Subgroups — C₃₇×#18882 #22640135

Order 9472.

1150 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3245	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3226	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#1649	C₂	1	2	yes	maximal, complemented
6	C₃₇×#1647	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1627	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1625	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₇×#332	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1480	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1477	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₃₇	—	2	1	no	—
13	C₂×#135×C₃₇	—	2	1	no	—
14	D₄×Q₈×C₃₇	—	2	1	no	—
15	D₄×Q₈×C₃₇	C₂²	1	2	yes	—
16	C₃₇×#547	—	2	2	no	—
17	C₃₇×#547	—	2	1	no	—
18	C₃₇×#547	—	2	2	no	—
19	C₃₇×#547	C₂²	1	2	yes	—
20	C₃₇×#536	—	2	2	no	—
21	C₃₇×#536	—	2	1	no	—
22	C₃₇×#532	—	2	1	no	—
23	C₃₇×#532	C₂²	1	1	yes	characteristic
24	C₃₇×#532	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₃₇	—	2	1	no	—
26	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
27	C₄×#41×C₃₇	C₂²	1	1	yes	characteristic
28	C₃₇×#500	C₂²	1	2	yes	—
29	C₃₇×#486	C₂²	1	2	yes	—
30	C₃₇×#480	—	2	2	no	—
31	C₃₇×#474	—	2	2	no	—
32	C₃₇×#474	—	2	1	no	—
33	C₃₇×#474	C₂²	1	2	yes	—
34	C₃₇×#466	—	2	2	no	—
35	C₃₇×#464	—	2	1	no	—
36	C₃₇×#463	—	2	1	no	—
37	C₃₇×#462	C₂²	1	1	yes	characteristic
38	C₃₇×#461	C₂²	1	1	yes	characteristic
39	C₃₇×#460	C₂²	1	1	yes	characteristic
40	C₃₇×#459	—	2	1	no	—
41	C₃₇×#459	C₂²	1	1	yes	characteristic
42	C₃₇×#459	C₂²	1	2	yes	—
43	C₃₇×#431	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
46	C₃₇×#416	—	2	1	no	—
47	C₃₇×#332	C₂²	1	2	yes	—
48	C₃₇×#332	C₂²	1	2	yes	—
49	C₃₇×Q₈⋊C₈	C₂²	1	2	yes	—
50	C₃₇×D₄⋊C₈	C₂²	1	2	yes	—
51	C₃₇×D₄⋊C₈	C₂²	1	2	yes	—
52	C₃₇×D₄⋊C₈	C₂²	1	2	yes	—
53	2₋¹⁺⁴×C₃₇	—	4	4	no	—
54	2₋¹⁺⁴×C₃₇	—	4	4	no	—
55	C₂×#41×C₃₇	—	2	2	no	—
56	C₂×#41×C₃₇	—	2	4	no	—
57	C₂×#41×C₃₇	—	2	2	no	—
58	C₂×#41×C₃₇	—	2	1	no	—
59	C₂×#41×C₃₇	—	2	1	no	—
60	C₂×#41×C₃₇	D₄	1	1	yes	characteristic
61	C₂²×Q₈×C₃₇	—	2	2	no	—
62	C₂²×Q₈×C₃₇	—	2	2	no	—
63	C₂²×Q₈×C₃₇	—	2	1	no	—
64	#135×C₃₇	—	4	4	no	—
65	C₂×Q₁₆×C₃₇	—	2	1	no	—
66	C₂×SD₁₆×C₃₇	—	2	1	no	—
67	C₂×SD₁₆×C₃₇	—	2	1	no	—
68	C₂×D₈×C₃₇	—	2	1	no	—
69	C₂×D₈×C₃₇	—	2	2	no	—
70	C₂²×C₈×C₃₇	—	2	1	no	—
71	C₂²×C₈×C₃₇	—	2	1	no	—
72	C₄⋊Q₈×C₃₇	—	2	2	no	—
73	C₄⋊Q₈×C₃₇	—	2	2	no	—
74	C₄⋊Q₈×C₃₇	—	2	2	no	—
75	C₄⋊Q₈×C₃₇	—	2	1	no	—
76	C₄⋊Q₈×C₃₇	—	2	1	no	—
77	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
78	C₄⋊Q₈×C₃₇	D₄	1	2	yes	—
79	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
80	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
