Subgroups — C₃₇×#25301 #22646554

Order 9472.

830 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#461	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#2568	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2538	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2068	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2055	C₂	1	2	yes	maximal
7	C₃₇×#1973	C₂	1	2	yes	maximal
8	C₃₇×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1947	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1935	C₂	1	2	yes	maximal, complemented
11	C₄×#102×C₃₇	C₂	1	1	yes	maximal, characteristic
12	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
13	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₃₇	—	2	1	no	—
15	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
17	C₃₇×#461	—	2	4	no	—
18	C₃₇×#446	—	2	4	no	—
19	C₂×#107×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×#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	1	yes	characteristic
27	C₂×#97×C₃₇	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
29	C₃₇×#400	—	2	2	no	—
30	C₃₇×#396	—	2	2	no	—
31	C₃₇×#391	—	2	1	no	—
32	C₃₇×#391	C₂²	1	2	yes	—
33	C₃₇×#391	C₂²	1	2	yes	—
34	C₃₇×#390	C₂²	1	2	yes	—
35	C₃₇×#389	C₂²	1	2	yes	—
36	C₃₇×#384	C₂²	1	1	yes	characteristic
37	C₃₇×#382	—	2	1	no	—
38	C₃₇×#380	—	2	1	no	—
39	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
40	C₃₇×#340	C₂²	1	1	yes	characteristic
41	C₃₇×#340	C₂²	1	2	yes	—
42	C₃₇×#340	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₃₇	D₄	1	1	yes	characteristic
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	C₂×SD₁₆×C₃₇	—	2	4	no	—
48	C₂×SD₁₆×C₃₇	—	2	4	no	—
49	C₂×SD₁₆×C₃₇	—	4	2	no	—
50	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
52	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
53	C₄⋊Q₈×C₃₇	—	2	2	no	—
54	C₄⋊Q₈×C₃₇	—	2	2	no	—
55	C₂²⋊Q₈×C₃₇	—	4	4	no	—
56	C₄×Q₈×C₃₇	—	2	2	no	—
57	C₄×Q₈×C₃₇	—	2	2	no	—
58	C₄×D₄×C₃₇	—	2	2	no	—
59	C₄×D₄×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	—	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	1	yes	characteristic
66	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
71	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
74	C₂×C₄²×C₃₇	—	2	1	no	—
75	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
76	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
77	#107×C₃₇	—	4	2	no	—
78	C₄⋊C₈×C₃₇	—	2	4	no	—
79	C₄⋊C₈×C₃₇	D₄	1	4	yes	—
80	#103×C₃₇	—	2	4	no	—
81	#103×C₃₇	—	2	4	no	—
82	#103×C₃₇	—	4	2	no	—
83	#102×C₃₇	—	2	2	no	—
84	#102×C₃₇	—	2	2	no	—
85	#97×C₃₇	—	2	4	no	—
86	C₄×C₈×C₃₇	—	2	2	no	—
87	#95×C₃₇	—	2	1	no	—
88	#95×C₃₇	—	2	2	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	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	—	2	2	no	—
101	C₂×Q₈×C₃₇	—	2	2	no	—
102	C₂×Q₈×C₃₇	—	2	2	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	—	2	1	no	—
108	C₂×D₄×C₃₇	#41	1	2	yes	—
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	1	no	—
113	C₂²×C₄×C₃₇	—	2	2	no	—
114	C₂²×C₄×C₃₇	—	4	2	no	—
115	C₂²×C₄×C₃₇	—	4	2	no	—
116	C₂²×C₄×C₃₇	—	4	2	no	—
117	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
