Subgroups — C₃₇×#28258 #22649511

Order 9472.

926 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#464	C₂	1	2	yes	maximal
2	C₂×C₃₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#461	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2327	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2326	C₂	1	1	yes	maximal, characteristic
6	C₃₇×#2056	C₂	1	2	yes	maximal, complemented
7	C₃₇×#2055	C₂	1	2	yes	maximal
8	C₃₇×#1843	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1804	C₂	1	1	yes	maximal, characteristic
11	C₃₇×#1803	C₂	1	2	yes	maximal, complemented
12	C₂²×Q₁₆×C₃₇	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₃₇	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
19	C₃₇×#464	—	2	8	no	—
20	C₃₇×#462	—	2	4	no	—
21	C₃₇×#461	—	2	4	no	—
22	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
25	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
26	C₂×#103×C₃₇	C₂²	1	2	yes	—
27	C₂×#103×C₃₇	C₂²	1	2	yes	—
28	C₂×#103×C₃₇	C₂²	1	2	yes	—
29	C₂×#102×C₃₇	C₂²	1	2	yes	—
30	C₃₇×#391	C₂²	1	2	yes	—
31	C₃₇×#391	C₂²	1	1	yes	characteristic
32	C₃₇×#390	C₂²	1	1	yes	characteristic
33	C₃₇×#388	—	2	2	no	—
34	C₃₇×#387	—	2	2	no	—
35	C₃₇×#387	—	2	2	no	—
36	C₃₇×#385	—	2	2	no	—
37	C₃₇×#384	C₂²	1	1	yes	characteristic
38	C₃₇×#382	C₂²	1	1	yes	characteristic
39	C₃₇×#376	C₂²	1	1	yes	characteristic
40	C₃₇×#340	C₂²	1	2	yes	—
41	C₃₇×#340	C₂²	1	2	yes	—
42	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
44	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₃₇	—	2	1	no	—
46	C₂×Q₁₆×C₃₇	—	2	4	no	—
47	C₂×Q₁₆×C₃₇	—	2	4	no	—
48	C₂×Q₁₆×C₃₇	—	4	2	no	—
49	C₂×SD₁₆×C₃₇	—	2	4	no	—
50	C₂×SD₁₆×C₃₇	—	2	4	no	—
51	C₂×SD₁₆×C₃₇	—	4	2	no	—
52	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
53	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₃₇	—	2	2	no	—
55	C₄⋊Q₈×C₃₇	D₄	1	4	yes	—
56	#124×C₃₇	—	2	2	no	—
57	#124×C₃₇	D₄	1	4	yes	—
58	C₄×Q₈×C₃₇	—	2	2	no	—
59	C₄×Q₈×C₃₇	—	2	4	no	—
60	C₄×Q₈×C₃₇	—	2	2	no	—
61	C₄×Q₈×C₃₇	—	2	4	no	—
62	C₄×D₄×C₃₇	—	2	2	no	—
63	C₄×D₄×C₃₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
75	C₂×C₄²×C₃₇	—	2	2	no	—
76	C₂×C₄²×C₃₇	—	2	1	no	—
77	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₃₇	—	2	2	no	—
81	C₄⋊C₈×C₃₇	—	2	2	no	—
82	C₄⋊C₈×C₃₇	—	2	4	no	—
83	C₄⋊C₈×C₃₇	—	4	2	no	—
84	#103×C₃₇	—	2	4	no	—
85	#103×C₃₇	—	2	4	no	—
86	#103×C₃₇	—	2	4	no	—
87	#102×C₃₇	—	2	4	no	—
88	#95×C₃₇	—	2	1	no	—
89	#95×C₃₇	—	2	1	no	—
90	#95×C₃₇	—	2	2	no	—
91	#95×C₃₇	—	2	4	no	—
92	#95×C₃₇	D₄	1	2	yes	—
93	#95×C₃₇	D₄	1	2	yes	—
94	C₂⁴×C₃₇	—	2	1	no	—
95	C₂×Q₈×C₃₇	—	2	1	no	—
96	C₂×Q₈×C₃₇	—	2	2	no	—
97	C₂×Q₈×C₃₇	—	2	2	no	—
98	C₂×Q₈×C₃₇	—	2	1	no	—
99	C₂×Q₈×C₃₇	—	2	1	no	—
100	C₂×Q₈×C₃₇	—	2	2	no	—
101	C₂×Q₈×C₃₇	—	2	2	no	—
102	C₂×Q₈×C₃₇	—	2	1	no	—
103	C₂×Q₈×C₃₇	—	2	1	no	—
104	C₂×Q₈×C₃₇	—	2	2	no	—
105	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
106	C₂×Q₈×C₃₇	C₂×D₄	1	4	yes	—
107	C₂×D₄×C₃₇	—	2	1	no	—
108	C₂×D₄×C₃₇	—	2	1	no	—
109	C₂×D₄×C₃₇	—	2	1	no	—
110	C₂×D₄×C₃₇	—	2	1	no	—
111	C₂×D₄×C₃₇	—	2	1	no	—