81	#127×C₃₇	D₄	1	1	yes	characteristic
82	#127×C₃₇	C₂³	1	1	yes	characteristic
83	#124×C₃₇	—	2	2	no	—
84	#124×C₃₇	—	2	1	no	—
85	#124×C₃₇	—	2	1	no	—
86	#123×C₃₇	—	2	4	no	—
87	#123×C₃₇	—	2	4	no	—
88	#123×C₃₇	—	2	4	no	—
89	C₂²⋊Q₈×C₃₇	—	2	4	no	—
90	C₂²⋊Q₈×C₃₇	—	2	2	no	—
91	C₂²⋊Q₈×C₃₇	—	2	4	no	—
92	C₂²⋊Q₈×C₃₇	—	2	2	no	—
93	#121×C₃₇	—	2	2	no	—
94	#121×C₃₇	—	2	2	no	—
95	#121×C₃₇	—	2	1	no	—
96	#121×C₃₇	—	2	1	no	—
97	#121×C₃₇	—	2	1	no	—
98	#121×C₃₇	D₄	1	2	yes	—
99	C₄×Q₈×C₃₇	D₄	1	1	yes	characteristic
100	C₄×Q₈×C₃₇	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₃₇	—	2	2	no	—
102	C₄×D₄×C₃₇	—	2	2	no	—
103	C₄×D₄×C₃₇	—	2	1	no	—
104	C₄×D₄×C₃₇	—	2	1	no	—
105	C₄×D₄×C₃₇	—	2	1	no	—
106	C₄×D₄×C₃₇	—	2	1	no	—
107	C₄×D₄×C₃₇	—	2	1	no	—
108	C₄×D₄×C₃₇	D₄	1	1	yes	characteristic
109	C₄×D₄×C₃₇	C₂³	1	2	yes	—
110	C₄×D₄×C₃₇	C₂³	1	1	yes	characteristic
111	#117×C₃₇	—	2	1	no	—
112	#117×C₃₇	D₄	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
114	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
115	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
116	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
117	C₂×C₄²×C₃₇	—	2	1	no	—
118	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
119	#107×C₃₇	—	2	2	no	—
120	#107×C₃₇	—	2	4	no	—
121	C₄⋊C₈×C₃₇	—	2	1	no	—
122	C₄⋊C₈×C₃₇	—	2	1	no	—
123	C₄⋊C₈×C₃₇	—	2	1	no	—
124	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
125	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
126	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
127	#103×C₃₇	—	2	1	no	—
128	#103×C₃₇	—	2	1	no	—
129	#102×C₃₇	—	2	2	no	—
130	#102×C₃₇	—	2	1	no	—
131	#102×C₃₇	—	2	1	no	—
132	#102×C₃₇	—	2	2	no	—
133	#102×C₃₇	—	2	4	no	—
134	C₂²⋊C₈×C₃₇	—	2	1	no	—
135	C₄×C₈×C₃₇	C₂³	1	2	yes	—
136	#41×C₃₇	—	2	2	no	—
137	#41×C₃₇	—	4	8	no	—
138	#41×C₃₇	—	4	16	no	—
139	#41×C₃₇	—	4	4	no	—
140	#41×C₃₇	—	4	4	no	—
141	#41×C₃₇	—	4	2	no	—
142	#41×C₃₇	—	4	2	no	—
143	#41×C₃₇	—	4	2	no	—
144	#41×C₃₇	—	4	2	no	—
145	#41×C₃₇	D₈	1	4	yes	complemented
146	C₂×Q₈×C₃₇	—	2	4	no	—
147	C₂×Q₈×C₃₇	—	2	2	no	—
148	C₂×Q₈×C₃₇	—	2	1	no	—
149	C₂×Q₈×C₃₇	—	2	2	no	—
150	C₂×Q₈×C₃₇	—	2	1	no	—
151	C₂×Q₈×C₃₇	—	4	8	no	—
152	C₂×Q₈×C₃₇	—	4	4	no	—
153	C₂×Q₈×C₃₇	—	4	4	no	—
154	C₂×Q₈×C₃₇	—	4	2	no	—
155	C₂×Q₈×C₃₇	—	4	2	no	—
156	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
157	C₂×D₄×C₃₇	—	2	1	no	—
158	C₂×D₄×C₃₇	—	2	4	no	—
159	C₂×D₄×C₃₇	—	2	2	no	—
160	C₂×D₄×C₃₇	—	2	1	no	—
161	C₂×D₄×C₃₇	—	2	1	no	—
162	C₂×D₄×C₃₇	—	2	1	no	—
163	C₂×D₄×C₃₇	—	2	1	no	—
164	C₂×D₄×C₃₇	—	2	1	no	—
165	C₂×D₄×C₃₇	—	4	1	no	—
166	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
167	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₃₇	—	2	1	no	—
