Subgroups — C₃₇×#28465 #22649718

Order 9472.

1226 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#495	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#493	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₇×#463	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×D₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2544	C₂	1	2	yes	maximal, complemented
7	C₃₇×#2014	C₂	1	2	yes	maximal, complemented
8	C₃₇×#2012	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1970	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1969	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₄⋊C₄×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
15	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
16	C₂²×D₈×C₃₇	C₂²	1	2	yes	—
17	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×#127×C₃₇	C₂²	1	2	yes	—
19	C₂×#124×C₃₇	C₂²	1	2	yes	—
20	C₂×#124×C₃₇	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₃₇	C₂²	1	2	yes	—
22	C₃₇×#495	—	2	4	no	—
23	C₃₇×#495	—	2	4	no	—
24	C₃₇×#493	—	2	4	no	—
25	C₃₇×#463	—	2	8	no	—
26	C₄×D₈×C₃₇	—	2	4	no	—
27	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
29	C₂×#103×C₃₇	C₂²	1	2	yes	—
30	C₂×#102×C₃₇	C₂²	1	2	yes	—
31	C₂×#102×C₃₇	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
35	C₃₇×#394	—	2	4	no	—
36	C₃₇×#391	C₂²	1	2	yes	—
37	C₃₇×#390	C₂²	1	2	yes	—
38	C₃₇×#386	—	2	4	no	—
39	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
40	C₃₇×#336	C₂²	1	1	yes	characteristic
41	C₃₇×#336	C₂²	1	1	yes	characteristic
42	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
43	C₂²×D₄×C₃₇	—	2	4	no	—
44	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
45	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
46	C₂³×C₄×C₃₇	—	2	2	no	—
47	C₂×Q₁₆×C₃₇	—	2	2	no	—
48	C₂×Q₁₆×C₃₇	—	2	2	no	—
49	C₂×Q₁₆×C₃₇	—	2	2	no	—
50	C₂×SD₁₆×C₃₇	—	2	4	no	—
51	C₂×SD₁₆×C₃₇	—	2	4	no	—
52	C₂×SD₁₆×C₃₇	—	2	4	no	—
53	C₂×SD₁₆×C₃₇	—	4	2	no	—
54	C₂×SD₁₆×C₃₇	—	4	2	no	—
55	C₂×SD₁₆×C₃₇	—	4	2	no	—
56	C₂×D₈×C₃₇	—	2	4	no	—
57	C₂×D₈×C₃₇	—	2	2	no	—
58	C₂×D₈×C₃₇	—	2	4	no	—
59	C₂×D₈×C₃₇	—	2	2	no	—
60	C₂×D₈×C₃₇	—	2	2	no	—
61	C₂×D₈×C₃₇	—	2	2	no	—
62	C₂×D₈×C₃₇	—	2	2	no	—
63	C₂×D₈×C₃₇	—	4	2	no	—
64	C₂×D₈×C₃₇	D₄	1	4	yes	—
65	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
69	#127×C₃₇	—	2	4	no	—
70	#127×C₃₇	—	4	2	no	—
71	#124×C₃₇	—	2	4	no	—
72	#124×C₃₇	—	2	4	no	—
73	#124×C₃₇	—	2	4	no	—
74	#124×C₃₇	—	4	2	no	—
75	C₄×D₄×C₃₇	—	2	4	no	—
76	C₄×D₄×C₃₇	—	2	4	no	—
77	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
78	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
81	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
84	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
87	#107×C₃₇	—	2	2	no	—
88	C₄⋊C₈×C₃₇	D₄	1	4	yes	complemented
89	#103×C₃₇	—	2	4	no	—
90	#102×C₃₇	—	2	4	no	—
