Subgroups — C₃₇×#17994 #22639247

Order 9472.

748 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3100	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×M₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#1589	C₂	1	2	yes	maximal, complemented
5	C₃₇×#1581	C₂	1	2	yes	maximal, complemented
6	C₃₇×#1581	C₂	1	2	yes	maximal, complemented
7	C₈×D₈×C₃₇	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1571	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1492	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₇×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#131×C₃₇	—	2	1	no	—
13	C₂²×M₁₆×C₃₇	—	2	1	no	—
14	C₃₇×#532	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
16	C₃₇×#480	C₄	1	2	yes	—
17	C₃₇×#474	C₄	1	1	yes	characteristic
18	C₃₇×#474	C₄	1	1	yes	characteristic
19	C₃₇×#459	C₄	1	1	yes	characteristic
20	C₃₇×#459	C₄	1	1	yes	characteristic
21	C₃₇×#447	C₄	1	2	yes	—
22	C₄×D₈×C₃₇	C₂²	1	2	yes	—
23	C₄×D₈×C₃₇	C₂²	1	2	yes	—
24	C₃₇×#436	C₂²	1	2	yes	—
25	C₃₇×#436	C₂²	1	2	yes	complemented
26	C₃₇×#435	—	2	2	no	—
27	C₃₇×#435	—	2	2	no	—
28	C₈×D₄×C₃₇	C₂²	1	2	yes	—
29	C₈×D₄×C₃₇	C₂²	1	2	yes	complemented
30	C₃₇×#431	C₂²	1	1	yes	characteristic
31	C₃₇×#423	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
33	C₃₇×#408	—	2	1	no	—
34	C₃₇×#407	—	2	1	no	—
35	C₄×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
37	C₃₇×#335	C₂²	1	2	yes	complemented
38	C₃₇×#335	C₂²	1	2	yes	complemented
39	C₃₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₃₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₃₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₃₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₃₇×D₄⋊C₈	C₂²	1	2	yes	complemented
44	C₃₇×D₄⋊C₈	C₂²	1	2	yes	complemented
45	C₃₇×#322	C₂²	1	2	yes	complemented
46	C₈²×C₃₇	C₂²	1	2	yes	complemented
47	C₂×#41×C₃₇	—	2	1	no	—
48	C₂²×D₄×C₃₇	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₃₇	—	2	1	no	—
50	C₂×D₈×C₃₇	C₂×C₄	1	2	yes	—
51	C₂×D₈×C₃₇	C₂×C₄	1	2	yes	—
52	#131×C₃₇	—	4	4	no	—
53	C₂×M₁₆×C₃₇	—	2	1	no	—
54	C₂×M₁₆×C₃₇	—	2	2	no	—
55	C₂×M₁₆×C₃₇	—	2	2	no	—
56	C₂×M₁₆×C₃₇	—	4	4	no	—
57	C₂×M₁₆×C₃₇	D₄	1	1	yes	characteristic
58	C₂×M₁₆×C₃₇	D₄	1	1	yes	characteristic
59	C₂²×C₈×C₃₇	—	2	1	no	—
60	C₂²×C₈×C₃₇	—	2	1	no	—
61	C₂²×C₈×C₃₇	—	2	2	no	—
62	C₂²×C₈×C₃₇	—	2	2	no	—
63	C₄⋊Q₈×C₃₇	C₂×C₄	1	1	yes	characteristic
64	#127×C₃₇	C₂×C₄	1	1	yes	characteristic
65	#124×C₃₇	—	2	1	no	—
66	#121×C₃₇	—	2	1	no	—
67	#121×C₃₇	C₂×C₄	1	2	yes	—
68	C₄×D₄×C₃₇	—	2	1	no	—
69	C₄×D₄×C₃₇	—	2	1	no	—
70	C₄×D₄×C₃₇	—	2	1	no	—
71	C₄×D₄×C₃₇	C₂×C₄	1	1	yes	characteristic
72	C₄×D₄×C₃₇	C₂×C₄	1	1	yes	characteristic
73	C₄×D₄×C₃₇	C₂³	1	2	yes	—
