Subgroups — C₃₇×#28628 #22649881

Order 9472.

832 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#497	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#2640	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2327	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2056	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2055	C₂	1	2	yes	maximal
7	C₃₇×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1958	C₂	1	1	yes	maximal, characteristic
9	C₃₇×#1880	C₂	1	2	yes	maximal
10	C₃₇×#1878	C₂	1	2	yes	maximal, complemented
11	C₃₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₃₇	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
16	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₃₇	C₂²	1	2	yes	—
18	C₃₇×#497	—	2	4	no	—
19	C₃₇×#487	—	2	4	no	—
20	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
21	C₂×#103×C₃₇	C₂²	1	2	yes	—
22	C₂×#103×C₃₇	C₂²	1	2	yes	—
23	C₂×#103×C₃₇	C₂²	1	2	yes	—
24	C₂×#102×C₃₇	C₂²	1	2	yes	—
25	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
27	C₃₇×#397	—	2	2	no	—
28	C₃₇×#393	—	2	2	no	—
29	C₃₇×#391	C₂²	1	1	yes	characteristic
30	C₃₇×#391	C₂²	1	1	yes	characteristic
31	C₃₇×#391	C₂²	1	2	yes	—
32	C₃₇×#390	C₂²	1	1	yes	characteristic
33	C₃₇×#390	C₂²	1	1	yes	characteristic
34	C₃₇×#387	—	2	2	no	—
35	C₃₇×#387	—	2	2	no	—
36	C₃₇×#382	C₂²	1	1	yes	characteristic
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×Q₈×C₃₇	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
44	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
45	C₂×Q₁₆×C₃₇	—	2	4	no	—
46	C₂×Q₁₆×C₃₇	—	2	4	no	—
47	C₂×Q₁₆×C₃₇	—	4	2	no	—
48	C₂×SD₁₆×C₃₇	—	2	4	no	—
49	C₂×SD₁₆×C₃₇	—	2	4	no	—
50	C₂×SD₁₆×C₃₇	—	4	2	no	—
51	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
52	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
53	C₄⋊Q₈×C₃₇	—	2	2	no	—
54	C₄⋊Q₈×C₃₇	—	2	2	no	—
55	C₄⋊Q₈×C₃₇	—	2	2	no	—
56	C₄⋊Q₈×C₃₇	D₄	1	4	yes	—
57	#124×C₃₇	—	2	2	no	—
58	#124×C₃₇	—	2	2	no	—
59	C₄×Q₈×C₃₇	—	4	2	no	—
60	C₄×Q₈×C₃₇	—	4	2	no	—
61	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
72	C₂×C₄²×C₃₇	—	2	2	no	—
73	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
76	C₄⋊C₈×C₃₇	—	2	4	no	—
77	#103×C₃₇	—	2	4	no	—
78	#103×C₃₇	—	2	4	no	—
79	#103×C₃₇	—	4	2	no	—
80	#102×C₃₇	—	4	2	no	—
81	#97×C₃₇	—	2	2	no	—
82	C₄×C₈×C₃₇	—	2	2	no	—
83	#95×C₃₇	—	2	1	no	—
84	#95×C₃₇	—	2	1	no	—
85	#95×C₃₇	—	2	4	no	—
86	#95×C₃₇	—	2	2	no	—
87	#95×C₃₇	—	2	2	no	—
88	#95×C₃₇	D₄	1	2	yes	—
89	#95×C₃₇	D₄	1	2	yes	—
90	C₂⁴×C₃₇	—	2	1	no	—
91	C₂×Q₈×C₃₇	—	2	2	no	—
92	C₂×Q₈×C₃₇	—	2	1	no	—
93	C₂×Q₈×C₃₇	—	2	2	no	—
94	C₂×Q₈×C₃₇	—	2	2	no	—
95	C₂×Q₈×C₃₇	—	2	1	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	C₂×Q₈×C₃₇	—	4	2	no	—
101	C₂×Q₈×C₃₇	—	8	2	no	—