91	#102×C₃₇	—	2	4	no	—
92	C₄×C₈×C₃₇	—	2	2	no	—
93	C₄×C₈×C₃₇	—	2	2	no	—
94	C₄×C₈×C₃₇	D₄	1	4	yes	complemented
95	#95×C₃₇	—	2	4	no	—
96	#95×C₃₇	D₄	1	2	yes	—
97	C₂⁴×C₃₇	—	2	2	no	—
98	C₂⁴×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×Q₈×C₃₇	—	2	2	no	—
104	C₂×Q₈×C₃₇	—	2	2	no	—
105	C₂×D₄×C₃₇	—	2	2	no	—
106	C₂×D₄×C₃₇	—	2	2	no	—
107	C₂×D₄×C₃₇	—	2	2	no	—
108	C₂×D₄×C₃₇	—	2	2	no	—
109	C₂×D₄×C₃₇	—	2	2	no	—
110	C₂×D₄×C₃₇	—	2	2	no	—
111	C₂×D₄×C₃₇	—	2	2	no	—
112	C₂×D₄×C₃₇	—	2	2	no	—
113	C₂×D₄×C₃₇	—	2	2	no	—
114	C₂×D₄×C₃₇	—	2	2	no	—
115	C₂×D₄×C₃₇	—	2	2	no	—
116	C₂×D₄×C₃₇	—	4	8	no	—
117	C₂×D₄×C₃₇	—	4	8	no	—
118	C₂×D₄×C₃₇	—	8	4	no	—
119	C₂×D₄×C₃₇	C₂×D₄	1	4	yes	—
120	C₂²×C₄×C₃₇	—	2	2	no	—
121	C₂²×C₄×C₃₇	—	2	2	no	—
122	C₂²×C₄×C₃₇	—	4	4	no	—
123	C₂²×C₄×C₃₇	—	8	4	no	—
124	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
129	Q₁₆×C₃₇	—	4	4	no	—
130	SD₁₆×C₃₇	—	4	8	no	—
131	SD₁₆×C₃₇	—	4	8	no	—
132	D₈×C₃₇	—	2	8	no	—
133	D₈×C₃₇	—	4	8	no	—
134	D₈×C₃₇	—	4	4	no	—
135	C₂×C₈×C₃₇	—	2	1	no	—
136	C₂×C₈×C₃₇	—	2	1	no	—
137	C₂×C₈×C₃₇	—	2	1	no	—
138	C₂×C₈×C₃₇	—	2	1	no	—
139	C₂×C₈×C₃₇	—	2	1	no	—
140	C₂×C₈×C₃₇	—	2	1	no	—
141	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₃₇	#41	1	2	yes	—
147	C₄⋊C₄×C₃₇	—	2	4	no	—
148	C₄⋊C₄×C₃₇	—	2	2	no	—
149	C₄⋊C₄×C₃₇	—	2	2	no	—
150	C₂²⋊C₄×C₃₇	—	4	8	no	—
151	C₂²⋊C₄×C₃₇	—	4	4	no	—
152	C₂²⋊C₄×C₃₇	—	4	4	no	—
153	C₂²⋊C₄×C₃₇	—	4	4	no	—
154	C₂²⋊C₄×C₃₇	—	8	4	no	—
155	C₄²×C₃₇	—	2	1	no	—
156	C₄²×C₃₇	—	2	1	no	—
157	C₄²×C₃₇	—	2	1	no	—
158	C₄²×C₃₇	—	2	1	no	—
159	C₄²×C₃₇	C₂×D₄	1	2	yes	—
160	C₄²×C₃₇	C₂×D₄	1	2	yes	—
161	C₂³×C₃₇	—	2	4	no	—
162	C₂³×C₃₇	—	4	2	no	—
163	C₂³×C₃₇	—	4	2	no	—
164	C₂³×C₃₇	—	4	4	no	—
165	C₂³×C₃₇	—	4	4	no	—
166	C₂³×C₃₇	—	4	2	no	—
167	C₂³×C₃₇	—	4	2	no	—
168	C₂³×C₃₇	—	4	2	no	—
169	C₂³×C₃₇	—	4	4	no	—
170	C₂³×C₃₇	—	4	4	no	—
171	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₃₇	—	4	2	no	—
173	Q₈×C₃₇	—	4	2	no	—
174	Q₈×C₃₇	—	4	2	no	—
175	Q₈×C₃₇	—	4	2	no	—
176	D₄×C₃₇	—	2	4	no	—
177	D₄×C₃₇	—	2	4	no	—
178	D₄×C₃₇	—	4	2	no	—
179	D₄×C₃₇	—	4	2	no	—
180	D₄×C₃₇	—	4	2	no	—
181	D₄×C₃₇	—	4	2	no	—
182	D₄×C₃₇	—	4	2	no	—
183	D₄×C₃₇	—	4	2	no	—
184	D₄×C₃₇	—	8	16	no	—
185	C₂×C₄×C₃₇	—	2	2	no	—
186	C₂×C₄×C₃₇	—	2	2	no	—
187	C₂×C₄×C₃₇	—	2	2	no	—
188	C₂×C₄×C₃₇	—	2	2	no	—
189	C₂×C₄×C₃₇	—	2	2	no	—
190	C₂×C₄×C₃₇	—	2	2	no	—
191	C₂×C₄×C₃₇	—	2	2	no	—
192	C₂×C₄×C₃₇	—	4	2	no	—
193	C₂×C₄×C₃₇	—	4	2	no	—
194	C₂×C₄×C₃₇	—	4	2	no	—
195	C₂×C₄×C₃₇	—	4	2	no	—
196	C₂×C₄×C₃₇	—	4	4	no	—
197	C₂×C₄×C₃₇	—	8	8	no	—
198	C₂×C₄×C₃₇	#127	1	2	yes	—
199	C₂×C₄×C₃₇	#127	1	2	yes	—
200	C₂×C₄×C₃₇	#135	1	4	yes	—
201	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
206	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
207	C₈×C₃₇	—	2	2	no	—
208	C₈×C₃₇	—	2	2	no	—
209	C₈×C₃₇	—	2	2	no	—
