Subgroups — C₃₇×#21875 #22643128

Order 9472.

1158 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#529	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#2285	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#1996	C₂	1	2	yes	maximal, complemented
5	C₃₇×#1964	C₂	1	2	yes	maximal
6	C₃₇×#1899	C₂	1	4	yes	maximal, complemented
7	C₃₇×#1799	C₂	1	4	yes	maximal, complemented
8	C₃₇×#529	—	2	1	no	—
9	C₃₇×#529	—	2	1	no	—
10	C₃₇×#529	—	2	1	no	—
11	C₃₇×#529	—	2	1	no	—
12	C₃₇×#529	—	2	1	no	—
13	C₃₇×#529	—	2	1	no	—
14	C₃₇×#529	—	2	1	no	—
15	C₃₇×#529	—	2	1	no	—
16	C₂×#126×C₃₇	C₄	1	2	yes	complemented
17	C₂×#125×C₃₇	C₄	1	1	yes	characteristic, complemented
18	C₂×#124×C₃₇	C₄	1	1	yes	characteristic, complemented
19	C₂×#123×C₃₇	C₂²	1	2	yes	—
20	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
21	C₂×#121×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₃₇	C₄	1	1	yes	characteristic, complemented
23	C₂×C₄×D₄×C₃₇	C₄	1	1	yes	characteristic, complemented
24	C₂×C₄×D₄×C₃₇	C₂²	1	2	yes	—
25	C₂×#117×C₃₇	C₄	1	2	yes	complemented
26	C₂×#117×C₃₇	C₂²	1	2	yes	—
27	C₂²×C₄²×C₃₇	C₂²	1	1	yes	characteristic
28	C₂×#99×C₃₇	C₂²	1	8	yes	—
29	C₃₇×#384	—	2	1	no	—
30	C₃₇×#383	—	2	1	no	—
31	C₃₇×#382	—	2	1	no	—
32	C₃₇×#382	—	2	1	no	—
33	C₃₇×#381	C₂²	1	2	yes	—
34	C₃₇×#380	C₂²	1	2	yes	—
35	C₃₇×#380	C₂²	1	2	yes	—
36	C₃₇×#380	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₃₇	—	2	1	no	—
38	C₄×C₄⋊C₄×C₃₇	—	2	1	no	—
39	C₄×C₄⋊C₄×C₃₇	—	2	1	no	—
40	C₄×C₂²⋊C₄×C₃₇	C₂²	1	2	yes	—
41	C₃₇×#376	—	2	1	no	—
42	C₃₇×#342	C₂²	1	8	yes	—
43	C₂²×Q₈×C₃₇	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₃₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
46	C₂³×C₄×C₃₇	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
50	#126×C₃₇	—	2	2	no	—
51	#126×C₃₇	—	2	2	no	—
52	#126×C₃₇	—	2	2	no	—
53	#126×C₃₇	—	2	2	no	—
54	#125×C₃₇	—	2	1	no	—
55	#125×C₃₇	—	2	1	no	—
56	#125×C₃₇	—	2	1	no	—
57	#125×C₃₇	—	2	1	no	—
58	#124×C₃₇	—	2	1	no	—
59	#124×C₃₇	—	2	1	no	—
60	#124×C₃₇	—	2	1	no	—
61	#124×C₃₇	—	2	1	no	—
62	#123×C₃₇	—	2	2	no	—
63	#123×C₃₇	—	2	2	no	—
64	#123×C₃₇	—	2	2	no	—
65	#123×C₃₇	—	2	2	no	—
66	C₂²⋊Q₈×C₃₇	—	2	1	no	—
67	C₂²⋊Q₈×C₃₇	—	2	1	no	—
68	C₂²⋊Q₈×C₃₇	—	2	1	no	—
69	C₂²⋊Q₈×C₃₇	—	2	1	no	—
70	#121×C₃₇	—	2	1	no	—
71	#121×C₃₇	—	2	1	no	—
72	#121×C₃₇	—	2	1	no	—
73	#121×C₃₇	—	2	1	no	—
74	C₄×Q₈×C₃₇	—	2	1	no	—
75	C₄×Q₈×C₃₇	—	2	1	no	—
76	C₄×Q₈×C₃₇	—	2	1	no	—
77	C₄×Q₈×C₃₇	—	2	1	no	—
78	C₄×D₄×C₃₇	—	2	2	no	—
79	C₄×D₄×C₃₇	—	2	2	no	—
80	C₄×D₄×C₃₇	—	2	2	no	—
81	C₄×D₄×C₃₇	—	2	2	no	—
82	C₄×D₄×C₃₇	—	2	1	no	—
83	C₄×D₄×C₃₇	—	2	1	no	—
84	C₄×D₄×C₃₇	—	2	1	no	—
85	C₄×D₄×C₃₇	—	2	1	no	—
86	#117×C₃₇	—	2	2	no	—
87	#117×C₃₇	—	2	2	no	—