74	C₄×D₄×C₃₇	C₂³	1	1	yes	characteristic
75	C₄×D₄×C₃₇	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
78	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
79	#107×C₃₇	C₂×C₄	1	2	yes	—
80	#107×C₃₇	C₂×C₄	1	2	yes	—
81	C₄⋊C₈×C₃₇	—	2	1	no	—
82	C₄⋊C₈×C₃₇	—	2	1	no	—
83	C₄⋊C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
84	C₄⋊C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
85	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
88	#102×C₃₇	C₂×C₄	1	2	yes	—
89	#102×C₃₇	C₂×C₄	1	2	yes	—
90	#102×C₃₇	C₂×C₄	1	2	yes	—
91	#102×C₃₇	C₂×C₄	1	2	yes	—
92	C₂²⋊C₈×C₃₇	—	2	2	no	—
93	C₂²⋊C₈×C₃₇	—	2	2	no	—
94	C₂²⋊C₈×C₃₇	—	2	2	no	—
95	C₂²⋊C₈×C₃₇	—	2	2	no	—
96	C₂²⋊C₈×C₃₇	C₂×C₄	1	2	yes	—
97	#97×C₃₇	D₄	1	2	yes	—
98	C₄×C₈×C₃₇	—	2	1	no	—
99	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₃₇	C₂³	1	2	yes	—
102	C₄×C₈×C₃₇	C₂³	1	2	yes	—
103	C₂⁴×C₃₇	—	2	1	no	—
104	#41×C₃₇	—	4	2	no	—
105	#41×C₃₇	—	4	2	no	—
106	C₂×Q₈×C₃₇	—	2	1	no	—
107	C₂×D₄×C₃₇	—	2	2	no	—
108	C₂×D₄×C₃₇	—	2	2	no	—
109	C₂×D₄×C₃₇	—	2	1	no	—
110	C₂×D₄×C₃₇	—	2	1	no	—
111	C₂×D₄×C₃₇	—	2	1	no	—
112	C₂×D₄×C₃₇	—	4	1	no	—
113	C₂×D₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
114	C₂×D₄×C₃₇	C₂²×C₄	1	2	yes	—
115	C₂×D₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₃₇	—	2	1	no	—
117	C₂²×C₄×C₃₇	—	2	1	no	—
118	C₂²×C₄×C₃₇	—	2	1	no	—
119	C₂²×C₄×C₃₇	—	2	1	no	—
120	C₂²×C₄×C₃₇	—	2	2	no	—
121	C₂²×C₄×C₃₇	—	2	1	no	—
122	C₂²×C₄×C₃₇	—	4	2	no	—
123	C₂²×C₄×C₃₇	—	4	2	no	—
124	C₂²×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
127	D₈×C₃₇	—	2	4	no	—
128	D₈×C₃₇	—	4	2	no	—
129	M₁₆×C₃₇	—	2	2	no	—
130	M₁₆×C₃₇	—	4	2	no	—
131	M₁₆×C₃₇	—	4	4	no	—
132	M₁₆×C₃₇	—	4	4	no	—
133	M₁₆×C₃₇	D₈	1	4	yes	complemented
134	C₂×C₈×C₃₇	—	2	1	no	—
135	C₂×C₈×C₃₇	—	2	1	no	—
136	C₂×C₈×C₃₇	—	2	2	no	—
137	C₂×C₈×C₃₇	—	2	1	no	—
138	C₂×C₈×C₃₇	—	2	1	no	—
139	C₂×C₈×C₃₇	—	4	2	no	—
140	C₂×C₈×C₃₇	—	4	2	no	—
141	C₂×C₈×C₃₇	—	4	4	no	—
142	C₂×C₈×C₃₇	—	4	4	no	—
143	C₂×C₈×C₃₇	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₃₇	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
147	C₄⋊C₄×C₃₇	—	2	1	no	—
148	C₄⋊C₄×C₃₇	—	2	1	no	—
149	C₄⋊C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
150	C₄⋊C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
151	C₄⋊C₄×C₃₇	C₂²×C₄	1	2	yes	—
152	C₂²⋊C₄×C₃₇	—	2	1	no	—
153	C₂²⋊C₄×C₃₇	—	2	1	no	—
154	C₂²⋊C₄×C₃₇	—	2	2	no	—
155	C₂²⋊C₄×C₃₇	—	2	1	no	—
156	C₂²⋊C₄×C₃₇	—	2	1	no	—
157	C₂²⋊C₄×C₃₇	—	2	2	no	—
158	C₄²×C₃₇	C₂²×C₄	1	1	yes	characteristic
159	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₃₇	#41	1	1	yes	characteristic
161	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
162	C₂³×C₃₇	—	2	1	no	—
163	C₂³×C₃₇	—	2	1	no	—