169	C₂²×C₄×C₃₇	—	2	4	no	—
170	C₂²×C₄×C₃₇	—	2	4	no	—
171	C₂²×C₄×C₃₇	—	2	2	no	—
172	C₂²×C₄×C₃₇	—	2	1	no	—
173	C₂²×C₄×C₃₇	—	2	1	no	—
174	C₂²×C₄×C₃₇	—	2	2	no	—
175	C₂²×C₄×C₃₇	—	4	1	no	—
176	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
179	Q₁₆×C₃₇	—	4	2	no	—
180	SD₁₆×C₃₇	—	4	2	no	—
181	SD₁₆×C₃₇	—	4	2	no	—
182	D₈×C₃₇	—	4	2	no	—
183	D₈×C₃₇	—	8	2	no	—
184	C₂×C₈×C₃₇	—	2	2	no	—
185	C₂×C₈×C₃₇	—	2	2	no	—
186	C₂×C₈×C₃₇	—	2	1	no	—
187	C₂×C₈×C₃₇	—	2	1	no	—
188	C₂×C₈×C₃₇	—	4	2	no	—
189	C₂×C₈×C₃₇	—	8	1	no	—
190	C₄⋊C₄×C₃₇	—	2	4	no	—
191	C₄⋊C₄×C₃₇	—	2	4	no	—
192	C₄⋊C₄×C₃₇	—	2	1	no	—
193	C₄⋊C₄×C₃₇	—	2	2	no	—
194	C₄⋊C₄×C₃₇	—	2	2	no	—
195	C₄⋊C₄×C₃₇	—	2	1	no	—
196	C₄⋊C₄×C₃₇	—	2	2	no	—
197	C₄⋊C₄×C₃₇	—	2	1	no	—
198	C₄⋊C₄×C₃₇	—	2	1	no	—
199	C₄⋊C₄×C₃₇	—	2	1	no	—
200	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
201	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
202	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
203	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
204	C₂²⋊C₄×C₃₇	—	2	4	no	—
205	C₂²⋊C₄×C₃₇	—	2	4	no	—
206	C₂²⋊C₄×C₃₇	—	2	1	no	—
207	C₂²⋊C₄×C₃₇	—	2	1	no	—
208	C₂²⋊C₄×C₃₇	—	2	2	no	—
209	C₂²⋊C₄×C₃₇	—	2	1	no	—
210	C₂²⋊C₄×C₃₇	—	2	2	no	—
211	C₂²⋊C₄×C₃₇	—	4	1	no	—
212	C₂²⋊C₄×C₃₇	—	4	1	no	—
213	C₄²×C₃₇	—	2	1	no	—
214	C₄²×C₃₇	—	2	1	no	—
215	C₄²×C₃₇	—	2	1	no	—
216	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
220	C₂³×C₃₇	—	2	1	no	—
221	C₂³×C₃₇	—	2	2	no	—
222	C₂³×C₃₇	—	4	1	no	—
223	C₂³×C₃₇	#120	1	1	yes	characteristic
224	Q₈×C₃₇	—	2	1	no	—
225	Q₈×C₃₇	—	4	8	no	—
226	Q₈×C₃₇	—	4	2	no	—
227	Q₈×C₃₇	—	4	2	no	—
228	Q₈×C₃₇	—	4	2	no	—
229	Q₈×C₃₇	—	4	4	no	—
230	Q₈×C₃₇	—	4	1	no	—
231	Q₈×C₃₇	—	4	1	no	—
232	Q₈×C₃₇	C₂×D₈	1	2	yes	—
233	D₄×C₃₇	—	2	4	no	—
234	D₄×C₃₇	—	2	1	no	—
235	D₄×C₃₇	—	2	2	no	—
236	D₄×C₃₇	—	2	2	no	—
237	D₄×C₃₇	—	4	2	no	—
238	D₄×C₃₇	—	4	2	no	—
239	D₄×C₃₇	—	4	8	no	—
240	D₄×C₃₇	—	4	4	no	—
241	D₄×C₃₇	—	4	1	no	—
242	D₄×C₃₇	—	4	1	no	—
243	D₄×C₃₇	—	4	1	no	—
244	D₄×C₃₇	—	4	1	no	—
245	D₄×C₃₇	—	4	2	no	—
246	D₄×C₃₇	—	8	2	no	—
247	D₄×C₃₇	C₂×D₈	1	2	yes	—
248	C₂×C₄×C₃₇	—	2	1	no	—
249	C₂×C₄×C₃₇	—	2	1	no	—
250	C₂×C₄×C₃₇	—	2	1	no	—
251	C₂×C₄×C₃₇	—	2	4	no	—
252	C₂×C₄×C₃₇	—	2	1	no	—
253	C₂×C₄×C₃₇	—	2	1	no	—
254	C₂×C₄×C₃₇	—	2	4	no	—
255	C₂×C₄×C₃₇	—	2	2	no	—
256	C₂×C₄×C₃₇	—	4	1	no	—
257	C₂×C₄×C₃₇	—	4	2	no	—
258	C₂×C₄×C₃₇	—	4	8	no	—
259	C₂×C₄×C₃₇	—	4	8	no	—
260	C₂×C₄×C₃₇	—	4	4	no	—
261	C₂×C₄×C₃₇	—	4	2	no	—
262	C₂×C₄×C₃₇	—	4	2	no	—
263	C₂×C₄×C₃₇	—	4	1	no	—
264	C₂×C₄×C₃₇	—	4	1	no	—
265	C₂×C₄×C₃₇	—	4	1	no	—
266	C₂×C₄×C₃₇	—	8	2	no	—
267	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