112	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₃₇	—	2	1	no	—
114	C₂²×C₄×C₃₇	—	2	2	no	—
115	C₂²×C₄×C₃₇	—	2	2	no	—
116	C₂²×C₄×C₃₇	—	2	1	no	—
117	C₂²×C₄×C₃₇	—	2	1	no	—
118	C₂²×C₄×C₃₇	—	4	2	no	—
119	C₂²×C₄×C₃₇	—	8	2	no	—
120	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
125	Q₁₆×C₃₇	—	4	8	no	—
126	SD₁₆×C₃₇	—	4	8	no	—
127	C₂×C₈×C₃₇	—	2	2	no	—
128	C₂×C₈×C₃₇	—	2	2	no	—
129	C₂×C₈×C₃₇	—	2	2	no	—
130	C₂×C₈×C₃₇	—	2	2	no	—
131	C₂×C₈×C₃₇	—	2	2	no	—
132	C₂×C₈×C₃₇	—	2	2	no	—
133	C₄⋊C₄×C₃₇	—	2	4	no	—
134	C₄⋊C₄×C₃₇	—	2	4	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	1	no	—
139	C₄⋊C₄×C₃₇	—	2	2	no	—
140	C₄⋊C₄×C₃₇	—	2	1	no	—
141	C₄⋊C₄×C₃₇	—	4	4	no	—
142	C₄⋊C₄×C₃₇	—	4	2	no	—
143	C₄⋊C₄×C₃₇	—	8	2	no	—
144	C₂²⋊C₄×C₃₇	—	2	8	no	—
145	C₂²⋊C₄×C₃₇	—	4	2	no	—
146	C₂²⋊C₄×C₃₇	—	8	2	no	—
147	C₄²×C₃₇	—	2	1	no	—
148	C₄²×C₃₇	—	2	1	no	—
149	C₄²×C₃₇	—	4	4	no	—
150	C₄²×C₃₇	—	4	2	no	—
151	C₄²×C₃₇	C₂×D₄	1	2	yes	—
152	C₄²×C₃₇	C₂×D₄	1	2	yes	—
153	C₄²×C₃₇	#41	1	2	yes	—
154	C₄²×C₃₇	#41	1	2	yes	—
155	C₂³×C₃₇	—	2	2	no	—
156	C₂³×C₃₇	—	4	1	no	—
157	C₂³×C₃₇	—	4	1	no	—
158	C₂³×C₃₇	—	4	2	no	—
159	C₂³×C₃₇	—	4	2	no	—
160	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₃₇	—	2	4	no	—
162	Q₈×C₃₇	—	2	2	no	—
163	Q₈×C₃₇	—	2	2	no	—
164	Q₈×C₃₇	—	2	4	no	—
165	Q₈×C₃₇	—	4	2	no	—
166	Q₈×C₃₇	—	4	1	no	—
167	Q₈×C₃₇	—	4	1	no	—
168	Q₈×C₃₇	—	4	2	no	—
169	D₄×C₃₇	—	2	2	no	—
170	D₄×C₃₇	—	2	2	no	—
171	D₄×C₃₇	—	4	1	no	—
172	D₄×C₃₇	—	4	1	no	—
173	C₂×C₄×C₃₇	—	2	2	no	—
174	C₂×C₄×C₃₇	—	2	2	no	—
175	C₂×C₄×C₃₇	—	2	2	no	—
176	C₂×C₄×C₃₇	—	2	2	no	—
177	C₂×C₄×C₃₇	—	2	2	no	—
178	C₂×C₄×C₃₇	—	2	4	no	—
179	C₂×C₄×C₃₇	—	2	2	no	—
180	C₂×C₄×C₃₇	—	2	2	no	—
181	C₂×C₄×C₃₇	—	2	2	no	—
182	C₂×C₄×C₃₇	—	4	1	no	—
183	C₂×C₄×C₃₇	—	4	2	no	—
184	C₂×C₄×C₃₇	—	4	1	no	—
185	C₂×C₄×C₃₇	—	4	2	no	—
186	C₂×C₄×C₃₇	—	4	1	no	—
187	C₂×C₄×C₃₇	—	4	2	no	—
188	C₂×C₄×C₃₇	—	4	1	no	—
189	C₂×C₄×C₃₇	—	4	2	no	—
190	C₂×C₄×C₃₇	—	4	2	no	—
191	C₂×C₄×C₃₇	—	4	2	no	—
192	C₂×C₄×C₃₇	—	4	2	no	—
193	C₂×C₄×C₃₇	—	8	4	no	—
194	C₂×C₄×C₃₇	#121	1	4	yes	—
195	C₂×C₄×C₃₇	#121	1	2	yes	—
196	C₂×C₄×C₃₇	#121	1	2	yes	—
197	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
203	C₈×C₃₇	—	4	2	no	—
204	C₈×C₃₇	—	4	2	no	—
205	#28258	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂²×C₃₇	—	4	4	no	—
207	C₂²×C₃₇	—	4	2	no	—
208	C₂²×C₃₇	—	8	2	no	—
209	C₂²×C₃₇	—	8	1	no	—
210	C₂²×C₃₇	—	8	1	no	—
211	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
212	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
213	C₂²×C₃₇	#537	1	1	yes	characteristic
214	C₂²×C₃₇	#577	1	2	yes	—
215	C₂²×C₃₇	#578	1	2	yes	—
216	C₄×C₃₇	—	2	2	no	—
217	C₄×C₃₇	—	2	2	no	—
218	C₄×C₃₇	—	2	4	no	—
219	C₄×C₃₇	—	4	2	no	—
220	C₄×C₃₇	—	4	2	no	—
221	C₄×C₃₇	—	4	4	no	—
222	C₄×C₃₇	—	8	1	no	—
223	C₄×C₃₇	—	8	1	no	—
224	C₄×C₃₇	—	8	2	no	—
225	C₄×C₃₇	D₄²	1	1	yes	characteristic
226	C₄×C₃₇	#547	1	1	yes	characteristic
227	C₄×C₃₇	#547	1	1	yes	characteristic
228	C₄×C₃₇	#555	1	1	yes	characteristic
229	C₂×#464	C₂×C₃₇	1	2	yes	—
230	C₂×#462	C₂×C₃₇	1	1	yes	characteristic, complemented