164	C₂³×C₃₇	—	2	2	no	—
165	C₂³×C₃₇	—	4	2	no	—
166	C₂³×C₃₇	—	4	2	no	—
167	C₂³×C₃₇	—	8	1	no	—
168	C₂³×C₃₇	C₄×D₄	1	1	yes	characteristic
169	Q₈×C₃₇	—	4	2	no	—
170	D₄×C₃₇	—	2	2	no	—
171	D₄×C₃₇	—	2	1	no	—
172	D₄×C₃₇	—	2	1	no	—
173	D₄×C₃₇	—	2	1	no	—
174	D₄×C₃₇	—	2	2	no	—
175	D₄×C₃₇	—	4	2	no	—
176	D₄×C₃₇	—	4	4	no	—
177	D₄×C₃₇	—	4	2	no	—
178	D₄×C₃₇	—	8	1	no	—
179	D₄×C₃₇	#131	1	2	yes	complemented
180	C₂×C₄×C₃₇	—	2	1	no	—
181	C₂×C₄×C₃₇	—	2	1	no	—
182	C₂×C₄×C₃₇	—	2	1	no	—
183	C₂×C₄×C₃₇	—	2	1	no	—
184	C₂×C₄×C₃₇	—	2	2	no	—
185	C₂×C₄×C₃₇	—	4	1	no	—
186	C₂×C₄×C₃₇	—	4	2	no	—
187	C₂×C₄×C₃₇	—	4	1	no	—
188	C₂×C₄×C₃₇	—	4	2	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	2	no	—
194	C₂×C₄×C₃₇	—	4	2	no	—
195	C₂×C₄×C₃₇	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₃₇	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₃₇	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₃₇	C₂×D₈	1	2	yes	—
199	C₂×C₄×C₃₇	#135	1	2	yes	—
200	C₂×C₄×C₃₇	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
203	C₈×C₃₇	—	2	2	no	—
204	C₈×C₃₇	—	2	2	no	—
205	C₈×C₃₇	—	2	2	no	—
206	C₈×C₃₇	—	2	2	no	—
207	C₈×C₃₇	—	4	1	no	—
208	C₈×C₃₇	—	4	1	no	—
209	C₈×C₃₇	—	4	1	no	—
210	C₈×C₃₇	—	4	2	no	—
211	C₈×C₃₇	C₂×D₈	1	4	yes	—
212	#17994	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂²×C₃₇	—	2	1	no	—
214	C₂²×C₃₇	—	2	1	no	—
215	C₂²×C₃₇	—	2	2	no	—
216	C₂²×C₃₇	—	4	1	no	—
217	C₂²×C₃₇	—	4	1	no	—
218	C₂²×C₃₇	—	4	1	no	—
219	C₂²×C₃₇	—	4	2	no	—
220	C₂²×C₃₇	—	4	1	no	—
221	C₂²×C₃₇	—	4	2	no	—
222	C₂²×C₃₇	—	4	2	no	—
223	C₂²×C₃₇	—	4	1	no	—
224	C₂²×C₃₇	—	8	4	no	—
225	C₂²×C₃₇	C₄×D₈	1	2	yes	—
226	C₂²×C₃₇	C₂×C₄×D₄	1	1	yes	characteristic
227	C₄×C₃₇	—	2	1	no	—
228	C₄×C₃₇	—	2	1	no	—
229	C₄×C₃₇	—	2	1	no	—
230	C₄×C₃₇	—	4	1	no	—
231	C₄×C₃₇	—	4	1	no	—
232	C₄×C₃₇	—	4	2	no	—
233	C₄×C₃₇	C₄×D₈	1	2	yes	—
234	C₄×C₃₇	C₂×#131	1	1	yes	characteristic
235	C₄×C₃₇	#568	1	1	yes	characteristic
236	C₄×C₃₇	C₂²×D₈	1	1	yes	characteristic
237	C₄×C₃₇	C₂×#135	1	1	yes	characteristic
238	#3100	C₂×C₃₇	1	1	yes	characteristic
239	#2935	C₂×C₃₇	1	1	yes	characteristic, complemented
240	D₄×M₁₆	C₂×C₃₇	1	1	yes	characteristic, complemented
241	#1589	C₂×C₃₇	1	2	yes	complemented
242	#1581	C₂×C₃₇	1	2	yes	complemented
243	#1581	C₂×C₃₇	1	2	yes	complemented
244	C₈×D₈	C₂×C₃₇	1	2	yes	complemented
245	#1571	C₂×C₃₇	1	1	yes	characteristic, complemented
246	#1492	C₂×C₃₇	1	1	yes	characteristic, complemented
247	C₂×D₄⋊C₈	C₂×C₃₇	1	1	yes	characteristic, complemented
248	C₈×M₁₆	C₂×C₃₇	1	1	yes	characteristic, complemented
249	C₂×C₃₇	—	2	2	no	—
250	C₂×C₃₇	—	4	2	no	—
251	C₂×C₃₇	—	8	2	no	—
252	C₂×C₃₇	—	8	1	no	—
253	C₂×C₃₇	#2933	1	1	yes	characteristic
254	C₂×C₃₇	C₂×C₄×D₈	1	1	yes	characteristic
