Subgroups — C₃₇×#28667 #22649920

Order 9472.

782 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#486	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2641	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2331	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×#1991	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1961	C₂	1	1	yes	maximal, characteristic
9	C₃₇×#1926	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1925	C₂	1	2	yes	maximal, complemented
11	C₃₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
15	C₃₇×#501	—	2	4	no	—
16	C₃₇×#486	—	2	4	no	—
17	C₂×#107×C₃₇	C₂²	1	2	yes	—
18	C₂×#106×C₃₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
20	C₂×#102×C₃₇	C₂²	1	2	yes	—
21	C₂×#102×C₃₇	C₂²	1	2	yes	—
22	C₂×#102×C₃₇	C₂²	1	2	yes	—
23	C₂×#102×C₃₇	C₂²	1	2	yes	—
24	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
26	C₃₇×#394	—	2	2	no	—
27	C₃₇×#394	—	2	2	no	—
28	C₃₇×#391	—	2	2	no	—
29	C₃₇×#390	C₂²	1	1	yes	characteristic
30	C₃₇×#390	C₂²	1	1	yes	characteristic
31	C₃₇×#390	C₂²	1	1	yes	characteristic
32	C₃₇×#390	C₂²	1	1	yes	characteristic
33	C₃₇×#389	C₂²	1	2	yes	—
34	C₃₇×#387	—	2	2	no	—
35	C₃₇×#382	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
37	C₃₇×#376	C₂²	1	1	yes	characteristic
38	C₃₇×#340	C₂²	1	2	yes	—
39	C₃₇×#340	C₂²	1	2	yes	—
40	C₃₇×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₃₇	—	2	1	no	—
42	C₂²×D₄×C₃₇	—	2	1	no	—
43	C₂²×D₄×C₃₇	—	2	1	no	—
44	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
47	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
48	C₄⋊Q₈×C₃₇	—	2	2	no	—
49	C₄⋊Q₈×C₃₇	D₄	1	4	yes	—
50	#127×C₃₇	—	2	2	no	—
51	#127×C₃₇	—	2	2	no	—
52	#125×C₃₇	—	2	2	no	—
53	#125×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	2	no	—
58	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
66	C₂×C₄²×C₃₇	—	2	2	no	—
67	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
70	#107×C₃₇	—	2	4	no	—
71	#106×C₃₇	—	2	4	no	—
72	C₄⋊C₈×C₃₇	—	2	4	no	—
73	#102×C₃₇	—	2	4	no	—
74	#102×C₃₇	—	2	4	no	—
75	#102×C₃₇	—	2	4	no	—
76	#102×C₃₇	—	2	4	no	—
77	#97×C₃₇	—	2	2	no	—
78	C₄×C₈×C₃₇	—	2	2	no	—
79	#95×C₃₇	—	2	2	no	—
80	#95×C₃₇	—	2	1	no	—
81	#95×C₃₇	—	2	1	no	—
82	#95×C₃₇	—	2	2	no	—
83	#95×C₃₇	D₄	1	2	yes	—
84	#95×C₃₇	D₄	1	2	yes	—
85	C₂⁴×C₃₇	—	2	1	no	—
86	C₂⁴×C₃₇	—	2	1	no	—
87	C₂×Q₈×C₃₇	—	2	4	no	—
88	C₂×Q₈×C₃₇	—	8	2	no	—
89	C₂×D₄×C₃₇	—	2	1	no	—
90	C₂×D₄×C₃₇	—	2	1	no	—
91	C₂×D₄×C₃₇	—	2	2	no	—
92	C₂×D₄×C₃₇	—	2	2	no	—
93	C₂×D₄×C₃₇	—	2	1	no	—
94	C₂×D₄×C₃₇	—	2	1	no	—
95	C₂×D₄×C₃₇	—	2	2	no	—
96	C₂×D₄×C₃₇	—	2	2	no	—
97	C₂×D₄×C₃₇	—	4	2	no	—
98	C₂×D₄×C₃₇	—	4	2	no	—
99	C₂×D₄×C₃₇	—	8	2	no	—
100	C₂×D₄×C₃₇	—	8	2	no	—
101	C₂²×C₄×C₃₇	—	2	2	no	—
102	C₂²×C₄×C₃₇	—	2	2	no	—
103	C₂²×C₄×C₃₇	—	2	1	no	—
104	C₂²×C₄×C₃₇	—	2	1	no	—
