Subgroups — C₃₇×#29926 #22651179

Order 9472.

728 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#2857	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#2283	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2097	C₂	1	2	yes	maximal, complemented
4	C₃₇×#2074	C₂	1	2	yes	maximal, complemented
5	C₃₇×#2036	C₂	1	2	yes	maximal
6	C₃₇×#2035	C₂	1	2	yes	maximal
7	C₃₇×#1981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1981	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1948	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1947	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1797	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	—
14	C₂²×C₄²×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×#107×C₃₇	C₂²	1	2	yes	—
16	C₂×#106×C₃₇	C₂²	1	2	yes	—
17	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×#103×C₃₇	C₂²	1	2	yes	—
20	C₂×#103×C₃₇	C₂²	1	2	yes	—
21	C₂×#103×C₃₇	C₂²	1	2	yes	—
22	C₂×#103×C₃₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₃₇	C₂²	1	2	yes	—
24	C₃₇×#391	C₂²	1	2	yes	—
25	C₃₇×#389	—	2	1	no	—
26	C₃₇×#389	—	2	1	no	—
27	C₃₇×#384	C₂²	1	1	yes	characteristic
28	C₃₇×#383	—	2	1	no	—
29	C₃₇×#382	C₂²	1	1	yes	characteristic
30	C₃₇×#382	C₂²	1	1	yes	characteristic
31	C₃₇×#381	—	2	1	no	—
32	C₃₇×#380	—	2	1	no	—
33	C₃₇×#380	—	2	1	no	—
34	C₃₇×#380	C₂²	1	1	yes	characteristic
35	C₃₇×#380	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₃₇	—	2	1	no	—
39	C₃₇×#376	—	2	1	no	—
40	C₃₇×#340	C₂²	1	2	yes	—
41	C₃₇×#340	C₂²	1	2	yes	—
42	C₃₇×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
44	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
48	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
49	C₄⋊Q₈×C₃₇	—	2	2	no	—
50	C₄⋊Q₈×C₃₇	—	2	2	no	—
51	C₂²⋊Q₈×C₃₇	—	4	2	no	—
52	C₂²⋊Q₈×C₃₇	—	4	2	no	—
53	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
66	C₂×C₄²×C₃₇	—	2	2	no	—
67	C₂×C₄²×C₃₇	—	2	2	no	—
68	C₂×C₄²×C₃₇	—	2	1	no	—
69	C₂×C₄²×C₃₇	—	2	1	no	—
70	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
74	#107×C₃₇	—	4	2	no	—
75	#106×C₃₇	—	4	2	no	—
76	C₄⋊C₈×C₃₇	—	2	2	no	—
77	C₄⋊C₈×C₃₇	—	2	2	no	—
78	#103×C₃₇	—	4	2	no	—
79	#103×C₃₇	—	4	2	no	—
80	#103×C₃₇	—	4	2	no	—
81	#103×C₃₇	—	4	2	no	—
82	C₂²⋊C₈×C₃₇	—	4	2	no	—
83	#95×C₃₇	—	2	1	no	—
84	#95×C₃₇	—	2	1	no	—
85	#95×C₃₇	—	2	1	no	—
86	#95×C₃₇	—	2	1	no	—
87	#95×C₃₇	—	2	1	no	—
88	#95×C₃₇	—	2	1	no	—
89	#95×C₃₇	—	2	1	no	—
90	#95×C₃₇	—	2	1	no	—
91	#95×C₃₇	—	2	2	no	—
92	#95×C₃₇	—	2	2	no	—
93	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
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	C₂²×C₄×C₃₇	—	2	2	no	—
101	C₂²×C₄×C₃₇	—	2	2	no	—
102	C₂²×C₄×C₃₇	—	2	2	no	—
103	C₂²×C₄×C₃₇	—	2	2	no	—
104	C₂²×C₄×C₃₇	—	2	2	no	—
105	C₂²×C₄×C₃₇	—	2	1	no	—
106	C₂²×C₄×C₃₇	—	2	1	no	—
107	C₂²×C₄×C₃₇	—	2	1	no	—
108	C₂²×C₄×C₃₇	—	2	1	no	—
109	C₂²×C₄×C₃₇	—	2	1	no	—
110	C₂²×C₄×C₃₇	—	2	1	no	—
111	C₂²×C₄×C₃₇	—	2	1	no	—
112	C₂²×C₄×C₃₇	—	2	1	no	—
113	C₂²×C₄×C₃₇	—	2	1	no	—
114	C₂²×C₄×C₃₇	—	2	1	no	—
115	C₂²×C₄×C₃₇	—	2	2	no	—
116	C₂²×C₄×C₃₇	—	2	2	no	—
117	C₂²×C₄×C₃₇	—	4	1	no	—
118	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
124	C₂×C₈×C₃₇	—	2	2	no	—