255	C₂×C₃₇	#2956	1	1	yes	characteristic
256	C₂×#131	—	2	1	no	—
257	C₂²×M₁₆	—	2	1	no	—
258	#532	C₂²×C₃₇	1	1	yes	characteristic
259	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
260	#480	C₄×C₃₇	1	2	yes	—
261	#474	C₄×C₃₇	1	1	yes	characteristic
262	#474	C₄×C₃₇	1	1	yes	characteristic
263	#459	C₄×C₃₇	1	1	yes	characteristic
264	#459	C₄×C₃₇	1	1	yes	characteristic
265	#447	C₄×C₃₇	1	2	yes	—
266	C₄×D₈	C₂²×C₃₇	1	2	yes	—
267	C₄×D₈	C₂²×C₃₇	1	2	yes	—
268	#436	C₂²×C₃₇	1	2	yes	—
269	#436	C₂²×C₃₇	1	2	yes	complemented
270	#435	—	2	2	no	—
271	#435	—	2	2	no	—
272	C₈×D₄	C₂²×C₃₇	1	2	yes	—
273	C₈×D₄	C₂²×C₃₇	1	2	yes	complemented
274	#431	C₂²×C₃₇	1	1	yes	characteristic
275	#423	C₂²×C₃₇	1	1	yes	characteristic
276	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
277	#408	—	2	1	no	—
278	#407	—	2	1	no	—
279	C₄×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
280	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
281	#335	C₂²×C₃₇	1	2	yes	complemented
282	#335	C₂²×C₃₇	1	2	yes	complemented
283	D₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
284	D₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
285	D₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
286	D₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
287	D₄⋊C₈	C₂²×C₃₇	1	2	yes	complemented
288	D₄⋊C₈	C₂²×C₃₇	1	2	yes	complemented
289	#322	C₂²×C₃₇	1	2	yes	complemented
290	C₈²	C₂²×C₃₇	1	2	yes	complemented
291	C₃₇	#17994	1	1	yes	characteristic, direct product factor, Sylow
292	C₂×#41	—	2	1	no	—
293	C₂²×D₄	C₂×C₄×C₃₇	1	1	yes	characteristic
294	C₂³×C₄	—	2	1	no	—
295	C₂×D₈	C₂×C₄×C₃₇	1	2	yes	—
296	C₂×D₈	C₂×C₄×C₃₇	1	2	yes	—
297	#131	—	4	4	no	—
298	C₂×M₁₆	—	2	1	no	—
299	C₂×M₁₆	—	2	2	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	—	4	4	no	—
302	C₂×M₁₆	D₄×C₃₇	1	1	yes	characteristic
303	C₂×M₁₆	D₄×C₃₇	1	1	yes	characteristic
304	C₂²×C₈	—	2	1	no	—
305	C₂²×C₈	—	2	1	no	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	—	2	2	no	—
308	C₄⋊Q₈	C₂×C₄×C₃₇	1	1	yes	characteristic
309	#127	C₂×C₄×C₃₇	1	1	yes	characteristic
310	#124	—	2	1	no	—
311	#121	—	2	1	no	—
312	#121	C₂×C₄×C₃₇	1	2	yes	—
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	C₂×C₄×C₃₇	1	1	yes	characteristic
317	C₄×D₄	C₂×C₄×C₃₇	1	1	yes	characteristic
318	C₄×D₄	C₂³×C₃₇	1	1	yes	characteristic
319	C₄×D₄	C₂³×C₃₇	1	1	yes	characteristic
320	C₄×D₄	C₂³×C₃₇	1	2	yes	—
321	C₂×C₄⋊C₄	C₂×C₄×C₃₇	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
324	#107	C₂×C₄×C₃₇	1	2	yes	—
325	#107	C₂×C₄×C₃₇	1	2	yes	—
326	C₄⋊C₈	—	2	1	no	—
327	C₄⋊C₈	—	2	1	no	—
328	C₄⋊C₈	C₂×C₄×C₃₇	1	1	yes	characteristic
329	C₄⋊C₈	C₂×C₄×C₃₇	1	1	yes	characteristic
