Subgroups — C₃₇×#17904 #22639157

Order 9472.

634 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3102	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×#41×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#1584	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#1583	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#1582	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#1581	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×Q₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×SD₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×SD₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#1572	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₇×#1488	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#1482	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₇×#1450	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₇×#529	C₂²	1	1	yes	characteristic
17	C₄×#41×C₃₇	C₂²	1	1	yes	characteristic
18	C₃₇×#485	C₄	1	1	yes	characteristic
19	C₃₇×#482	C₄	1	1	yes	characteristic
20	C₃₇×#479	C₄	1	1	yes	characteristic
21	C₃₇×#478	C₄	1	1	yes	characteristic
22	C₃₇×#464	C₄	1	1	yes	characteristic
23	C₃₇×#463	C₄	1	1	yes	characteristic
24	C₃₇×#452	C₄	1	1	yes	characteristic
25	C₃₇×#449	C₄	1	1	yes	characteristic
26	C₃₇×#446	C₂²	1	1	yes	characteristic
27	C₈×Q₈×C₃₇	C₂²	1	1	yes	characteristic
28	C₈×Q₈×C₃₇	C₂²	1	1	yes	characteristic
29	C₈×Q₈×C₃₇	C₂²	1	1	yes	characteristic
30	C₄×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
31	C₄×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
32	C₄×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
33	C₄×D₈×C₃₇	C₂²	1	1	yes	characteristic
34	C₃₇×#436	C₂²	1	1	yes	characteristic
35	C₃₇×#435	—	2	1	no	—
36	C₈×D₄×C₃₇	—	2	1	no	—
37	C₈×D₄×C₃₇	—	2	1	no	—
38	C₈×D₄×C₃₇	—	2	1	no	—
39	C₈×D₄×C₃₇	C₂²	1	1	yes	characteristic
40	C₈×D₄×C₃₇	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₃₇	C₂²	1	1	yes	characteristic
42	C₃₇×#433	—	2	1	no	—
43	C₃₇×#432	C₂²	1	1	yes	characteristic
44	C₃₇×#431	—	2	1	no	—
45	C₃₇×#431	C₂²	1	1	yes	characteristic
46	C₃₇×#431	C₂²	1	1	yes	characteristic
47	C₃₇×#431	C₂²	1	1	yes	characteristic
48	C₃₇×#405	—	2	1	no	—
49	C₂×C₄×C₈×C₃₇	—	2	1	no	—
50	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
51	C₃₇×#335	C₂²	1	1	yes	characteristic
52	C₃₇×#335	C₂²	1	1	yes	characteristic
53	C₃₇×#334	C₂²	1	1	yes	characteristic
54	C₃₇×#334	C₂²	1	1	yes	characteristic
55	C₃₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
56	C₃₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
57	C₃₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
58	C₃₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
59	C₃₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
60	C₃₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
61	C₃₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₃₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₃₇×#322	C₂²	1	1	yes	characteristic