268	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
269	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
270	C₂×C₄×C₃₇	C₂×D₈	1	2	yes	—
271	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
272	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
275	C₈×C₃₇	—	4	2	no	—
276	C₈×C₃₇	—	4	1	no	—
277	C₈×C₃₇	—	4	1	no	—
278	C₈×C₃₇	—	4	2	no	—
279	#18882	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
280	C₂²×C₃₇	—	2	1	no	—
281	C₂²×C₃₇	—	2	1	no	—
282	C₂²×C₃₇	—	2	2	no	—
283	C₂²×C₃₇	—	4	1	no	—
284	C₂²×C₃₇	—	4	1	no	—
285	C₂²×C₃₇	—	4	2	no	—
286	C₂²×C₃₇	—	4	2	no	—
287	C₂²×C₃₇	—	4	2	no	—
288	C₂²×C₃₇	—	8	1	no	—
289	C₂²×C₃₇	—	8	1	no	—
290	C₂²×C₃₇	—	8	1	no	—
291	C₂²×C₃₇	#447	1	2	yes	—
292	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
293	C₄×C₃₇	—	2	2	no	—
294	C₄×C₃₇	—	2	1	no	—
295	C₄×C₃₇	—	2	1	no	—
296	C₄×C₃₇	—	2	1	no	—
297	C₄×C₃₇	—	4	4	no	—
298	C₄×C₃₇	—	4	2	no	—
299	C₄×C₃₇	—	4	1	no	—
300	C₄×C₃₇	—	4	1	no	—
301	C₄×C₃₇	—	8	1	no	—
302	C₄×C₃₇	#447	1	2	yes	—
303	C₄×C₃₇	C₂²×D₈	1	1	yes	characteristic
304	C₄×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
305	C₄×C₃₇	#577	1	1	yes	characteristic
306	C₄×C₃₇	#578	1	1	yes	characteristic
307	#3499	C₂×C₃₇	1	1	yes	characteristic, complemented
308	#3245	C₂×C₃₇	1	1	yes	characteristic, complemented
309	#3226	C₂×C₃₇	1	1	yes	characteristic, complemented
310	#3035	C₂×C₃₇	1	1	yes	characteristic, complemented
311	#1649	C₂×C₃₇	1	2	yes	complemented
312	#1647	C₂×C₃₇	1	2	yes	complemented
313	#1627	C₂×C₃₇	1	2	yes	complemented
314	#1625	C₂×C₃₇	1	2	yes	complemented
315	C₂×#332	C₂×C₃₇	1	1	yes	characteristic, complemented
316	#1480	C₂×C₃₇	1	1	yes	characteristic, complemented
317	#1477	C₂×C₃₇	1	1	yes	characteristic, complemented
318	C₂×C₃₇	—	2	2	no	—
319	C₂×C₃₇	—	4	2	no	—
320	C₂×C₃₇	—	8	2	no	—
321	C₂×C₃₇	—	16	1	no	—
322	C₂×C₃₇	C₂×#447	1	1	yes	characteristic
323	C₂×C₃₇	#3013	1	1	yes	characteristic
324	C₂×C₃₇	#3020	1	1	yes	characteristic
325	C₂×2₋¹⁺⁴	—	2	1	no	—
326	C₂×#135	—	2	1	no	—
327	D₄×Q₈	—	2	1	no	—
328	D₄×Q₈	C₂²×C₃₇	1	2	yes	—
329	#547	—	2	2	no	—
330	#547	—	2	1	no	—
331	#547	—	2	2	no	—
332	#547	C₂²×C₃₇	1	2	yes	—
333	#536	—	2	2	no	—
334	#536	—	2	1	no	—
335	#532	—	2	1	no	—
336	#532	C₂²×C₃₇	1	1	yes	characteristic
337	#532	C₂²×C₃₇	1	1	yes	characteristic
338	C₂×C₄⋊Q₈	—	2	1	no	—
339	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
340	C₄×#41	C₂²×C₃₇	1	1	yes	characteristic
341	#500	C₂²×C₃₇	1	2	yes	—
342	#486	C₂²×C₃₇	1	2	yes	—
343	#480	—	2	2	no	—
344	#474	—	2	2	no	—
345	#474	—	2	1	no	—
346	#474	C₂²×C₃₇	1	2	yes	—
347	#466	—	2	2	no	—
348	#464	—	2	1	no	—
349	#463	—	2	1	no	—
350	#462	C₂²×C₃₇	1	1	yes	characteristic