102	C₂×Q₈×C₃₇	C₂×D₄	1	4	yes	—
103	C₂×D₄×C₃₇	—	2	1	no	—
104	C₂×D₄×C₃₇	—	2	1	no	—
105	C₂×D₄×C₃₇	—	2	2	no	—
106	C₂×D₄×C₃₇	—	2	2	no	—
107	C₂²×C₄×C₃₇	—	2	2	no	—
108	C₂²×C₄×C₃₇	—	2	2	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	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
117	Q₁₆×C₃₇	—	4	8	no	—
118	SD₁₆×C₃₇	—	4	8	no	—
119	C₂×C₈×C₃₇	—	2	2	no	—
120	C₂×C₈×C₃₇	—	2	2	no	—
121	C₂×C₈×C₃₇	—	2	2	no	—
122	C₂×C₈×C₃₇	—	2	2	no	—
123	C₂×C₈×C₃₇	—	2	2	no	—
124	C₂×C₈×C₃₇	#41	1	4	yes	—
125	C₄⋊C₄×C₃₇	—	2	4	no	—
126	C₄⋊C₄×C₃₇	—	2	4	no	—
127	C₄⋊C₄×C₃₇	—	2	1	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	2	no	—
132	C₄⋊C₄×C₃₇	—	2	2	no	—
133	C₄⋊C₄×C₃₇	—	4	4	no	—
134	C₄⋊C₄×C₃₇	—	4	2	no	—
135	C₂²⋊C₄×C₃₇	—	4	2	no	—
136	C₂²⋊C₄×C₃₇	—	4	2	no	—
137	C₂²⋊C₄×C₃₇	—	8	2	no	—
138	C₂²⋊C₄×C₃₇	—	8	2	no	—
139	C₄²×C₃₇	—	2	2	no	—
140	C₄²×C₃₇	—	2	2	no	—
141	C₄²×C₃₇	—	4	4	no	—
142	C₄²×C₃₇	C₂×D₄	1	2	yes	—
143	C₄²×C₃₇	#41	1	2	yes	—
144	C₂³×C₃₇	—	4	1	no	—
145	C₂³×C₃₇	—	4	1	no	—
146	C₂³×C₃₇	—	4	1	no	—
147	C₂³×C₃₇	—	4	2	no	—
148	C₂³×C₃₇	—	4	2	no	—
149	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₃₇	—	2	4	no	—
151	Q₈×C₃₇	—	2	4	no	—
152	Q₈×C₃₇	—	4	2	no	—
153	Q₈×C₃₇	—	4	2	no	—
154	Q₈×C₃₇	—	4	2	no	—
155	Q₈×C₃₇	—	4	2	no	—
156	Q₈×C₃₇	—	8	4	no	—
157	D₄×C₃₇	—	4	2	no	—
158	D₄×C₃₇	—	4	2	no	—
159	C₂×C₄×C₃₇	—	2	2	no	—
160	C₂×C₄×C₃₇	—	2	2	no	—
161	C₂×C₄×C₃₇	—	2	4	no	—
162	C₂×C₄×C₃₇	—	2	2	no	—
163	C₂×C₄×C₃₇	—	2	2	no	—
164	C₂×C₄×C₃₇	—	2	2	no	—
165	C₂×C₄×C₃₇	—	2	2	no	—
166	C₂×C₄×C₃₇	—	2	2	no	—
167	C₂×C₄×C₃₇	—	2	2	no	—
168	C₂×C₄×C₃₇	—	4	2	no	—
169	C₂×C₄×C₃₇	—	4	2	no	—
170	C₂×C₄×C₃₇	—	4	1	no	—
171	C₂×C₄×C₃₇	—	4	1	no	—
172	C₂×C₄×C₃₇	—	4	1	no	—
173	C₂×C₄×C₃₇	—	4	1	no	—
174	C₂×C₄×C₃₇	—	4	2	no	—
175	C₂×C₄×C₃₇	—	4	1	no	—
176	C₂×C₄×C₃₇	—	4	2	no	—
177	C₂×C₄×C₃₇	—	4	2	no	—
178	C₂×C₄×C₃₇	—	4	2	no	—
179	C₂×C₄×C₃₇	—	4	2	no	—
180	C₂×C₄×C₃₇	#121	1	2	yes	—
181	C₂×C₄×C₃₇	#121	1	2	yes	—
182	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
184	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
186	C₈×C₃₇	—	2	4	no	—
187	C₈×C₃₇	—	4	2	no	—
188	#28628	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂²×C₃₇	—	8	2	no	—
190	C₂²×C₃₇	—	8	2	no	—
191	C₂²×C₃₇	—	8	1	no	—
192	C₂²×C₃₇	—	8	1	no	—
193	C₂²×C₃₇	—	8	1	no	—
194	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
195	C₂²×C₃₇	#532	1	1	yes	characteristic
196	C₂²×C₃₇	#535	1	1	yes	characteristic
197	C₂²×C₃₇	#577	1	2	yes	—
198	C₂²×C₃₇	#578	1	2	yes	—
199	C₄×C₃₇	—	2	2	no	—
200	C₄×C₃₇	—	2	2	no	—
201	C₄×C₃₇	—	4	2	no	—
202	C₄×C₃₇	—	4	2	no	—
203	C₄×C₃₇	—	4	4	no	—
204	C₄×C₃₇	—	8	2	no	—
205	C₄×C₃₇	—	8	1	no	—
206	C₄×C₃₇	—	8	1	no	—
207	C₄×C₃₇	—	8	1	no	—
208	C₄×C₃₇	#546	1	2	yes	—
209	C₄×C₃₇	#559	1	2	yes	—
210	C₂×#497	C₂×C₃₇	1	1	yes	characteristic