64	C₃₇×#322	C₂²	1	1	yes	characteristic
65	C₈²×C₃₇	C₂²	1	1	yes	characteristic
66	C₈²×C₃₇	C₂²	1	1	yes	characteristic
67	C₂×#41×C₃₇	C₂×C₄	1	1	yes	characteristic
68	C₂×Q₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
69	C₂×SD₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
70	C₂×SD₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
71	C₂×D₈×C₃₇	C₂×C₄	1	1	yes	characteristic
72	C₂×M₁₆×C₃₇	—	2	1	no	—
73	C₂²×C₈×C₃₇	—	2	1	no	—
74	C₂²×C₈×C₃₇	—	2	1	no	—
75	C₂²×C₈×C₃₇	—	2	1	no	—
76	C₂²×C₈×C₃₇	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₃₇	D₄	1	1	yes	characteristic
78	#126×C₃₇	—	2	1	no	—
79	#125×C₃₇	C₂×C₄	1	1	yes	characteristic
80	#124×C₃₇	C₂×C₄	1	1	yes	characteristic
81	#123×C₃₇	—	2	1	no	—
82	C₂²⋊Q₈×C₃₇	C₂×C₄	1	1	yes	characteristic
83	#121×C₃₇	C₂×C₄	1	1	yes	characteristic
84	C₄×Q₈×C₃₇	C₂×C₄	1	1	yes	characteristic
85	C₄×Q₈×C₃₇	C₂³	1	1	yes	characteristic
86	C₄×Q₈×C₃₇	C₂³	1	1	yes	characteristic
87	C₄×D₄×C₃₇	—	2	1	no	—
88	C₄×D₄×C₃₇	—	2	1	no	—
89	C₄×D₄×C₃₇	—	2	1	no	—
90	C₄×D₄×C₃₇	C₂×C₄	1	1	yes	characteristic
91	C₄×D₄×C₃₇	C₂³	1	1	yes	characteristic
92	C₄×D₄×C₃₇	C₂³	1	1	yes	characteristic
93	#117×C₃₇	—	2	1	no	—
94	#117×C₃₇	—	2	1	no	—
95	#117×C₃₇	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₃₇	—	2	1	no	—
97	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
98	#107×C₃₇	C₂×C₄	1	1	yes	characteristic
99	#107×C₃₇	C₂×C₄	1	1	yes	characteristic
100	#106×C₃₇	C₂×C₄	1	1	yes	characteristic
101	#106×C₃₇	C₂×C₄	1	1	yes	characteristic
102	C₄⋊C₈×C₃₇	—	2	1	no	—
103	C₄⋊C₈×C₃₇	—	2	1	no	—
104	C₄⋊C₈×C₃₇	—	2	1	no	—
105	C₄⋊C₈×C₃₇	—	2	1	no	—
106	C₄⋊C₈×C₃₇	—	2	1	no	—
107	C₄⋊C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
108	C₄⋊C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
109	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
110	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
111	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
112	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
113	#103×C₃₇	C₂×C₄	1	1	yes	characteristic
114	#103×C₃₇	C₂×C₄	1	1	yes	characteristic
115	#103×C₃₇	C₂×C₄	1	1	yes	characteristic
116	#103×C₃₇	C₂×C₄	1	1	yes	characteristic
117	#102×C₃₇	C₂×C₄	1	1	yes	characteristic
118	#102×C₃₇	C₂×C₄	1	1	yes	characteristic
119	#102×C₃₇	C₂×C₄	1	1	yes	characteristic
120	#102×C₃₇	C₂×C₄	1	1	yes	characteristic
121	C₂²⋊C₈×C₃₇	—	2	1	no	—
122	C₂²⋊C₈×C₃₇	—	2	1	no	—
123	C₂²⋊C₈×C₃₇	—	2	1	no	—
124	C₂²⋊C₈×C₃₇	—	2	1	no	—
125	C₂²⋊C₈×C₃₇	—	2	1	no	—
126	C₂²⋊C₈×C₃₇	—	2	1	no	—
127	C₂²⋊C₈×C₃₇	—	2	1	no	—
128	C₂²⋊C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
129	C₂²⋊C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
130	#97×C₃₇	—	2	1	no	—
131	#97×C₃₇	—	2	1	no	—
132	C₄×C₈×C₃₇	—	2	1	no	—
133	C₄×C₈×C₃₇	—	2	1	no	—
134	C₄×C₈×C₃₇	—	2	1	no	—
135	C₄×C₈×C₃₇	—	2	1	no	—
136	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