210	C₈×C₃₇	#121	1	4	yes	—
211	#28465	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂²×C₃₇	—	4	8	no	—
213	C₂²×C₃₇	—	4	4	no	—
214	C₂²×C₃₇	—	8	4	no	—
215	C₂²×C₃₇	—	8	2	no	—
216	C₂²×C₃₇	—	8	2	no	—
217	C₂²×C₃₇	—	8	4	no	—
218	C₂²×C₃₇	—	8	2	no	—
219	C₂²×C₃₇	—	8	2	no	—
220	C₂²×C₃₇	—	8	4	no	—
221	C₂²×C₃₇	—	8	2	no	—
222	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
223	C₂²×C₃₇	D₄²	1	1	yes	characteristic
224	C₂²×C₃₇	#550	1	1	yes	characteristic
225	C₂²×C₃₇	C₂×#135	1	2	yes	—
226	C₂²×C₃₇	#576	1	2	yes	—
227	C₄×C₃₇	—	2	2	no	—
228	C₄×C₃₇	—	2	2	no	—
229	C₄×C₃₇	—	2	4	no	—
230	C₄×C₃₇	—	4	2	no	—
231	C₄×C₃₇	—	8	2	no	—
232	C₄×C₃₇	—	8	2	no	—
233	C₄×C₃₇	C₂×#121	1	1	yes	characteristic
234	C₄×C₃₇	#535	1	1	yes	characteristic
235	C₄×C₃₇	D₄²	1	1	yes	characteristic
236	C₄×C₃₇	#550	1	1	yes	characteristic
237	C₂×#495	C₂×C₃₇	1	1	yes	characteristic, complemented
238	C₂×#495	C₂×C₃₇	1	1	yes	characteristic, complemented
239	C₂×#493	C₂×C₃₇	1	1	yes	characteristic
240	C₂×#463	C₂×C₃₇	1	2	yes	complemented
241	C₂×C₄×D₈	C₂×C₃₇	1	1	yes	characteristic, complemented
242	#2544	C₂×C₃₇	1	2	yes	complemented
243	#2014	C₂×C₃₇	1	2	yes	complemented
244	#2012	C₂×C₃₇	1	2	yes	complemented
245	#1970	C₂×C₃₇	1	1	yes	characteristic, complemented
246	#1969	C₂×C₃₇	1	1	yes	characteristic, complemented
247	C₈×C₄⋊C₄	C₂×C₃₇	1	1	yes	characteristic, complemented
248	C₂×C₃₇	—	8	4	no	—
249	C₂×C₃₇	—	16	2	no	—
250	C₂×C₃₇	#2541	1	1	yes	characteristic
251	C₂×C₃₇	#3147	1	1	yes	characteristic
252	C₂×C₃₇	#3155	1	1	yes	characteristic
253	C₂×C₃₇	#3280	1	2	yes	—
254	C₂×C₃₇	#3396	1	2	yes	—
255	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
256	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
257	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
258	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
259	C₂²×D₈	C₂²×C₃₇	1	2	yes	—
260	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
261	C₂×#127	C₂²×C₃₇	1	2	yes	—
262	C₂×#124	C₂²×C₃₇	1	2	yes	—
263	C₂×#124	C₂²×C₃₇	1	2	yes	—
264	C₂×C₄×D₄	C₂²×C₃₇	1	2	yes	—
265	#495	—	2	4	no	—
266	#495	—	2	4	no	—
267	#493	—	2	4	no	—
268	#463	—	2	8	no	—
269	C₄×D₈	—	2	4	no	—
270	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
272	C₂×#103	C₂²×C₃₇	1	2	yes	—
273	C₂×#102	C₂²×C₃₇	1	2	yes	—
274	C₂×#102	C₂²×C₃₇	1	2	yes	—
275	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
276	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
277	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
278	#394	—	2	4	no	—
279	#391	C₂²×C₃₇	1	2	yes	—
280	#390	C₂²×C₃₇	1	2	yes	—
281	#386	—	2	4	no	—
282	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
283	#336	C₂²×C₃₇	1	1	yes	characteristic
284	#336	C₂²×C₃₇	1	1	yes	characteristic
285	C₃₇	#28465	1	1	yes	characteristic, direct product factor, Sylow