211	C₂×#487	C₂×C₃₇	1	1	yes	characteristic, complemented
212	#2640	C₂×C₃₇	1	1	yes	characteristic
213	#2327	C₂×C₃₇	1	1	yes	characteristic, complemented
214	#2056	C₂×C₃₇	1	2	yes	complemented
215	#2055	C₂×C₃₇	1	2	yes	—
216	#1993	C₂×C₃₇	1	1	yes	characteristic, complemented
217	#1958	C₂×C₃₇	1	1	yes	characteristic
218	#1880	C₂×C₃₇	1	2	yes	—
219	#1878	C₂×C₃₇	1	2	yes	complemented
220	#1768	C₂×C₃₇	1	1	yes	characteristic, complemented
221	C₂×C₃₇	—	16	1	no	—
222	C₂×C₃₇	#2544	1	1	yes	characteristic
223	C₂×C₃₇	#3043	1	1	yes	characteristic
224	C₂×C₃₇	#3044	1	1	yes	characteristic
225	C₂×C₃₇	#3178	1	2	yes	—
226	C₂×C₃₇	#3225	1	2	yes	—
227	C₂²×Q₁₆	C₂²×C₃₇	1	2	yes	—
228	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
229	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
230	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
231	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
232	C₂×C₄×Q₈	C₂²×C₃₇	1	2	yes	—
233	#497	—	2	4	no	—
234	#487	—	2	4	no	—
235	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
236	C₂×#103	C₂²×C₃₇	1	2	yes	—
237	C₂×#103	C₂²×C₃₇	1	2	yes	—
238	C₂×#103	C₂²×C₃₇	1	2	yes	—
239	C₂×#102	C₂²×C₃₇	1	2	yes	—
240	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
241	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
242	#397	—	2	2	no	—
243	#393	—	2	2	no	—
244	#391	C₂²×C₃₇	1	2	yes	—
245	#391	C₂²×C₃₇	1	1	yes	characteristic
246	#391	C₂²×C₃₇	1	1	yes	characteristic
247	#390	C₂²×C₃₇	1	1	yes	characteristic
248	#390	C₂²×C₃₇	1	1	yes	characteristic
249	#387	—	2	2	no	—
250	#387	—	2	2	no	—
251	#382	C₂²×C₃₇	1	1	yes	characteristic
252	#376	C₂²×C₃₇	1	1	yes	characteristic
253	#340	C₂²×C₃₇	1	2	yes	—
254	#340	C₂²×C₃₇	1	2	yes	—
255	#336	C₂²×C₃₇	1	2	yes	—
256	C₃₇	#28628	1	1	yes	characteristic, direct product factor, Sylow
257	C₂²×Q₈	—	2	1	no	—
258	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
259	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
260	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
261	C₂×Q₁₆	—	2	4	no	—
262	C₂×Q₁₆	—	2	4	no	—
263	C₂×Q₁₆	—	4	2	no	—
264	C₂×SD₁₆	—	2	4	no	—
265	C₂×SD₁₆	—	2	4	no	—
266	C₂×SD₁₆	—	4	2	no	—
267	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
268	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
269	C₄⋊Q₈	—	2	2	no	—
270	C₄⋊Q₈	—	2	2	no	—
271	C₄⋊Q₈	—	2	2	no	—
272	C₄⋊Q₈	D₄×C₃₇	1	4	yes	—
273	#124	—	2	2	no	—
274	#124	—	2	2	no	—
275	C₄×Q₈	—	4	2	no	—
276	C₄×Q₈	—	4	2	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
292	C₄⋊C₈	—	2	4	no	—
293	#103	—	2	4	no	—
294	#103	—	2	4	no	—
295	#103	—	4	2	no	—
296	#102	—	4	2	no	—
297	#97	—	2	2	no	—
298	C₄×C₈	—	2	2	no	—
299	#95	—	2	1	no	—
300	#95	—	2	1	no	—
301	#95	—	2	4	no	—
302	#95	—	2	2	no	—
303	#95	—	2	2	no	—
