Subgroups — C₃₇×#28290 #22649543

Order 9472.

858 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#474	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#2331	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2328	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2067	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2065	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1982	C₂	1	2	yes	maximal
8	C₃₇×#1949	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1843	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1804	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1804	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
16	C₃₇×#476	—	2	4	no	—
17	C₃₇×#474	—	2	4	no	—
18	C₂×#107×C₃₇	C₂²	1	2	yes	—
19	C₂×#106×C₃₇	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
24	C₂×#102×C₃₇	C₂²	1	2	yes	—
25	C₂×#102×C₃₇	C₂²	1	2	yes	—
26	C₂×#102×C₃₇	C₂²	1	2	yes	—
27	C₂×#102×C₃₇	C₂²	1	2	yes	—
28	C₃₇×#391	—	2	2	no	—
29	C₃₇×#390	C₂²	1	1	yes	characteristic
30	C₃₇×#390	C₂²	1	1	yes	characteristic
31	C₃₇×#389	C₂²	1	2	yes	—
32	C₃₇×#387	—	2	2	no	—
33	C₃₇×#386	—	2	2	no	—
34	C₃₇×#386	—	2	2	no	—
35	C₃₇×#382	C₂²	1	1	yes	characteristic
36	C₃₇×#382	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
38	C₃₇×#376	C₂²	1	1	yes	characteristic
39	C₃₇×#340	C₂²	1	2	yes	—
40	C₃₇×#340	C₂²	1	2	yes	—
41	C₂²×Q₈×C₃₇	—	2	1	no	—
42	C₂²×D₄×C₃₇	—	2	2	no	—
43	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₃₇	—	2	1	no	—
46	C₂³×C₄×C₃₇	—	2	1	no	—
47	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
48	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
49	C₄⋊Q₈×C₃₇	—	2	2	no	—
50	C₄⋊Q₈×C₃₇	D₄	1	4	yes	complemented
51	#127×C₃₇	—	2	2	no	—
52	#127×C₃₇	Q₈	1	4	yes	complemented
53	C₄×D₄×C₃₇	—	2	2	no	—
54	C₄×D₄×C₃₇	—	2	2	no	—
55	C₄×D₄×C₃₇	—	2	2	no	—
56	C₄×D₄×C₃₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
67	C₂×C₄²×C₃₇	—	2	2	no	—
68	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
71	#107×C₃₇	—	2	4	no	—
72	#106×C₃₇	—	2	4	no	—
73	C₄⋊C₈×C₃₇	—	2	2	no	—
74	C₄⋊C₈×C₃₇	—	2	2	no	—
75	C₄⋊C₈×C₃₇	—	2	4	no	—
76	C₄⋊C₈×C₃₇	—	4	2	no	—
77	#102×C₃₇	—	2	4	no	—
78	#102×C₃₇	—	2	4	no	—
79	#102×C₃₇	—	4	2	no	—
80	#102×C₃₇	—	4	2	no	—
81	#95×C₃₇	—	2	2	no	—
82	#95×C₃₇	—	2	2	no	—
83	#95×C₃₇	—	2	1	no	—
84	#95×C₃₇	—	2	1	no	—
85	#95×C₃₇	—	2	2	no	—
86	#95×C₃₇	D₄	1	2	yes	—
87	#95×C₃₇	D₄	1	2	yes	—
88	C₂⁴×C₃₇	—	2	1	no	—
89	C₂⁴×C₃₇	—	2	1	no	—
90	C₂×Q₈×C₃₇	—	2	4	no	—
91	C₂×Q₈×C₃₇	—	8	2	no	—
92	C₂×D₄×C₃₇	—	2	8	no	—
93	C₂×D₄×C₃₇	—	2	1	no	—
94	C₂×D₄×C₃₇	—	2	1	no	—
95	C₂×D₄×C₃₇	—	2	1	no	—
96	C₂×D₄×C₃₇	—	2	1	no	—
97	C₂×D₄×C₃₇	—	2	1	no	—
98	C₂×D₄×C₃₇	—	2	1	no	—
99	C₂×D₄×C₃₇	—	2	1	no	—
100	C₂×D₄×C₃₇	—	2	1	no	—
101	C₂×D₄×C₃₇	—	2	1	no	—
102	C₂×D₄×C₃₇	—	2	1	no	—
103	C₂×D₄×C₃₇	—	8	2	no	—
104	C₂×D₄×C₃₇	—	8	2	no	—
105	C₂×D₄×C₃₇	C₂×Q₈	1	2	yes	—
106	C₂×D₄×C₃₇	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₃₇	—	2	2	no	—
108	C₂²×C₄×C₃₇	—	2	2	no	—
109	C₂²×C₄×C₃₇	—	2	1	no	—
110	C₂²×C₄×C₃₇	—	2	1	no	—
111	C₂²×C₄×C₃₇	—	4	2	no	—
112	C₂²×C₄×C₃₇	—	4	2	no	—
