Subgroups — C₃₇×#28435 #22649688

Order 9472.

1074 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#490	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#478	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#440	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2565	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2541	C₂	1	1	yes	maximal, characteristic
7	C₃₇×#2093	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2092	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#2014	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#2014	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#1968	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₇×#1961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#1957	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₇×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
20	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
21	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×#121×C₃₇	—	2	2	no	—
24	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
26	C₃₇×#490	—	2	4	no	—
27	C₃₇×#478	—	2	4	no	—
28	C₃₇×#460	—	2	4	no	—
29	C₃₇×#440	—	2	4	no	—
30	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
32	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
34	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
35	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
36	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
37	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
38	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
39	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
40	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
41	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
42	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
43	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
44	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
45	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
47	C₃₇×#398	—	2	2	no	—
48	C₃₇×#392	—	2	2	no	—
49	C₃₇×#391	C₂²	1	1	yes	characteristic
50	C₃₇×#391	C₂²	1	1	yes	characteristic
51	C₃₇×#390	C₂²	1	1	yes	characteristic
52	C₃₇×#390	C₂²	1	1	yes	characteristic
53	C₃₇×#387	—	2	2	no	—
54	C₃₇×#384	C₂²	1	1	yes	characteristic
55	C₃₇×#382	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
57	C₃₇×#336	C₂²	1	1	yes	characteristic
58	C₃₇×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₃₇	—	2	1	no	—
61	C₂²×D₄×C₃₇	—	2	2	no	—
62	C₂²×D₄×C₃₇	—	2	2	no	—
63	C₂²×D₄×C₃₇	—	2	1	no	—
64	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₃₇	—	2	1	no	—
68	C₂×SD₁₆×C₃₇	—	2	2	no	—
69	C₂×SD₁₆×C₃₇	—	2	2	no	—
70	C₂×SD₁₆×C₃₇	—	2	2	no	—
71	C₂×SD₁₆×C₃₇	—	2	2	no	—
72	C₂×SD₁₆×C₃₇	—	2	2	no	—
73	C₂×SD₁₆×C₃₇	—	2	2	no	—
74	C₂×SD₁₆×C₃₇	—	2	2	no	—
75	C₂×SD₁₆×C₃₇	—	4	1	no	—
76	C₂×SD₁₆×C₃₇	—	4	1	no	—
77	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
81	#127×C₃₇	—	2	2	no	—
82	#127×C₃₇	—	2	2	no	—
83	#127×C₃₇	—	2	2	no	—
84	#127×C₃₇	—	2	2	no	—
85	#127×C₃₇	—	4	1	no	—
86	#127×C₃₇	—	4	1	no	—
87	#125×C₃₇	—	2	2	no	—
88	#125×C₃₇	—	2	2	no	—
89	#121×C₃₇	—	4	8	no	—
90	C₄×Q₈×C₃₇	—	2	2	no	—
91	C₄×Q₈×C₃₇	—	2	2	no	—
92	C₄×D₄×C₃₇	—	2	2	no	—
93	C₄×D₄×C₃₇	—	2	2	no	—
94	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
95	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
