Subgroups — C₃₇×#18952 #22640205

Order 9472.

880 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3246	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3228	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#3214	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#1651	C₂	1	2	yes	maximal, complemented
6	C₃₇×#1650	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1628	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1627	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1552	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1497	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1480	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#563	—	2	2	no	—
13	C₃₇×#559	—	2	1	no	—
14	Q₈²×C₃₇	—	2	1	no	—
15	C₃₇×#556	—	2	1	no	—
16	C₃₇×#556	C₂²	1	2	yes	—
17	D₄×Q₈×C₃₇	—	2	1	no	—
18	D₄×Q₈×C₃₇	C₂²	1	2	yes	—
19	C₃₇×#542	—	2	2	no	—
20	C₃₇×#542	—	2	2	no	—
21	C₃₇×#536	—	2	2	no	—
22	C₃₇×#533	C₂²	1	1	yes	characteristic
23	C₃₇×#533	C₂²	1	1	yes	characteristic
24	C₃₇×#532	C₂²	1	1	yes	characteristic
25	C₃₇×#532	C₂²	1	1	yes	characteristic
26	C₃₇×#500	C₂²	1	1	yes	characteristic
27	C₃₇×#498	C₂²	1	1	yes	characteristic
28	C₃₇×#496	—	2	1	no	—
29	C₃₇×#489	—	2	1	no	—
30	C₃₇×#486	C₂²	1	1	yes	characteristic
31	C₃₇×#486	C₂²	1	1	yes	characteristic
32	C₃₇×#482	—	2	2	no	—
33	C₃₇×#478	—	2	2	no	—
34	C₃₇×#476	—	2	1	no	—
35	C₃₇×#475	C₂²	1	2	yes	—
36	C₃₇×#465	—	2	2	no	—
37	C₃₇×#461	—	2	1	no	—
38	C₃₇×#461	C₂²	1	2	yes	—
39	C₃₇×#460	C₂²	1	2	yes	—
40	C₃₇×#459	C₂²	1	2	yes	—
41	C₃₇×#449	—	2	2	no	—
42	C₃₇×#432	C₂²	1	1	yes	characteristic
43	C₃₇×#431	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
45	C₃₇×#332	C₂²	1	2	yes	—
46	C₃₇×#332	C₂²	1	2	yes	—
47	C₃₇×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₃₇×Q₈⋊C₈	C₂²	1	2	yes	—
49	C₃₇×D₄⋊C₈	C₂²	1	2	yes	—
50	C₃₇×D₄⋊C₈	C₂²	1	2	yes	—
51	C₂×#41×C₃₇	—	2	1	no	—
52	C₂×#41×C₃₇	—	2	1	no	—
53	C₂²×Q₈×C₃₇	—	2	2	no	—
54	C₂×SD₁₆×C₃₇	—	2	2	no	—
55	C₂×SD₁₆×C₃₇	—	2	2	no	—
56	C₂×D₈×C₃₇	—	2	2	no	—
57	C₂²×C₈×C₃₇	—	2	1	no	—
58	C₄⋊Q₈×C₃₇	—	2	4	no	—
59	C₄⋊Q₈×C₃₇	—	2	2	no	—
60	C₄⋊Q₈×C₃₇	—	2	2	no	—
61	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
62	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
63	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
64	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
65	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
66	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
67	#127×C₃₇	D₄	1	1	yes	characteristic
68	#127×C₃₇	C₂³	1	1	yes	characteristic
69	#126×C₃₇	—	2	4	no	—
70	#126×C₃₇	—	2	4	no	—
71	#125×C₃₇	—	2	1	no	—