88	#117×C₃₇	—	2	2	no	—
89	#117×C₃₇	—	2	2	no	—
90	#117×C₃₇	—	4	4	no	—
91	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
92	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
93	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
94	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
95	C₂×C₄⋊C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₃₇	C₂×C₄	1	2	yes	—
98	C₂×C₄⋊C₄×C₃₇	C₂×C₄	1	2	yes	—
99	C₂×C₄⋊C₄×C₃₇	C₂×C₄	1	2	yes	—
100	C₂×C₄⋊C₄×C₃₇	C₂×C₄	1	2	yes	—
101	C₂×C₂²⋊C₄×C₃₇	C₂×C₄	1	2	yes	—
102	C₂×C₂²⋊C₄×C₃₇	C₂×C₄	1	2	yes	—
103	C₂×C₂²⋊C₄×C₃₇	C₂×C₄	1	2	yes	—
104	C₂×C₂²⋊C₄×C₃₇	C₂×C₄	1	2	yes	—
105	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
108	C₂×C₄²×C₃₇	—	2	2	no	—
109	C₂×C₄²×C₃₇	—	2	2	no	—
110	C₂×C₄²×C₃₇	C₂×C₄	1	2	yes	—
111	C₂×C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
121	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
122	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
123	#99×C₃₇	—	4	8	no	—
124	#95×C₃₇	—	2	2	no	—
125	#95×C₃₇	—	2	2	no	—
126	#95×C₃₇	—	2	2	no	—
127	#95×C₃₇	—	2	2	no	—
128	#95×C₃₇	—	2	2	no	—
129	#95×C₃₇	—	2	2	no	—
130	C₂⁴×C₃₇	C₂²×C₄	1	2	yes	—
131	C₂⁴×C₃₇	C₂⁴	1	1	yes	characteristic
132	C₂×Q₈×C₃₇	—	2	1	no	—
133	C₂×Q₈×C₃₇	—	2	1	no	—
134	C₂×Q₈×C₃₇	—	4	2	no	—
135	C₂×D₄×C₃₇	—	2	2	no	—
136	C₂×D₄×C₃₇	—	2	2	no	—
137	C₂×D₄×C₃₇	—	2	4	no	—
138	C₂×D₄×C₃₇	—	2	4	no	—
139	C₂×D₄×C₃₇	—	2	1	no	—
140	C₂×D₄×C₃₇	—	2	1	no	—
141	C₂×D₄×C₃₇	—	4	2	no	—
142	C₂²×C₄×C₃₇	—	2	2	no	—
143	C₂²×C₄×C₃₇	—	2	2	no	—
144	C₂²×C₄×C₃₇	—	2	2	no	—
145	C₂²×C₄×C₃₇	—	2	2	no	—
146	C₂²×C₄×C₃₇	—	2	4	no	—
147	C₂²×C₄×C₃₇	—	2	4	no	—
148	C₂²×C₄×C₃₇	—	4	2	no	—
149	C₂²×C₄×C₃₇	—	4	2	no	—
150	C₂²×C₄×C₃₇	—	4	4	no	—
151	C₂²×C₄×C₃₇	C₂²×C₄	1	2	yes	—
152	C₂²×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₃₇	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₃₇	C₂²×C₄	1	2	yes	—
158	C₂²×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
172	C₄⋊C₄×C₃₇	—	2	2	no	—
173	C₄⋊C₄×C₃₇	—	2	2	no	—
174	C₄⋊C₄×C₃₇	—	2	2	no	—
175	C₄⋊C₄×C₃₇	—	2	2	no	—
176	C₄⋊C₄×C₃₇	—	2	1	no	—
177	C₄⋊C₄×C₃₇	—	2	1	no	—
178	C₄⋊C₄×C₃₇	—	2	2	no	—
179	C₄⋊C₄×C₃₇	—	2	2	no	—
180	C₄⋊C₄×C₃₇	—	2	1	no	—
181	C₄⋊C₄×C₃₇	—	2	1	no	—
182	C₄⋊C₄×C₃₇	—	2	2	no	—
183	C₄⋊C₄×C₃₇	—	2	2	no	—
184	C₄⋊C₄×C₃₇	—	4	4	no	—
185	C₄⋊C₄×C₃₇	—	4	4	no	—
186	C₄⋊C₄×C₃₇	—	4	4	no	—
187	C₄⋊C₄×C₃₇	—	4	4	no	—
188	C₂²⋊C₄×C₃₇	—	2	2	no	—
189	C₂²⋊C₄×C₃₇	—	2	2	no	—
190	C₂²⋊C₄×C₃₇	—	2	2	no	—
191	C₂²⋊C₄×C₃₇	—	2	2	no	—
192	C₂²⋊C₄×C₃₇	—	2	2	no	—
193	C₂²⋊C₄×C₃₇	—	2	2	no	—
194	C₂²⋊C₄×C₃₇	—	2	2	no	—
195	C₂²⋊C₄×C₃₇	—	2	2	no	—
196	C₂²⋊C₄×C₃₇	—	2	2	no	—
197	C₂²⋊C₄×C₃₇	—	2	2	no	—
198	C₂²⋊C₄×C₃₇	—	2	4	no	—
199	C₂²⋊C₄×C₃₇	—	2	8	no	—