137	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
138	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
144	#41×C₃₇	—	2	2	no	—
145	#41×C₃₇	—	2	2	no	—
146	C₂×Q₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×Q₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₃₇	—	2	1	no	—
149	C₂×D₄×C₃₇	—	2	1	no	—
150	C₂×D₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
151	C₂×D₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₃₇	—	2	1	no	—
153	C₂²×C₄×C₃₇	—	2	1	no	—
154	C₂²×C₄×C₃₇	—	2	1	no	—
155	C₂²×C₄×C₃₇	—	2	1	no	—
156	C₂²×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
159	Q₁₆×C₃₇	—	2	2	no	—
160	SD₁₆×C₃₇	—	2	2	no	—
161	SD₁₆×C₃₇	—	2	2	no	—
162	D₈×C₃₇	—	2	2	no	—
163	M₁₆×C₃₇	—	4	2	no	—
164	C₂×C₈×C₃₇	—	2	2	no	—
165	C₂×C₈×C₃₇	—	2	2	no	—
166	C₂×C₈×C₃₇	—	2	1	no	—
167	C₂×C₈×C₃₇	—	2	1	no	—
168	C₂×C₈×C₃₇	—	2	1	no	—
169	C₂×C₈×C₃₇	—	2	1	no	—
170	C₂×C₈×C₃₇	—	2	1	no	—
171	C₂×C₈×C₃₇	—	2	1	no	—
172	C₂×C₈×C₃₇	—	4	2	no	—
173	C₂×C₈×C₃₇	—	4	2	no	—
174	C₂×C₈×C₃₇	—	4	2	no	—
175	C₂×C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
180	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
183	C₄⋊C₄×C₃₇	—	2	1	no	—
184	C₄⋊C₄×C₃₇	—	2	1	no	—
185	C₄⋊C₄×C₃₇	—	2	1	no	—
186	C₄⋊C₄×C₃₇	—	2	1	no	—
187	C₄⋊C₄×C₃₇	—	2	1	no	—
188	C₄⋊C₄×C₃₇	—	2	1	no	—
189	C₄⋊C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
190	C₄⋊C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
191	C₄⋊C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
192	C₄⋊C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
193	C₂²⋊C₄×C₃₇	—	2	1	no	—
194	C₂²⋊C₄×C₃₇	—	2	1	no	—
195	C₂²⋊C₄×C₃₇	—	2	1	no	—
196	C₂²⋊C₄×C₃₇	—	2	1	no	—
197	C₂²⋊C₄×C₃₇	—	2	1	no	—
198	C₂²⋊C₄×C₃₇	—	2	1	no	—
199	C₂²⋊C₄×C₃₇	—	2	1	no	—
200	C₂²⋊C₄×C₃₇	—	2	1	no	—
201	C₄²×C₃₇	—	2	1	no	—
202	C₄²×C₃₇	—	2	1	no	—
203	C₄²×C₃₇	—	2	1	no	—
204	C₄²×C₃₇	—	2	1	no	—
205	C₄²×C₃₇	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₃₇	#41	1	1	yes	characteristic
208	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
209	C₂³×C₃₇	—	2	1	no	—
210	C₂³×C₃₇	—	2	1	no	—
211	C₂³×C₃₇	C₄×D₄	1	1	yes	characteristic
212	Q₈×C₃₇	—	2	1	no	—
213	Q₈×C₃₇	—	2	1	no	—
214	Q₈×C₃₇	—	2	1	no	—
215	Q₈×C₃₇	#131	1	2	yes	—
216	D₄×C₃₇	—	2	4	no	—
217	D₄×C₃₇	—	2	1	no	—
218	D₄×C₃₇	—	2	1	no	—
219	D₄×C₃₇	—	2	1	no	—
220	D₄×C₃₇	—	4	2	no	—
221	D₄×C₃₇	#131	1	2	yes	—
222	C₂×C₄×C₃₇	—	2	4	no	—
223	C₂×C₄×C₃₇	—	2	1	no	—
224	C₂×C₄×C₃₇	—	2	1	no	—
225	C₂×C₄×C₃₇	—	2	1	no	—
226	C₂×C₄×C₃₇	—	2	1	no	—
227	C₂×C₄×C₃₇	—	2	1	no	—
228	C₂×C₄×C₃₇	—	2	1	no	—
229	C₂×C₄×C₃₇	—	2	1	no	—
230	C₂×C₄×C₃₇	—	2	1	no	—
231	C₂×C₄×C₃₇	—	2	1	no	—
232	C₂×C₄×C₃₇	—	2	1	no	—
233	C₂×C₄×C₃₇	—	4	1	no	—
234	C₂×C₄×C₃₇	—	4	2	no	—
235	C₂×C₄×C₃₇	—	4	1	no	—
236	C₂×C₄×C₃₇	—	4	1	no	—
237	C₂×C₄×C₃₇	—	4	1	no	—
238	C₂×C₄×C₃₇	—	4	1	no	—
239	C₂×C₄×C₃₇	C₄×D₄	1	1	yes	characteristic