72	#125×C₃₇	D₄	1	2	yes	—
73	#124×C₃₇	—	2	4	no	—
74	#124×C₃₇	—	2	2	no	—
75	#124×C₃₇	—	2	2	no	—
76	#124×C₃₇	—	2	1	no	—
77	#124×C₃₇	—	2	1	no	—
78	#123×C₃₇	—	2	4	no	—
79	#123×C₃₇	—	2	4	no	—
80	C₂²⋊Q₈×C₃₇	—	2	4	no	—
81	C₂²⋊Q₈×C₃₇	—	2	2	no	—
82	C₂²⋊Q₈×C₃₇	—	2	1	no	—
83	C₂²⋊Q₈×C₃₇	—	2	1	no	—
84	C₂²⋊Q₈×C₃₇	—	2	1	no	—
85	C₂²⋊Q₈×C₃₇	—	2	2	no	—
86	C₂²⋊Q₈×C₃₇	—	2	4	no	—
87	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
88	#121×C₃₇	—	2	1	no	—
89	#121×C₃₇	—	2	1	no	—
90	#121×C₃₇	—	2	1	no	—
91	#121×C₃₇	D₄	1	2	yes	—
92	C₄×Q₈×C₃₇	—	2	2	no	—
93	C₄×Q₈×C₃₇	—	2	2	no	—
94	C₄×Q₈×C₃₇	—	2	1	no	—
95	C₄×Q₈×C₃₇	—	2	1	no	—
96	C₄×Q₈×C₃₇	—	2	1	no	—
97	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
98	C₄×D₄×C₃₇	—	2	2	no	—
99	C₄×D₄×C₃₇	—	2	2	no	—
100	C₄×D₄×C₃₇	—	2	1	no	—
101	C₄×D₄×C₃₇	—	2	1	no	—
102	C₄×D₄×C₃₇	—	2	1	no	—
103	C₄×D₄×C₃₇	C₂³	1	2	yes	—
104	#117×C₃₇	—	2	1	no	—
105	#117×C₃₇	—	2	2	no	—
106	#117×C₃₇	D₄	1	2	yes	—
107	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
108	#107×C₃₇	—	2	2	no	—
109	#106×C₃₇	—	2	2	no	—
110	#106×C₃₇	—	2	2	no	—
111	C₄⋊C₈×C₃₇	—	2	1	no	—
112	C₄⋊C₈×C₃₇	—	2	1	no	—
113	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
114	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
115	#103×C₃₇	—	2	2	no	—
116	#103×C₃₇	—	2	2	no	—
117	#102×C₃₇	—	2	2	no	—
118	#102×C₃₇	—	2	2	no	—
119	#102×C₃₇	—	2	2	no	—
120	#102×C₃₇	—	2	2	no	—
121	C₂²⋊C₈×C₃₇	—	2	1	no	—
122	C₂²⋊C₈×C₃₇	—	2	1	no	—
123	#97×C₃₇	—	2	1	no	—
124	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
126	#41×C₃₇	—	8	1	no	—
127	#41×C₃₇	—	8	1	no	—
128	#41×C₃₇	—	8	2	no	—
129	C₂×Q₈×C₃₇	—	2	4	no	—
130	C₂×Q₈×C₃₇	—	2	1	no	—
131	C₂×Q₈×C₃₇	—	2	1	no	—
132	C₂×Q₈×C₃₇	—	2	1	no	—
133	C₂×Q₈×C₃₇	—	2	1	no	—
134	C₂×Q₈×C₃₇	—	2	1	no	—
135	C₂×Q₈×C₃₇	—	8	2	no	—
136	C₂×Q₈×C₃₇	—	8	2	no	—
137	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
138	C₂×D₄×C₃₇	—	2	2	no	—
139	C₂×D₄×C₃₇	—	2	1	no	—
140	C₂×D₄×C₃₇	—	2	1	no	—
141	C₂×D₄×C₃₇	—	2	1	no	—
142	C₂×D₄×C₃₇	—	2	1	no	—
143	C₂×D₄×C₃₇	—	2	1	no	—
144	C₂×D₄×C₃₇	—	4	1	no	—
145	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₃₇	—	2	4	no	—
147	C₂²×C₄×C₃₇	—	2	2	no	—
148	C₂²×C₄×C₃₇	—	4	1	no	—
149	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
152	SD₁₆×C₃₇	—	8	2	no	—
153	SD₁₆×C₃₇	—	8	2	no	—
154	D₈×C₃₇	—	8	2	no	—
155	C₂×C₈×C₃₇	—	2	1	no	—
156	C₂×C₈×C₃₇	—	2	1	no	—
157	C₂×C₈×C₃₇	—	2	2	no	—
158	C₂×C₈×C₃₇	—	2	2	no	—
159	C₂×C₈×C₃₇	—	8	1	no	—
160	C₄⋊C₄×C₃₇	—	2	4	no	—
161	C₄⋊C₄×C₃₇	—	2	4	no	—
162	C₄⋊C₄×C₃₇	—	2	1	no	—
163	C₄⋊C₄×C₃₇	—	2	1	no	—
164	C₄⋊C₄×C₃₇	—	2	1	no	—
165	C₄⋊C₄×C₃₇	—	2	1	no	—