200	C₂²⋊C₄×C₃₇	—	2	4	no	—
201	C₄²×C₃₇	—	2	2	no	—
202	C₄²×C₃₇	—	2	2	no	—
203	C₄²×C₃₇	—	4	4	no	—
204	C₄²×C₃₇	—	4	4	no	—
205	C₄²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
206	C₄²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
207	C₄²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
208	C₄²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
209	C₄²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
210	C₄²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
211	C₄²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
212	C₄²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
213	C₄²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
214	C₄²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
215	C₄²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
216	C₄²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
217	C₄²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
218	C₄²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
219	C₄²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
220	C₄²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
221	C₂³×C₃₇	—	2	2	no	—
222	C₂³×C₃₇	—	2	4	no	—
223	C₂³×C₃₇	—	4	1	no	—
224	C₂³×C₃₇	—	4	1	no	—
225	C₂³×C₃₇	—	4	2	no	—
226	C₂³×C₃₇	—	4	2	no	—
227	C₂³×C₃₇	C₂³×C₄	1	1	yes	characteristic
228	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
229	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
230	C₂³×C₃₇	H(5,𝔽₂)	1	2	yes	—
231	C₂³×C₃₇	2₋¹⁺⁴	1	2	yes	—
232	Q₈×C₃₇	—	4	2	no	—
233	Q₈×C₃₇	—	4	2	no	—
234	D₄×C₃₇	—	4	2	no	—
235	D₄×C₃₇	—	4	2	no	—
236	D₄×C₃₇	—	4	2	no	—
237	D₄×C₃₇	—	4	4	no	—
238	D₄×C₃₇	—	4	2	no	—
239	C₂×C₄×C₃₇	—	2	2	no	—
240	C₂×C₄×C₃₇	—	2	2	no	—
241	C₂×C₄×C₃₇	—	2	1	no	—
242	C₂×C₄×C₃₇	—	2	1	no	—
243	C₂×C₄×C₃₇	—	2	1	no	—
244	C₂×C₄×C₃₇	—	2	1	no	—
245	C₂×C₄×C₃₇	—	2	2	no	—
246	C₂×C₄×C₃₇	—	2	2	no	—
247	C₂×C₄×C₃₇	—	2	2	no	—
248	C₂×C₄×C₃₇	—	2	2	no	—
249	C₂×C₄×C₃₇	—	2	2	no	—
250	C₂×C₄×C₃₇	—	2	2	no	—
251	C₂×C₄×C₃₇	—	2	2	no	—
252	C₂×C₄×C₃₇	—	2	2	no	—
253	C₂×C₄×C₃₇	—	2	2	no	—
254	C₂×C₄×C₃₇	—	2	2	no	—
255	C₂×C₄×C₃₇	—	2	2	no	—
256	C₂×C₄×C₃₇	—	2	4	no	—
257	C₂×C₄×C₃₇	—	4	1	no	—
258	C₂×C₄×C₃₇	—	4	1	no	—
259	C₂×C₄×C₃₇	—	4	1	no	—
260	C₂×C₄×C₃₇	—	4	1	no	—
261	C₂×C₄×C₃₇	—	4	1	no	—
262	C₂×C₄×C₃₇	—	4	1	no	—
263	C₂×C₄×C₃₇	—	4	4	no	—
264	C₂×C₄×C₃₇	—	4	4	no	—
265	C₂×C₄×C₃₇	—	4	2	no	—
266	C₂×C₄×C₃₇	—	4	2	no	—
267	C₂×C₄×C₃₇	—	4	4	no	—
268	C₂×C₄×C₃₇	—	4	4	no	—
269	C₂×C₄×C₃₇	—	4	4	no	—
270	C₂×C₄×C₃₇	—	4	4	no	—
271	C₂×C₄×C₃₇	—	4	4	no	—
272	C₂×C₄×C₃₇	—	4	4	no	—
273	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
281	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
282	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