240	C₂×C₄×C₃₇	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₃₇	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₃₇	C₂³×C₄	1	1	yes	characteristic
243	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
245	C₈×C₃₇	—	2	1	no	—
246	C₈×C₃₇	—	2	1	no	—
247	C₈×C₃₇	—	2	1	no	—
248	C₈×C₃₇	—	2	1	no	—
249	C₈×C₃₇	—	2	1	no	—
250	C₈×C₃₇	—	2	1	no	—
251	C₈×C₃₇	—	4	1	no	—
252	C₈×C₃₇	—	4	1	no	—
253	C₈×C₃₇	—	4	1	no	—
254	C₈×C₃₇	—	4	1	no	—
255	C₈×C₃₇	—	4	1	no	—
256	C₈×C₃₇	—	4	1	no	—
257	C₈×C₃₇	#135	1	2	yes	—
258	C₈×C₃₇	#135	1	2	yes	—
259	#17904	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
260	C₂²×C₃₇	—	2	1	no	—
261	C₂²×C₃₇	—	2	2	no	—
262	C₂²×C₃₇	—	2	1	no	—
263	C₂²×C₃₇	—	2	1	no	—
264	C₂²×C₃₇	—	4	1	no	—
265	C₂²×C₃₇	—	4	1	no	—
266	C₂²×C₃₇	—	4	1	no	—
267	C₂²×C₃₇	—	4	1	no	—
268	C₂²×C₃₇	—	4	1	no	—
269	C₂²×C₃₇	C₂×C₄×D₄	1	1	yes	characteristic
270	C₄×C₃₇	—	2	1	no	—
271	C₄×C₃₇	—	2	2	no	—
272	C₄×C₃₇	—	2	1	no	—
273	C₄×C₃₇	—	2	1	no	—
274	C₄×C₃₇	—	2	1	no	—
275	C₄×C₃₇	—	4	1	no	—
276	C₄×C₃₇	—	4	1	no	—
277	C₄×C₃₇	—	4	1	no	—
278	C₄×C₃₇	—	4	1	no	—
279	C₄×C₃₇	—	4	1	no	—
280	C₄×C₃₇	C₂×#131	1	1	yes	characteristic
281	C₄×C₃₇	C₂×#131	1	1	yes	characteristic
282	C₄×C₃₇	C₂×#135	1	1	yes	characteristic
283	C₄×C₃₇	C₂×#135	1	1	yes	characteristic
284	#3102	C₂×C₃₇	1	1	yes	characteristic
285	#2966	C₂×C₃₇	1	1	yes	characteristic, complemented
286	C₈×#41	C₂×C₃₇	1	1	yes	characteristic, complemented
287	#1584	C₂×C₃₇	1	1	yes	characteristic, complemented
288	#1583	C₂×C₃₇	1	1	yes	characteristic, complemented
289	#1582	C₂×C₃₇	1	1	yes	characteristic, complemented
290	#1581	C₂×C₃₇	1	1	yes	characteristic, complemented
291	C₈×Q₁₆	C₂×C₃₇	1	1	yes	characteristic, complemented
292	C₈×SD₁₆	C₂×C₃₇	1	1	yes	characteristic, complemented
293	C₈×SD₁₆	C₂×C₃₇	1	1	yes	characteristic, complemented
294	C₈×D₈	C₂×C₃₇	1	1	yes	characteristic, complemented
295	#1572	C₂×C₃₇	1	1	yes	characteristic, complemented
296	#1488	C₂×C₃₇	1	1	yes	characteristic, complemented
297	#1482	C₂×C₃₇	1	1	yes	characteristic, complemented
298	#1450	C₂×C₃₇	1	1	yes	characteristic, complemented
299	C₂×C₃₇	—	4	1	no	—
300	C₂×C₃₇	—	4	2	no	—
301	C₂×C₃₇	—	8	1	no	—
302	C₂×C₃₇	#2929	1	1	yes	characteristic
303	C₂×C₃₇	C₄×#135	1	1	yes	characteristic
304	C₂×C₃₇	#2955	1	1	yes	characteristic
305	#529	C₂²×C₃₇	1	1	yes	characteristic
306	C₄×#41	C₂²×C₃₇	1	1	yes	characteristic
307	#485	C₄×C₃₇	1	1	yes	characteristic
308	#482	C₄×C₃₇	1	1	yes	characteristic
309	#479	C₄×C₃₇	1	1	yes	characteristic
310	#478	C₄×C₃₇	1	1	yes	characteristic
311	#464	C₄×C₃₇	1	1	yes	characteristic
312	#463	C₄×C₃₇	1	1	yes	characteristic
313	#452	C₄×C₃₇	1	1	yes	characteristic
314	#449	C₄×C₃₇	1	1	yes	characteristic
315	#446	C₂²×C₃₇	1	1	yes	characteristic
316	C₈×Q₈	C₂²×C₃₇	1	1	yes	characteristic
317	C₈×Q₈	C₂²×C₃₇	1	1	yes	characteristic
318	C₈×Q₈	C₂²×C₃₇	1	1	yes	characteristic
319	C₄×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
320	C₄×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