96	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
97	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
98	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
99	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
104	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
105	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
106	C₂×C₄²×C₃₇	—	2	1	no	—
107	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
110	#107×C₃₇	—	2	2	no	—
111	#107×C₃₇	—	2	2	no	—
112	#106×C₃₇	—	2	2	no	—
113	C₄⋊C₈×C₃₇	D₄	1	4	yes	complemented
114	#103×C₃₇	—	2	2	no	—
115	#102×C₃₇	—	2	2	no	—
116	#102×C₃₇	—	2	2	no	—
117	#102×C₃₇	—	2	2	no	—
118	#102×C₃₇	—	2	2	no	—
119	#102×C₃₇	—	2	2	no	—
120	#102×C₃₇	—	2	2	no	—
121	#102×C₃₇	—	2	2	no	—
122	#102×C₃₇	—	2	2	no	—
123	#102×C₃₇	—	2	2	no	—
124	#97×C₃₇	—	4	1	no	—
125	#97×C₃₇	D₄	1	4	yes	complemented
126	C₄×C₈×C₃₇	—	4	1	no	—
127	#95×C₃₇	—	2	2	no	—
128	#95×C₃₇	—	2	2	no	—
129	#95×C₃₇	—	2	2	no	—
130	#95×C₃₇	D₄	1	2	yes	—
131	C₂⁴×C₃₇	—	2	1	no	—
132	C₂⁴×C₃₇	—	2	1	no	—
133	C₂⁴×C₃₇	—	2	1	no	—
134	C₂×Q₈×C₃₇	—	2	1	no	—
135	C₂×Q₈×C₃₇	—	2	1	no	—
136	C₂×Q₈×C₃₇	—	2	1	no	—
137	C₂×Q₈×C₃₇	—	2	1	no	—
138	C₂×Q₈×C₃₇	—	2	1	no	—
139	C₂×Q₈×C₃₇	#41	1	2	yes	—
140	C₂×D₄×C₃₇	—	2	1	no	—
141	C₂×D₄×C₃₇	—	2	1	no	—
142	C₂×D₄×C₃₇	—	2	1	no	—
143	C₂×D₄×C₃₇	—	2	1	no	—
144	C₂×D₄×C₃₇	—	2	1	no	—
145	C₂×D₄×C₃₇	—	2	1	no	—
146	C₂×D₄×C₃₇	—	2	1	no	—
147	C₂×D₄×C₃₇	—	2	1	no	—
148	C₂×D₄×C₃₇	—	2	1	no	—
149	C₂×D₄×C₃₇	—	2	1	no	—
150	C₂×D₄×C₃₇	—	2	1	no	—
151	C₂×D₄×C₃₇	—	2	1	no	—
152	C₂×D₄×C₃₇	—	2	1	no	—
153	C₂×D₄×C₃₇	—	2	1	no	—
154	C₂×D₄×C₃₇	—	2	1	no	—
155	C₂×D₄×C₃₇	—	2	1	no	—
156	C₂×D₄×C₃₇	—	2	1	no	—
157	C₂×D₄×C₃₇	—	4	4	no	—
158	C₂×D₄×C₃₇	—	4	4	no	—
159	C₂×D₄×C₃₇	—	4	4	no	—
160	C₂×D₄×C₃₇	—	4	4	no	—
161	C₂×D₄×C₃₇	—	4	2	no	—
162	C₂×D₄×C₃₇	—	4	2	no	—
163	C₂×D₄×C₃₇	—	4	4	no	—
164	C₂×D₄×C₃₇	—	8	2	no	—
165	C₂×D₄×C₃₇	—	8	2	no	—
166	C₂×D₄×C₃₇	—	8	2	no	—
167	C₂×D₄×C₃₇	#41	1	2	yes	—
168	C₂²×C₄×C₃₇	—	2	1	no	—
169	C₂²×C₄×C₃₇	—	2	1	no	—
170	C₂²×C₄×C₃₇	—	2	1	no	—
171	C₂²×C₄×C₃₇	—	2	1	no	—
172	C₂²×C₄×C₃₇	—	2	1	no	—
173	C₂²×C₄×C₃₇	—	4	4	no	—
174	C₂²×C₄×C₃₇	—	4	2	no	—
175	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
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	2	yes	—
179	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
180	SD₁₆×C₃₇	—	2	8	no	—
181	SD₁₆×C₃₇	—	4	4	no	—
182	SD₁₆×C₃₇	—	4	4	no	—
183	C₂×C₈×C₃₇	—	2	1	no	—
184	C₂×C₈×C₃₇	—	2	1	no	—
185	C₂×C₈×C₃₇	—	2	1	no	—
186	C₂×C₈×C₃₇	—	2	1	no	—
187	C₂×C₈×C₃₇	—	2	1	no	—
188	C₂×C₈×C₃₇	—	2	1	no	—
189	C₂×C₈×C₃₇	—	2	1	no	—
190	C₂×C₈×C₃₇	—	2	1	no	—
191	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
192	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
193	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
194	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
195	C₄⋊C₄×C₃₇	—	2	4	no	—
196	C₄⋊C₄×C₃₇	—	2	1	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	—	2	1	no	—
201	C₄⋊C₄×C₃₇	—	2	1	no	—
202	C₄⋊C₄×C₃₇	—	2	1	no	—
203	C₄⋊C₄×C₃₇	—	2	1	no	—
204	C₄⋊C₄×C₃₇	—	4	2	no	—
205	C₄⋊C₄×C₃₇	—	4	2	no	—
206	C₄⋊C₄×C₃₇	—	4	2	no	—
207	C₄⋊C₄×C₃₇	—	4	4	no	—
208	C₂²⋊C₄×C₃₇	—	4	4	no	—
209	C₂²⋊C₄×C₃₇	—	4	2	no	—
210	C₂²⋊C₄×C₃₇	—	4	4	no	—
211	C₄²×C₃₇	—	2	1	no	—
212	C₄²×C₃₇	—	2	1	no	—
213	C₄²×C₃₇	—	2	1	no	—
214	C₄²×C₃₇	—	2	1	no	—
215	C₄²×C₃₇	—	4	2	no	—
216	C₄²×C₃₇	C₂×D₄	1	2	yes	—
