	1	no	—
73	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
74	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
75	#107×C₃₇	—	2	4	no	—
76	#107×C₃₇	—	2	4	no	—
77	#106×C₃₇	—	2	2	no	—
78	#106×C₃₇	—	2	4	no	—
79	#106×C₃₇	—	2	4	no	—
80	C₄⋊C₈×C₃₇	D₄	1	4	yes	—
81	#103×C₃₇	—	2	2	no	—
82	#103×C₃₇	—	2	4	no	—
83	#102×C₃₇	—	2	2	no	—
84	#102×C₃₇	—	2	4	no	—
85	C₄×C₈×C₃₇	—	2	4	no	—
86	C₄×C₈×C₃₇	D₄	1	4	yes	—
87	#95×C₃₇	—	2	4	no	—
88	#95×C₃₇	—	2	4	no	—
89	#95×C₃₇	—	2	4	no	—
90	#95×C₃₇	D₄	1	2	yes	—
91	C₂⁴×C₃₇	—	2	1	no	—
92	C₂×Q₈×C₃₇	—	2	1	no	—
93	C₂×Q₈×C₃₇	—	2	1	no	—
94	C₂×Q₈×C₃₇	—	2	1	no	—
95	C₂×Q₈×C₃₇	—	2	1	no	—
96	C₂×Q₈×C₃₇	—	2	1	no	—
97	C₂×Q₈×C₃₇	—	4	2	no	—
98	C₂×Q₈×C₃₇	—	4	2	no	—
99	C₂×Q₈×C₃₇	—	4	4	no	—
100	C₂×Q₈×C₃₇	—	8	2	no	—
101	C₂×Q₈×C₃₇	C₂×Q₈	1	2	yes	—
102	C₂×D₄×C₃₇	—	2	1	no	—
103	C₂×D₄×C₃₇	—	2	1	no	—
104	C₂×D₄×C₃₇	—	2	1	no	—
105	C₂×D₄×C₃₇	—	2	1	no	—
106	C₂×D₄×C₃₇	—	2	1	no	—
107	C₂×D₄×C₃₇	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₃₇	—	2	1	no	—
109	C₂²×C₄×C₃₇	—	2	1	no	—
110	C₂²×C₄×C₃₇	—	2	1	no	—
111	C₂²×C₄×C₃₇	—	2	2	no	—
112	C₂²×C₄×C₃₇	—	2	2	no	—
113	C₂²×C₄×C₃₇	—	4	2	no	—
114	C₂²×C₄×C₃₇	—	4	4	no	—
115	C₂²×C₄×C₃₇	C₂×D₄	1	4	yes	—
116	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
119	SD₁₆×C₃₇	—	2	8	no	—
120	C₂×C₈×C₃₇	—	2	2	no	—
121	C₂×C₈×C₃₇	—	2	1	no	—
122	C₂×C₈×C₃₇	—	2	1	no	—
123	C₂×C₈×C₃₇	—	2	2	no	—
124	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
126	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₃₇	C₂×Q₈	1	2	yes	—
128	C₂×C₈×C₃₇	#41	1	2	yes	—
129	C₄⋊C₄×C₃₇	—	2	4	no	—
130	C₄⋊C₄×C₃₇	—	2	1	no	—
131	C₄⋊C₄×C₃₇	—	2	2	no	—
132	C₄⋊C₄×C₃₇	—	2	1	no	—
133	C₄⋊C₄×C₃₇	—	2	2	no	—
134	C₄⋊C₄×C₃₇	—	2	2	no	—
135	C₄⋊C₄×C₃₇	—	2	2	no	—
136	C₄⋊C₄×C₃₇	—	2	1	no	—
137	C₄⋊C₄×C₃₇	—	2	1	no	—
138	C₄⋊C₄×C₃₇	—	4	2	no	—
139	C₄⋊C₄×C₃₇	—	4	2	no	—
140	C₄⋊C₄×C₃₇	—	4	2	no	—
141	C₂²⋊C₄×C₃₇	—	4	2	no	—
142	C₂²⋊C₄×C₃₇	—	8	4	no	—
143	C₄²×C₃₇	—	2	2	no	—
144	C₄²×C₃₇	—	2	2	no	—
145	C₄²×C₃₇	—	4	2	no	—
146	C₄²×C₃₇	C₂×D₄	1	2	yes	—
147	C₄²×C₃₇	C₂×D₄	1	2	yes	—
148	C₂³×C₃₇	—	2	2	no	—
149	C₂³×C₃₇	—	4	1	no	—
150	C₂³×C₃₇	—	4	1	no	—
151	C₂³×C₃₇	—	4	2	no	—
152	C₂³×C₃₇	—	4	2	no	—
153	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
154	Q₈×C₃₇	—	2	2	no	—
155	Q₈×C₃₇	—	2	2	no	—
156	Q₈×C₃₇	—	4	1	no	—
157	Q₈×C₃₇	—	4	1	no	—
158	Q₈×C₃₇	—	8	4	no	—
159	Q₈×C₃₇	—	8	4	no	—
160	D₄×C₃₇	—	2	2	no	—
161	D₄×C₃₇	—	2	2	no	—
162	D₄×C₃₇	—	4	1	no	—
163	D₄×C₃₇	—	4	1	no	—
164	C₂×C₄×C₃₇	—	2	2	no	—
165	C₂×C₄×C₃₇	—	2	4	no	—
166	C₂×C₄×C₃₇	—	2	2	no	—
167	C₂×C₄×C₃₇	—	2	4	no	—
168	C₂×C₄×C₃₇	—	2	4	no	—
169	C₂×C₄×C₃₇	—	4	1	no	—
170	C₂×C₄×C₃₇	—	4	1	no	—