321	C₄×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
322	C₄×D₈	C₂²×C₃₇	1	1	yes	characteristic
323	#436	C₂²×C₃₇	1	1	yes	characteristic
324	#435	—	2	1	no	—
325	C₈×D₄	—	2	1	no	—
326	C₈×D₄	—	2	1	no	—
327	C₈×D₄	—	2	1	no	—
328	C₈×D₄	C₂²×C₃₇	1	1	yes	characteristic
329	C₈×D₄	C₂²×C₃₇	1	1	yes	characteristic
330	C₈×D₄	C₂²×C₃₇	1	1	yes	characteristic
331	#433	—	2	1	no	—
332	#432	C₂²×C₃₇	1	1	yes	characteristic
333	#431	—	2	1	no	—
334	#431	C₂²×C₃₇	1	1	yes	characteristic
335	#431	C₂²×C₃₇	1	1	yes	characteristic
336	#431	C₂²×C₃₇	1	1	yes	characteristic
337	#405	—	2	1	no	—
338	C₂×C₄×C₈	—	2	1	no	—
339	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
340	#335	C₂²×C₃₇	1	1	yes	characteristic
341	#335	C₂²×C₃₇	1	1	yes	characteristic
342	#334	C₂²×C₃₇	1	1	yes	characteristic
343	#334	C₂²×C₃₇	1	1	yes	characteristic
344	Q₈⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
345	Q₈⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
346	Q₈⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
347	Q₈⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
348	D₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
349	D₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
350	D₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
351	D₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
352	#322	C₂²×C₃₇	1	1	yes	characteristic
353	#322	C₂²×C₃₇	1	1	yes	characteristic
354	C₈²	C₂²×C₃₇	1	1	yes	characteristic
355	C₈²	C₂²×C₃₇	1	1	yes	characteristic
356	C₃₇	#17904	1	1	yes	characteristic, direct product factor, Sylow
357	C₂×#41	C₂×C₄×C₃₇	1	1	yes	characteristic
358	C₂×Q₁₆	C₂×C₄×C₃₇	1	1	yes	characteristic
359	C₂×SD₁₆	C₂×C₄×C₃₇	1	1	yes	characteristic
360	C₂×SD₁₆	C₂×C₄×C₃₇	1	1	yes	characteristic
361	C₂×D₈	C₂×C₄×C₃₇	1	1	yes	characteristic
362	C₂×M₁₆	—	2	1	no	—
363	C₂²×C₈	—	2	1	no	—
364	C₂²×C₈	—	2	1	no	—
365	C₂²×C₈	—	2	1	no	—
366	C₂²×C₈	D₄×C₃₇	1	1	yes	characteristic
367	C₂²×C₈	D₄×C₃₇	1	1	yes	characteristic
368	#126	—	2	1	no	—
369	#125	C₂×C₄×C₃₇	1	1	yes	characteristic
370	#124	C₂×C₄×C₃₇	1	1	yes	characteristic
371	#123	—	2	1	no	—
372	C₂²⋊Q₈	C₂×C₄×C₃₇	1	1	yes	characteristic
373	#121	C₂×C₄×C₃₇	1	1	yes	characteristic
374	C₄×Q₈	C₂×C₄×C₃₇	1	1	yes	characteristic
375	C₄×Q₈	C₂³×C₃₇	1	1	yes	characteristic
376	C₄×Q₈	C₂³×C₃₇	1	1	yes	characteristic
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	C₂×C₄×C₃₇	1	1	yes	characteristic
381	C₄×D₄	C₂³×C₃₇	1	1	yes	characteristic
382	C₄×D₄	C₂³×C₃₇	1	1	yes	characteristic
383	#117	—	2	1	no	—
384	#117	—	2	1	no	—
385	#117	C₂×C₄×C₃₇	1	1	yes	characteristic
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
388	#107	C₂×C₄×C₃₇	1	1	yes	characteristic
389	#107	C₂×C₄×C₃₇	1	1	yes	characteristic
390	#106	C₂×C₄×C₃₇	1	1	yes	characteristic
391	#106	C₂×C₄×C₃₇	1	1	yes	characteristic
392	C₄⋊C₈	—	2	1	no	—
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	—	2	1	no	—