166	C₄⋊C₄×C₃₇	—	2	2	no	—
167	C₄⋊C₄×C₃₇	—	2	2	no	—
168	C₄⋊C₄×C₃₇	—	2	2	no	—
169	C₄⋊C₄×C₃₇	—	2	1	no	—
170	C₄⋊C₄×C₃₇	—	2	1	no	—
171	C₄⋊C₄×C₃₇	—	2	2	no	—
172	C₄⋊C₄×C₃₇	—	2	1	no	—
173	C₄⋊C₄×C₃₇	—	2	1	no	—
174	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
175	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
176	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
177	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
178	C₂²⋊C₄×C₃₇	—	2	4	no	—
179	C₂²⋊C₄×C₃₇	—	2	4	no	—
180	C₂²⋊C₄×C₃₇	—	2	4	no	—
181	C₂²⋊C₄×C₃₇	—	2	2	no	—
182	C₂²⋊C₄×C₃₇	—	2	2	no	—
183	C₂²⋊C₄×C₃₇	—	2	2	no	—
184	C₂²⋊C₄×C₃₇	—	2	2	no	—
185	C₂²⋊C₄×C₃₇	—	4	1	no	—
186	C₂²⋊C₄×C₃₇	—	4	1	no	—
187	C₄²×C₃₇	—	2	4	no	—
188	C₄²×C₃₇	—	2	2	no	—
189	C₄²×C₃₇	—	2	2	no	—
190	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
194	C₂³×C₃₇	—	2	2	no	—
195	C₂³×C₃₇	—	4	1	no	—
196	C₂³×C₃₇	#120	1	1	yes	characteristic
197	Q₈×C₃₇	—	2	2	no	—
198	Q₈×C₃₇	—	2	2	no	—
199	Q₈×C₃₇	—	4	2	no	—
200	Q₈×C₃₇	—	4	1	no	—
201	Q₈×C₃₇	—	4	2	no	—
202	Q₈×C₃₇	—	4	1	no	—
203	Q₈×C₃₇	—	4	2	no	—
204	Q₈×C₃₇	—	8	1	no	—
205	Q₈×C₃₇	—	8	4	no	—
206	D₄×C₃₇	—	2	2	no	—
207	D₄×C₃₇	—	2	2	no	—
208	D₄×C₃₇	—	4	2	no	—
209	D₄×C₃₇	—	4	2	no	—
210	D₄×C₃₇	—	4	1	no	—
211	D₄×C₃₇	—	4	2	no	—
212	D₄×C₃₇	—	4	1	no	—
213	D₄×C₃₇	—	8	1	no	—
214	D₄×C₃₇	—	8	2	no	—
215	D₄×C₃₇	—	8	2	no	—
216	C₂×C₄×C₃₇	—	2	1	no	—
217	C₂×C₄×C₃₇	—	2	2	no	—
218	C₂×C₄×C₃₇	—	2	1	no	—
219	C₂×C₄×C₃₇	—	2	2	no	—
220	C₂×C₄×C₃₇	—	2	2	no	—
221	C₂×C₄×C₃₇	—	2	2	no	—
222	C₂×C₄×C₃₇	—	2	2	no	—
223	C₂×C₄×C₃₇	—	2	2	no	—
224	C₂×C₄×C₃₇	—	4	1	no	—
225	C₂×C₄×C₃₇	—	4	2	no	—
226	C₂×C₄×C₃₇	—	4	2	no	—
227	C₂×C₄×C₃₇	—	4	1	no	—
228	C₂×C₄×C₃₇	—	8	2	no	—
229	C₂×C₄×C₃₇	—	8	4	no	—
230	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
231	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
232	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
233	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
236	C₈×C₃₇	—	4	1	no	—
237	C₈×C₃₇	—	4	1	no	—
238	C₈×C₃₇	—	4	2	no	—
239	C₈×C₃₇	—	4	2	no	—
240	#18952	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₂²×C₃₇	—	2	1	no	—
242	C₂²×C₃₇	—	2	1	no	—
243	C₂²×C₃₇	—	2	1	no	—
244	C₂²×C₃₇	—	4	2	no	—
245	C₂²×C₃₇	—	4	2	no	—
246	C₂²×C₃₇	—	4	2	no	—
247	C₂²×C₃₇	—	8	1	no	—
248	C₂²×C₃₇	—	8	1	no	—
249	C₂²×C₃₇	—	8	1	no	—
250	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
251	C₄×C₃₇	—	2	1	no	—
252	C₄×C₃₇	—	2	1	no	—
253	C₄×C₃₇	—	2	1	no	—
254	C₄×C₃₇	—	2	1	no	—
255	C₄×C₃₇	—	4	2	no	—
256	C₄×C₃₇	—	4	2	no	—
257	C₄×C₃₇	—	4	2	no	—
258	C₄×C₃₇	—	4	2	no	—
259	C₄×C₃₇	—	4	2	no	—
260	C₄×C₃₇	—	8	1	no	—