171	C₂×C₄×C₃₇	—	4	1	no	—
172	C₂×C₄×C₃₇	—	4	1	no	—
173	C₂×C₄×C₃₇	—	4	2	no	—
174	C₂×C₄×C₃₇	—	4	2	no	—
175	C₂×C₄×C₃₇	—	4	2	no	—
176	C₂×C₄×C₃₇	—	4	4	no	—
177	C₂×C₄×C₃₇	—	4	4	no	—
178	C₂×C₄×C₃₇	—	4	2	no	—
179	C₂×C₄×C₃₇	—	8	4	no	—
180	C₂×C₄×C₃₇	#127	1	2	yes	—
181	C₂×C₄×C₃₇	#127	1	2	yes	—
182	C₂×C₄×C₃₇	#135	1	4	yes	—
183	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
188	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
189	C₈×C₃₇	—	2	2	no	—
190	C₈×C₃₇	—	2	4	no	—
191	C₈×C₃₇	C₂²⋊Q₈	1	4	yes	—
192	#28529	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂²×C₃₇	—	4	4	no	—
194	C₂²×C₃₇	—	4	2	no	—
195	C₂²×C₃₇	—	8	2	no	—
196	C₂²×C₃₇	—	8	1	no	—
197	C₂²×C₃₇	—	8	1	no	—
198	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
199	C₂²×C₃₇	#547	1	1	yes	characteristic
200	C₂²×C₃₇	D₄×Q₈	1	1	yes	characteristic
201	C₂²×C₃₇	C₂×#135	1	2	yes	—
202	C₂²×C₃₇	#577	1	2	yes	—
203	C₄×C₃₇	—	2	2	no	—
204	C₄×C₃₇	—	4	4	no	—
205	C₄×C₃₇	—	4	2	no	—
206	C₄×C₃₇	—	8	1	no	—
207	C₄×C₃₇	—	8	2	no	—
208	C₄×C₃₇	—	8	1	no	—
209	C₄×C₃₇	—	8	2	no	—
210	C₄×C₃₇	#495	1	4	yes	—
211	C₄×C₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
212	C₄×C₃₇	#536	1	1	yes	characteristic
213	C₄×C₃₇	#547	1	1	yes	characteristic
214	C₄×C₃₇	D₄×Q₈	1	1	yes	characteristic
215	C₂×#498	C₂×C₃₇	1	1	yes	characteristic, complemented
216	C₂×#477	C₂×C₃₇	1	1	yes	characteristic, complemented
217	C₂×#474	C₂×C₃₇	1	1	yes	characteristic
218	C₂×C₄×SD₁₆	C₂×C₃₇	1	1	yes	characteristic
219	#2568	C₂×C₃₇	1	1	yes	characteristic, complemented
220	#2563	C₂×C₃₇	1	1	yes	characteristic
221	#2097	C₂×C₃₇	1	2	yes	complemented
222	#2092	C₂×C₃₇	1	2	yes	—
223	#1968	C₂×C₃₇	1	2	yes	—
224	#1846	C₂×C₃₇	1	2	yes	complemented
225	C₈×C₄⋊C₄	C₂×C₃₇	1	1	yes	characteristic, complemented
226	C₂×C₃₇	—	8	2	no	—
227	C₂×C₃₇	#2542	1	1	yes	characteristic
228	C₂×C₃₇	C₂×#495	1	1	yes	characteristic
229	C₂×C₃₇	#3154	1	1	yes	characteristic
230	C₂×C₃₇	#3340	1	2	yes	—
231	C₂×C₃₇	#3381	1	2	yes	—
232	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
233	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
234	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
235	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
237	#498	—	2	4	no	—
238	#477	—	2	4	no	—
239	#474	—	2	4	no	—
240	C₄×SD₁₆	—	2	4	no	—
241	C₂×#107	C₂²×C₃₇	1	2	yes	—
242	C₂×#107	C₂²×C₃₇	1	2	yes	—
243	C₂×#106	C₂²×C₃₇	1	2	yes	—
244	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
245	C₂×#106	C₂²×C₃₇	1	2	yes	—
246	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
247	C₂×#103	C₂²×C₃₇	1	2	yes	—
248	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