283	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
285	#21875	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
286	C₂²×C₃₇	—	2	1	no	—
287	C₂²×C₃₇	—	2	1	no	—
288	C₂²×C₃₇	—	2	1	no	—
289	C₂²×C₃₇	—	2	1	no	—
290	C₂²×C₃₇	—	2	1	no	—
291	C₂²×C₃₇	—	2	1	no	—
292	C₂²×C₃₇	—	4	2	no	—
293	C₂²×C₃₇	—	4	2	no	—
294	C₂²×C₃₇	—	4	2	no	—
295	C₂²×C₃₇	—	4	2	no	—
296	C₂²×C₃₇	—	4	2	no	—
297	C₂²×C₃₇	—	8	4	no	—
298	C₂²×C₃₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
299	C₂²×C₃₇	#520	1	2	yes	—
300	C₂²×C₃₇	#535	1	1	yes	characteristic
301	C₂²×C₃₇	#536	1	1	yes	characteristic
302	C₂²×C₃₇	#537	1	2	yes	—
303	C₄×C₃₇	—	2	1	no	—
304	C₄×C₃₇	—	2	1	no	—
305	C₄×C₃₇	—	2	1	no	—
306	C₄×C₃₇	—	2	1	no	—
307	C₄×C₃₇	—	2	1	no	—
308	C₄×C₃₇	—	2	1	no	—
309	C₄×C₃₇	—	2	1	no	—
310	C₄×C₃₇	—	2	1	no	—
311	C₄×C₃₇	—	2	1	no	—
312	C₄×C₃₇	—	2	1	no	—
313	C₄×C₃₇	—	4	2	no	—
314	C₄×C₃₇	—	4	2	no	—
315	C₄×C₃₇	—	4	2	no	—
316	C₄×C₃₇	—	8	4	no	—
317	C₄×C₃₇	—	8	4	no	—
318	C₄×C₃₇	#410	1	2	yes	—
319	C₄×C₃₇	#410	1	2	yes	—
320	C₂×#529	C₂×C₃₇	1	1	yes	characteristic
321	#2285	C₂×C₃₇	1	1	yes	characteristic, complemented
322	#2283	C₂×C₃₇	1	1	yes	characteristic, complemented
323	#1996	C₂×C₃₇	1	2	yes	complemented
324	#1964	C₂×C₃₇	1	2	yes	—
325	#1899	C₂×C₃₇	1	4	yes	complemented
326	#1799	C₂×C₃₇	1	4	yes	complemented
327	C₂×C₃₇	—	2	1	no	—
328	C₂×C₃₇	—	2	2	no	—
329	C₂×C₃₇	—	2	2	no	—
330	C₂×C₃₇	—	2	1	no	—
331	C₂×C₃₇	—	8	2	no	—
332	C₂×C₃₇	#2311	1	1	yes	characteristic
333	C₂×C₃₇	C₂×#410	1	1	yes	characteristic
334	C₂×C₃₇	C₂×#410	1	1	yes	characteristic
335	#529	—	2	1	no	—
336	#529	—	2	1	no	—
337	#529	—	2	1	no	—
338	#529	—	2	1	no	—
339	#529	—	2	1	no	—
340	#529	—	2	1	no	—
341	#529	—	2	1	no	—
342	#529	—	2	1	no	—
343	C₂×#126	C₄×C₃₇	1	2	yes	complemented
344	C₂×#125	C₄×C₃₇	1	1	yes	characteristic, complemented
345	C₂×#124	C₄×C₃₇	1	1	yes	characteristic, complemented
346	C₂×#123	C₂²×C₃₇	1	2	yes	—
347	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
348	C₂×#121	C₂²×C₃₇	1	1	yes	characteristic
349	C₂×C₄×Q₈	C₄×C₃₇	1	1	yes	characteristic, complemented
350	C₂×C₄×D₄	C₄×C₃₇	1	1	yes	characteristic, complemented
351	C₂×C₄×D₄	C₂²×C₃₇	1	2	yes	—
352	C₂×#117	C₄×C₃₇	1	2	yes	complemented
353	C₂×#117	C₂²×C₃₇	1	2	yes	—
354	C₂²×C₄²	C₂²×C₃₇	1	1	yes	characteristic
355	C₂×#99	C₂²×C₃₇	1	8	yes	—
356	#384	—	2	1	no	—
357	#383	—	2	1	no	—
358	#382	—	2	1	no	—
359	#382	—	2	1	no	—
360	#381	C₂²×C₃₇	1	2	yes	—
361	#380	C₂²×C₃₇	1	2	yes	—
362	#380	C₂²×C₃₇	1	2	yes	—
363	#380	C₂²×C₃₇	1	2	yes	—
364	C₄×C₄⋊C₄	—	2	1	no	—
365	C₄×C₄⋊C₄	—	2	1	no	—
366	C₄×C₄⋊C₄	—	2	1	no	—
367	C₄×C₂²⋊C₄	C₂²×C₃₇	1	2	yes	—
368	#376	—	2	1	no	—
369	#342	C₂²×C₃₇	1	8	yes	—