261	C₄×C₃₇	#576	1	1	yes	characteristic
262	C₄×C₃₇	#577	1	2	yes	—
263	C₄×C₃₇	#577	1	1	yes	characteristic
264	#3550	C₂×C₃₇	1	1	yes	characteristic, complemented
265	#3246	C₂×C₃₇	1	1	yes	characteristic, complemented
266	#3228	C₂×C₃₇	1	1	yes	characteristic, complemented
267	#3214	C₂×C₃₇	1	1	yes	characteristic
268	#1651	C₂×C₃₇	1	2	yes	complemented
269	#1650	C₂×C₃₇	1	2	yes	complemented
270	#1628	C₂×C₃₇	1	2	yes	complemented
271	#1627	C₂×C₃₇	1	2	yes	complemented
272	#1552	C₂×C₃₇	1	1	yes	characteristic, complemented
273	#1497	C₂×C₃₇	1	1	yes	characteristic, complemented
274	#1480	C₂×C₃₇	1	1	yes	characteristic, complemented
275	C₂×C₃₇	—	4	1	no	—
276	C₂×C₃₇	—	8	2	no	—
277	C₂×C₃₇	—	16	1	no	—
278	C₂×C₃₇	#3010	1	1	yes	characteristic
279	C₂×C₃₇	#3012	1	1	yes	characteristic
280	C₂×C₃₇	#3020	1	1	yes	characteristic
281	#563	—	2	2	no	—
282	#559	—	2	1	no	—
283	Q₈²	—	2	1	no	—
284	#556	—	2	1	no	—
285	#556	C₂²×C₃₇	1	2	yes	—
286	D₄×Q₈	—	2	1	no	—
287	D₄×Q₈	C₂²×C₃₇	1	2	yes	—
288	#542	—	2	2	no	—
289	#542	—	2	2	no	—
290	#536	—	2	2	no	—
291	#533	C₂²×C₃₇	1	1	yes	characteristic
292	#533	C₂²×C₃₇	1	1	yes	characteristic
293	#532	C₂²×C₃₇	1	1	yes	characteristic
294	#532	C₂²×C₃₇	1	1	yes	characteristic
295	#500	C₂²×C₃₇	1	1	yes	characteristic
296	#498	C₂²×C₃₇	1	1	yes	characteristic
297	#496	—	2	1	no	—
298	#489	—	2	1	no	—
299	#486	C₂²×C₃₇	1	1	yes	characteristic
300	#486	C₂²×C₃₇	1	1	yes	characteristic
301	#482	—	2	2	no	—
302	#478	—	2	2	no	—
303	#476	—	2	1	no	—
304	#475	C₂²×C₃₇	1	2	yes	—
305	#465	—	2	2	no	—
306	#461	—	2	1	no	—
307	#461	C₂²×C₃₇	1	2	yes	—
308	#460	C₂²×C₃₇	1	2	yes	—
309	#459	C₂²×C₃₇	1	2	yes	—
310	#449	—	2	2	no	—
311	#432	C₂²×C₃₇	1	1	yes	characteristic
312	#431	C₂²×C₃₇	1	1	yes	characteristic
313	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
314	#332	C₂²×C₃₇	1	2	yes	—
315	#332	C₂²×C₃₇	1	2	yes	—
316	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
317	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
318	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
319	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
320	C₃₇	#18952	1	1	yes	characteristic, direct product factor, Sylow
321	C₂×#41	—	2	1	no	—
322	C₂×#41	—	2	1	no	—
323	C₂²×Q₈	—	2	2	no	—
324	C₂×SD₁₆	—	2	2	no	—
325	C₂×SD₁₆	—	2	2	no	—
326	C₂×D₈	—	2	2	no	—
327	C₂²×C₈	—	2	1	no	—
328	C₄⋊Q₈	—	2	4	no	—
329	C₄⋊Q₈	—	2	2	no	—
330	C₄⋊Q₈	—	2	2	no	—
331	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
332	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
333	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
334	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