286	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
287	C₂²×D₄	—	2	4	no	—
288	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
289	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
290	C₂³×C₄	—	2	2	no	—
291	C₂×Q₁₆	—	2	2	no	—
292	C₂×Q₁₆	—	2	2	no	—
293	C₂×Q₁₆	—	2	2	no	—
294	C₂×SD₁₆	—	2	4	no	—
295	C₂×SD₁₆	—	2	4	no	—
296	C₂×SD₁₆	—	2	4	no	—
297	C₂×SD₁₆	—	4	2	no	—
298	C₂×SD₁₆	—	4	2	no	—
299	C₂×SD₁₆	—	4	2	no	—
300	C₂×D₈	—	2	4	no	—
301	C₂×D₈	—	2	2	no	—
302	C₂×D₈	—	2	4	no	—
303	C₂×D₈	—	2	2	no	—
304	C₂×D₈	—	2	2	no	—
305	C₂×D₈	—	2	2	no	—
306	C₂×D₈	—	2	2	no	—
307	C₂×D₈	—	4	2	no	—
308	C₂×D₈	D₄×C₃₇	1	4	yes	—
309	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
313	#127	—	2	4	no	—
314	#127	—	4	2	no	—
315	#124	—	2	4	no	—
316	#124	—	2	4	no	—
317	#124	—	2	4	no	—
318	#124	—	4	2	no	—
319	C₄×D₄	—	2	4	no	—
320	C₄×D₄	—	2	4	no	—
321	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	2	4	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	4	no	—
328	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
330	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
331	#107	—	2	2	no	—
332	C₄⋊C₈	D₄×C₃₇	1	4	yes	complemented
333	#103	—	2	4	no	—
334	#102	—	2	4	no	—
335	#102	—	2	4	no	—
336	C₄×C₈	—	2	2	no	—
337	C₄×C₈	—	2	2	no	—
338	C₄×C₈	D₄×C₃₇	1	4	yes	complemented
339	#95	—	2	4	no	—
340	#95	D₄×C₃₇	1	2	yes	—
341	C₂⁴	—	2	2	no	—
342	C₂⁴	—	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×Q₈	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	4	8	no	—
361	C₂×D₄	—	4	8	no	—
362	C₂×D₄	—	8	4	no	—
363	C₂×D₄	C₂×D₄×C₃₇	1	4	yes	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	4	4	no	—
367	C₂²×C₄	—	8	4	no	—
368	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
372	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
373	Q₁₆	—	4	4	no	—
374	SD₁₆	—	4	8	no	—
375	SD₁₆	—	4	8	no	—
376	D₈	—	2	8	no	—
377	D₈	—	4	8	no	—
378	D₈	—	4	4	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
386	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
387	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
388	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
389	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
390	C₂×C₈	#41×C₃₇	1	2	yes	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	4	8	no	—
395	C₂²⋊C₄	—	4	4	no	—
396	C₂²⋊C₄	—	4	4	no	—
397	C₂²⋊C₄	—	4	4	no	—
398	C₂²⋊C₄	—	8	4	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	1	no	—
401	C₄²	—	2	1	no	—
402	C₄²	—	2	1	no	—
403	C₄²	C₂×D₄×C₃₇	1	2	yes	—
404	C₄²	C₂×D₄×C₃₇	1	2	yes	—
405	C₂³	—	2	4	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	4	no	—
409	C₂³	—	4	4	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	4	no	—
414	C₂³	—	4	4	no	—
415	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
416	Q₈	—	4	2	no	—