370	C₃₇	#21875	1	1	yes	characteristic, direct product factor, Sylow
371	C₂²×Q₈	C₂×C₄×C₃₇	1	1	yes	characteristic
372	C₂²×D₄	C₂×C₄×C₃₇	1	1	yes	characteristic
373	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
374	C₂³×C₄	C₂×C₄×C₃₇	1	2	yes	—
375	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
376	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
377	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
378	#126	—	2	2	no	—
379	#126	—	2	2	no	—
380	#126	—	2	2	no	—
381	#126	—	2	2	no	—
382	#125	—	2	1	no	—
383	#125	—	2	1	no	—
384	#125	—	2	1	no	—
385	#125	—	2	1	no	—
386	#124	—	2	1	no	—
387	#124	—	2	1	no	—
388	#124	—	2	1	no	—
389	#124	—	2	1	no	—
390	#123	—	2	2	no	—
391	#123	—	2	2	no	—
392	#123	—	2	2	no	—
393	#123	—	2	2	no	—
394	C₂²⋊Q₈	—	2	1	no	—
395	C₂²⋊Q₈	—	2	1	no	—
396	C₂²⋊Q₈	—	2	1	no	—
397	C₂²⋊Q₈	—	2	1	no	—
398	#121	—	2	1	no	—
399	#121	—	2	1	no	—
400	#121	—	2	1	no	—
401	#121	—	2	1	no	—
402	C₄×Q₈	—	2	1	no	—
403	C₄×Q₈	—	2	1	no	—
404	C₄×Q₈	—	2	1	no	—
405	C₄×Q₈	—	2	1	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	—	2	1	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	2	1	no	—
414	#117	—	2	2	no	—
415	#117	—	2	2	no	—
416	#117	—	2	2	no	—
417	#117	—	2	2	no	—
418	#117	—	4	4	no	—
419	C₂×C₄⋊C₄	—	2	2	no	—
420	C₂×C₄⋊C₄	—	2	2	no	—
421	C₂×C₄⋊C₄	—	2	2	no	—
422	C₂×C₄⋊C₄	—	2	2	no	—
423	C₂×C₄⋊C₄	C₂×C₄×C₃₇	1	2	yes	—
424	C₂×C₄⋊C₄	C₂×C₄×C₃₇	1	2	yes	—
425	C₂×C₄⋊C₄	C₂×C₄×C₃₇	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂×C₄×C₃₇	1	2	yes	—
427	C₂×C₄⋊C₄	C₂×C₄×C₃₇	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂×C₄×C₃₇	1	2	yes	—
429	C₂×C₂²⋊C₄	C₂×C₄×C₃₇	1	2	yes	—
430	C₂×C₂²⋊C₄	C₂×C₄×C₃₇	1	2	yes	—
431	C₂×C₂²⋊C₄	C₂×C₄×C₃₇	1	2	yes	—
432	C₂×C₂²⋊C₄	C₂×C₄×C₃₇	1	2	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₃₇	1	2	yes	—
436	C₂×C₄²	—	2	2	no	—
437	C₂×C₄²	—	2	2	no	—
438	C₂×C₄²	C₂×C₄×C₃₇	1	2	yes	—
439	C₂×C₄²	C₂×C₄×C₃₇	1	1	yes	characteristic
440	C₂×C₄²	C₂×C₄×C₃₇	1	1	yes	characteristic
441	C₂×C₄²	C₂×C₄×C₃₇	1	1	yes	characteristic
442	C₂×C₄²	C₂×C₄×C₃₇	1	1	yes	characteristic
443	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
444	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
445	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
446	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
447	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
448	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
449	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
450	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
451	#99	—	4	8	no	—
452	#95	—	2	2	no	—
453	#95	—	2	2	no	—
454	#95	—	2	2	no	—
455	#95	—	2	2	no	—
456	#95	—	2	2	no	—