397	C₄⋊C₈	C₂×C₄×C₃₇	1	1	yes	characteristic
398	C₄⋊C₈	C₂×C₄×C₃₇	1	1	yes	characteristic
399	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
400	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
401	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
402	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
403	#103	C₂×C₄×C₃₇	1	1	yes	characteristic
404	#103	C₂×C₄×C₃₇	1	1	yes	characteristic
405	#103	C₂×C₄×C₃₇	1	1	yes	characteristic
406	#103	C₂×C₄×C₃₇	1	1	yes	characteristic
407	#102	C₂×C₄×C₃₇	1	1	yes	characteristic
408	#102	C₂×C₄×C₃₇	1	1	yes	characteristic
409	#102	C₂×C₄×C₃₇	1	1	yes	characteristic
410	#102	C₂×C₄×C₃₇	1	1	yes	characteristic
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	2	1	no	—
414	C₂²⋊C₈	—	2	1	no	—
415	C₂²⋊C₈	—	2	1	no	—
416	C₂²⋊C₈	—	2	1	no	—
417	C₂²⋊C₈	—	2	1	no	—
418	C₂²⋊C₈	C₂×C₄×C₃₇	1	1	yes	characteristic
419	C₂²⋊C₈	C₂×C₄×C₃₇	1	1	yes	characteristic
420	#97	—	2	1	no	—
421	#97	—	2	1	no	—
422	C₄×C₈	—	2	1	no	—
423	C₄×C₈	—	2	1	no	—
424	C₄×C₈	—	2	1	no	—
425	C₄×C₈	—	2	1	no	—
426	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
427	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
428	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
429	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
430	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
431	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
432	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
433	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
434	#41	—	2	2	no	—
435	#41	—	2	2	no	—
436	C₂×Q₈	C₂²×C₄×C₃₇	1	1	yes	characteristic
437	C₂×Q₈	C₂²×C₄×C₃₇	1	1	yes	characteristic
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	C₂²×C₄×C₃₇	1	1	yes	characteristic
441	C₂×D₄	C₂²×C₄×C₃₇	1	1	yes	characteristic
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	C₂²×C₄×C₃₇	1	1	yes	characteristic
447	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
448	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
449	Q₁₆	—	2	2	no	—
450	SD₁₆	—	2	2	no	—
451	SD₁₆	—	2	2	no	—
452	D₈	—	2	2	no	—
453	M₁₆	—	4	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	4	2	no	—
463	C₂×C₈	—	4	2	no	—
464	C₂×C₈	—	4	2	no	—
465	C₂×C₈	C₂²×C₄×C₃₇	1	1	yes	characteristic
466	C₂×C₈	C₂²×C₄×C₃₇	1	1	yes	characteristic
467	C₂×C₈	C₂²×C₄×C₃₇	1	1	yes	characteristic
468	C₂×C₈	C₂²×C₄×C₃₇	1	1	yes	characteristic
469	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
470	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
471	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
472	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	C₂²×C₄×C₃₇	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×C₄×C₃₇	1	1	yes	characteristic
481	C₄⋊C₄	C₂²×C₄×C₃₇	1	1	yes	characteristic
482	C₄⋊C₄	C₂²×C₄×C₃₇	1	1	yes	characteristic
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	1	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	C₂²×C₄×C₃₇	1	1	yes	characteristic
