Subgroups — C₃₇×#29835 #22651088

Order 9472.

796 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#479	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#460	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2641	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2320	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2067	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2065	C₂	1	2	yes	maximal, complemented
7	C₃₇×#2055	C₂	1	2	yes	maximal, complemented
8	C₃₇×#2055	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1989	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1982	C₂	1	1	yes	maximal, characteristic
11	C₃₇×#1843	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
13	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
16	C₃₇×#479	—	2	4	no	—
17	C₃₇×#460	—	2	4	no	—
18	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
23	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
24	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
26	C₂×#102×C₃₇	C₂²	1	2	yes	—
27	C₂×#102×C₃₇	C₂²	1	2	yes	—
28	C₂×#102×C₃₇	C₂²	1	2	yes	—
29	C₃₇×#394	—	2	1	no	—
30	C₃₇×#394	—	2	1	no	—
31	C₃₇×#394	—	2	2	no	—
32	C₃₇×#391	C₂²	1	2	yes	—
33	C₃₇×#390	C₂²	1	2	yes	—
34	C₃₇×#390	C₂²	1	2	yes	—
35	C₃₇×#389	C₂²	1	2	yes	—
36	C₃₇×#387	—	2	2	no	—
37	C₃₇×#383	—	2	1	no	—
38	C₃₇×#382	—	2	1	no	—
39	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
40	C₃₇×#376	C₂²	1	1	yes	characteristic
41	C₃₇×#340	C₂²	1	2	yes	—
42	C₃₇×#340	C₂²	1	2	yes	—
43	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₃₇	—	2	1	no	—
45	C₂²×D₄×C₃₇	—	2	1	no	—
46	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
47	C₂×SD₁₆×C₃₇	—	2	4	no	—
48	C₂×SD₁₆×C₃₇	—	4	2	no	—
49	C₂×SD₁₆×C₃₇	—	4	2	no	—
50	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
51	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
53	#127×C₃₇	—	2	2	no	—
54	#127×C₃₇	—	2	2	no	—
55	#125×C₃₇	—	2	2	no	—
56	#125×C₃₇	—	2	2	no	—
57	C₄×Q₈×C₃₇	—	2	2	no	—
58	C₄×Q₈×C₃₇	D₄	1	4	yes	—
59	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
71	C₂×C₄²×C₃₇	—	2	1	no	—
72	C₂×C₄²×C₃₇	—	2	1	no	—
73	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
74	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
75	#107×C₃₇	—	2	2	no	—
76	#106×C₃₇	—	2	2	no	—
77	C₄⋊C₈×C₃₇	—	2	2	no	—
78	C₄⋊C₈×C₃₇	—	2	2	no	—
79	C₄⋊C₈×C₃₇	—	4	2	no	—
80	C₄⋊C₈×C₃₇	—	4	2	no	—
81	#103×C₃₇	—	2	2	no	—
82	#103×C₃₇	—	2	2	no	—
83	#102×C₃₇	—	2	4	no	—
84	#102×C₃₇	—	4	2	no	—
85	#102×C₃₇	—	4	2	no	—
86	#95×C₃₇	—	2	1	no	—
87	#95×C₃₇	—	2	2	no	—
88	#95×C₃₇	—	2	2	no	—
89	#95×C₃₇	—	2	2	no	—
90	#95×C₃₇	D₄	1	1	yes	characteristic
91	#95×C₃₇	D₄	1	1	yes	characteristic
92	#95×C₃₇	D₄	1	2	yes	—
93	C₂⁴×C₃₇	—	2	2	no	—
94	C₂×Q₈×C₃₇	—	2	1	no	—
95	C₂×Q₈×C₃₇	—	2	2	no	—
96	C₂×Q₈×C₃₇	—	2	2	no	—
97	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
98	C₂×D₄×C₃₇	—	2	2	no	—
99	C₂×D₄×C₃₇	—	2	2	no	—
100	C₂×D₄×C₃₇	—	2	2	no	—
101	C₂×D₄×C₃₇	—	2	2	no	—
102	C₂×D₄×C₃₇	—	2	2	no	—
