Subgroups — C₃₇×#25273 #22646526

Order 9472.

814 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#476	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2547	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2369	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2066	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2042	C₂	1	2	yes	maximal
7	C₃₇×#1983	C₂	1	2	yes	maximal
8	C₃₇×#1981	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1927	C₂	1	2	yes	maximal, complemented
11	C₄×#102×C₃₇	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×#124×C₃₇	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
16	C₃₇×#487	—	2	4	no	—
17	C₃₇×#476	—	2	4	no	—
18	C₂×#106×C₃₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
21	C₂×#103×C₃₇	C₂²	1	2	yes	—
22	C₂×#103×C₃₇	C₂²	1	2	yes	—
23	C₂×#103×C₃₇	C₂²	1	2	yes	—
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×#102×C₃₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
29	C₃₇×#397	—	2	2	no	—
30	C₃₇×#391	—	2	2	no	—
31	C₃₇×#391	C₂²	1	2	yes	—
32	C₃₇×#389	—	2	1	no	—
33	C₃₇×#389	C₂²	1	2	yes	—
34	C₃₇×#380	—	2	1	no	—
35	C₃₇×#380	—	2	1	no	—
36	C₄×C₄⋊C₄×C₃₇	—	2	1	no	—
37	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
38	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
40	C₃₇×#340	C₂²	1	1	yes	characteristic
41	C₃₇×#340	C₂²	1	1	yes	characteristic
42	C₃₇×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₃₇	—	2	1	no	—
44	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
45	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₃₇	—	2	1	no	—
47	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
50	C₄⋊Q₈×C₃₇	—	2	2	no	—
51	C₄⋊Q₈×C₃₇	—	2	2	no	—
52	C₄⋊Q₈×C₃₇	—	2	2	no	—
53	C₄⋊Q₈×C₃₇	D₄	1	4	yes	—
54	#124×C₃₇	—	2	4	no	—
55	#124×C₃₇	—	4	2	no	—
56	C₄×D₄×C₃₇	—	2	2	no	—
57	C₄×D₄×C₃₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
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	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
71	C₂×C₄²×C₃₇	—	2	1	no	—
72	C₂×C₄²×C₃₇	—	2	2	no	—
73	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
74	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
75	#106×C₃₇	—	2	4	no	—
76	C₄⋊C₈×C₃₇	—	2	2	no	—
77	C₄⋊C₈×C₃₇	—	4	2	no	—
78	#103×C₃₇	—	2	4	no	—
79	#103×C₃₇	—	2	4	no	—
80	#103×C₃₇	—	2	4	no	—
81	#103×C₃₇	—	4	2	no	—
82	#102×C₃₇	—	2	2	no	—
83	#102×C₃₇	—	2	4	no	—
84	#102×C₃₇	—	2	2	no	—
85	C₄×C₈×C₃₇	—	2	2	no	—
86	#95×C₃₇	—	2	2	no	—
87	#95×C₃₇	—	2	2	no	—
88	#95×C₃₇	—	2	1	no	—
89	#95×C₃₇	—	2	2	no	—
90	#95×C₃₇	—	2	2	no	—
91	#95×C₃₇	D₄	1	2	yes	—
92	C₂⁴×C₃₇	—	2	1	no	—
93	C₂×Q₈×C₃₇	—	2	4	no	—
94	C₂×Q₈×C₃₇	—	2	2	no	—
95	C₂×Q₈×C₃₇	—	2	2	no	—
96	C₂×Q₈×C₃₇	—	2	2	no	—
97	C₂×Q₈×C₃₇	—	2	2	no	—
98	C₂×Q₈×C₃₇	—	2	2	no	—
99	C₂×Q₈×C₃₇	—	2	2	no	—
100	C₂×Q₈×C₃₇	—	8	1	no	—
101	C₂×Q₈×C₃₇	—	8	1	no	—
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	#41	1	2	yes	—
108	C₂²×C₄×C₃₇	—	2	1	no	—
109	C₂²×C₄×C₃₇	—	2	2	no	—
110	C₂²×C₄×C₃₇	—	2	1	no	—
111	C₂²×C₄×C₃₇	—	2	1	no	—
112	C₂²×C₄×C₃₇	—	2	2	no	—
113	C₂²×C₄×C₃₇	—	4	2	no	—
114	C₂²×C₄×C₃₇	—	4	2	no	—
115	C₂²×C₄×C₃₇	—	4	2	no	—
