Subgroups — C₃₇×#28266 #22649519

Order 9472.

814 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×SD₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2581	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2580	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2068	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2067	C₂	1	2	yes	maximal
7	C₃₇×#1968	C₂	1	2	yes	maximal
8	C₃₇×#1941	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1846	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1804	C₂	1	1	yes	maximal, characteristic
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×D₄×C₃₇	C₂²	1	1	yes	characteristic
16	C₈×Q₈×C₃₇	—	2	4	no	—
17	C₄×SD₁₆×C₃₇	—	2	4	no	—
18	C₂×#107×C₃₇	C₂²	1	2	yes	—
19	C₂×#106×C₃₇	C₂²	1	2	yes	—
20	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
23	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
24	C₂×#103×C₃₇	C₂²	1	2	yes	—
25	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
26	C₂×#102×C₃₇	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₃₇	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
29	C₃₇×#400	—	2	1	no	—
30	C₃₇×#399	—	2	1	no	—
31	C₃₇×#395	—	2	1	no	—
32	C₃₇×#393	—	2	1	no	—
33	C₃₇×#391	C₂²	1	2	yes	—
34	C₃₇×#390	C₂²	1	2	yes	—
35	C₃₇×#389	C₂²	1	2	yes	—
36	C₃₇×#389	C₂²	1	2	yes	—
37	C₃₇×#387	—	2	2	no	—
38	C₃₇×#385	—	2	2	no	—
39	C₃₇×#382	C₂²	1	1	yes	characteristic
40	C₃₇×#382	C₂²	1	1	yes	characteristic
41	C₃₇×#340	C₂²	1	2	yes	—
42	C₃₇×#340	C₂²	1	2	yes	—
43	C₂²×Q₈×C₃₇	D₄	1	1	yes	characteristic
44	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₃₇	—	2	1	no	—
47	C₂×SD₁₆×C₃₇	—	2	2	no	—
48	C₂×SD₁₆×C₃₇	—	2	2	no	—
49	C₂×SD₁₆×C₃₇	Q₈	1	4	yes	complemented
50	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
51	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
53	C₄×Q₈×C₃₇	—	2	2	no	—
54	C₄×Q₈×C₃₇	—	2	2	no	—
55	C₄×Q₈×C₃₇	—	2	2	no	—
56	C₄×Q₈×C₃₇	—	2	2	no	—
57	C₄×D₄×C₃₇	—	2	2	no	—
58	C₄×D₄×C₃₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
63	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
71	C₂×C₄²×C₃₇	—	2	1	no	—
72	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
73	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
74	#107×C₃₇	—	4	2	no	—
75	#106×C₃₇	—	2	2	no	—
76	#106×C₃₇	—	2	4	no	—
77	C₄⋊C₈×C₃₇	—	2	4	no	—
78	C₄⋊C₈×C₃₇	—	2	2	no	—
79	#103×C₃₇	—	2	2	no	—
80	#103×C₃₇	—	4	2	no	—
81	#102×C₃₇	—	2	2	no	—
82	#102×C₃₇	—	4	2	no	—
83	C₄×C₈×C₃₇	—	2	4	no	—
84	C₄×C₈×C₃₇	D₄	1	4	yes	—
85	#95×C₃₇	—	2	1	no	—
86	#95×C₃₇	—	2	1	no	—
87	#95×C₃₇	—	2	1	no	—
88	#95×C₃₇	—	2	1	no	—
89	#95×C₃₇	—	2	2	no	—
90	#95×C₃₇	—	2	2	no	—
91	#95×C₃₇	—	2	2	no	—
92	#95×C₃₇	—	2	2	no	—
93	C₂⁴×C₃₇	—	2	1	no	—
94	C₂×Q₈×C₃₇	—	2	2	no	—
95	C₂×Q₈×C₃₇	—	2	4	no	—
96	C₂×Q₈×C₃₇	—	2	1	no	—
97	C₂×Q₈×C₃₇	—	2	1	no	—
98	C₂×Q₈×C₃₇	—	2	1	no	—
99	C₂×Q₈×C₃₇	—	2	1	no	—
100	C₂×Q₈×C₃₇	—	2	1	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	2	no	—
110	C₂²×C₄×C₃₇	—	2	2	no	—
111	C₂²×C₄×C₃₇	—	2	1	no	—
112	C₂²×C₄×C₃₇	—	2	1	no	—
113	C₂²×C₄×C₃₇	—	4	2	no	—
114	C₂²×C₄×C₃₇	—	8	2	no	—