457	#95	—	2	2	no	—
458	C₂⁴	C₂²×C₄×C₃₇	1	2	yes	—
459	C₂⁴	C₂⁴×C₃₇	1	1	yes	characteristic
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	4	2	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	4	no	—
466	C₂×D₄	—	2	4	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	4	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	4	2	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	4	no	—
479	C₂²×C₄	C₂²×C₄×C₃₇	1	2	yes	—
480	C₂²×C₄	C₂²×C₄×C₃₇	1	1	yes	characteristic
481	C₂²×C₄	C₂²×C₄×C₃₇	1	1	yes	characteristic
482	C₂²×C₄	C₂²×C₄×C₃₇	1	1	yes	characteristic
483	C₂²×C₄	C₂²×C₄×C₃₇	1	1	yes	characteristic
484	C₂²×C₄	C₂²×C₄×C₃₇	1	2	yes	—
485	C₂²×C₄	C₂²×C₄×C₃₇	1	2	yes	—
486	C₂²×C₄	C₂²×C₄×C₃₇	1	1	yes	characteristic
487	C₂²×C₄	C₂²×C₄×C₃₇	1	1	yes	characteristic
488	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
489	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
490	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
491	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
492	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
496	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	4	4	no	—
513	C₄⋊C₄	—	4	4	no	—
514	C₄⋊C₄	—	4	4	no	—
515	C₄⋊C₄	—	4	4	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	4	no	—
527	C₂²⋊C₄	—	2	8	no	—
528	C₂²⋊C₄	—	2	4	no	—
529	C₄²	—	2	2	no	—
530	C₄²	—	2	2	no	—
531	C₄²	—	4	4	no	—
532	C₄²	—	4	4	no	—
533	C₄²	C₂²⋊C₄×C₃₇	1	1	yes	characteristic
534	C₄²	C₂²⋊C₄×C₃₇	1	1	yes	characteristic
535	C₄²	C₂²⋊C₄×C₃₇	1	1	yes	characteristic
536	C₄²	C₂²⋊C₄×C₃₇	1	1	yes	characteristic
537	C₄²	C₂²⋊C₄×C₃₇	1	1	yes	characteristic
538	C₄²	C₂²⋊C₄×C₃₇	1	1	yes	characteristic
539	C₄²	C₂²⋊C₄×C₃₇	1	1	yes	characteristic
540	C₄²	C₂²⋊C₄×C₃₇	1	1	yes	characteristic
541	C₄²	C₂²⋊C₄×C₃₇	1	1	yes	characteristic
542	C₄²	C₂²⋊C₄×C₃₇	1	1	yes	characteristic
543	C₄²	C₂²⋊C₄×C₃₇	1	1	yes	characteristic
544	C₄²	C₂²⋊C₄×C₃₇	1	1	yes	characteristic
545	C₄²	C₂²⋊C₄×C₃₇	1	1	yes	characteristic
546	C₄²	C₂²⋊C₄×C₃₇	1	1	yes	characteristic
547	C₄²	C₂²⋊C₄×C₃₇	1	1	yes	characteristic
548	C₄²	C₂²⋊C₄×C₃₇	1	1	yes	characteristic
549	C₂³	—	2	2	no	—
550	C₂³	—	2	4	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	2	no	—
554	C₂³	—	4	2	no	—
555	C₂³	C₂³×C₄×C₃₇	1	1	yes	characteristic
556	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
557	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
558	C₂³	H(5,𝔽₂)×C₃₇	1	2	yes	—
559	C₂³	2₋¹⁺⁴×C₃₇	1	2	yes	—
560	Q₈	—	4	2	no	—
561	Q₈	—	4	2	no	—
562	D₄	—	4	2	no	—
563	D₄	—	4	2	no	—
564	D₄	—	4	2	no	—
565	D₄	—	4	4	no	—
566	D₄	—	4	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	4	no	—
592	C₂×C₄	—	4	4	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	4	no	—