231	C₂×#461	C₂×C₃₇	1	1	yes	characteristic
232	#2327	C₂×C₃₇	1	1	yes	characteristic, complemented
233	#2326	C₂×C₃₇	1	1	yes	characteristic
234	#2056	C₂×C₃₇	1	2	yes	complemented
235	#2055	C₂×C₃₇	1	2	yes	—
236	#1843	C₂×C₃₇	1	1	yes	characteristic, complemented
237	#1805	C₂×C₃₇	1	1	yes	characteristic, complemented
238	#1804	C₂×C₃₇	1	1	yes	characteristic
239	#1803	C₂×C₃₇	1	2	yes	complemented
240	C₂×C₃₇	—	8	2	no	—
241	C₂×C₃₇	#2537	1	1	yes	characteristic
242	C₂×C₃₇	#3043	1	1	yes	characteristic
243	C₂×C₃₇	#3044	1	1	yes	characteristic
244	C₂×C₃₇	#3046	1	2	yes	—
245	C₂×C₃₇	#3258	1	2	yes	—
246	C₂²×Q₁₆	C₂²×C₃₇	1	2	yes	—
247	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
248	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
249	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
250	C₂×C₄×Q₈	C₂²×C₃₇	1	2	yes	—
251	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
252	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
253	#464	—	2	8	no	—
254	#462	—	2	4	no	—
255	#461	—	2	4	no	—
256	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
257	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
258	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
259	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
260	C₂×#103	C₂²×C₃₇	1	2	yes	—
261	C₂×#103	C₂²×C₃₇	1	2	yes	—
262	C₂×#103	C₂²×C₃₇	1	2	yes	—
263	C₂×#102	C₂²×C₃₇	1	2	yes	—
264	#391	C₂²×C₃₇	1	2	yes	—
265	#391	C₂²×C₃₇	1	1	yes	characteristic
266	#390	C₂²×C₃₇	1	1	yes	characteristic
267	#388	—	2	2	no	—
268	#387	—	2	2	no	—
269	#387	—	2	2	no	—
270	#385	—	2	2	no	—
271	#384	C₂²×C₃₇	1	1	yes	characteristic
272	#382	C₂²×C₃₇	1	1	yes	characteristic
273	#376	C₂²×C₃₇	1	1	yes	characteristic
274	#340	C₂²×C₃₇	1	2	yes	—
275	#340	C₂²×C₃₇	1	2	yes	—
276	C₃₇	#28258	1	1	yes	characteristic, direct product factor, Sylow
277	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
278	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
279	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
280	C₂³×C₄	—	2	1	no	—
281	C₂×Q₁₆	—	2	4	no	—
282	C₂×Q₁₆	—	2	4	no	—
283	C₂×Q₁₆	—	4	2	no	—
284	C₂×SD₁₆	—	2	4	no	—
285	C₂×SD₁₆	—	2	4	no	—
286	C₂×SD₁₆	—	4	2	no	—
287	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
288	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
289	C₄⋊Q₈	—	2	2	no	—
290	C₄⋊Q₈	D₄×C₃₇	1	4	yes	—
291	#124	—	2	2	no	—
292	#124	D₄×C₃₇	1	4	yes	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×Q₈	—	2	4	no	—
295	C₄×Q₈	—	2	2	no	—
296	C₄×Q₈	—	2	4	no	—
297	C₄×D₄	—	2	2	no	—
298	C₄×D₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
315	C₄⋊C₈	—	2	2	no	—
316	C₄⋊C₈	—	2	2	no	—
317	C₄⋊C₈	—	2	4	no	—
318	C₄⋊C₈	—	4	2	no	—
319	#103	—	2	4	no	—
320	#103	—	2	4	no	—
321	#103	—	2	4	no	—
322	#102	—	2	4	no	—
323	#95	—	2	1	no	—
324	#95	—	2	1	no	—
325	#95	—	2	2	no	—
326	#95	—	2	4	no	—
327	#95	D₄×C₃₇	1	2	yes	—
328	#95	D₄×C₃₇	1	2	yes	—
329	C₂⁴	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
341	C₂×Q₈	C₂×D₄×C₃₇	1	4	yes	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	—	8	2	no	—