351	#461	C₂²×C₃₇	1	1	yes	characteristic
352	#460	C₂²×C₃₇	1	1	yes	characteristic
353	#459	—	2	1	no	—
354	#459	C₂²×C₃₇	1	1	yes	characteristic
355	#459	C₂²×C₃₇	1	2	yes	—
356	#431	C₂²×C₃₇	1	1	yes	characteristic
357	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
358	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
359	#416	—	2	1	no	—
360	#332	C₂²×C₃₇	1	2	yes	—
361	#332	C₂²×C₃₇	1	2	yes	—
362	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
363	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
364	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
365	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
366	C₃₇	#18882	1	1	yes	characteristic, direct product factor, Sylow
367	2₋¹⁺⁴	—	4	4	no	—
368	2₋¹⁺⁴	—	4	4	no	—
369	C₂×#41	—	2	2	no	—
370	C₂×#41	—	2	4	no	—
371	C₂×#41	—	2	2	no	—
372	C₂×#41	—	2	1	no	—
373	C₂×#41	—	2	1	no	—
374	C₂×#41	D₄×C₃₇	1	1	yes	characteristic
375	C₂²×Q₈	—	2	2	no	—
376	C₂²×Q₈	—	2	2	no	—
377	C₂²×Q₈	—	2	1	no	—
378	#135	—	4	4	no	—
379	C₂×Q₁₆	—	2	1	no	—
380	C₂×SD₁₆	—	2	1	no	—
381	C₂×SD₁₆	—	2	1	no	—
382	C₂×D₈	—	2	1	no	—
383	C₂×D₈	—	2	2	no	—
384	C₂²×C₈	—	2	1	no	—
385	C₂²×C₈	—	2	1	no	—
386	C₄⋊Q₈	—	2	2	no	—
387	C₄⋊Q₈	—	2	2	no	—
388	C₄⋊Q₈	—	2	2	no	—
389	C₄⋊Q₈	—	2	1	no	—
390	C₄⋊Q₈	—	2	1	no	—
391	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
392	C₄⋊Q₈	D₄×C₃₇	1	2	yes	—
393	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
394	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
395	#127	D₄×C₃₇	1	1	yes	characteristic
396	#127	C₂³×C₃₇	1	1	yes	characteristic
397	#124	—	2	2	no	—
398	#124	—	2	1	no	—
399	#124	—	2	1	no	—
400	#123	—	2	4	no	—
401	#123	—	2	4	no	—
402	#123	—	2	4	no	—
403	C₂²⋊Q₈	—	2	4	no	—
404	C₂²⋊Q₈	—	2	2	no	—
405	C₂²⋊Q₈	—	2	4	no	—
406	C₂²⋊Q₈	—	2	2	no	—
407	#121	—	2	2	no	—
408	#121	—	2	2	no	—
409	#121	—	2	1	no	—
410	#121	—	2	1	no	—
411	#121	—	2	1	no	—
412	#121	D₄×C₃₇	1	2	yes	—
413	C₄×Q₈	D₄×C₃₇	1	1	yes	characteristic
414	C₄×Q₈	C₂³×C₃₇	1	1	yes	characteristic
415	C₄×D₄	—	2	2	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	2	1	no	—
418	C₄×D₄	—	2	1	no	—
419	C₄×D₄	—	2	1	no	—
420	C₄×D₄	—	2	1	no	—
421	C₄×D₄	—	2	1	no	—
422	C₄×D₄	D₄×C₃₇	1	1	yes	characteristic
423	C₄×D₄	C₂³×C₃₇	1	1	yes	characteristic
424	C₄×D₄	C₂³×C₃₇	1	2	yes	—
425	#117	—	2	1	no	—
426	#117	D₄×C₃₇	1	1	yes	characteristic
427	C₂×C₄⋊C₄	—	2	2	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	2	no	—
430	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
431	C₂×C₄²	—	2	1	no	—
432	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
433	#107	—	2	2	no	—
434	#107	—	2	4	no	—
435	C₄⋊C₈	—	2	1	no	—
436	C₄⋊C₈	—	2	1	no	—