116	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
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	1	no	—
125	C₂×C₈×C₃₇	—	2	1	no	—
126	C₂×C₈×C₃₇	—	2	2	no	—
127	C₂×C₈×C₃₇	—	2	2	no	—
128	C₂×C₈×C₃₇	—	2	1	no	—
129	C₂×C₈×C₃₇	—	2	1	no	—
130	C₄⋊C₄×C₃₇	—	2	4	no	—
131	C₄⋊C₄×C₃₇	—	2	2	no	—
132	C₄⋊C₄×C₃₇	—	2	2	no	—
133	C₄⋊C₄×C₃₇	—	2	2	no	—
134	C₄⋊C₄×C₃₇	—	2	1	no	—
135	C₄⋊C₄×C₃₇	—	2	1	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	—	4	2	no	—
140	C₄⋊C₄×C₃₇	—	4	2	no	—
141	C₄⋊C₄×C₃₇	—	8	2	no	—
142	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
143	C₄⋊C₄×C₃₇	#41	1	2	yes	—
144	C₂²⋊C₄×C₃₇	—	4	4	no	—
145	C₂²⋊C₄×C₃₇	—	4	4	no	—
146	C₂²⋊C₄×C₃₇	—	4	2	no	—
147	C₄²×C₃₇	—	2	2	no	—
148	C₄²×C₃₇	—	2	2	no	—
149	C₄²×C₃₇	—	4	2	no	—
150	C₄²×C₃₇	—	8	2	no	—
151	C₄²×C₃₇	C₂×D₄	1	2	yes	—
152	C₄²×C₃₇	#41	1	2	yes	—
153	C₂³×C₃₇	—	2	2	no	—
154	C₂³×C₃₇	—	4	1	no	—
155	C₂³×C₃₇	—	4	1	no	—
156	C₂³×C₃₇	—	4	1	no	—
157	C₂³×C₃₇	—	4	1	no	—
158	C₂³×C₃₇	—	4	1	no	—
159	C₂³×C₃₇	—	4	1	no	—
160	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₃₇	—	4	2	no	—
162	Q₈×C₃₇	—	4	2	no	—
163	Q₈×C₃₇	—	4	2	no	—
164	Q₈×C₃₇	—	4	2	no	—
165	Q₈×C₃₇	—	8	4	no	—
166	D₄×C₃₇	—	2	2	no	—
167	D₄×C₃₇	—	2	2	no	—
168	D₄×C₃₇	—	4	1	no	—
169	D₄×C₃₇	—	4	1	no	—
170	C₂×C₄×C₃₇	—	2	1	no	—
171	C₂×C₄×C₃₇	—	2	1	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	—	2	2	no	—
177	C₂×C₄×C₃₇	—	2	2	no	—
178	C₂×C₄×C₃₇	—	2	2	no	—
179	C₂×C₄×C₃₇	—	2	2	no	—
180	C₂×C₄×C₃₇	—	4	1	no	—
181	C₂×C₄×C₃₇	—	4	1	no	—
182	C₂×C₄×C₃₇	—	4	2	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	2	no	—
187	C₂×C₄×C₃₇	—	4	1	no	—
188	C₂×C₄×C₃₇	—	4	2	no	—
189	C₂×C₄×C₃₇	—	4	1	no	—
190	C₂×C₄×C₃₇	—	4	1	no	—
191	C₂×C₄×C₃₇	—	4	1	no	—
192	C₂×C₄×C₃₇	—	4	1	no	—
193	C₂×C₄×C₃₇	—	8	4	no	—
194	C₂×C₄×C₃₇	#121	1	2	yes	—
195	C₂×C₄×C₃₇	#121	1	2	yes	—
196	C₂×C₄×C₃₇	#135	1	2	yes	—
197	C₂×C₄×C₃₇	#137	1	2	yes	—
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	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
203	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
204	C₈×C₃₇	—	4	1	no	—
205	C₈×C₃₇	—	4	1	no	—
206	C₈×C₃₇	—	4	2	no	—
207	#25273	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂²×C₃₇	—	4	2	no	—
209	C₂²×C₃₇	—	4	2	no	—
210	C₂²×C₃₇	—	4	2	no	—
211	C₂²×C₃₇	—	8	1	no	—
212	C₂²×C₃₇	—	8	1	no	—
213	C₂²×C₃₇	—	8	1	no	—
214	C₂²×C₃₇	—	8	1	no	—
215	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
216	C₂²×C₃₇	#546	1	1	yes	characteristic
217	C₂²×C₃₇	#548	1	1	yes	characteristic
218	C₂²×C₃₇	C₂×#135	1	1	yes	characteristic
219	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
220	C₂²×C₃₇	#577	1	1	yes	characteristic
221	C₂²×C₃₇	#577	1	1	yes	characteristic
222	C₄×C₃₇	—	2	2	no	—
223	C₄×C₃₇	—	4	2	no	—
224	C₄×C₃₇	—	4	2	no	—
225	C₄×C₃₇	—	4	4	no	—
226	C₄×C₃₇	—	4	2	no	—
227	C₄×C₃₇	—	8	2	no	—
228	C₄×C₃₇	—	8	1	no	—
229	C₄×C₃₇	—	8	1	no	—
230	C₄×C₃₇	#464	1	4	yes	—
231	C₄×C₃₇	#529	1	1	yes	characteristic
232	C₄×C₃₇	#542	1	1	yes	characteristic
233	C₄×C₃₇	#548	1	1	yes	characteristic
234	C₄×C₃₇	#550	1	1	yes	characteristic
235	C₂×#487	C₂×C₃₇	1	1	yes	characteristic, complemented