217	C₄²×C₃₇	C₂×D₄	1	2	yes	—
218	C₂³×C₃₇	—	2	2	no	—
219	C₂³×C₃₇	—	4	1	no	—
220	C₂³×C₃₇	—	4	1	no	—
221	C₂³×C₃₇	—	4	2	no	—
222	C₂³×C₃₇	—	4	2	no	—
223	C₂³×C₃₇	—	4	1	no	—
224	C₂³×C₃₇	—	4	1	no	—
225	C₂³×C₃₇	—	4	1	no	—
226	C₂³×C₃₇	—	4	1	no	—
227	C₂³×C₃₇	—	4	1	no	—
228	C₂³×C₃₇	—	4	1	no	—
229	C₂³×C₃₇	—	4	2	no	—
230	C₂³×C₃₇	—	4	2	no	—
231	C₂³×C₃₇	—	4	2	no	—
232	C₂³×C₃₇	—	4	2	no	—
233	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
234	Q₈×C₃₇	—	2	2	no	—
235	Q₈×C₃₇	—	2	2	no	—
236	Q₈×C₃₇	—	4	1	no	—
237	Q₈×C₃₇	—	4	1	no	—
238	D₄×C₃₇	—	2	2	no	—
239	D₄×C₃₇	—	2	2	no	—
240	D₄×C₃₇	—	4	1	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	1	no	—
246	D₄×C₃₇	—	4	1	no	—
247	D₄×C₃₇	—	4	1	no	—
248	D₄×C₃₇	—	4	1	no	—
249	D₄×C₃₇	—	4	1	no	—
250	D₄×C₃₇	—	8	8	no	—
251	D₄×C₃₇	—	8	4	no	—
252	D₄×C₃₇	—	8	4	no	—
253	D₄×C₃₇	—	8	8	no	—
254	C₂×C₄×C₃₇	—	2	2	no	—
255	C₂×C₄×C₃₇	—	2	2	no	—
256	C₂×C₄×C₃₇	—	2	2	no	—
257	C₂×C₄×C₃₇	—	2	2	no	—
258	C₂×C₄×C₃₇	—	2	2	no	—
259	C₂×C₄×C₃₇	—	2	2	no	—
260	C₂×C₄×C₃₇	—	2	2	no	—
261	C₂×C₄×C₃₇	—	2	2	no	—
262	C₂×C₄×C₃₇	—	4	1	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	—	4	1	no	—
267	C₂×C₄×C₃₇	—	4	1	no	—
268	C₂×C₄×C₃₇	—	4	2	no	—
269	C₂×C₄×C₃₇	—	4	2	no	—
270	C₂×C₄×C₃₇	—	4	2	no	—
271	C₂×C₄×C₃₇	—	4	2	no	—
272	C₂×C₄×C₃₇	—	8	4	no	—
273	C₂×C₄×C₃₇	#127	1	2	yes	—
274	C₂×C₄×C₃₇	#127	1	2	yes	—
275	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	4	yes	—
276	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
279	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
280	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
281	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
282	C₈×C₃₇	—	2	2	no	—
283	C₈×C₃₇	—	2	2	no	—
284	C₈×C₃₇	—	2	2	no	—
285	C₈×C₃₇	—	2	2	no	—
286	#28435	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂²×C₃₇	—	4	2	no	—
288	C₂²×C₃₇	—	4	4	no	—
289	C₂²×C₃₇	—	8	2	no	—
290	C₂²×C₃₇	—	8	1	no	—
291	C₂²×C₃₇	—	8	1	no	—
292	C₂²×C₃₇	—	8	2	no	—
293	C₂²×C₃₇	—	8	2	no	—
294	C₂²×C₃₇	—	8	1	no	—
295	C₂²×C₃₇	—	8	1	no	—
296	C₂²×C₃₇	—	8	1	no	—
297	C₂²×C₃₇	—	8	1	no	—
298	C₂²×C₃₇	—	8	1	no	—
299	C₂²×C₃₇	—	8	1	no	—
300	C₂²×C₃₇	—	8	2	no	—
301	C₂²×C₃₇	—	8	2	no	—
302	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
303	C₂²×C₃₇	#546	1	1	yes	characteristic
304	C₂²×C₃₇	#548	1	1	yes	characteristic
305	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
306	C₂²×C₃₇	#577	1	2	yes	—
307	C₄×C₃₇	—	2	2	no	—
308	C₄×C₃₇	—	2	2	no	—
309	C₄×C₃₇	—	2	4	no	—
310	C₄×C₃₇	—	4	2	no	—
311	C₄×C₃₇	—	4	2	no	—
312	C₄×C₃₇	—	8	1	no	—
313	C₄×C₃₇	—	8	1	no	—
314	C₄×C₃₇	—	8	1	no	—
315	C₄×C₃₇	—	8	1	no	—
316	C₄×C₃₇	#525	1	1	yes	characteristic
317	C₄×C₃₇	#537	1	1	yes	characteristic
318	C₄×C₃₇	#546	1	1	yes	characteristic
319	C₄×C₃₇	#548	1	1	yes	characteristic
320	C₂×#490	C₂×C₃₇	1	1	yes	characteristic, complemented
321	C₂×#478	C₂×C₃₇	1	1	yes	characteristic, complemented
322	C₂×#460	C₂×C₃₇	1	1	yes	characteristic, complemented
323	C₂×#440	C₂×C₃₇	1	1	yes	characteristic, complemented
324	#2565	C₂×C₃₇	1	1	yes	characteristic, complemented
325	#2541	C₂×C₃₇	1	1	yes	characteristic
326	#2093	C₂×C₃₇	1	1	yes	characteristic, complemented
327	#2092	C₂×C₃₇	1	1	yes	characteristic, complemented
328	#2014	C₂×C₃₇	1	1	yes	characteristic, complemented
329	#2014	C₂×C₃₇	1	1	yes	characteristic, complemented
330	#1973	C₂×C₃₇	1	1	yes	characteristic, complemented