437	C₄⋊C₈	—	2	1	no	—
438	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
439	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
440	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
441	#103	—	2	1	no	—
442	#103	—	2	1	no	—
443	#102	—	2	2	no	—
444	#102	—	2	1	no	—
445	#102	—	2	1	no	—
446	#102	—	2	2	no	—
447	#102	—	2	4	no	—
448	C₂²⋊C₈	—	2	1	no	—
449	C₄×C₈	C₂³×C₃₇	1	2	yes	—
450	#41	—	2	2	no	—
451	#41	—	4	8	no	—
452	#41	—	4	16	no	—
453	#41	—	4	4	no	—
454	#41	—	4	4	no	—
455	#41	—	4	2	no	—
456	#41	—	4	2	no	—
457	#41	—	4	2	no	—
458	#41	—	4	2	no	—
459	#41	D₈×C₃₇	1	4	yes	complemented
460	C₂×Q₈	—	2	4	no	—
461	C₂×Q₈	—	2	2	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	2	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	4	8	no	—
466	C₂×Q₈	—	4	4	no	—
467	C₂×Q₈	—	4	4	no	—
468	C₂×Q₈	—	4	2	no	—
469	C₂×Q₈	—	4	2	no	—
470	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	4	no	—
473	C₂×D₄	—	2	2	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	4	1	no	—
480	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
481	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	4	1	no	—
490	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
491	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
492	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
493	Q₁₆	—	4	2	no	—
494	SD₁₆	—	4	2	no	—
495	SD₁₆	—	4	2	no	—
496	D₈	—	4	2	no	—
497	D₈	—	8	2	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	4	2	no	—
503	C₂×C₈	—	8	1	no	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	4	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
515	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
516	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
517	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	2	4	no	—
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	1	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	4	1	no	—
526	C₂²⋊C₄	—	4	1	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
531	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
532	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
533	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
534	C₂³	—	2	1	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	4	1	no	—
537	C₂³	#120×C₃₇	1	1	yes	characteristic
538	Q₈	—	2	1	no	—
539	Q₈	—	4	8	no	—
540	Q₈	—	4	2	no	—
541	Q₈	—	4	2	no	—
542	Q₈	—	4	2	no	—
543	Q₈	—	4	4	no	—
544	Q₈	—	4	1	no	—
545	Q₈	—	4	1	no	—
546	Q₈	C₂×D₈×C₃₇	1	2	yes	—
547	D₄	—	2	4	no	—
548	D₄	—	2	1	no	—
549	D₄	—	2	2	no	—
550	D₄	—	2	2	no	—
551	D₄	—	4	2	no	—
552	D₄	—	4	2	no	—
553	D₄	—	4	8	no	—
554	D₄	—	4	4	no	—
555	D₄	—	4	1	no	—
556	D₄	—	4	1	no	—