115	C₂²×C₄×C₃₇	C₂×D₄	1	2	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	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
120	SD₁₆×C₃₇	—	2	8	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	—	2	2	no	—
125	C₂×C₈×C₃₇	—	2	2	no	—
126	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₃₇	C₂×Q₈	1	2	yes	—
129	C₂×C₈×C₃₇	#41	1	2	yes	—
130	C₄⋊C₄×C₃₇	—	2	4	no	—
131	C₄⋊C₄×C₃₇	—	2	2	no	—
132	C₄⋊C₄×C₃₇	—	2	1	no	—
133	C₄⋊C₄×C₃₇	—	2	1	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	—	2	2	no	—
139	C₄⋊C₄×C₃₇	—	2	2	no	—
140	C₄⋊C₄×C₃₇	—	4	2	no	—
141	C₄⋊C₄×C₃₇	—	4	4	no	—
142	C₄⋊C₄×C₃₇	—	8	2	no	—
143	C₂²⋊C₄×C₃₇	—	4	2	no	—
144	C₂²⋊C₄×C₃₇	—	4	4	no	—
145	C₂²⋊C₄×C₃₇	—	8	2	no	—
146	C₄²×C₃₇	—	2	2	no	—
147	C₄²×C₃₇	—	2	2	no	—
148	C₄²×C₃₇	—	4	2	no	—
149	C₄²×C₃₇	C₂×D₄	1	2	yes	—
150	C₄²×C₃₇	#41	1	2	yes	—
151	C₂³×C₃₇	—	2	2	no	—
152	C₂³×C₃₇	—	4	1	no	—
153	C₂³×C₃₇	—	4	1	no	—
154	C₂³×C₃₇	—	4	2	no	—
155	C₂³×C₃₇	—	4	2	no	—
156	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₃₇	—	2	8	no	—
158	Q₈×C₃₇	—	2	2	no	—
159	Q₈×C₃₇	—	2	2	no	—
160	Q₈×C₃₇	—	4	1	no	—
161	Q₈×C₃₇	—	4	1	no	—
162	D₄×C₃₇	—	2	2	no	—
163	D₄×C₃₇	—	2	2	no	—
164	D₄×C₃₇	—	4	1	no	—
165	D₄×C₃₇	—	4	1	no	—
166	C₂×C₄×C₃₇	—	2	2	no	—
167	C₂×C₄×C₃₇	—	2	2	no	—
168	C₂×C₄×C₃₇	—	2	2	no	—
169	C₂×C₄×C₃₇	—	2	2	no	—
170	C₂×C₄×C₃₇	—	2	2	no	—
171	C₂×C₄×C₃₇	—	2	2	no	—
172	C₂×C₄×C₃₇	—	2	2	no	—
173	C₂×C₄×C₃₇	—	2	2	no	—
174	C₂×C₄×C₃₇	—	4	1	no	—
175	C₂×C₄×C₃₇	—	4	1	no	—
176	C₂×C₄×C₃₇	—	4	1	no	—
177	C₂×C₄×C₃₇	—	4	1	no	—
178	C₂×C₄×C₃₇	—	4	2	no	—
179	C₂×C₄×C₃₇	—	4	2	no	—
180	C₂×C₄×C₃₇	—	4	2	no	—
181	C₂×C₄×C₃₇	—	4	2	no	—
182	C₂×C₄×C₃₇	—	4	2	no	—
183	C₂×C₄×C₃₇	—	4	2	no	—
184	C₂×C₄×C₃₇	—	4	2	no	—
185	C₂×C₄×C₃₇	—	4	2	no	—
186	C₂×C₄×C₃₇	—	8	4	no	—
187	C₂×C₄×C₃₇	#121	1	2	yes	—
188	C₂×C₄×C₃₇	#121	1	2	yes	—
189	C₂×C₄×C₃₇	#135	1	4	yes	—
190	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
192	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
196	C₈×C₃₇	—	2	2	no	—
197	C₈×C₃₇	—	4	2	no	—
198	C₈×C₃₇	C₂²⋊Q₈	1	4	yes	—
199	#28266	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂²×C₃₇	—	4	4	no	—
201	C₂²×C₃₇	—	4	2	no	—
202	C₂²×C₃₇	—	8	2	no	—
203	C₂²×C₃₇	—	8	1	no	—
204	C₂²×C₃₇	—	8	1	no	—
205	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
206	C₂²×C₃₇	D₄×Q₈	1	1	yes	characteristic
207	C₂²×C₃₇	#550	1	1	yes	characteristic
208	C₂²×C₃₇	C₂×#135	1	2	yes	—
209	C₂²×C₃₇	#577	1	2	yes	—
210	C₄×C₃₇	—	2	2	no	—
211	C₄×C₃₇	—	2	4	no	—
212	C₄×C₃₇	—	2	2	no	—
213	C₄×C₃₇	—	4	2	no	—
214	C₄×C₃₇	—	4	2	no	—
215	C₄×C₃₇	—	8	2	no	—
216	C₄×C₃₇	—	8	2	no	—
217	C₄×C₃₇	—	8	1	no	—
218	C₄×C₃₇	—	8	1	no	—
219	C₄×C₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
220	C₄×C₃₇	#537	1	1	yes	characteristic
221	C₄×C₃₇	#554	1	1	yes	characteristic
222	C₄×C₃₇	#556	1	1	yes	characteristic
223	C₂×C₈×Q₈	C₂×C₃₇	1	1	yes	characteristic, complemented
224	C₂×C₄×SD₁₆	C₂×C₃₇	1	1	yes	characteristic
225	#2581	C₂×C₃₇	1	1	yes	characteristic, complemented
226	#2580	C₂×C₃₇	1	1	yes	characteristic
227	#2068	C₂×C₃₇	1	2	yes	complemented