113	C₂²×C₄×C₃₇	—	8	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	C₂×C₈×C₃₇	—	2	2	no	—
121	C₂×C₈×C₃₇	—	2	2	no	—
122	C₂×C₈×C₃₇	—	2	2	no	—
123	C₂×C₈×C₃₇	—	2	2	no	—
124	C₂×C₈×C₃₇	—	2	2	no	—
125	C₂×C₈×C₃₇	—	2	2	no	—
126	C₄⋊C₄×C₃₇	—	2	4	no	—
127	C₄⋊C₄×C₃₇	—	2	2	no	—
128	C₄⋊C₄×C₃₇	—	2	1	no	—
129	C₄⋊C₄×C₃₇	—	2	1	no	—
130	C₄⋊C₄×C₃₇	—	2	1	no	—
131	C₄⋊C₄×C₃₇	—	2	1	no	—
132	C₄⋊C₄×C₃₇	—	2	2	no	—
133	C₄⋊C₄×C₃₇	—	2	2	no	—
134	C₄⋊C₄×C₃₇	—	8	2	no	—
135	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
136	C₂²⋊C₄×C₃₇	—	4	2	no	—
137	C₂²⋊C₄×C₃₇	—	4	2	no	—
138	C₂²⋊C₄×C₃₇	—	8	2	no	—
139	C₂²⋊C₄×C₃₇	—	8	2	no	—
140	C₄²×C₃₇	—	2	1	no	—
141	C₄²×C₃₇	—	2	1	no	—
142	C₄²×C₃₇	—	8	2	no	—
143	C₄²×C₃₇	C₂×D₄	1	2	yes	—
144	C₄²×C₃₇	C₂×Q₈	1	2	yes	—
145	C₄²×C₃₇	#41	1	2	yes	—
146	C₄²×C₃₇	#41	1	2	yes	—
147	C₂³×C₃₇	—	2	2	no	—
148	C₂³×C₃₇	—	2	2	no	—
149	C₂³×C₃₇	—	4	1	no	—
150	C₂³×C₃₇	—	4	1	no	—
151	C₂³×C₃₇	—	4	1	no	—
152	C₂³×C₃₇	—	4	1	no	—
153	C₂³×C₃₇	—	4	2	no	—
154	C₂³×C₃₇	—	4	2	no	—
155	C₂³×C₃₇	—	4	2	no	—
156	C₂³×C₃₇	—	4	2	no	—
157	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₃₇	—	8	4	no	—
159	D₄×C₃₇	—	2	2	no	—
160	D₄×C₃₇	—	2	2	no	—
161	D₄×C₃₇	—	2	2	no	—
162	D₄×C₃₇	—	2	2	no	—
163	D₄×C₃₇	—	4	1	no	—
164	D₄×C₃₇	—	4	1	no	—
165	D₄×C₃₇	—	4	1	no	—
166	D₄×C₃₇	—	4	1	no	—
167	D₄×C₃₇	—	8	8	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	4	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	—	4	2	no	—
177	C₂×C₄×C₃₇	—	4	2	no	—
178	C₂×C₄×C₃₇	—	4	1	no	—
179	C₂×C₄×C₃₇	—	4	1	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	—	8	4	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	C₂²⋊Q₈	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	—	4	2	no	—
197	C₈×C₃₇	—	4	2	no	—
198	#28290	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₃₇	—	4	4	no	—
200	C₂²×C₃₇	—	4	4	no	—
201	C₂²×C₃₇	—	4	2	no	—
202	C₂²×C₃₇	—	4	2	no	—
203	C₂²×C₃₇	—	8	2	no	—
204	C₂²×C₃₇	—	8	2	no	—
205	C₂²×C₃₇	—	8	1	no	—
206	C₂²×C₃₇	—	8	1	no	—
207	C₂²×C₃₇	—	8	1	no	—
208	C₂²×C₃₇	—	8	1	no	—
209	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
210	C₂²×C₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
211	C₂²×C₃₇	#537	1	1	yes	characteristic
212	C₂²×C₃₇	#576	1	2	yes	—
213	C₂²×C₃₇	#577	1	2	yes	—
214	C₄×C₃₇	—	2	4	no	—
215	C₄×C₃₇	—	2	2	no	—
216	C₄×C₃₇	—	2	2	no	—
217	C₄×C₃₇	—	4	2	no	—
218	C₄×C₃₇	—	4	4	no	—
219	C₄×C₃₇	—	8	2	no	—
220	C₄×C₃₇	—	8	1	no	—
221	C₄×C₃₇	—	8	1	no	—
222	C₄×C₃₇	D₄×Q₈	1	1	yes	characteristic
223	C₄×C₃₇	#550	1	1	yes	characteristic
224	C₄×C₃₇	#554	1	1	yes	characteristic
225	C₄×C₃₇	#556	1	1	yes	characteristic
226	C₂×#476	C₂×C₃₇	1	1	yes	characteristic, complemented
227	C₂×#474	C₂×C₃₇	1	1	yes	characteristic, complemented
228	#2331	C₂×C₃₇	1	1	yes	characteristic, complemented
229	#2328	C₂×C₃₇	1	1	yes	characteristic
230	#2067	C₂×C₃₇	1	2	yes	complemented
231	#2065	C₂×C₃₇	1	2	yes	complemented
232	#1982	C₂×C₃₇	1	2	yes	—
233	#1949	C₂×C₃₇	1	2	yes	complemented
234	#1843	C₂×C₃₇	1	1	yes	characteristic, complemented
235	#1804	C₂×C₃₇	1	1	yes	characteristic, complemented
236	#1804	C₂×C₃₇	1	1	yes	characteristic, complemented