249	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
250	C₂×#102	C₂²×C₃₇	1	2	yes	—
251	C₂×C₄×C₈	C₂²×C₃₇	1	2	yes	—
252	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
253	#400	—	2	2	no	—
254	#393	—	2	2	no	—
255	#391	—	2	2	no	—
256	#391	C₂²×C₃₇	1	2	yes	—
257	#390	C₂²×C₃₇	1	2	yes	—
258	#382	C₂²×C₃₇	1	2	yes	—
259	#382	C₂²×C₃₇	1	2	yes	—
260	#380	—	2	2	no	—
261	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
262	#336	C₂²×C₃₇	1	2	yes	—
263	C₃₇	#28529	1	1	yes	characteristic, direct product factor, Sylow
264	C₂²×Q₈	—	2	1	no	—
265	C₂²×Q₈	—	2	1	no	—
266	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
267	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
268	C₂³×C₄	—	2	1	no	—
269	C₂×SD₁₆	—	2	2	no	—
270	C₂×SD₁₆	—	2	2	no	—
271	C₂×SD₁₆	Q₈×C₃₇	1	4	yes	complemented
272	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
274	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
275	C₄⋊Q₈	—	2	2	no	—
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	—	2	2	no	—
278	C₄⋊Q₈	—	2	2	no	—
279	C₄×Q₈	—	2	2	no	—
280	C₄×Q₈	—	2	2	no	—
281	C₄×D₄	—	2	2	no	—
282	C₄×D₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	4	no	—
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
295	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
296	#107	—	2	4	no	—
297	#107	—	2	4	no	—
298	#106	—	2	2	no	—
299	#106	—	2	4	no	—
300	#106	—	2	4	no	—
301	C₄⋊C₈	D₄×C₃₇	1	4	yes	—
302	#103	—	2	2	no	—
303	#103	—	2	4	no	—
304	#102	—	2	2	no	—
305	#102	—	2	4	no	—
306	C₄×C₈	—	2	4	no	—
307	C₄×C₈	D₄×C₃₇	1	4	yes	—
308	#95	—	2	4	no	—
309	#95	—	2	4	no	—
310	#95	—	2	4	no	—
311	#95	D₄×C₃₇	1	2	yes	—
312	C₂⁴	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	4	2	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×Q₈	—	4	4	no	—
321	C₂×Q₈	—	8	2	no	—
322	C₂×Q₈	C₂×Q₈×C₃₇	1	2	yes	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	C₂×Q₈×C₃₇	1	2	yes	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	4	no	—
336	C₂²×C₄	C₂×D₄×C₃₇	1	4	yes	—
337	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
339	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
340	SD₁₆	—	2	8	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
346	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
347	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
348	C₂×C₈	C₂×Q₈×C₃₇	1	2	yes	—
349	C₂×C₈	#41×C₃₇	1	2	yes	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	—	4	2	no	—
361	C₄⋊C₄	—	4	2	no	—
362	C₂²⋊C₄	—	4	2	no	—
363	C₂²⋊C₄	—	8	4	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	4	2	no	—
367	C₄²	C₂×D₄×C₃₇	1	2	yes	—