331	#1968	C₂×C₃₇	1	1	yes	characteristic, complemented
332	#1961	C₂×C₃₇	1	1	yes	characteristic, complemented
333	#1957	C₂×C₃₇	1	1	yes	characteristic, complemented
334	#1771	C₂×C₃₇	1	1	yes	characteristic, complemented
335	C₂×C₃₇	—	8	2	no	—
336	C₂×C₃₇	—	16	1	no	—
337	C₂×C₃₇	—	16	1	no	—
338	C₂×C₃₇	#2540	1	1	yes	characteristic
339	C₂×C₃₇	#3151	1	1	yes	characteristic
340	C₂×C₃₇	#3154	1	1	yes	characteristic
341	C₂×C₃₇	#3310	1	2	yes	—
342	C₂×C₃₇	#3368	1	2	yes	—
343	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
344	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
345	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
346	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
347	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
348	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
349	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
350	C₂×#121	—	2	2	no	—
351	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
352	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
353	#490	—	2	4	no	—
354	#478	—	2	4	no	—
355	#460	—	2	4	no	—
356	#440	—	2	4	no	—
357	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
358	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
359	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
360	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
361	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
362	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
363	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
364	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
365	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
366	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
367	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
368	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
369	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
370	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
371	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
372	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
373	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
374	#398	—	2	2	no	—
375	#392	—	2	2	no	—
376	#391	C₂²×C₃₇	1	1	yes	characteristic
377	#391	C₂²×C₃₇	1	1	yes	characteristic
378	#390	C₂²×C₃₇	1	1	yes	characteristic
379	#390	C₂²×C₃₇	1	1	yes	characteristic
380	#387	—	2	2	no	—
381	#384	C₂²×C₃₇	1	1	yes	characteristic
382	#382	C₂²×C₃₇	1	1	yes	characteristic
383	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
384	#336	C₂²×C₃₇	1	1	yes	characteristic
385	#336	C₂²×C₃₇	1	1	yes	characteristic
386	C₃₇	#28435	1	1	yes	characteristic, direct product factor, Sylow
387	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
388	C₂²×D₄	—	2	1	no	—
389	C₂²×D₄	—	2	2	no	—
390	C₂²×D₄	—	2	2	no	—
391	C₂²×D₄	—	2	1	no	—
392	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
393	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
394	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
395	C₂³×C₄	—	2	1	no	—
396	C₂×SD₁₆	—	2	2	no	—
397	C₂×SD₁₆	—	2	2	no	—
398	C₂×SD₁₆	—	2	2	no	—
399	C₂×SD₁₆	—	2	2	no	—
400	C₂×SD₁₆	—	2	2	no	—
401	C₂×SD₁₆	—	2	2	no	—
402	C₂×SD₁₆	—	2	2	no	—
403	C₂×SD₁₆	—	4	1	no	—
404	C₂×SD₁₆	—	4	1	no	—
405	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
406	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