335	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
336	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
337	#127	D₄×C₃₇	1	1	yes	characteristic
338	#127	C₂³×C₃₇	1	1	yes	characteristic
339	#126	—	2	4	no	—
340	#126	—	2	4	no	—
341	#125	—	2	1	no	—
342	#125	D₄×C₃₇	1	2	yes	—
343	#124	—	2	4	no	—
344	#124	—	2	2	no	—
345	#124	—	2	2	no	—
346	#124	—	2	1	no	—
347	#124	—	2	1	no	—
348	#123	—	2	4	no	—
349	#123	—	2	4	no	—
350	C₂²⋊Q₈	—	2	4	no	—
351	C₂²⋊Q₈	—	2	2	no	—
352	C₂²⋊Q₈	—	2	1	no	—
353	C₂²⋊Q₈	—	2	1	no	—
354	C₂²⋊Q₈	—	2	1	no	—
355	C₂²⋊Q₈	—	2	2	no	—
356	C₂²⋊Q₈	—	2	4	no	—
357	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
358	#121	—	2	1	no	—
359	#121	—	2	1	no	—
360	#121	—	2	1	no	—
361	#121	D₄×C₃₇	1	2	yes	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	—	2	2	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	—	2	2	no	—
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	C₂³×C₃₇	1	2	yes	—
374	#117	—	2	1	no	—
375	#117	—	2	2	no	—
376	#117	D₄×C₃₇	1	2	yes	—
377	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
378	#107	—	2	2	no	—
379	#106	—	2	2	no	—
380	#106	—	2	2	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	2	1	no	—
383	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
384	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
385	#103	—	2	2	no	—
386	#103	—	2	2	no	—
387	#102	—	2	2	no	—
388	#102	—	2	2	no	—
389	#102	—	2	2	no	—
390	#102	—	2	2	no	—
391	C₂²⋊C₈	—	2	1	no	—
392	C₂²⋊C₈	—	2	1	no	—
393	#97	—	2	1	no	—
394	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
395	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
396	#41	—	8	1	no	—
397	#41	—	8	1	no	—
398	#41	—	8	2	no	—
399	C₂×Q₈	—	2	4	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	2	1	no	—
404	C₂×Q₈	—	2	1	no	—
405	C₂×Q₈	—	8	2	no	—
406	C₂×Q₈	—	8	2	no	—
407	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	4	1	no	—
415	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	4	1	no	—
419	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
422	SD₁₆	—	8	2	no	—
423	SD₁₆	—	8	2	no	—
424	D₈	—	8	2	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	8	1	no	—
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	4	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
445	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
446	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
447	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	4	1	no	—
456	C₂²⋊C₄	—	4	1	no	—
457	C₄²	—	2	4	no	—
458	C₄²	—	2	2	no	—
459	C₄²	—	2	2	no	—
460	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