330	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
331	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
332	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
333	#102	C₂×C₄×C₃₇	1	2	yes	—
334	#102	C₂×C₄×C₃₇	1	2	yes	—
335	#102	C₂×C₄×C₃₇	1	2	yes	—
336	#102	C₂×C₄×C₃₇	1	2	yes	—
337	C₂²⋊C₈	—	2	2	no	—
338	C₂²⋊C₈	—	2	2	no	—
339	C₂²⋊C₈	—	2	2	no	—
340	C₂²⋊C₈	—	2	2	no	—
341	C₂²⋊C₈	C₂×C₄×C₃₇	1	2	yes	—
342	#97	D₄×C₃₇	1	2	yes	—
343	C₄×C₈	—	2	1	no	—
344	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
345	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
346	C₄×C₈	C₂³×C₃₇	1	2	yes	—
347	C₄×C₈	C₂³×C₃₇	1	2	yes	—
348	C₂⁴	—	2	1	no	—
349	#41	—	4	2	no	—
350	#41	—	4	2	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	4	1	no	—
358	C₂×D₄	C₂²×C₄×C₃₇	1	1	yes	characteristic
359	C₂×D₄	C₂²×C₄×C₃₇	1	2	yes	—
360	C₂×D₄	C₂²×C₄×C₃₇	1	1	yes	characteristic
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	2	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	C₂²×C₄×C₃₇	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
371	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
372	D₈	—	2	4	no	—
373	D₈	—	4	2	no	—
374	M₁₆	—	2	2	no	—
375	M₁₆	—	4	2	no	—
376	M₁₆	—	4	4	no	—
377	M₁₆	—	4	4	no	—
378	M₁₆	D₈×C₃₇	1	4	yes	complemented
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	4	2	no	—
385	C₂×C₈	—	4	2	no	—
386	C₂×C₈	—	4	4	no	—
387	C₂×C₈	—	4	4	no	—
388	C₂×C₈	C₂²×C₄×C₃₇	1	2	yes	—
389	C₂×C₈	C₂²×C₄×C₃₇	1	2	yes	—
390	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
391	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	C₂²×C₄×C₃₇	1	1	yes	characteristic
395	C₄⋊C₄	C₂²×C₄×C₃₇	1	1	yes	characteristic
396	C₄⋊C₄	C₂²×C₄×C₃₇	1	2	yes	—
397	C₂²⋊C₄	—	2	1	no	—
398	C₂²⋊C₄	—	2	1	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	2	1	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₄²	C₂²×C₄×C₃₇	1	1	yes	characteristic
404	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
405	C₄²	#41×C₃₇	1	1	yes	characteristic
406	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	8	1	no	—
413	C₂³	C₄×D₄×C₃₇	1	1	yes	characteristic
414	Q₈	—	4	2	no	—
415	D₄	—	2	2	no	—
416	D₄	—	2	1	no	—
417	D₄	—	2	1	no	—
418	D₄	—	2	1	no	—
419	D₄	—	2	2	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	4	no	—
422	D₄	—	4	2	no	—
423	D₄	—	8	1	no	—
424	D₄	#131×C₃₇	1	2	yes	complemented
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	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	C₄×D₄×C₃₇	1	1	yes	characteristic
441	C₂×C₄	C₄×D₄×C₃₇	1	1	yes	characteristic
442	C₂×C₄	C₄×D₄×C₃₇	1	1	yes	characteristic
443	C₂×C₄	C₂×D₈×C₃₇	1	2	yes	—
444	C₂×C₄	#135×C₃₇	1	2	yes	—
445	C₂×C₄	C₂³×C₄×C₃₇	1	1	yes	characteristic