105	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
110	C₂×C₈×C₃₇	—	2	2	no	—
111	C₂×C₈×C₃₇	—	2	2	no	—
112	C₂×C₈×C₃₇	—	2	2	no	—
113	C₂×C₈×C₃₇	—	2	2	no	—
114	C₂×C₈×C₃₇	—	2	2	no	—
115	C₂×C₈×C₃₇	#41	1	4	yes	—
116	C₄⋊C₄×C₃₇	—	2	4	no	—
117	C₄⋊C₄×C₃₇	—	2	2	no	—
118	C₄⋊C₄×C₃₇	—	2	1	no	—
119	C₄⋊C₄×C₃₇	—	2	1	no	—
120	C₄⋊C₄×C₃₇	—	2	2	no	—
121	C₄⋊C₄×C₃₇	—	2	2	no	—
122	C₄⋊C₄×C₃₇	—	2	1	no	—
123	C₄⋊C₄×C₃₇	—	2	1	no	—
124	C₄⋊C₄×C₃₇	—	4	2	no	—
125	C₄⋊C₄×C₃₇	—	4	2	no	—
126	C₄⋊C₄×C₃₇	—	8	2	no	—
127	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
128	C₂²⋊C₄×C₃₇	—	8	2	no	—
129	C₂²⋊C₄×C₃₇	—	8	2	no	—
130	C₂²⋊C₄×C₃₇	—	8	2	no	—
131	C₂²⋊C₄×C₃₇	—	8	2	no	—
132	C₄²×C₃₇	—	2	2	no	—
133	C₄²×C₃₇	—	2	2	no	—
134	C₄²×C₃₇	—	8	2	no	—
135	C₄²×C₃₇	C₂×D₄	1	2	yes	—
136	C₄²×C₃₇	#41	1	2	yes	—
137	C₂³×C₃₇	—	4	1	no	—
138	C₂³×C₃₇	—	4	1	no	—
139	C₂³×C₃₇	—	4	1	no	—
140	C₂³×C₃₇	—	4	1	no	—
141	C₂³×C₃₇	—	4	1	no	—
142	C₂³×C₃₇	—	4	1	no	—
143	C₂³×C₃₇	—	4	2	no	—
144	C₂³×C₃₇	—	4	2	no	—
145	C₂³×C₃₇	—	4	2	no	—
146	C₂³×C₃₇	—	4	2	no	—
147	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₃₇	—	8	4	no	—
149	D₄×C₃₇	—	4	2	no	—
150	D₄×C₃₇	—	4	2	no	—
151	D₄×C₃₇	—	4	2	no	—
152	D₄×C₃₇	—	4	2	no	—
153	D₄×C₃₇	—	8	4	no	—
154	D₄×C₃₇	—	8	4	no	—
155	C₂×C₄×C₃₇	—	2	2	no	—
156	C₂×C₄×C₃₇	—	2	2	no	—
157	C₂×C₄×C₃₇	—	2	4	no	—
158	C₂×C₄×C₃₇	—	2	2	no	—
159	C₂×C₄×C₃₇	—	2	2	no	—
160	C₂×C₄×C₃₇	—	2	2	no	—
161	C₂×C₄×C₃₇	—	2	2	no	—
162	C₂×C₄×C₃₇	—	2	2	no	—
163	C₂×C₄×C₃₇	—	2	2	no	—
164	C₂×C₄×C₃₇	—	4	2	no	—
165	C₂×C₄×C₃₇	—	4	2	no	—
166	C₂×C₄×C₃₇	—	4	1	no	—
167	C₂×C₄×C₃₇	—	4	1	no	—
168	C₂×C₄×C₃₇	—	4	2	no	—
169	C₂×C₄×C₃₇	—	4	2	no	—
170	C₂×C₄×C₃₇	—	4	2	no	—
171	C₂×C₄×C₃₇	—	4	2	no	—
172	C₂×C₄×C₃₇	—	4	2	no	—
173	C₂×C₄×C₃₇	#121	1	2	yes	—
174	C₂×C₄×C₃₇	#121	1	2	yes	—
175	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
177	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₃₇	2₋¹⁺⁴	1	2	yes	—
179	C₈×C₃₇	—	2	4	no	—
180	C₈×C₃₇	—	4	2	no	—
181	#28667	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂²×C₃₇	—	8	2	no	—
183	C₂²×C₃₇	—	8	2	no	—
184	C₂²×C₃₇	—	8	2	no	—
185	C₂²×C₃₇	—	8	2	no	—
186	C₂²×C₃₇	—	8	1	no	—
187	C₂²×C₃₇	—	8	1	no	—
188	C₂²×C₃₇	—	8	1	no	—
189	C₂²×C₃₇	—	8	1	no	—
190	C₂²×C₃₇	—	8	1	no	—
191	C₂²×C₃₇	—	8	1	no	—
192	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
193	C₂²×C₃₇	#532	1	1	yes	characteristic
194	C₂²×C₃₇	#536	1	1	yes	characteristic
195	C₂²×C₃₇	#576	1	2	yes	—
196	C₂²×C₃₇	#577	1	2	yes	—
197	C₄×C₃₇	—	2	2	no	—
198	C₄×C₃₇	—	2	2	no	—
199	C₄×C₃₇	—	4	2	no	—
200	C₄×C₃₇	—	4	2	no	—
201	C₄×C₃₇	—	4	4	no	—
202	C₄×C₃₇	—	8	2	no	—
203	C₄×C₃₇	—	8	1	no	—
204	C₄×C₃₇	—	8	1	no	—
205	C₄×C₃₇	#548	1	2	yes	—
206	C₄×C₃₇	#556	1	2	yes	—
207	C₂×#501	C₂×C₃₇	1	1	yes	characteristic, complemented