122	SD₁₆×C₃₇	—	4	8	no	—
123	C₂×C₈×C₃₇	—	2	1	no	—
124	C₂×C₈×C₃₇	—	2	2	no	—
125	C₂×C₈×C₃₇	—	2	2	no	—
126	C₂×C₈×C₃₇	—	2	1	no	—
127	C₂×C₈×C₃₇	—	2	1	no	—
128	C₂×C₈×C₃₇	—	2	1	no	—
129	C₂×C₈×C₃₇	—	2	1	no	—
130	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
131	C₂×C₈×C₃₇	#41	1	2	yes	—
132	C₄⋊C₄×C₃₇	—	2	2	no	—
133	C₄⋊C₄×C₃₇	—	2	4	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	2	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	—	2	1	no	—
142	C₄⋊C₄×C₃₇	—	4	4	no	—
143	C₄⋊C₄×C₃₇	—	4	2	no	—
144	C₄⋊C₄×C₃₇	—	4	2	no	—
145	C₄⋊C₄×C₃₇	—	4	2	no	—
146	C₄⋊C₄×C₃₇	—	8	1	no	—
147	C₂²⋊C₄×C₃₇	—	4	4	no	—
148	C₂²⋊C₄×C₃₇	—	4	2	no	—
149	C₂²⋊C₄×C₃₇	—	8	2	no	—
150	C₄²×C₃₇	—	2	2	no	—
151	C₄²×C₃₇	—	2	2	no	—
152	C₄²×C₃₇	—	4	2	no	—
153	C₄²×C₃₇	C₂×D₄	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	1	no	—
159	C₂³×C₃₇	—	4	1	no	—
160	C₂³×C₃₇	—	4	1	no	—
161	C₂³×C₃₇	—	4	1	no	—
162	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₃₇	—	4	4	no	—
164	Q₈×C₃₇	—	4	2	no	—
165	Q₈×C₃₇	—	4	2	no	—
166	Q₈×C₃₇	—	4	2	no	—
167	Q₈×C₃₇	—	4	2	no	—
168	D₄×C₃₇	—	2	2	no	—
169	D₄×C₃₇	—	2	2	no	—
170	D₄×C₃₇	—	4	1	no	—
171	D₄×C₃₇	—	4	1	no	—
172	C₂×C₄×C₃₇	—	2	1	no	—
173	C₂×C₄×C₃₇	—	2	1	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	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	2	no	—
187	C₂×C₄×C₃₇	—	4	1	no	—
188	C₂×C₄×C₃₇	—	4	1	no	—
189	C₂×C₄×C₃₇	—	4	2	no	—
190	C₂×C₄×C₃₇	—	4	1	no	—
191	C₂×C₄×C₃₇	—	4	1	no	—
192	C₂×C₄×C₃₇	—	4	2	no	—
193	C₂×C₄×C₃₇	—	4	1	no	—
194	C₂×C₄×C₃₇	—	4	1	no	—
195	C₂×C₄×C₃₇	—	8	4	no	—
196	C₂×C₄×C₃₇	#121	1	2	yes	—
197	C₂×C₄×C₃₇	#121	1	2	yes	—
198	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
199	C₂×C₄×C₃₇	#137	1	2	yes	—
200	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
205	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
206	C₈×C₃₇	—	2	4	no	—
207	C₈×C₃₇	—	2	2	no	—
208	C₈×C₃₇	—	4	1	no	—
209	#25301	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂²×C₃₇	—	4	2	no	—
211	C₂²×C₃₇	—	4	2	no	—
212	C₂²×C₃₇	—	4	2	no	—
213	C₂²×C₃₇	—	8	1	no	—
214	C₂²×C₃₇	—	8	1	no	—
215	C₂²×C₃₇	—	8	1	no	—
216	C₂²×C₃₇	—	8	1	no	—
217	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
218	C₂²×C₃₇	#548	1	1	yes	characteristic
219	C₂²×C₃₇	#550	1	1	yes	characteristic
220	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
221	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
222	C₂²×C₃₇	#577	1	1	yes	characteristic
223	C₂²×C₃₇	#578	1	1	yes	characteristic
224	C₄×C₃₇	—	2	2	no	—
225	C₄×C₃₇	—	4	2	no	—
226	C₄×C₃₇	—	4	2	no	—
227	C₄×C₃₇	—	8	1	no	—
228	C₄×C₃₇	—	8	1	no	—
229	C₄×C₃₇	—	8	2	no	—
230	C₄×C₃₇	—	8	2	no	—
231	C₄×C₃₇	—	8	1	no	—
232	C₄×C₃₇	#468	1	4	yes	—
233	C₄×C₃₇	#529	1	1	yes	characteristic
234	C₄×C₃₇	#542	1	1	yes	characteristic
235	C₄×C₃₇	#546	1	1	yes	characteristic
236	C₄×C₃₇	#548	1	1	yes	characteristic
237	C₂×#461	C₂×C₃₇	1	1	yes	characteristic
238	C₂×#446	C₂×C₃₇	1	1	yes	characteristic, complemented
239	#2568	C₂×C₃₇	1	1	yes	characteristic, complemented
240	#2538	C₂×C₃₇	1	1	yes	characteristic
241	#2068	C₂×C₃₇	1	2	yes	complemented
242	#2055	C₂×C₃₇	1	2	yes	—