407	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
408	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
409	#127	—	2	2	no	—
410	#127	—	2	2	no	—
411	#127	—	2	2	no	—
412	#127	—	2	2	no	—
413	#127	—	4	1	no	—
414	#127	—	4	1	no	—
415	#125	—	2	2	no	—
416	#125	—	2	2	no	—
417	#121	—	4	8	no	—
418	C₄×Q₈	—	2	2	no	—
419	C₄×Q₈	—	2	2	no	—
420	C₄×D₄	—	2	2	no	—
421	C₄×D₄	—	2	2	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	—	2	2	no	—
426	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
427	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	2	no	—
433	C₂×C₂²⋊C₄	—	2	2	no	—
434	C₂×C₄²	—	2	1	no	—
435	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
436	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
437	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
438	#107	—	2	2	no	—
439	#107	—	2	2	no	—
440	#106	—	2	2	no	—
441	C₄⋊C₈	D₄×C₃₇	1	4	yes	complemented
442	#103	—	2	2	no	—
443	#102	—	2	2	no	—
444	#102	—	2	2	no	—
445	#102	—	2	2	no	—
446	#102	—	2	2	no	—
447	#102	—	2	2	no	—
448	#102	—	2	2	no	—
449	#102	—	2	2	no	—
450	#102	—	2	2	no	—
451	#102	—	2	2	no	—
452	#97	—	4	1	no	—
453	#97	D₄×C₃₇	1	4	yes	complemented
454	C₄×C₈	—	4	1	no	—
455	#95	—	2	2	no	—
456	#95	—	2	2	no	—
457	#95	—	2	2	no	—
458	#95	D₄×C₃₇	1	2	yes	—
459	C₂⁴	—	2	1	no	—
460	C₂⁴	—	2	1	no	—
461	C₂⁴	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	#41×C₃₇	1	2	yes	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	1	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	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	4	4	no	—
486	C₂×D₄	—	4	4	no	—
487	C₂×D₄	—	4	4	no	—
488	C₂×D₄	—	4	4	no	—
489	C₂×D₄	—	4	2	no	—
490	C₂×D₄	—	4	2	no	—
491	C₂×D₄	—	4	4	no	—
492	C₂×D₄	—	8	2	no	—
493	C₂×D₄	—	8	2	no	—
494	C₂×D₄	—	8	2	no	—
495	C₂×D₄	#41×C₃₇	1	2	yes	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	4	4	no	—
502	C₂²×C₄	—	4	2	no	—
503	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
504	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
505	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
507	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
508	SD₁₆	—	2	8	no	—
509	SD₁₆	—	4	4	no	—
510	SD₁₆	—	4	4	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
520	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
521	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
522	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
523	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	4	2	no	—
533	C₄⋊C₄	—	4	2	no	—
534	C₄⋊C₄	—	4	2	no	—
535	C₄⋊C₄	—	4	4	no	—
536	C₂²⋊C₄	—	4	4	no	—
537	C₂²⋊C₄	—	4	2	no	—
538	C₂²⋊C₄	—	4	4	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	4	2	no	—
544	C₄²	C₂×D₄×C₃₇	1	2	yes	—
545	C₄²	C₂×D₄×C₃₇	1	2	yes	—
546	C₂³	—	2	2	no	—
547	C₂³	—	4	1	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	2	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	1	no	—
554	C₂³	—	4	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	2	no	—
558	C₂³	—	4	2	no	—
559	C₂³	—	4	2	no	—
560	C₂³	—	4	2	no	—
561	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
562	Q₈	—	2	2	no	—
563	Q₈	—	2	2	no	—
564	Q₈	—	4	1	no	—
565	Q₈	—	4	1	no	—
566	D₄	—	2	2	no	—
567	D₄	—	2	2	no	—
568	D₄	—	4	1	no	—
569	D₄	—	4	1	no	—
570	D₄	—	4	1	no	—
571	D₄	—	4	1	no	—
572	D₄	—	4	1	no	—
573	D₄	—	4	1	no	—