461	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
462	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
463	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
464	C₂³	—	2	2	no	—
465	C₂³	—	4	1	no	—
466	C₂³	#120×C₃₇	1	1	yes	characteristic
467	Q₈	—	2	2	no	—
468	Q₈	—	2	2	no	—
469	Q₈	—	4	2	no	—
470	Q₈	—	4	1	no	—
471	Q₈	—	4	1	no	—
472	Q₈	—	4	2	no	—
473	Q₈	—	4	2	no	—
474	Q₈	—	8	1	no	—
475	Q₈	—	8	4	no	—
476	D₄	—	2	2	no	—
477	D₄	—	2	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	4	2	no	—
480	D₄	—	4	1	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	1	no	—
483	D₄	—	8	1	no	—
484	D₄	—	8	2	no	—
485	D₄	—	8	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	8	2	no	—
499	C₂×C₄	—	8	4	no	—
500	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
501	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
502	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
504	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
505	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
506	C₈	—	4	1	no	—
507	C₈	—	4	1	no	—
508	C₈	—	4	2	no	—
509	C₈	—	4	2	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	8	1	no	—
517	C₂²	—	8	1	no	—
518	C₂²	—	8	1	no	—
519	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	2	no	—
529	C₄	—	8	1	no	—
530	C₄	C₃₇×#576	1	1	yes	characteristic
531	C₄	C₃₇×#577	1	2	yes	—
532	C₄	C₃₇×#577	1	1	yes	characteristic
533	C₂	—	4	1	no	—
534	C₂	—	8	2	no	—
535	C₂	—	16	1	no	—
536	C₂	C₃₇×#3010	1	1	yes	characteristic
537	C₂	C₃₇×#3012	1	1	yes	characteristic
538	C₂	C₃₇×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
prime radical	C₃₇×#3214	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3550	C₂	semidirect
2. C₃₇×#3246	C₂	semidirect
3. C₃₇×#3228	C₂	semidirect
5. C₃₇×#1651	C₂	semidirect
6. C₃₇×#1650	C₂	semidirect
7. C₃₇×#1628	C₂	semidirect
8. C₃₇×#1627	C₂	semidirect
9. C₃₇×#1552	C₂	semidirect
10. C₃₇×#1497	C₂	semidirect
11. C₃₇×#1480	C₂	semidirect
240. #18952	C₃₇	direct (N × H)
264. #3550	C₂×C₃₇	semidirect
265. #3246	C₂×C₃₇	semidirect
266. #3228	C₂×C₃₇	semidirect
268. #1651	C₂×C₃₇	semidirect
269. #1650	C₂×C₃₇	semidirect
270. #1628	C₂×C₃₇	semidirect
271. #1627	C₂×C₃₇	semidirect
272. #1552	C₂×C₃₇	semidirect
273. #1497	C₂×C₃₇	semidirect
274. #1480	C₂×C₃₇	semidirect
320. C₃₇	#18952	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×#3550	2
C₃₇×#3246	2
C₃₇×#3228	2
C₃₇×#3214	2
C₃₇×#1651	2
C₃₇×#1650	2
C₃₇×#1628	2
C₃₇×#1627	2
C₃₇×#1552	2
C₃₇×#1497	2
C₃₇×#1480	2
#18952	37

Subgroups — C37×#18952 #22640205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18952 #22640205