243	#1973	C₂×C₃₇	1	2	yes	—
244	#1956	C₂×C₃₇	1	1	yes	characteristic, complemented
245	#1947	C₂×C₃₇	1	1	yes	characteristic, complemented
246	#1935	C₂×C₃₇	1	2	yes	complemented
247	C₄×#102	C₂×C₃₇	1	1	yes	characteristic
248	C₂×C₃₇	—	8	2	no	—
249	C₂×C₃₇	#2426	1	1	yes	characteristic
250	C₂×C₃₇	C₂×#468	1	1	yes	characteristic
251	C₂×C₃₇	#3063	1	1	yes	characteristic
252	C₂×C₃₇	#3367	1	1	yes	characteristic
253	C₂×C₃₇	#3372	1	1	yes	characteristic
254	C₂×C₃₇	#3397	1	1	yes	characteristic
255	C₂×C₃₇	#3398	1	1	yes	characteristic
256	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
257	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
258	C₂×C₂²⋊Q₈	—	2	1	no	—
259	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
260	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
261	#461	—	2	4	no	—
262	#446	—	2	4	no	—
263	C₂×#107	C₂²×C₃₇	1	2	yes	—
264	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
265	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
266	C₂×#103	C₂²×C₃₇	1	2	yes	—
267	C₂×#103	C₂²×C₃₇	1	2	yes	—
268	C₂×#103	C₂²×C₃₇	1	2	yes	—
269	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
270	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
271	C₂×#97	C₂²×C₃₇	1	2	yes	—
272	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
273	#400	—	2	2	no	—
274	#396	—	2	2	no	—
275	#391	—	2	1	no	—
276	#391	C₂²×C₃₇	1	2	yes	—
277	#391	C₂²×C₃₇	1	2	yes	—
278	#390	C₂²×C₃₇	1	2	yes	—
279	#389	C₂²×C₃₇	1	2	yes	—
280	#384	C₂²×C₃₇	1	1	yes	characteristic
281	#382	—	2	1	no	—
282	#380	—	2	1	no	—
283	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
284	#340	C₂²×C₃₇	1	2	yes	—
285	#340	C₂²×C₃₇	1	1	yes	characteristic
286	#340	C₂²×C₃₇	1	1	yes	characteristic
287	C₃₇	#25301	1	1	yes	characteristic, direct product factor, Sylow
288	C₂²×Q₈	D₄×C₃₇	1	1	yes	characteristic
289	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
290	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
291	C₂³×C₄	—	2	1	no	—
292	C₂×SD₁₆	—	2	4	no	—
293	C₂×SD₁₆	—	2	4	no	—
294	C₂×SD₁₆	—	4	2	no	—
295	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
297	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
298	C₄⋊Q₈	—	2	2	no	—
299	C₄⋊Q₈	—	2	2	no	—
300	C₂²⋊Q₈	—	4	4	no	—
301	C₄×Q₈	—	2	2	no	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
311	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
321	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
322	#107	—	4	2	no	—
323	C₄⋊C₈	—	2	4	no	—
324	C₄⋊C₈	D₄×C₃₇	1	4	yes	—
325	#103	—	2	4	no	—
326	#103	—	2	4	no	—
327	#103	—	4	2	no	—
328	#102	—	2	2	no	—
329	#102	—	2	2	no	—
330	#97	—	2	4	no	—
331	C₄×C₈	—	2	2	no	—
332	#95	—	2	1	no	—
333	#95	—	2	2	no	—
334	#95	—	2	2	no	—
335	#95	—	2	2	no	—
336	#95	—	2	2	no	—
337	#95	—	2	2	no	—
338	C₂⁴	—	2	1	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	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	#41×C₃₇	1	2	yes	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
367	SD₁₆	—	4	8	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	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