368	C₄²	C₂×D₄×C₃₇	1	2	yes	—
369	C₂³	—	2	2	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
375	Q₈	—	2	2	no	—
376	Q₈	—	2	2	no	—
377	Q₈	—	4	1	no	—
378	Q₈	—	4	1	no	—
379	Q₈	—	8	4	no	—
380	Q₈	—	8	4	no	—
381	D₄	—	2	2	no	—
382	D₄	—	2	2	no	—
383	D₄	—	4	1	no	—
384	D₄	—	4	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	8	4	no	—
401	C₂×C₄	#127×C₃₇	1	2	yes	—
402	C₂×C₄	#127×C₃₇	1	2	yes	—
403	C₂×C₄	#135×C₃₇	1	4	yes	—
404	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
405	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
406	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
407	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
408	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
409	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
410	C₈	—	2	2	no	—
411	C₈	—	2	4	no	—
412	C₈	C₂²⋊Q₈×C₃₇	1	4	yes	—
413	C₂²	—	4	4	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	1	no	—
417	C₂²	—	8	2	no	—
418	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
419	C₂²	C₃₇×#547	1	1	yes	characteristic
420	C₂²	D₄×Q₈×C₃₇	1	1	yes	characteristic
421	C₂²	C₂×#135×C₃₇	1	2	yes	—
422	C₂²	C₃₇×#577	1	2	yes	—
423	C₄	—	2	2	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	4	no	—
426	C₄	—	8	1	no	—
427	C₄	—	8	2	no	—
428	C₄	—	8	2	no	—
429	C₄	—	8	1	no	—
430	C₄	C₃₇×#495	1	4	yes	—
431	C₄	C₂×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
432	C₄	C₃₇×#536	1	1	yes	characteristic
433	C₄	C₃₇×#547	1	1	yes	characteristic
434	C₄	D₄×Q₈×C₃₇	1	1	yes	characteristic
435	C₂	—	8	2	no	—
436	C₂	C₃₇×#2542	1	1	yes	characteristic
437	C₂	C₂×C₃₇×#495	1	1	yes	characteristic
438	C₂	C₃₇×#3154	1	1	yes	characteristic
439	C₂	C₃₇×#3340	1	2	yes	—
440	C₂	C₃₇×#3381	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂²×D₄×C₃₇	C₂³
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×#498	C₂	semidirect
2. C₂×C₃₇×#477	C₂	semidirect
5. C₃₇×#2568	C₂	semidirect
7. C₃₇×#2097	C₂	semidirect
10. C₃₇×#1846	C₂	semidirect
11. C₈×C₄⋊C₄×C₃₇	C₂	semidirect
50. C₂×SD₁₆×C₃₇	Q₈	semidirect
192. #28529	C₃₇	direct (N × H)
215. C₂×#498	C₂×C₃₇	semidirect
216. C₂×#477	C₂×C₃₇	semidirect
219. #2568	C₂×C₃₇	semidirect
221. #2097	C₂×C₃₇	semidirect
224. #1846	C₂×C₃₇	semidirect
225. C₈×C₄⋊C₄	C₂×C₃₇	semidirect
263. C₃₇	#28529	direct (N × H)
271. C₂×SD₁₆	Q₈×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×#498	2
C₂×C₃₇×#477	2
C₂×C₃₇×#474	2
C₂×C₄×SD₁₆×C₃₇	2
C₃₇×#2568	2
C₃₇×#2563	2
C₃₇×#2097	2
C₃₇×#2092	2
C₃₇×#1968	2
C₃₇×#1846	2
C₈×C₄⋊C₄×C₃₇	2
#28529	37

Subgroups — C37×#28529 #22649782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28529 #22649782