103	C₂×D₄×C₃₇	—	2	2	no	—
104	C₂×D₄×C₃₇	—	4	2	no	—
105	C₂×D₄×C₃₇	—	4	2	no	—
106	C₂×D₄×C₃₇	—	8	1	no	—
107	C₂×D₄×C₃₇	—	8	2	no	—
108	C₂×D₄×C₃₇	—	8	1	no	—
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	1	no	—
114	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
119	SD₁₆×C₃₇	—	4	8	no	—
120	C₂×C₈×C₃₇	—	2	2	no	—
121	C₂×C₈×C₃₇	—	2	1	no	—
122	C₂×C₈×C₃₇	—	2	1	no	—
123	C₂×C₈×C₃₇	—	2	2	no	—
124	C₂×C₈×C₃₇	—	2	2	no	—
125	C₂×C₈×C₃₇	—	2	2	no	—
126	C₂×C₈×C₃₇	—	2	2	no	—
127	C₄⋊C₄×C₃₇	—	2	4	no	—
128	C₄⋊C₄×C₃₇	—	2	1	no	—
129	C₄⋊C₄×C₃₇	—	2	1	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	2	no	—
134	C₄⋊C₄×C₃₇	—	2	2	no	—
135	C₄⋊C₄×C₃₇	—	4	2	no	—
136	C₄⋊C₄×C₃₇	—	4	2	no	—
137	C₄⋊C₄×C₃₇	—	8	2	no	—
138	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
139	C₂²⋊C₄×C₃₇	—	8	2	no	—
140	C₂²⋊C₄×C₃₇	—	8	2	no	—
141	C₂²⋊C₄×C₃₇	—	8	2	no	—
142	C₂²⋊C₄×C₃₇	—	8	2	no	—
143	C₄²×C₃₇	—	2	4	no	—
144	C₄²×C₃₇	—	2	2	no	—
145	C₄²×C₃₇	—	2	2	no	—
146	C₄²×C₃₇	—	8	1	no	—
147	C₄²×C₃₇	C₂×D₄	1	2	yes	—
148	C₄²×C₃₇	#41	1	2	yes	—
149	C₂³×C₃₇	—	4	2	no	—
150	C₂³×C₃₇	—	4	2	no	—
151	C₂³×C₃₇	—	4	2	no	—
152	C₂³×C₃₇	—	4	2	no	—
153	C₂³×C₃₇	—	4	2	no	—
154	C₂³×C₃₇	—	4	2	no	—
155	C₂³×C₃₇	—	4	2	no	—
156	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₃₇	—	2	2	no	—
158	Q₈×C₃₇	—	2	2	no	—
159	Q₈×C₃₇	—	4	2	no	—
160	D₄×C₃₇	—	4	2	no	—
161	D₄×C₃₇	—	4	2	no	—
162	D₄×C₃₇	—	4	2	no	—
163	D₄×C₃₇	—	4	2	no	—
164	D₄×C₃₇	—	8	4	no	—
165	D₄×C₃₇	—	8	4	no	—
166	C₂×C₄×C₃₇	—	2	1	no	—
167	C₂×C₄×C₃₇	—	2	2	no	—
168	C₂×C₄×C₃₇	—	2	1	no	—
169	C₂×C₄×C₃₇	—	2	2	no	—
170	C₂×C₄×C₃₇	—	2	2	no	—
171	C₂×C₄×C₃₇	—	2	2	no	—
172	C₂×C₄×C₃₇	—	2	2	no	—
173	C₂×C₄×C₃₇	—	2	2	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	—	4	2	no	—
178	C₂×C₄×C₃₇	—	4	1	no	—
179	C₂×C₄×C₃₇	—	4	1	no	—
180	C₂×C₄×C₃₇	—	4	1	no	—
181	C₂×C₄×C₃₇	—	4	1	no	—
182	C₂×C₄×C₃₇	—	4	2	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	1	no	—
187	C₂×C₄×C₃₇	—	4	2	no	—
188	C₂×C₄×C₃₇	#121	1	2	yes	—
189	C₂×C₄×C₃₇	#121	1	2	yes	—
190	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
193	C₂×C₄×C₃₇	2₋¹⁺⁴	1	2	yes	—
194	C₈×C₃₇	—	4	1	no	—
195	C₈×C₃₇	—	4	1	no	—
196	C₈×C₃₇	—	4	2	no	—
197	#29835	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂²×C₃₇	—	8	2	no	—
199	C₂²×C₃₇	—	8	2	no	—
200	C₂²×C₃₇	—	8	2	no	—
201	C₂²×C₃₇	—	8	2	no	—
202	C₂²×C₃₇	—	8	2	no	—
203	C₂²×C₃₇	—	8	2	no	—
204	C₂²×C₃₇	—	8	2	no	—
205	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
206	C₂²×C₃₇	#537	1	2	yes	—
207	C₂²×C₃₇	#576	1	1	yes	characteristic
208	C₂²×C₃₇	#577	1	2	yes	—
209	C₂²×C₃₇	#577	1	1	yes	characteristic
210	C₄×C₃₇	—	2	2	no	—
211	C₄×C₃₇	—	2	2	no	—
212	C₄×C₃₇	—	4	2	no	—
213	C₄×C₃₇	—	4	2	no	—
214	C₄×C₃₇	—	4	2	no	—
215	C₄×C₃₇	—	4	2	no	—
216	C₄×C₃₇	—	8	2	no	—
217	C₄×C₃₇	—	8	1	no	—
218	C₄×C₃₇	—	8	1	no	—
219	C₄×C₃₇	#535	1	1	yes	characteristic
220	C₄×C₃₇	#536	1	1	yes	characteristic
221	C₄×C₃₇	#542	1	2	yes	—
222	C₂×#479	C₂×C₃₇	1	1	yes	characteristic, complemented
223	C₂×#460	C₂×C₃₇	1	1	yes	characteristic