446	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
447	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
448	C₈	—	2	2	no	—
449	C₈	—	2	2	no	—
450	C₈	—	2	2	no	—
451	C₈	—	2	2	no	—
452	C₈	—	4	1	no	—
453	C₈	—	4	1	no	—
454	C₈	—	4	1	no	—
455	C₈	—	4	2	no	—
456	C₈	C₂×D₈×C₃₇	1	4	yes	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	4	1	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	8	4	no	—
469	C₂²	C₄×D₈×C₃₇	1	2	yes	—
470	C₂²	C₂×C₄×D₄×C₃₇	1	1	yes	characteristic
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	2	no	—
477	C₄	C₄×D₈×C₃₇	1	2	yes	—
478	C₄	C₂×#131×C₃₇	1	1	yes	characteristic
479	C₄	C₃₇×#568	1	1	yes	characteristic
480	C₄	C₂²×D₈×C₃₇	1	1	yes	characteristic
481	C₄	C₂×#135×C₃₇	1	1	yes	characteristic
482	C₂	—	2	2	no	—
483	C₂	—	4	2	no	—
484	C₂	—	8	1	no	—
485	C₂	—	8	2	no	—
486	C₂	C₃₇×#2933	1	1	yes	characteristic
487	C₂	C₂×C₄×D₈×C₃₇	1	1	yes	characteristic
488	C₂	C₃₇×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₇
Frattini, cosocle	C₄²	C₂⁴×C₃₇
socle	C₂²×C₃₇	C₂×C₄×D₄
prime radical	C₃₇×#3100	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ C₄×M₁₆×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₇×#2935	C₂	semidirect
3. D₄×M₁₆×C₃₇	C₂	semidirect
4. C₃₇×#1589	C₂	semidirect
5. C₃₇×#1581	C₂	semidirect
6. C₃₇×#1581	C₂	semidirect
7. C₈×D₈×C₃₇	C₂	semidirect
8. C₃₇×#1571	C₂	semidirect
9. C₃₇×#1492	C₂	semidirect
10. C₂×C₃₇×D₄⋊C₈	C₂	semidirect
11. C₈×M₁₆×C₃₇	C₂	semidirect
25. C₃₇×#436	C₂²	semidirect
29. C₈×D₄×C₃₇	C₂²	semidirect
37. C₃₇×#335	C₂²	semidirect
38. C₃₇×#335	C₂²	semidirect
43. C₃₇×D₄⋊C₈	C₂²	semidirect
44. C₃₇×D₄⋊C₈	C₂²	semidirect
45. C₃₇×#322	C₂²	semidirect
46. C₈²×C₃₇	C₂²	semidirect
133. M₁₆×C₃₇	D₈	semidirect
179. D₄×C₃₇	#131	semidirect
212. #17994	C₃₇	direct (N × H)
239. #2935	C₂×C₃₇	semidirect
240. D₄×M₁₆	C₂×C₃₇	semidirect
241. #1589	C₂×C₃₇	semidirect
242. #1581	C₂×C₃₇	semidirect
243. #1581	C₂×C₃₇	semidirect
244. C₈×D₈	C₂×C₃₇	semidirect
245. #1571	C₂×C₃₇	semidirect
246. #1492	C₂×C₃₇	semidirect
247. C₂×D₄⋊C₈	C₂×C₃₇	semidirect
248. C₈×M₁₆	C₂×C₃₇	semidirect
269. #436	C₂²×C₃₇	semidirect
273. C₈×D₄	C₂²×C₃₇	semidirect
281. #335	C₂²×C₃₇	semidirect
282. #335	C₂²×C₃₇	semidirect
287. D₄⋊C₈	C₂²×C₃₇	semidirect
288. D₄⋊C₈	C₂²×C₃₇	semidirect
289. #322	C₂²×C₃₇	semidirect
290. C₈²	C₂²×C₃₇	semidirect
291. C₃₇	#17994	direct (N × H)
378. M₁₆	D₈×C₃₇	semidirect
424. D₄	#131×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#3100	2
C₃₇×#2935	2
D₄×M₁₆×C₃₇	2
C₃₇×#1589	2
C₃₇×#1581	2
C₈×D₈×C₃₇	2
C₃₇×#1571	2
C₃₇×#1492	2
C₂×C₃₇×D₄⋊C₈	2
C₈×M₁₆×C₃₇	2
#17994	37

Subgroups — C37×#17994 #22639247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#17994 #22639247