208	C₂×#486	C₂×C₃₇	1	1	yes	characteristic
209	#2641	C₂×C₃₇	1	1	yes	characteristic
210	#2331	C₂×C₃₇	1	1	yes	characteristic, complemented
211	#2067	C₂×C₃₇	1	2	yes	complemented
212	#2065	C₂×C₃₇	1	2	yes	complemented
213	#1991	C₂×C₃₇	1	1	yes	characteristic, complemented
214	#1961	C₂×C₃₇	1	1	yes	characteristic
215	#1926	C₂×C₃₇	1	2	yes	complemented
216	#1925	C₂×C₃₇	1	2	yes	complemented
217	#1768	C₂×C₃₇	1	1	yes	characteristic, complemented
218	C₂×C₃₇	—	16	1	no	—
219	C₂×C₃₇	—	16	1	no	—
220	C₂×C₃₇	#2545	1	1	yes	characteristic
221	C₂×C₃₇	#3041	1	1	yes	characteristic
222	C₂×C₃₇	#3043	1	1	yes	characteristic
223	C₂×C₃₇	#3179	1	2	yes	—
224	C₂×C₃₇	#3241	1	2	yes	—
225	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
226	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
227	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
228	#501	—	2	4	no	—
229	#486	—	2	4	no	—
230	C₂×#107	C₂²×C₃₇	1	2	yes	—
231	C₂×#106	C₂²×C₃₇	1	2	yes	—
232	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
233	C₂×#102	C₂²×C₃₇	1	2	yes	—
234	C₂×#102	C₂²×C₃₇	1	2	yes	—
235	C₂×#102	C₂²×C₃₇	1	2	yes	—
236	C₂×#102	C₂²×C₃₇	1	2	yes	—
237	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
238	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
239	#394	—	2	2	no	—
240	#394	—	2	2	no	—
241	#391	—	2	2	no	—
242	#390	C₂²×C₃₇	1	1	yes	characteristic
243	#390	C₂²×C₃₇	1	1	yes	characteristic
244	#390	C₂²×C₃₇	1	1	yes	characteristic
245	#390	C₂²×C₃₇	1	1	yes	characteristic
246	#389	C₂²×C₃₇	1	2	yes	—
247	#387	—	2	2	no	—
248	#382	C₂²×C₃₇	1	1	yes	characteristic
249	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
250	#376	C₂²×C₃₇	1	1	yes	characteristic
251	#340	C₂²×C₃₇	1	2	yes	—
252	#340	C₂²×C₃₇	1	2	yes	—
253	#336	C₂²×C₃₇	1	2	yes	—
254	C₃₇	#28667	1	1	yes	characteristic, direct product factor, Sylow
255	C₂²×Q₈	—	2	1	no	—
256	C₂²×D₄	—	2	1	no	—
257	C₂²×D₄	—	2	1	no	—
258	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
259	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
261	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
262	C₄⋊Q₈	—	2	2	no	—
263	C₄⋊Q₈	D₄×C₃₇	1	4	yes	—
264	#127	—	2	2	no	—
265	#127	—	2	2	no	—
266	#125	—	2	2	no	—
267	#125	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₄²	—	2	2	no	—
281	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
284	#107	—	2	4	no	—
285	#106	—	2	4	no	—
286	C₄⋊C₈	—	2	4	no	—
287	#102	—	2	4	no	—
288	#102	—	2	4	no	—
289	#102	—	2	4	no	—
290	#102	—	2	4	no	—
291	#97	—	2	2	no	—
292	C₄×C₈	—	2	2	no	—
293	#95	—	2	2	no	—
294	#95	—	2	1	no	—
295	#95	—	2	1	no	—
296	#95	—	2	2	no	—
297	#95	D₄×C₃₇	1	2	yes	—
298	#95	D₄×C₃₇	1	2	yes	—
299	C₂⁴	—	2	1	no	—
300	C₂⁴	—	2	1	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	—	8	2	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	8	2	no	—