224	#2641	C₂×C₃₇	1	1	yes	characteristic
225	#2320	C₂×C₃₇	1	1	yes	characteristic, complemented
226	#2067	C₂×C₃₇	1	2	yes	complemented
227	#2065	C₂×C₃₇	1	2	yes	complemented
228	#2055	C₂×C₃₇	1	2	yes	complemented
229	#2055	C₂×C₃₇	1	2	yes	complemented
230	#1989	C₂×C₃₇	1	1	yes	characteristic, complemented
231	#1982	C₂×C₃₇	1	1	yes	characteristic
232	#1843	C₂×C₃₇	1	1	yes	characteristic, complemented
233	C₂×C₃₇	—	16	2	no	—
234	C₂×C₃₇	#2620	1	1	yes	characteristic
235	C₂×C₃₇	#3043	1	1	yes	characteristic
236	C₂×C₃₇	#3045	1	1	yes	characteristic
237	C₂×C₃₇	#3257	1	2	yes	—
238	C₂×C₃₇	#3260	1	2	yes	—
239	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
240	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
241	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
242	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
243	#479	—	2	4	no	—
244	#460	—	2	4	no	—
245	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
246	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
247	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
248	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
249	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
250	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
251	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
252	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
253	C₂×#102	C₂²×C₃₇	1	2	yes	—
254	C₂×#102	C₂²×C₃₇	1	2	yes	—
255	C₂×#102	C₂²×C₃₇	1	2	yes	—
256	#394	—	2	1	no	—
257	#394	—	2	1	no	—
258	#394	—	2	2	no	—
259	#391	C₂²×C₃₇	1	2	yes	—
260	#390	C₂²×C₃₇	1	2	yes	—
261	#390	C₂²×C₃₇	1	2	yes	—
262	#389	C₂²×C₃₇	1	2	yes	—
263	#387	—	2	2	no	—
264	#383	—	2	1	no	—
265	#382	—	2	1	no	—
266	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
267	#376	C₂²×C₃₇	1	1	yes	characteristic
268	#340	C₂²×C₃₇	1	2	yes	—
269	#340	C₂²×C₃₇	1	2	yes	—
270	C₃₇	#29835	1	1	yes	characteristic, direct product factor, Sylow
271	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
272	C₂²×D₄	—	2	1	no	—
273	C₂²×D₄	—	2	1	no	—
274	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
275	C₂×SD₁₆	—	2	4	no	—
276	C₂×SD₁₆	—	4	2	no	—
277	C₂×SD₁₆	—	4	2	no	—
278	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
279	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
281	#127	—	2	2	no	—
282	#127	—	2	2	no	—
283	#125	—	2	2	no	—
284	#125	—	2	2	no	—
285	C₄×Q₈	—	2	2	no	—
286	C₄×Q₈	D₄×C₃₇	1	4	yes	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
302	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
303	#107	—	2	2	no	—
304	#106	—	2	2	no	—
305	C₄⋊C₈	—	2	2	no	—
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	—	4	2	no	—
308	C₄⋊C₈	—	4	2	no	—
309	#103	—	2	2	no	—
310	#103	—	2	2	no	—
311	#102	—	2	4	no	—
312	#102	—	4	2	no	—
313	#102	—	4	2	no	—
314	#95	—	2	1	no	—
315	#95	—	2	2	no	—
316	#95	—	2	2	no	—
317	#95	—	2	2	no	—
318	#95	D₄×C₃₇	1	1	yes	characteristic
319	#95	D₄×C₃₇	1	1	yes	characteristic
320	#95	D₄×C₃₇	1	2	yes	—