125	C₂×C₈×C₃₇	—	2	2	no	—
126	C₂×C₈×C₃₇	—	2	2	no	—
127	C₂×C₈×C₃₇	—	2	2	no	—
128	C₂×C₈×C₃₇	—	2	2	no	—
129	C₂×C₈×C₃₇	—	2	2	no	—
130	C₄⋊C₄×C₃₇	—	2	1	no	—
131	C₄⋊C₄×C₃₇	—	2	1	no	—
132	C₄⋊C₄×C₃₇	—	2	1	no	—
133	C₄⋊C₄×C₃₇	—	2	1	no	—
134	C₄⋊C₄×C₃₇	—	2	1	no	—
135	C₄⋊C₄×C₃₇	—	2	2	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	1	no	—
140	C₄⋊C₄×C₃₇	—	4	2	no	—
141	C₄⋊C₄×C₃₇	—	4	4	no	—
142	C₄⋊C₄×C₃₇	—	4	2	no	—
143	C₄⋊C₄×C₃₇	—	4	2	no	—
144	C₄⋊C₄×C₃₇	—	4	2	no	—
145	C₂²⋊C₄×C₃₇	—	4	2	no	—
146	C₂²⋊C₄×C₃₇	—	4	4	no	—
147	C₂²⋊C₄×C₃₇	—	4	2	no	—
148	C₄²×C₃₇	—	2	2	no	—
149	C₄²×C₃₇	—	2	2	no	—
150	C₄²×C₃₇	—	2	1	no	—
151	C₄²×C₃₇	—	2	1	no	—
152	C₄²×C₃₇	—	4	2	no	—
153	C₄²×C₃₇	—	4	2	no	—
154	C₄²×C₃₇	#41	1	2	yes	—
155	C₄²×C₃₇	#41	1	2	yes	—
156	C₂³×C₃₇	—	2	1	no	—
157	C₂³×C₃₇	—	2	1	no	—
158	C₂³×C₃₇	—	2	1	no	—
159	C₂³×C₃₇	—	2	1	no	—
160	C₂³×C₃₇	—	2	1	no	—
161	C₂³×C₃₇	—	2	1	no	—
162	C₂³×C₃₇	#137	1	2	yes	—
163	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
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	C₂×C₄×C₃₇	—	2	1	no	—
169	C₂×C₄×C₃₇	—	2	1	no	—
170	C₂×C₄×C₃₇	—	2	1	no	—
171	C₂×C₄×C₃₇	—	2	1	no	—
172	C₂×C₄×C₃₇	—	2	1	no	—
173	C₂×C₄×C₃₇	—	2	1	no	—
174	C₂×C₄×C₃₇	—	2	1	no	—
175	C₂×C₄×C₃₇	—	2	1	no	—
176	C₂×C₄×C₃₇	—	2	1	no	—
177	C₂×C₄×C₃₇	—	2	1	no	—
178	C₂×C₄×C₃₇	—	2	1	no	—
179	C₂×C₄×C₃₇	—	4	4	no	—
180	C₂×C₄×C₃₇	—	4	1	no	—
181	C₂×C₄×C₃₇	—	4	1	no	—
182	C₂×C₄×C₃₇	—	4	1	no	—
183	C₂×C₄×C₃₇	—	4	1	no	—
184	C₂×C₄×C₃₇	—	4	4	no	—
185	C₂×C₄×C₃₇	—	4	2	no	—
186	C₂×C₄×C₃₇	—	4	2	no	—
187	C₂×C₄×C₃₇	—	4	2	no	—
188	C₂×C₄×C₃₇	—	4	1	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	2	no	—
193	C₂×C₄×C₃₇	—	4	1	no	—
194	C₂×C₄×C₃₇	—	4	1	no	—
195	C₂×C₄×C₃₇	—	4	2	no	—
196	C₂×C₄×C₃₇	—	4	1	no	—
197	C₂×C₄×C₃₇	—	4	1	no	—
198	C₂×C₄×C₃₇	—	4	1	no	—
199	C₂×C₄×C₃₇	—	4	1	no	—
200	C₂×C₄×C₃₇	—	4	1	no	—
201	C₂×C₄×C₃₇	—	4	1	no	—
202	C₂×C₄×C₃₇	—	4	2	no	—
203	C₂×C₄×C₃₇	#123	1	2	yes	—
204	C₂×C₄×C₃₇	#123	1	2	yes	—
205	C₂×C₄×C₃₇	#135	1	2	yes	—
206	C₂×C₄×C₃₇	#137	1	2	yes	—
207	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
213	C₈×C₃₇	—	4	2	no	—
214	C₈×C₃₇	—	4	2	no	—
215	#29926	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂²×C₃₇	—	2	2	no	—
217	C₂²×C₃₇	—	2	2	no	—
218	C₂²×C₃₇	—	2	2	no	—
219	C₂²×C₃₇	—	4	1	no	—
220	C₂²×C₃₇	—	4	1	no	—
221	C₂²×C₃₇	—	4	1	no	—
222	C₂²×C₃₇	—	4	1	no	—
223	C₂²×C₃₇	C₂×#123	1	1	yes	characteristic
224	C₂²×C₃₇	#535	1	1	yes	characteristic
225	C₂²×C₃₇	#537	1	1	yes	characteristic
226	C₂²×C₃₇	C₂×#135	1	1	yes	characteristic
227	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
228	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
229	C₂²×C₃₇	#575	1	1	yes	characteristic
230	C₄×C₃₇	—	2	2	no	—
231	C₄×C₃₇	—	4	1	no	—
232	C₄×C₃₇	—	4	1	no	—
233	C₄×C₃₇	—	4	1	no	—
234	C₄×C₃₇	—	8	2	no	—
235	C₄×C₃₇	—	8	2	no	—
236	C₄×C₃₇	—	8	1	no	—
237	C₄×C₃₇	—	8	1	no	—
238	C₄×C₃₇	—	8	1	no	—
239	C₄×C₃₇	—	8	1	no	—
240	C₄×C₃₇	#485	1	4	yes	—
241	C₄×C₃₇	#540	1	1	yes	characteristic
242	C₄×C₃₇	#540	1	1	yes	characteristic
243	C₄×C₃₇	#542	1	1	yes	characteristic
244	C₄×C₃₇	#542	1	1	yes	characteristic
245	#2857	C₂×C₃₇	1	1	yes	characteristic