237	C₂×C₃₇	—	8	2	no	—
238	C₂×C₃₇	—	8	2	no	—
239	C₂×C₃₇	#2538	1	1	yes	characteristic
240	C₂×C₃₇	#3041	1	1	yes	characteristic
241	C₂×C₃₇	#3043	1	1	yes	characteristic
242	C₂×C₃₇	#3081	1	2	yes	—
243	C₂×C₃₇	#3257	1	2	yes	—
244	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
245	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
246	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
247	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
248	#476	—	2	4	no	—
249	#474	—	2	4	no	—
250	C₂×#107	C₂²×C₃₇	1	2	yes	—
251	C₂×#106	C₂²×C₃₇	1	2	yes	—
252	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
253	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
255	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
256	C₂×#102	C₂²×C₃₇	1	2	yes	—
257	C₂×#102	C₂²×C₃₇	1	2	yes	—
258	C₂×#102	C₂²×C₃₇	1	2	yes	—
259	C₂×#102	C₂²×C₃₇	1	2	yes	—
260	#391	—	2	2	no	—
261	#390	C₂²×C₃₇	1	1	yes	characteristic
262	#390	C₂²×C₃₇	1	1	yes	characteristic
263	#389	C₂²×C₃₇	1	2	yes	—
264	#387	—	2	2	no	—
265	#386	—	2	2	no	—
266	#386	—	2	2	no	—
267	#382	C₂²×C₃₇	1	1	yes	characteristic
268	#382	C₂²×C₃₇	1	1	yes	characteristic
269	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
270	#376	C₂²×C₃₇	1	1	yes	characteristic
271	#340	C₂²×C₃₇	1	2	yes	—
272	#340	C₂²×C₃₇	1	2	yes	—
273	C₃₇	#28290	1	1	yes	characteristic, direct product factor, Sylow
274	C₂²×Q₈	—	2	1	no	—
275	C₂²×D₄	—	2	2	no	—
276	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
277	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
278	C₂³×C₄	—	2	1	no	—
279	C₂³×C₄	—	2	1	no	—
280	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
281	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
282	C₄⋊Q₈	—	2	2	no	—
283	C₄⋊Q₈	D₄×C₃₇	1	4	yes	complemented
284	#127	—	2	2	no	—
285	#127	Q₈×C₃₇	1	4	yes	complemented
286	C₄×D₄	—	2	2	no	—
287	C₄×D₄	—	2	2	no	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
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	2	no	—
301	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
304	#107	—	2	4	no	—
305	#106	—	2	4	no	—
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	—	2	2	no	—
308	C₄⋊C₈	—	2	4	no	—
309	C₄⋊C₈	—	4	2	no	—
310	#102	—	2	4	no	—
311	#102	—	2	4	no	—
312	#102	—	4	2	no	—
313	#102	—	4	2	no	—
314	#95	—	2	2	no	—
315	#95	—	2	2	no	—
316	#95	—	2	1	no	—
317	#95	—	2	1	no	—
318	#95	—	2	2	no	—
319	#95	D₄×C₃₇	1	2	yes	—
320	#95	D₄×C₃₇	1	2	yes	—
321	C₂⁴	—	2	1	no	—
322	C₂⁴	—	2	1	no	—
323	C₂×Q₈	—	2	4	no	—
324	C₂×Q₈	—	8	2	no	—
325	C₂×D₄	—	2	8	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
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	—	8	2	no	—
337	C₂×D₄	—	8	2	no	—
338	C₂×D₄	C₂×Q₈×C₃₇	1	2	yes	—
339	C₂×D₄	C₂×Q₈×C₃₇	1	2	yes	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	8	2	no	—
347	C₂²×C₄	—	8	2	no	—
348	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
352	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
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	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	8	2	no	—