596	C₂×C₄	—	4	4	no	—
597	C₂×C₄	—	4	4	no	—
598	C₂×C₄	—	4	4	no	—
599	C₂×C₄	—	4	4	no	—
600	C₂×C₄	—	4	4	no	—
601	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
602	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
603	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
604	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
605	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
606	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
607	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
608	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
609	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
610	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
611	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
612	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	8	4	no	—
625	C₂²	C₂²×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
626	C₂²	C₃₇×#520	1	2	yes	—
627	C₂²	C₃₇×#535	1	1	yes	characteristic
628	C₂²	C₃₇×#536	1	1	yes	characteristic
629	C₂²	C₃₇×#537	1	2	yes	—
630	C₄	—	2	1	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	1	no	—
640	C₄	—	4	2	no	—
641	C₄	—	4	2	no	—
642	C₄	—	4	2	no	—
643	C₄	—	8	4	no	—
644	C₄	—	8	4	no	—
645	C₄	C₃₇×#410	1	2	yes	—
646	C₄	C₃₇×#410	1	2	yes	—
647	C₂	—	2	1	no	—
648	C₂	—	2	2	no	—
649	C₂	—	2	2	no	—
650	C₂	—	2	1	no	—
651	C₂	—	8	2	no	—
652	C₂	C₃₇×#2311	1	1	yes	characteristic
653	C₂	C₂×C₃₇×#410	1	1	yes	characteristic
654	C₂	C₂×C₃₇×#410	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₃₇
Frattini, cosocle	C₂⁴	C₂⁴×C₃₇
prime radical	C₂×#121×C₃₇	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂²×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₇×#2285	C₂	semidirect
3. C₃₇×#2283	C₂	semidirect
4. C₃₇×#1996	C₂	semidirect
6. C₃₇×#1899	C₂	semidirect
7. C₃₇×#1799	C₂	semidirect
16. C₂×#126×C₃₇	C₄	semidirect
17. C₂×#125×C₃₇	C₄	semidirect
18. C₂×#124×C₃₇	C₄	semidirect
22. C₂×C₄×Q₈×C₃₇	C₄	semidirect
23. C₂×C₄×D₄×C₃₇	C₄	semidirect
25. C₂×#117×C₃₇	C₄	semidirect
285. #21875	C₃₇	direct (N × H)
321. #2285	C₂×C₃₇	semidirect
322. #2283	C₂×C₃₇	semidirect
323. #1996	C₂×C₃₇	semidirect
325. #1899	C₂×C₃₇	semidirect
326. #1799	C₂×C₃₇	semidirect
343. C₂×#126	C₄×C₃₇	semidirect
344. C₂×#125	C₄×C₃₇	semidirect
345. C₂×#124	C₄×C₃₇	semidirect
349. C₂×C₄×Q₈	C₄×C₃₇	semidirect
350. C₂×C₄×D₄	C₄×C₃₇	semidirect
352. C₂×#117	C₄×C₃₇	semidirect
370. C₃₇	#21875	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×#529	2
C₃₇×#2285	2
C₃₇×#2283	2
C₃₇×#1996	2
C₃₇×#1964	2
C₃₇×#1899	2
C₃₇×#1799	2
#21875	37

Subgroups — C37×#21875 #22643128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#21875 #22643128