228	#2067	C₂×C₃₇	1	2	yes	—
229	#1968	C₂×C₃₇	1	2	yes	—
230	#1941	C₂×C₃₇	1	2	yes	complemented
231	#1846	C₂×C₃₇	1	1	yes	characteristic, complemented
232	#1805	C₂×C₃₇	1	1	yes	characteristic, complemented
233	#1804	C₂×C₃₇	1	1	yes	characteristic
234	C₂×C₃₇	—	8	2	no	—
235	C₂×C₃₇	#2538	1	1	yes	characteristic
236	C₂×C₃₇	#3050	1	1	yes	characteristic
237	C₂×C₃₇	#3057	1	1	yes	characteristic
238	C₂×C₃₇	#3381	1	2	yes	—
239	C₂×C₃₇	#3394	1	2	yes	—
240	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
242	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
243	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
244	C₈×Q₈	—	2	4	no	—
245	C₄×SD₁₆	—	2	4	no	—
246	C₂×#107	C₂²×C₃₇	1	2	yes	—
247	C₂×#106	C₂²×C₃₇	1	2	yes	—
248	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
249	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
250	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
251	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
252	C₂×#103	C₂²×C₃₇	1	2	yes	—
253	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
254	C₂×#102	C₂²×C₃₇	1	2	yes	—
255	C₂×C₄×C₈	C₂²×C₃₇	1	2	yes	—
256	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
257	#400	—	2	1	no	—
258	#399	—	2	1	no	—
259	#395	—	2	1	no	—
260	#393	—	2	1	no	—
261	#391	C₂²×C₃₇	1	2	yes	—
262	#390	C₂²×C₃₇	1	2	yes	—
263	#389	C₂²×C₃₇	1	2	yes	—
264	#389	C₂²×C₃₇	1	2	yes	—
265	#387	—	2	2	no	—
266	#385	—	2	2	no	—
267	#382	C₂²×C₃₇	1	1	yes	characteristic
268	#382	C₂²×C₃₇	1	1	yes	characteristic
269	#340	C₂²×C₃₇	1	2	yes	—
270	#340	C₂²×C₃₇	1	2	yes	—
271	C₃₇	#28266	1	1	yes	characteristic, direct product factor, Sylow
272	C₂²×Q₈	D₄×C₃₇	1	1	yes	characteristic
273	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
274	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
275	C₂³×C₄	—	2	1	no	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×SD₁₆	—	2	2	no	—
278	C₂×SD₁₆	Q₈×C₃₇	1	4	yes	complemented
279	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
280	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
282	C₄×Q₈	—	2	2	no	—
283	C₄×Q₈	—	2	2	no	—
284	C₄×Q₈	—	2	2	no	—
285	C₄×Q₈	—	2	2	no	—
286	C₄×D₄	—	2	2	no	—
287	C₄×D₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
292	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
296	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
302	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
303	#107	—	4	2	no	—
304	#106	—	2	2	no	—
305	#106	—	2	4	no	—
306	C₄⋊C₈	—	2	4	no	—
307	C₄⋊C₈	—	2	2	no	—
308	#103	—	2	2	no	—
309	#103	—	4	2	no	—
310	#102	—	2	2	no	—
311	#102	—	4	2	no	—
312	C₄×C₈	—	2	4	no	—
313	C₄×C₈	D₄×C₃₇	1	4	yes	—
314	#95	—	2	1	no	—
315	#95	—	2	1	no	—
316	#95	—	2	1	no	—
317	#95	—	2	1	no	—
318	#95	—	2	2	no	—
319	#95	—	2	2	no	—
320	#95	—	2	2	no	—
321	#95	—	2	2	no	—
322	C₂⁴	—	2	1	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	4	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	C₂×Q₈×C₃₇	1	2	yes	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	C₂×Q₈×C₃₇	1	2	yes	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	8	2	no	—