574	D₄	—	4	1	no	—
575	D₄	—	4	1	no	—
576	D₄	—	4	1	no	—
577	D₄	—	4	1	no	—
578	D₄	—	8	8	no	—
579	D₄	—	8	4	no	—
580	D₄	—	8	4	no	—
581	D₄	—	8	8	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	8	4	no	—
601	C₂×C₄	#127×C₃₇	1	2	yes	—
602	C₂×C₄	#127×C₃₇	1	2	yes	—
603	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	4	yes	—
604	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
605	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
606	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
607	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
608	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
609	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
610	C₈	—	2	2	no	—
611	C₈	—	2	2	no	—
612	C₈	—	2	2	no	—
613	C₈	—	2	2	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	8	1	no	—
617	C₂²	—	8	1	no	—
618	C₂²	—	8	2	no	—
619	C₂²	—	8	1	no	—
620	C₂²	—	8	1	no	—
621	C₂²	—	8	1	no	—
622	C₂²	—	8	1	no	—
623	C₂²	—	8	1	no	—
624	C₂²	—	8	1	no	—
625	C₂²	—	8	2	no	—
626	C₂²	—	8	2	no	—
627	C₂²	—	8	2	no	—
628	C₂²	—	8	2	no	—
629	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
630	C₂²	C₃₇×#546	1	1	yes	characteristic
631	C₂²	C₃₇×#548	1	1	yes	characteristic
632	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	2	yes	—
633	C₂²	C₃₇×#577	1	2	yes	—
634	C₄	—	2	2	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	4	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	2	no	—
639	C₄	—	8	1	no	—
640	C₄	—	8	1	no	—
641	C₄	—	8	1	no	—
642	C₄	—	8	1	no	—
643	C₄	C₃₇×#525	1	1	yes	characteristic
644	C₄	C₃₇×#537	1	1	yes	characteristic
645	C₄	C₃₇×#546	1	1	yes	characteristic
646	C₄	C₃₇×#548	1	1	yes	characteristic
647	C₂	—	8	2	no	—
648	C₂	—	16	1	no	—
649	C₂	—	16	1	no	—
650	C₂	C₃₇×#2540	1	1	yes	characteristic
651	C₂	C₃₇×#3151	1	1	yes	characteristic
652	C₂	C₃₇×#3154	1	1	yes	characteristic
653	C₂	C₃₇×#3310	1	2	yes	—
654	C₂	C₃₇×#3368	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#2541	C₂
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×#490	C₂	semidirect
2. C₂×C₃₇×#478	C₂	semidirect
3. C₂×C₃₇×#460	C₂	semidirect
4. C₂×C₃₇×#440	C₂	semidirect
5. C₃₇×#2565	C₂	semidirect
7. C₃₇×#2093	C₂	semidirect
8. C₃₇×#2092	C₂	semidirect
9. C₃₇×#2014	C₂	semidirect
10. C₃₇×#2014	C₂	semidirect
11. C₃₇×#1973	C₂	semidirect
12. C₃₇×#1968	C₂	semidirect
13. C₃₇×#1961	C₂	semidirect
14. C₃₇×#1957	C₂	semidirect
15. C₃₇×#1771	C₂	semidirect
113. C₄⋊C₈×C₃₇	D₄	semidirect
125. #97×C₃₇	D₄	semidirect
286. #28435	C₃₇	direct (N × H)
320. C₂×#490	C₂×C₃₇	semidirect
321. C₂×#478	C₂×C₃₇	semidirect
322. C₂×#460	C₂×C₃₇	semidirect
323. C₂×#440	C₂×C₃₇	semidirect
324. #2565	C₂×C₃₇	semidirect
326. #2093	C₂×C₃₇	semidirect
327. #2092	C₂×C₃₇	semidirect
328. #2014	C₂×C₃₇	semidirect
329. #2014	C₂×C₃₇	semidirect
330. #1973	C₂×C₃₇	semidirect
331. #1968	C₂×C₃₇	semidirect
332. #1961	C₂×C₃₇	semidirect
333. #1957	C₂×C₃₇	semidirect
334. #1771	C₂×C₃₇	semidirect
386. C₃₇	#28435	direct (N × H)
441. C₄⋊C₈	D₄×C₃₇	semidirect
453. #97	D₄×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×#490	2
C₂×C₃₇×#478	2
C₂×C₃₇×#460	2
C₂×C₃₇×#440	2
C₃₇×#2565	2
C₃₇×#2541	2
C₃₇×#2093	2
C₃₇×#2092	2
C₃₇×#2014	2
C₃₇×#1973	2
C₃₇×#1968	2
C₃₇×#1961	2
C₃₇×#1957	2
C₃₇×#1771	2
#28435	37

Subgroups — C37×#28435 #22649688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28435 #22649688