321	C₂⁴	—	2	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂×D₄	—	8	1	no	—
335	C₂×D₄	—	8	2	no	—
336	C₂×D₄	—	8	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
343	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
344	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
346	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
347	SD₁₆	—	4	8	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	—	8	2	no	—
366	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
367	C₂²⋊C₄	—	8	2	no	—
368	C₂²⋊C₄	—	8	2	no	—
369	C₂²⋊C₄	—	8	2	no	—
370	C₂²⋊C₄	—	8	2	no	—
371	C₄²	—	2	4	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	8	1	no	—
375	C₄²	C₂×D₄×C₃₇	1	2	yes	—
376	C₄²	#41×C₃₇	1	2	yes	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	4	2	no	—
384	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
385	Q₈	—	2	2	no	—
386	Q₈	—	2	2	no	—
387	Q₈	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	8	4	no	—
393	D₄	—	8	4	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	#121×C₃₇	1	2	yes	—
417	C₂×C₄	#121×C₃₇	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
419	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
420	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
421	C₂×C₄	2₋¹⁺⁴×C₃₇	1	2	yes	—
422	C₈	—	4	2	no	—
423	C₈	—	4	1	no	—
424	C₈	—	4	1	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	2	no	—
432	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
433	C₂²	C₃₇×#537	1	2	yes	—
434	C₂²	C₃₇×#576	1	1	yes	characteristic
435	C₂²	C₃₇×#577	1	2	yes	—
436	C₂²	C₃₇×#577	1	1	yes	characteristic
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	2	no	—
443	C₄	—	8	2	no	—
444	C₄	—	8	1	no	—
445	C₄	—	8	1	no	—
446	C₄	C₃₇×#535	1	1	yes	characteristic
447	C₄	C₃₇×#536	1	1	yes	characteristic
448	C₄	C₃₇×#542	1	2	yes	—
449	C₂	—	16	2	no	—
450	C₂	C₃₇×#2620	1	1	yes	characteristic
451	C₂	C₃₇×#3043	1	1	yes	characteristic
452	C₂	C₃₇×#3045	1	1	yes	characteristic
453	C₂	C₃₇×#3257	1	2	yes	—
454	C₂	C₃₇×#3260	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×#127×C₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₃₇×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#479	C₂	semidirect
4. C₃₇×#2320	C₂	semidirect
5. C₃₇×#2067	C₂	semidirect
6. C₃₇×#2065	C₂	semidirect
7. C₃₇×#2055	C₂	semidirect
8. C₃₇×#2055	C₂	semidirect
9. C₃₇×#1989	C₂	semidirect
11. C₃₇×#1843	C₂	semidirect
197. #29835	C₃₇	direct (N × H)
222. C₂×#479	C₂×C₃₇	semidirect
225. #2320	C₂×C₃₇	semidirect
226. #2067	C₂×C₃₇	semidirect
227. #2065	C₂×C₃₇	semidirect
228. #2055	C₂×C₃₇	semidirect
229. #2055	C₂×C₃₇	semidirect
230. #1989	C₂×C₃₇	semidirect
232. #1843	C₂×C₃₇	semidirect
270. C₃₇	#29835	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×#479	2
C₂×C₃₇×#460	2
C₃₇×#2641	2
C₃₇×#2320	2
C₃₇×#2067	2
C₃₇×#2065	2
C₃₇×#2055	2
C₃₇×#1989	2
C₃₇×#1982	2
C₃₇×#1843	2
#29835	37

Subgroups — C37×#29835 #22651088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#29835 #22651088