417	Q₈	—	4	2	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	4	2	no	—
420	D₄	—	2	4	no	—
421	D₄	—	2	4	no	—
422	D₄	—	4	2	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	2	no	—
426	D₄	—	4	2	no	—
427	D₄	—	4	2	no	—
428	D₄	—	8	16	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	8	8	no	—
442	C₂×C₄	#127×C₃₇	1	2	yes	—
443	C₂×C₄	#127×C₃₇	1	2	yes	—
444	C₂×C₄	#135×C₃₇	1	4	yes	—
445	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
446	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₄×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	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
451	C₈	—	2	2	no	—
452	C₈	—	2	2	no	—
453	C₈	—	2	2	no	—
454	C₈	#121×C₃₇	1	4	yes	—
455	C₂²	—	4	8	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	8	4	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	4	no	—
461	C₂²	—	8	2	no	—
462	C₂²	—	8	2	no	—
463	C₂²	—	8	4	no	—
464	C₂²	—	8	2	no	—
465	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
466	C₂²	D₄²×C₃₇	1	1	yes	characteristic
467	C₂²	C₃₇×#550	1	1	yes	characteristic
468	C₂²	C₂×#135×C₃₇	1	2	yes	—
469	C₂²	C₃₇×#576	1	2	yes	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	4	no	—
473	C₄	—	4	2	no	—
474	C₄	—	8	2	no	—
475	C₄	—	8	2	no	—
476	C₄	C₂×#121×C₃₇	1	1	yes	characteristic
477	C₄	C₃₇×#535	1	1	yes	characteristic
478	C₄	D₄²×C₃₇	1	1	yes	characteristic
479	C₄	C₃₇×#550	1	1	yes	characteristic
480	C₂	—	8	4	no	—
481	C₂	—	16	2	no	—
482	C₂	C₃₇×#2541	1	1	yes	characteristic
483	C₂	C₃₇×#3147	1	1	yes	characteristic
484	C₂	C₃₇×#3155	1	1	yes	characteristic
485	C₂	C₃₇×#3280	1	2	yes	—
486	C₂	C₃₇×#3396	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×C₃₇×#493	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×#495	C₂	semidirect
2. C₂×C₃₇×#495	C₂	semidirect
4. C₂×C₃₇×#463	C₂	semidirect
5. C₂×C₄×D₈×C₃₇	C₂	semidirect
6. C₃₇×#2544	C₂	semidirect
7. C₃₇×#2014	C₂	semidirect
8. C₃₇×#2012	C₂	semidirect
9. C₃₇×#1970	C₂	semidirect
10. C₃₇×#1969	C₂	semidirect
11. C₈×C₄⋊C₄×C₃₇	C₂	semidirect
88. C₄⋊C₈×C₃₇	D₄	semidirect
94. C₄×C₈×C₃₇	D₄	semidirect
211. #28465	C₃₇	direct (N × H)
237. C₂×#495	C₂×C₃₇	semidirect
238. C₂×#495	C₂×C₃₇	semidirect
240. C₂×#463	C₂×C₃₇	semidirect
241. C₂×C₄×D₈	C₂×C₃₇	semidirect
242. #2544	C₂×C₃₇	semidirect
243. #2014	C₂×C₃₇	semidirect
244. #2012	C₂×C₃₇	semidirect
245. #1970	C₂×C₃₇	semidirect
246. #1969	C₂×C₃₇	semidirect
247. C₈×C₄⋊C₄	C₂×C₃₇	semidirect
285. C₃₇	#28465	direct (N × H)
332. C₄⋊C₈	D₄×C₃₇	semidirect
338. C₄×C₈	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×#495	2
C₂×C₃₇×#493	2
C₂×C₃₇×#463	2
C₂×C₄×D₈×C₃₇	2
C₃₇×#2544	2
C₃₇×#2014	2
C₃₇×#2012	2
C₃₇×#1970	2
C₃₇×#1969	2
C₈×C₄⋊C₄×C₃₇	2
#28465	37

Subgroups — C37×#28465 #22649718

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28465 #22649718