304	#95	D₄×C₃₇	1	2	yes	—
305	#95	D₄×C₃₇	1	2	yes	—
306	C₂⁴	—	2	1	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	4	2	no	—
317	C₂×Q₈	—	8	2	no	—
318	C₂×Q₈	C₂×D₄×C₃₇	1	4	yes	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
330	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
332	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
333	Q₁₆	—	4	8	no	—
334	SD₁₆	—	4	8	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	#41×C₃₇	1	4	yes	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	4	4	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₂²⋊C₄	—	4	2	no	—
353	C₂²⋊C₄	—	8	2	no	—
354	C₂²⋊C₄	—	8	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	4	4	no	—
358	C₄²	C₂×D₄×C₃₇	1	2	yes	—
359	C₄²	#41×C₃₇	1	2	yes	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	1	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
366	Q₈	—	2	4	no	—
367	Q₈	—	2	4	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	8	4	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	#121×C₃₇	1	2	yes	—
397	C₂×C₄	#121×C₃₇	1	2	yes	—
398	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
399	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
400	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
401	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
402	C₈	—	2	4	no	—
403	C₈	—	4	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
410	C₂²	C₃₇×#532	1	1	yes	characteristic
411	C₂²	C₃₇×#535	1	1	yes	characteristic
412	C₂²	C₃₇×#577	1	2	yes	—
413	C₂²	C₃₇×#578	1	2	yes	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	4	no	—
419	C₄	—	8	2	no	—
420	C₄	—	8	1	no	—
421	C₄	—	8	1	no	—
422	C₄	—	8	1	no	—
423	C₄	C₃₇×#546	1	2	yes	—
424	C₄	C₃₇×#559	1	2	yes	—
425	C₂	—	16	1	no	—
426	C₂	C₃₇×#2544	1	1	yes	characteristic
427	C₂	C₃₇×#3043	1	1	yes	characteristic
428	C₂	C₃₇×#3044	1	1	yes	characteristic
429	C₂	C₃₇×#3178	1	2	yes	—
430	C₂	C₃₇×#3225	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂²×D₄×C₃₇	C₂³
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
2. C₂×C₃₇×#487	C₂	semidirect
4. C₃₇×#2327	C₂	semidirect
5. C₃₇×#2056	C₂	semidirect
7. C₃₇×#1993	C₂	semidirect
10. C₃₇×#1878	C₂	semidirect
11. C₃₇×#1768	C₂	semidirect
188. #28628	C₃₇	direct (N × H)
211. C₂×#487	C₂×C₃₇	semidirect
213. #2327	C₂×C₃₇	semidirect
214. #2056	C₂×C₃₇	semidirect
216. #1993	C₂×C₃₇	semidirect
219. #1878	C₂×C₃₇	semidirect
220. #1768	C₂×C₃₇	semidirect
256. C₃₇	#28628	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×#497	2
C₂×C₃₇×#487	2
C₃₇×#2640	2
C₃₇×#2327	2
C₃₇×#2056	2
C₃₇×#2055	2
C₃₇×#1993	2
C₃₇×#1958	2
C₃₇×#1880	2
C₃₇×#1878	2
C₃₇×#1768	2
#28628	37

Subgroups — C37×#28628 #22649881

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28628 #22649881