368	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
369	C₂²⋊C₄	—	4	2	no	—
370	C₂²⋊C₄	—	4	2	no	—
371	C₂²⋊C₄	—	8	2	no	—
372	C₂²⋊C₄	—	8	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	8	2	no	—
376	C₄²	C₂×D₄×C₃₇	1	2	yes	—
377	C₄²	C₂×Q₈×C₃₇	1	2	yes	—
378	C₄²	#41×C₃₇	1	2	yes	—
379	C₄²	#41×C₃₇	1	2	yes	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	4	1	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
391	Q₈	—	8	4	no	—
392	D₄	—	2	2	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	4	1	no	—
397	D₄	—	4	1	no	—
398	D₄	—	4	1	no	—
399	D₄	—	4	1	no	—
400	D₄	—	8	8	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	8	4	no	—
419	C₂×C₄	—	8	4	no	—
420	C₂×C₄	#121×C₃₇	1	2	yes	—
421	C₂×C₄	#121×C₃₇	1	2	yes	—
422	C₂×C₄	C₂²⋊Q₈×C₃₇	1	4	yes	—
423	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
424	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
426	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
427	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
428	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
429	C₈	—	4	2	no	—
430	C₈	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	1	no	—
439	C₂²	—	8	1	no	—
440	C₂²	—	8	1	no	—
441	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
442	C₂²	C₂×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
443	C₂²	C₃₇×#537	1	1	yes	characteristic
444	C₂²	C₃₇×#576	1	2	yes	—
445	C₂²	C₃₇×#577	1	2	yes	—
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	4	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	4	no	—
451	C₄	—	8	2	no	—
452	C₄	—	8	1	no	—
453	C₄	—	8	1	no	—
454	C₄	D₄×Q₈×C₃₇	1	1	yes	characteristic
455	C₄	C₃₇×#550	1	1	yes	characteristic
456	C₄	C₃₇×#554	1	1	yes	characteristic
457	C₄	C₃₇×#556	1	1	yes	characteristic
458	C₂	—	8	2	no	—
459	C₂	—	8	2	no	—
460	C₂	C₃₇×#2538	1	1	yes	characteristic
461	C₂	C₃₇×#3041	1	1	yes	characteristic
462	C₂	C₃₇×#3043	1	1	yes	characteristic
463	C₂	C₃₇×#3081	1	2	yes	—
464	C₂	C₃₇×#3257	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×#127×C₃₇	C₂²
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
1. C₂×C₃₇×#476	C₂	semidirect
2. C₂×C₃₇×#474	C₂	semidirect
3. C₃₇×#2331	C₂	semidirect
5. C₃₇×#2067	C₂	semidirect
6. C₃₇×#2065	C₂	semidirect
8. C₃₇×#1949	C₂	semidirect
9. C₃₇×#1843	C₂	semidirect
10. C₃₇×#1804	C₂	semidirect
11. C₃₇×#1804	C₂	semidirect
50. C₄⋊Q₈×C₃₇	D₄	semidirect
52. #127×C₃₇	Q₈	semidirect
198. #28290	C₃₇	direct (N × H)
226. C₂×#476	C₂×C₃₇	semidirect
227. C₂×#474	C₂×C₃₇	semidirect
228. #2331	C₂×C₃₇	semidirect
230. #2067	C₂×C₃₇	semidirect
231. #2065	C₂×C₃₇	semidirect
233. #1949	C₂×C₃₇	semidirect
234. #1843	C₂×C₃₇	semidirect
235. #1804	C₂×C₃₇	semidirect
236. #1804	C₂×C₃₇	semidirect
273. C₃₇	#28290	direct (N × H)
283. C₄⋊Q₈	D₄×C₃₇	semidirect
285. #127	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×#476	2
C₂×C₃₇×#474	2
C₃₇×#2331	2
C₃₇×#2328	2
C₃₇×#2067	2
C₃₇×#2065	2
C₃₇×#1982	2
C₃₇×#1949	2
C₃₇×#1843	2
C₃₇×#1804	2
#28290	37

Subgroups — C37×#28290 #22649543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28290 #22649543