236	C₂×#476	C₂×C₃₇	1	1	yes	characteristic
237	#2547	C₂×C₃₇	1	1	yes	characteristic
238	#2369	C₂×C₃₇	1	1	yes	characteristic, complemented
239	#2066	C₂×C₃₇	1	2	yes	complemented
240	#2042	C₂×C₃₇	1	2	yes	—
241	#1983	C₂×C₃₇	1	2	yes	—
242	#1981	C₂×C₃₇	1	1	yes	characteristic, complemented
243	#1939	C₂×C₃₇	1	1	yes	characteristic, complemented
244	#1927	C₂×C₃₇	1	2	yes	complemented
245	C₄×#102	C₂×C₃₇	1	1	yes	characteristic
246	C₂×C₃₇	—	8	2	no	—
247	C₂×C₃₇	#2426	1	1	yes	characteristic
248	C₂×C₃₇	C₂×#464	1	1	yes	characteristic
249	C₂×C₃₇	#3042	1	1	yes	characteristic
250	C₂×C₃₇	#3303	1	1	yes	characteristic
251	C₂×C₃₇	#3331	1	1	yes	characteristic
252	C₂×C₃₇	#3360	1	1	yes	characteristic
253	C₂×C₃₇	#3369	1	1	yes	characteristic
254	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
255	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
256	C₂×#124	C₂²×C₃₇	1	2	yes	—
257	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
258	#487	—	2	4	no	—
259	#476	—	2	4	no	—
260	C₂×#106	C₂²×C₃₇	1	2	yes	—
261	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
263	C₂×#103	C₂²×C₃₇	1	2	yes	—
264	C₂×#103	C₂²×C₃₇	1	2	yes	—
265	C₂×#103	C₂²×C₃₇	1	2	yes	—
266	C₂×#103	C₂²×C₃₇	1	2	yes	—
267	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
268	C₂×#102	C₂²×C₃₇	1	2	yes	—
269	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
270	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
271	#397	—	2	2	no	—
272	#391	—	2	2	no	—
273	#391	C₂²×C₃₇	1	2	yes	—
274	#389	—	2	1	no	—
275	#389	C₂²×C₃₇	1	2	yes	—
276	#380	—	2	1	no	—
277	#380	—	2	1	no	—
278	C₄×C₄⋊C₄	—	2	1	no	—
279	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
280	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
281	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
282	#340	C₂²×C₃₇	1	1	yes	characteristic
283	#340	C₂²×C₃₇	1	1	yes	characteristic
284	#336	C₂²×C₃₇	1	2	yes	—
285	C₃₇	#25273	1	1	yes	characteristic, direct product factor, Sylow
286	C₂²×Q₈	—	2	1	no	—
287	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
288	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
289	C₂³×C₄	—	2	1	no	—
290	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
292	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
293	C₄⋊Q₈	—	2	2	no	—
294	C₄⋊Q₈	—	2	2	no	—
295	C₄⋊Q₈	—	2	2	no	—
296	C₄⋊Q₈	D₄×C₃₇	1	4	yes	—
297	#124	—	2	4	no	—
298	#124	—	4	2	no	—
299	C₄×D₄	—	2	2	no	—
300	C₄×D₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
306	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₄²	—	2	1	no	—
315	C₂×C₄²	—	2	2	no	—
316	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
317	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
318	#106	—	2	4	no	—
319	C₄⋊C₈	—	2	2	no	—
320	C₄⋊C₈	—	4	2	no	—
321	#103	—	2	4	no	—
322	#103	—	2	4	no	—
323	#103	—	2	4	no	—
324	#103	—	4	2	no	—
325	#102	—	2	2	no	—
326	#102	—	2	4	no	—
327	#102	—	2	2	no	—
328	C₄×C₈	—	2	2	no	—
329	#95	—	2	2	no	—
330	#95	—	2	2	no	—
331	#95	—	2	1	no	—
332	#95	—	2	2	no	—
333	#95	—	2	2	no	—
334	#95	D₄×C₃₇	1	2	yes	—
335	C₂⁴	—	2	1	no	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	8	1	no	—