557	D₄	—	4	1	no	—
558	D₄	—	4	1	no	—
559	D₄	—	4	2	no	—
560	D₄	—	8	2	no	—
561	D₄	C₂×D₈×C₃₇	1	2	yes	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	8	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	8	no	—
574	C₂×C₄	—	4	4	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	8	2	no	—
581	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
582	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
583	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
584	C₂×C₄	C₂×D₈×C₃₇	1	2	yes	—
585	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
586	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
587	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
588	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
589	C₈	—	4	2	no	—
590	C₈	—	4	1	no	—
591	C₈	—	4	1	no	—
592	C₈	—	4	2	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	8	1	no	—
602	C₂²	—	8	1	no	—
603	C₂²	—	8	1	no	—
604	C₂²	C₃₇×#447	1	2	yes	—
605	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
606	C₄	—	2	2	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	4	4	no	—
611	C₄	—	4	2	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	8	1	no	—
615	C₄	C₃₇×#447	1	2	yes	—
616	C₄	C₂²×D₈×C₃₇	1	1	yes	characteristic
617	C₄	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
618	C₄	C₃₇×#577	1	1	yes	characteristic
619	C₄	C₃₇×#578	1	1	yes	characteristic
620	C₂	—	2	2	no	—
621	C₂	—	4	2	no	—
622	C₂	—	8	2	no	—
623	C₂	—	16	1	no	—
624	C₂	C₂×C₃₇×#447	1	1	yes	characteristic
625	C₂	C₃₇×#3013	1	1	yes	characteristic
626	C₂	C₃₇×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3499	C₂	semidirect
2. C₃₇×#3245	C₂	semidirect
3. C₃₇×#3226	C₂	semidirect
4. C₃₇×#3035	C₂	semidirect
5. C₃₇×#1649	C₂	semidirect
6. C₃₇×#1647	C₂	semidirect
7. C₃₇×#1627	C₂	semidirect
8. C₃₇×#1625	C₂	semidirect
9. C₂×C₃₇×#332	C₂	semidirect
10. C₃₇×#1480	C₂	semidirect
11. C₃₇×#1477	C₂	semidirect
145. #41×C₃₇	D₈	semidirect
279. #18882	C₃₇	direct (N × H)
307. #3499	C₂×C₃₇	semidirect
308. #3245	C₂×C₃₇	semidirect
309. #3226	C₂×C₃₇	semidirect
310. #3035	C₂×C₃₇	semidirect
311. #1649	C₂×C₃₇	semidirect
312. #1647	C₂×C₃₇	semidirect
313. #1627	C₂×C₃₇	semidirect
314. #1625	C₂×C₃₇	semidirect
315. C₂×#332	C₂×C₃₇	semidirect
316. #1480	C₂×C₃₇	semidirect
317. #1477	C₂×C₃₇	semidirect
366. C₃₇	#18882	direct (N × H)
459. #41	D₈×C₃₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₇×#3499	2
C₃₇×#3245	2
C₃₇×#3226	2
C₃₇×#3035	2
C₃₇×#1649	2
C₃₇×#1647	2
C₃₇×#1627	2
C₃₇×#1625	2
C₂×C₃₇×#332	2
C₃₇×#1480	2
C₃₇×#1477	2
#18882	37

Subgroups — C37×#18882 #22640135

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18882 #22640135