344	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
348	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
349	SD₁₆	—	2	8	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
356	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
357	C₂×C₈	C₂×Q₈×C₃₇	1	2	yes	—
358	C₂×C₈	#41×C₃₇	1	2	yes	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	—	8	2	no	—
372	C₂²⋊C₄	—	4	2	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₂²⋊C₄	—	8	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	4	2	no	—
378	C₄²	C₂×D₄×C₃₇	1	2	yes	—
379	C₄²	#41×C₃₇	1	2	yes	—
380	C₂³	—	2	2	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
386	Q₈	—	2	8	no	—
387	Q₈	—	2	2	no	—
388	Q₈	—	2	2	no	—
389	Q₈	—	4	1	no	—
390	Q₈	—	4	1	no	—
391	D₄	—	2	2	no	—
392	D₄	—	2	2	no	—
393	D₄	—	4	1	no	—
394	D₄	—	4	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	8	4	no	—
416	C₂×C₄	#121×C₃₇	1	2	yes	—
417	C₂×C₄	#121×C₃₇	1	2	yes	—
418	C₂×C₄	#135×C₃₇	1	4	yes	—
419	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
420	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
421	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
422	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
423	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
424	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	4	2	no	—
427	C₈	C₂²⋊Q₈×C₃₇	1	4	yes	—
428	C₂²	—	4	4	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
434	C₂²	D₄×Q₈×C₃₇	1	1	yes	characteristic
435	C₂²	C₃₇×#550	1	1	yes	characteristic
436	C₂²	C₂×#135×C₃₇	1	2	yes	—
437	C₂²	C₃₇×#577	1	2	yes	—
438	C₄	—	2	2	no	—
439	C₄	—	2	4	no	—
440	C₄	—	2	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	2	no	—
443	C₄	—	8	2	no	—
444	C₄	—	8	2	no	—
445	C₄	—	8	1	no	—
446	C₄	—	8	1	no	—
447	C₄	C₂×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
448	C₄	C₃₇×#537	1	1	yes	characteristic
449	C₄	C₃₇×#554	1	1	yes	characteristic
450	C₄	C₃₇×#556	1	1	yes	characteristic
451	C₂	—	8	2	no	—
452	C₂	C₃₇×#2538	1	1	yes	characteristic
453	C₂	C₃₇×#3050	1	1	yes	characteristic
454	C₂	C₃₇×#3057	1	1	yes	characteristic
455	C₂	C₃₇×#3381	1	2	yes	—
456	C₂	C₃₇×#3394	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 ◁ C₂×C₄×Q₈×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×Q₈×C₃₇	C₂	semidirect
3. C₃₇×#2581	C₂	semidirect
5. C₃₇×#2068	C₂	semidirect
8. C₃₇×#1941	C₂	semidirect
9. C₃₇×#1846	C₂	semidirect
10. C₃₇×#1805	C₂	semidirect
49. C₂×SD₁₆×C₃₇	Q₈	semidirect
199. #28266	C₃₇	direct (N × H)
223. C₂×C₈×Q₈	C₂×C₃₇	semidirect
225. #2581	C₂×C₃₇	semidirect
227. #2068	C₂×C₃₇	semidirect
230. #1941	C₂×C₃₇	semidirect
231. #1846	C₂×C₃₇	semidirect
232. #1805	C₂×C₃₇	semidirect
271. C₃₇	#28266	direct (N × H)
278. 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×C₈×Q₈×C₃₇	2
C₂×C₄×SD₁₆×C₃₇	2
C₃₇×#2581	2
C₃₇×#2580	2
C₃₇×#2068	2
C₃₇×#2067	2
C₃₇×#1968	2
C₃₇×#1941	2
C₃₇×#1846	2
C₃₇×#1805	2
C₃₇×#1804	2
#28266	37

Subgroups — C37×#28266 #22649519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28266 #22649519