246	#2283	C₂×C₃₇	1	1	yes	characteristic
247	#2097	C₂×C₃₇	1	2	yes	complemented
248	#2074	C₂×C₃₇	1	2	yes	complemented
249	#2036	C₂×C₃₇	1	2	yes	—
250	#2035	C₂×C₃₇	1	2	yes	—
251	#1981	C₂×C₃₇	1	1	yes	characteristic, complemented
252	#1981	C₂×C₃₇	1	1	yes	characteristic, complemented
253	#1948	C₂×C₃₇	1	1	yes	characteristic, complemented
254	#1947	C₂×C₃₇	1	1	yes	characteristic, complemented
255	#1797	C₂×C₃₇	1	1	yes	characteristic
256	C₂×C₃₇	—	4	2	no	—
257	C₂×C₃₇	#2624	1	1	yes	characteristic
258	C₂×C₃₇	C₂×#485	1	1	yes	characteristic
259	C₂×C₃₇	#3095	1	1	yes	characteristic
260	C₂×C₃₇	#3212	1	1	yes	characteristic
261	C₂×C₃₇	#3218	1	1	yes	characteristic
262	C₂×C₃₇	#3248	1	1	yes	characteristic
263	C₂×C₃₇	#3252	1	1	yes	characteristic
264	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
265	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	2	yes	—
266	C₂²×C₄²	C₂²×C₃₇	1	1	yes	characteristic
267	C₂×#107	C₂²×C₃₇	1	2	yes	—
268	C₂×#106	C₂²×C₃₇	1	2	yes	—
269	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
270	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
271	C₂×#103	C₂²×C₃₇	1	2	yes	—
272	C₂×#103	C₂²×C₃₇	1	2	yes	—
273	C₂×#103	C₂²×C₃₇	1	2	yes	—
274	C₂×#103	C₂²×C₃₇	1	2	yes	—
275	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	—
276	#391	C₂²×C₃₇	1	2	yes	—
277	#389	—	2	1	no	—
278	#389	—	2	1	no	—
279	#384	C₂²×C₃₇	1	1	yes	characteristic
280	#383	—	2	1	no	—
281	#382	C₂²×C₃₇	1	1	yes	characteristic
282	#382	C₂²×C₃₇	1	1	yes	characteristic
283	#381	—	2	1	no	—
284	#380	—	2	1	no	—
285	#380	—	2	1	no	—
286	#380	C₂²×C₃₇	1	1	yes	characteristic
287	#380	C₂²×C₃₇	1	1	yes	characteristic
288	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
289	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
290	C₄×C₂²⋊C₄	—	2	1	no	—
291	#376	—	2	1	no	—
292	#340	C₂²×C₃₇	1	2	yes	—
293	#340	C₂²×C₃₇	1	2	yes	—
294	#336	C₂²×C₃₇	1	2	yes	—
295	C₃₇	#29926	1	1	yes	characteristic, direct product factor, Sylow
296	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
297	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
298	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
299	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
301	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
302	C₄⋊Q₈	—	2	2	no	—
303	C₄⋊Q₈	—	2	2	no	—
304	C₂²⋊Q₈	—	4	2	no	—
305	C₂²⋊Q₈	—	4	2	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	—	2	1	no	—
311	C₂×C₄⋊C₄	C₂³×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	1	yes	characteristic
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
324	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
326	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
327	#107	—	4	2	no	—
328	#106	—	4	2	no	—
329	C₄⋊C₈	—	2	2	no	—
330	C₄⋊C₈	—	2	2	no	—
331	#103	—	4	2	no	—
332	#103	—	4	2	no	—
333	#103	—	4	2	no	—
334	#103	—	4	2	no	—
335	C₂²⋊C₈	—	4	2	no	—
336	#95	—	2	1	no	—
337	#95	—	2	1	no	—
338	#95	—	2	1	no	—
339	#95	—	2	1	no	—
340	#95	—	2	1	no	—
341	#95	—	2	1	no	—
342	#95	—	2	1	no	—
343	#95	—	2	1	no	—
344	#95	—	2	2	no	—
345	#95	—	2	2	no	—
346	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	4	1	no	—