355	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
359	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
360	Q₁₆	—	4	8	no	—
361	SD₁₆	—	4	8	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	4	4	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	—	8	2	no	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	8	2	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	4	4	no	—
385	C₄²	—	4	2	no	—
386	C₄²	C₂×D₄×C₃₇	1	2	yes	—
387	C₄²	C₂×D₄×C₃₇	1	2	yes	—
388	C₄²	#41×C₃₇	1	2	yes	—
389	C₄²	#41×C₃₇	1	2	yes	—
390	C₂³	—	2	2	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
396	Q₈	—	2	4	no	—
397	Q₈	—	2	2	no	—
398	Q₈	—	2	2	no	—
399	Q₈	—	2	4	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	4	1	no	—
402	Q₈	—	4	1	no	—
403	Q₈	—	4	2	no	—
404	D₄	—	2	2	no	—
405	D₄	—	2	2	no	—
406	D₄	—	4	1	no	—
407	D₄	—	4	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	8	4	no	—
429	C₂×C₄	#121×C₃₇	1	4	yes	—
430	C₂×C₄	#121×C₃₇	1	2	yes	—
431	C₂×C₄	#121×C₃₇	1	2	yes	—
432	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
433	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
434	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
435	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
436	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
437	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
438	C₈	—	4	2	no	—
439	C₈	—	4	2	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	8	1	no	—
444	C₂²	—	8	1	no	—
445	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
446	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
447	C₂²	C₃₇×#537	1	1	yes	characteristic
448	C₂²	C₃₇×#577	1	2	yes	—
449	C₂²	C₃₇×#578	1	2	yes	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	4	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	4	no	—
456	C₄	—	8	1	no	—
457	C₄	—	8	1	no	—
458	C₄	—	8	2	no	—
459	C₄	D₄²×C₃₇	1	1	yes	characteristic
460	C₄	C₃₇×#547	1	1	yes	characteristic
461	C₄	C₃₇×#547	1	1	yes	characteristic
462	C₄	C₃₇×#555	1	1	yes	characteristic
463	C₂	—	8	2	no	—
464	C₂	C₃₇×#2537	1	1	yes	characteristic
465	C₂	C₃₇×#3043	1	1	yes	characteristic
466	C₂	C₃₇×#3044	1	1	yes	characteristic
467	C₂	C₃₇×#3046	1	2	yes	—
468	C₂	C₃₇×#3258	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 ◁ C₃₇×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₇×#462	C₂	semidirect
4. C₃₇×#2327	C₂	semidirect
6. C₃₇×#2056	C₂	semidirect
8. C₃₇×#1843	C₂	semidirect
9. C₃₇×#1805	C₂	semidirect
11. C₃₇×#1803	C₂	semidirect
205. #28258	C₃₇	direct (N × H)
230. C₂×#462	C₂×C₃₇	semidirect
232. #2327	C₂×C₃₇	semidirect
234. #2056	C₂×C₃₇	semidirect
236. #1843	C₂×C₃₇	semidirect
237. #1805	C₂×C₃₇	semidirect
239. #1803	C₂×C₃₇	semidirect
276. C₃₇	#28258	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×#464	2
C₂×C₃₇×#462	2
C₂×C₃₇×#461	2
C₃₇×#2327	2
C₃₇×#2326	2
C₃₇×#2056	2
C₃₇×#2055	2
C₃₇×#1843	2
C₃₇×#1805	2
C₃₇×#1804	2
C₃₇×#1803	2
#28258	37

Subgroups — C37×#28258 #22649511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28258 #22649511