314	C₂×D₄	—	8	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
321	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
323	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	#41×C₃₇	1	4	yes	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₄⋊C₄	—	8	2	no	—
341	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
342	C₂²⋊C₄	—	8	2	no	—
343	C₂²⋊C₄	—	8	2	no	—
344	C₂²⋊C₄	—	8	2	no	—
345	C₂²⋊C₄	—	8	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	8	2	no	—
349	C₄²	C₂×D₄×C₃₇	1	2	yes	—
350	C₄²	#41×C₃₇	1	2	yes	—
351	C₂³	—	4	1	no	—
352	C₂³	—	4	1	no	—
353	C₂³	—	4	1	no	—
354	C₂³	—	4	1	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	4	1	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	2	no	—
361	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
362	Q₈	—	8	4	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	8	4	no	—
368	D₄	—	8	4	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	#121×C₃₇	1	2	yes	—
388	C₂×C₄	#121×C₃₇	1	2	yes	—
389	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
390	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
391	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
392	C₂×C₄	2₋¹⁺⁴×C₃₇	1	2	yes	—
393	C₈	—	2	4	no	—
394	C₈	—	4	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	1	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
406	C₂²	C₃₇×#532	1	1	yes	characteristic
407	C₂²	C₃₇×#536	1	1	yes	characteristic
408	C₂²	C₃₇×#576	1	2	yes	—
409	C₂²	C₃₇×#577	1	2	yes	—
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	4	no	—
415	C₄	—	8	2	no	—
416	C₄	—	8	1	no	—
417	C₄	—	8	1	no	—
418	C₄	C₃₇×#548	1	2	yes	—
419	C₄	C₃₇×#556	1	2	yes	—
420	C₂	—	16	1	no	—
421	C₂	—	16	1	no	—
422	C₂	C₃₇×#2545	1	1	yes	characteristic
423	C₂	C₃₇×#3041	1	1	yes	characteristic
424	C₂	C₃₇×#3043	1	1	yes	characteristic
425	C₂	C₃₇×#3179	1	2	yes	—
426	C₂	C₃₇×#3241	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×#501	C₂	semidirect
4. C₃₇×#2331	C₂	semidirect
5. C₃₇×#2067	C₂	semidirect
6. C₃₇×#2065	C₂	semidirect
7. C₃₇×#1991	C₂	semidirect
9. C₃₇×#1926	C₂	semidirect
10. C₃₇×#1925	C₂	semidirect
11. C₃₇×#1768	C₂	semidirect
181. #28667	C₃₇	direct (N × H)
207. C₂×#501	C₂×C₃₇	semidirect
210. #2331	C₂×C₃₇	semidirect
211. #2067	C₂×C₃₇	semidirect
212. #2065	C₂×C₃₇	semidirect
213. #1991	C₂×C₃₇	semidirect
215. #1926	C₂×C₃₇	semidirect
216. #1925	C₂×C₃₇	semidirect
217. #1768	C₂×C₃₇	semidirect
254. C₃₇	#28667	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×#501	2
C₂×C₃₇×#486	2
C₃₇×#2641	2
C₃₇×#2331	2
C₃₇×#2067	2
C₃₇×#2065	2
C₃₇×#1991	2
C₃₇×#1961	2
C₃₇×#1926	2
C₃₇×#1925	2
C₃₇×#1768	2
#28667	37

Subgroups — C37×#28667 #22649920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28667 #22649920