371	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
376	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₄⋊C₄	—	4	4	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₄⋊C₄	—	4	2	no	—
397	C₄⋊C₄	—	4	2	no	—
398	C₂²⋊C₄	—	4	2	no	—
399	C₂²⋊C₄	—	4	4	no	—
400	C₂²⋊C₄	—	4	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	4	2	no	—
406	C₄²	—	4	2	no	—
407	C₄²	#41×C₃₇	1	2	yes	—
408	C₄²	#41×C₃₇	1	2	yes	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	1	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	#137×C₃₇	1	2	yes	—
416	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
417	Q₈	—	4	2	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	4	2	no	—
420	Q₈	—	4	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	#123×C₃₇	1	2	yes	—
457	C₂×C₄	#123×C₃₇	1	2	yes	—
458	C₂×C₄	#135×C₃₇	1	2	yes	—
459	C₂×C₄	#137×C₃₇	1	2	yes	—
460	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
461	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
462	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
463	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
464	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
465	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
466	C₈	—	4	2	no	—
467	C₈	—	4	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	C₂×#123×C₃₇	1	1	yes	characteristic
476	C₂²	C₃₇×#535	1	1	yes	characteristic
477	C₂²	C₃₇×#537	1	1	yes	characteristic
478	C₂²	C₂×#135×C₃₇	1	1	yes	characteristic
479	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
480	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
481	C₂²	C₃₇×#575	1	1	yes	characteristic
482	C₄	—	2	2	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	8	2	no	—
487	C₄	—	8	2	no	—
488	C₄	—	8	1	no	—
489	C₄	—	8	1	no	—
490	C₄	—	8	1	no	—
491	C₄	—	8	1	no	—
492	C₄	C₃₇×#485	1	4	yes	—
493	C₄	C₃₇×#540	1	1	yes	characteristic
494	C₄	C₃₇×#540	1	1	yes	characteristic
495	C₄	C₃₇×#542	1	1	yes	characteristic
496	C₄	C₃₇×#542	1	1	yes	characteristic
497	C₂	—	4	2	no	—
498	C₂	C₃₇×#2624	1	1	yes	characteristic
499	C₂	C₂×C₃₇×#485	1	1	yes	characteristic
500	C₂	C₃₇×#3095	1	1	yes	characteristic
501	C₂	C₃₇×#3212	1	1	yes	characteristic
502	C₂	C₃₇×#3218	1	1	yes	characteristic
503	C₂	C₃₇×#3248	1	1	yes	characteristic
504	C₂	C₃₇×#3252	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂⁴×C₃₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂²×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₇×#2097	C₂	semidirect
4. C₃₇×#2074	C₂	semidirect
7. C₃₇×#1981	C₂	semidirect
8. C₃₇×#1981	C₂	semidirect
9. C₃₇×#1948	C₂	semidirect
10. C₃₇×#1947	C₂	semidirect
215. #29926	C₃₇	direct (N × H)
247. #2097	C₂×C₃₇	semidirect
248. #2074	C₂×C₃₇	semidirect
251. #1981	C₂×C₃₇	semidirect
252. #1981	C₂×C₃₇	semidirect
253. #1948	C₂×C₃₇	semidirect
254. #1947	C₂×C₃₇	semidirect
295. C₃₇	#29926	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₇×#2857	2
C₃₇×#2283	2
C₃₇×#2097	2
C₃₇×#2074	2
C₃₇×#2036	2
C₃₇×#2035	2
C₃₇×#1981	2
C₃₇×#1948	2
C₃₇×#1947	2
C₃₇×#1797	2
#29926	37

Subgroups — C37×#29926 #22651179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#29926 #22651179