376	C₂×C₈	#41×C₃₇	1	2	yes	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	4	4	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	—	8	1	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₂²⋊C₄	—	4	2	no	—
394	C₂²⋊C₄	—	8	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	4	2	no	—
398	C₄²	C₂×D₄×C₃₇	1	2	yes	—
399	C₄²	#41×C₃₇	1	2	yes	—
400	C₂³	—	2	2	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
408	Q₈	—	4	4	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	4	2	no	—
412	Q₈	—	4	2	no	—
413	D₄	—	2	2	no	—
414	D₄	—	2	2	no	—
415	D₄	—	4	1	no	—
416	D₄	—	4	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	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	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	8	4	no	—
441	C₂×C₄	#121×C₃₇	1	2	yes	—
442	C₂×C₄	#121×C₃₇	1	2	yes	—
443	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
444	C₂×C₄	#137×C₃₇	1	2	yes	—
445	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
446	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
447	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
448	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
449	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
450	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
451	C₈	—	2	4	no	—
452	C₈	—	2	2	no	—
453	C₈	—	4	1	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	—	8	1	no	—
460	C₂²	—	8	1	no	—
461	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
462	C₂²	C₃₇×#548	1	1	yes	characteristic
463	C₂²	C₃₇×#550	1	1	yes	characteristic
464	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
465	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
466	C₂²	C₃₇×#577	1	1	yes	characteristic
467	C₂²	C₃₇×#578	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	8	1	no	—
472	C₄	—	8	2	no	—
473	C₄	—	8	2	no	—
474	C₄	—	8	1	no	—
475	C₄	—	8	1	no	—
476	C₄	C₃₇×#468	1	4	yes	—
477	C₄	C₃₇×#529	1	1	yes	characteristic
478	C₄	C₃₇×#542	1	1	yes	characteristic
479	C₄	C₃₇×#546	1	1	yes	characteristic
480	C₄	C₃₇×#548	1	1	yes	characteristic
481	C₂	—	8	2	no	—
482	C₂	C₃₇×#2426	1	1	yes	characteristic
483	C₂	C₂×C₃₇×#468	1	1	yes	characteristic
484	C₂	C₃₇×#3063	1	1	yes	characteristic
485	C₂	C₃₇×#3367	1	1	yes	characteristic
486	C₂	C₃₇×#3372	1	1	yes	characteristic
487	C₂	C₃₇×#3397	1	1	yes	characteristic
488	C₂	C₃₇×#3398	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 ◁ C₂×C₄×Q₈×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₇×#446	C₂	semidirect
3. C₃₇×#2568	C₂	semidirect
5. C₃₇×#2068	C₂	semidirect
8. C₃₇×#1956	C₂	semidirect
9. C₃₇×#1947	C₂	semidirect
10. C₃₇×#1935	C₂	semidirect
209. #25301	C₃₇	direct (N × H)
238. C₂×#446	C₂×C₃₇	semidirect
239. #2568	C₂×C₃₇	semidirect
241. #2068	C₂×C₃₇	semidirect
244. #1956	C₂×C₃₇	semidirect
245. #1947	C₂×C₃₇	semidirect
246. #1935	C₂×C₃₇	semidirect
287. C₃₇	#25301	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×#461	2
C₂×C₃₇×#446	2
C₃₇×#2568	2
C₃₇×#2538	2
C₃₇×#2068	2
C₃₇×#2055	2
C₃₇×#1973	2
C₃₇×#1956	2
C₃₇×#1947	2
C₃₇×#1935	2
C₄×#102×C₃₇	2
#25301	37

Subgroups — C37×#25301 #22646554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#25301 #22646554