344	C₂×Q₈	—	8	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	#41×C₃₇	1	2	yes	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
363	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	—	8	2	no	—
385	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
386	C₄⋊C₄	#41×C₃₇	1	2	yes	—
387	C₂²⋊C₄	—	4	4	no	—
388	C₂²⋊C₄	—	4	4	no	—
389	C₂²⋊C₄	—	4	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	4	2	no	—
393	C₄²	—	8	2	no	—
394	C₄²	C₂×D₄×C₃₇	1	2	yes	—
395	C₄²	#41×C₃₇	1	2	yes	—
396	C₂³	—	2	2	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
404	Q₈	—	4	2	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	4	2	no	—
407	Q₈	—	4	2	no	—
408	Q₈	—	8	4	no	—
409	D₄	—	2	2	no	—
410	D₄	—	2	2	no	—
411	D₄	—	4	1	no	—
412	D₄	—	4	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	8	4	no	—
437	C₂×C₄	#121×C₃₇	1	2	yes	—
438	C₂×C₄	#121×C₃₇	1	2	yes	—
439	C₂×C₄	#135×C₃₇	1	2	yes	—
440	C₂×C₄	#137×C₃₇	1	2	yes	—
441	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
442	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
443	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
444	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
445	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
446	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
447	C₈	—	4	1	no	—
448	C₈	—	4	1	no	—
449	C₈	—	4	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	8	1	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
458	C₂²	C₃₇×#546	1	1	yes	characteristic
459	C₂²	C₃₇×#548	1	1	yes	characteristic
460	C₂²	C₂×#135×C₃₇	1	1	yes	characteristic
461	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
462	C₂²	C₃₇×#577	1	1	yes	characteristic
463	C₂²	C₃₇×#577	1	1	yes	characteristic
464	C₄	—	2	2	no	—
465	C₄	—	4	4	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	8	2	no	—
470	C₄	—	8	1	no	—
471	C₄	—	8	1	no	—
472	C₄	C₃₇×#464	1	4	yes	—
473	C₄	C₃₇×#529	1	1	yes	characteristic
474	C₄	C₃₇×#542	1	1	yes	characteristic
475	C₄	C₃₇×#548	1	1	yes	characteristic
476	C₄	C₃₇×#550	1	1	yes	characteristic
477	C₂	—	8	2	no	—
478	C₂	C₃₇×#2426	1	1	yes	characteristic
479	C₂	C₂×C₃₇×#464	1	1	yes	characteristic
480	C₂	C₃₇×#3042	1	1	yes	characteristic
481	C₂	C₃₇×#3303	1	1	yes	characteristic
482	C₂	C₃₇×#3331	1	1	yes	characteristic
483	C₂	C₃₇×#3360	1	1	yes	characteristic
484	C₂	C₃₇×#3369	1	1	yes	characteristic

	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×#487	C₂	semidirect
4. C₃₇×#2369	C₂	semidirect
5. C₃₇×#2066	C₂	semidirect
8. C₃₇×#1981	C₂	semidirect
9. C₃₇×#1939	C₂	semidirect
10. C₃₇×#1927	C₂	semidirect
207. #25273	C₃₇	direct (N × H)
235. C₂×#487	C₂×C₃₇	semidirect
238. #2369	C₂×C₃₇	semidirect
239. #2066	C₂×C₃₇	semidirect
242. #1981	C₂×C₃₇	semidirect
243. #1939	C₂×C₃₇	semidirect
244. #1927	C₂×C₃₇	semidirect
285. C₃₇	#25273	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×#487	2
C₂×C₃₇×#476	2
C₃₇×#2547	2
C₃₇×#2369	2
C₃₇×#2066	2
C₃₇×#2042	2
C₃₇×#1983	2
C₃₇×#1981	2
C₃₇×#1939	2
C₃₇×#1927	2
C₄×#102×C₃₇	2
#25273	37

Subgroups — C37×#25273 #22646526

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#25273 #22646526