496	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
497	C₄²	#41×C₃₇	1	1	yes	characteristic
498	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	C₄×D₄×C₃₇	1	1	yes	characteristic
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	Q₈	—	2	1	no	—
505	Q₈	#131×C₃₇	1	2	yes	—
506	D₄	—	2	4	no	—
507	D₄	—	2	1	no	—
508	D₄	—	2	1	no	—
509	D₄	—	2	1	no	—
510	D₄	—	4	2	no	—
511	D₄	#131×C₃₇	1	2	yes	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	C₄×D₄×C₃₇	1	1	yes	characteristic
530	C₂×C₄	C₄×D₄×C₃₇	1	1	yes	characteristic
531	C₂×C₄	C₄×D₄×C₃₇	1	1	yes	characteristic
532	C₂×C₄	C₂³×C₄×C₃₇	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
534	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	1	no	—
546	C₈	—	4	1	no	—
547	C₈	#135×C₃₇	1	2	yes	—
548	C₈	#135×C₃₇	1	2	yes	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	C₂×C₄×D₄×C₃₇	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	2	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	C₂×#131×C₃₇	1	1	yes	characteristic
570	C₄	C₂×#131×C₃₇	1	1	yes	characteristic
571	C₄	C₂×#135×C₃₇	1	1	yes	characteristic
572	C₄	C₂×#135×C₃₇	1	1	yes	characteristic
573	C₂	—	4	1	no	—
574	C₂	—	4	2	no	—
575	C₂	—	8	1	no	—
576	C₂	C₃₇×#2929	1	1	yes	characteristic
577	C₂	C₄×#135×C₃₇	1	1	yes	characteristic
578	C₂	C₃₇×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₃₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₇
Frattini, cosocle	C₄²	C₂⁴×C₃₇
socle	C₂²×C₃₇	C₂×C₄×D₄
prime radical	C₃₇×#449	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₃₇ ◁ C₂×C₄×C₈×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₇×#2966	C₂	semidirect
3. C₈×#41×C₃₇	C₂	semidirect
4. C₃₇×#1584	C₂	semidirect
5. C₃₇×#1583	C₂	semidirect
6. C₃₇×#1582	C₂	semidirect
7. C₃₇×#1581	C₂	semidirect
8. C₈×Q₁₆×C₃₇	C₂	semidirect
9. C₈×SD₁₆×C₃₇	C₂	semidirect
10. C₈×SD₁₆×C₃₇	C₂	semidirect
11. C₈×D₈×C₃₇	C₂	semidirect
12. C₃₇×#1572	C₂	semidirect
13. C₃₇×#1488	C₂	semidirect
14. C₃₇×#1482	C₂	semidirect
15. C₃₇×#1450	C₂	semidirect
259. #17904	C₃₇	direct (N × H)
285. #2966	C₂×C₃₇	semidirect
286. C₈×#41	C₂×C₃₇	semidirect
287. #1584	C₂×C₃₇	semidirect
288. #1583	C₂×C₃₇	semidirect
289. #1582	C₂×C₃₇	semidirect
290. #1581	C₂×C₃₇	semidirect
291. C₈×Q₁₆	C₂×C₃₇	semidirect
292. C₈×SD₁₆	C₂×C₃₇	semidirect
293. C₈×SD₁₆	C₂×C₃₇	semidirect
294. C₈×D₈	C₂×C₃₇	semidirect
295. #1572	C₂×C₃₇	semidirect
296. #1488	C₂×C₃₇	semidirect
297. #1482	C₂×C₃₇	semidirect
298. #1450	C₂×C₃₇	semidirect
356. C₃₇	#17904	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₇×#3102	2
C₃₇×#2966	2
C₈×#41×C₃₇	2
C₃₇×#1584	2
C₃₇×#1583	2
C₃₇×#1582	2
C₃₇×#1581	2
C₈×Q₁₆×C₃₇	2
C₈×SD₁₆×C₃₇	2
C₈×D₈×C₃₇	2
C₃₇×#1572	2
C₃₇×#1488	2
C₃₇×#1482	2
C₃₇×#1450	2
#17904	37

Subgroups — C37×#17904 #22639157

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#17904 #22639157