Subgroups — C₃₇×#18938 #22640191

Order 9472.

892 conjugacy classes of subgroups.

The subgroup lattice has 538 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×#3216	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#3207	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#1645	C₂	1	2	yes	maximal, complemented
6	C₃₇×#1640	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1623	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1620	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1551	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1497	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1481	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#563	—	2	2	no	—
13	C₃₇×#559	C₂²	1	2	yes	—
14	Q₈²×C₃₇	C₂²	1	2	yes	—
15	C₃₇×#556	—	2	1	no	—
16	C₃₇×#556	—	2	1	no	—
17	D₄×Q₈×C₃₇	—	2	1	no	—
18	D₄×Q₈×C₃₇	—	2	1	no	—
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×#497	—	2	1	no	—
27	C₃₇×#493	C₂²	1	1	yes	characteristic
28	C₃₇×#492	C₂²	1	1	yes	characteristic
29	C₃₇×#489	—	2	1	no	—
30	C₃₇×#487	C₂²	1	1	yes	characteristic
31	C₃₇×#486	C₂²	1	1	yes	characteristic
32	C₃₇×#476	—	2	1	no	—
33	C₃₇×#475	C₂²	1	2	yes	—
34	C₃₇×#465	—	2	2	no	—
35	C₃₇×#463	—	2	2	no	—
36	C₃₇×#462	C₂²	1	2	yes	—
37	C₃₇×#461	—	2	1	no	—
38	C₃₇×#460	C₂²	1	2	yes	—
39	C₃₇×#460	C₂²	1	2	yes	—
40	C₃₇×#452	—	2	2	no	—
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×#333	C₂²	1	2	yes	—
46	C₃₇×#331	C₂²	1	2	yes	—
47	C₃₇×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₃₇×Q₈⋊C₈	C₂²	1	2	yes	—
49	C₃₇×Q₈⋊C₈	C₂²	1	2	yes	—
50	C₃₇×Q₈⋊C₈	C₂²	1	2	yes	—
51	C₂×#41×C₃₇	—	2	1	no	—
52	C₂×#41×C₃₇	D₄	1	2	yes	—
53	C₂²×Q₈×C₃₇	—	2	2	no	—
54	C₂×Q₁₆×C₃₇	—	2	2	no	—
55	C₂×SD₁₆×C₃₇	—	2	2	no	—
56	C₂×SD₁₆×C₃₇	—	2	2	no	—
57	C₂×SD₁₆×C₃₇	—	2	2	no	—
58	C₂×D₈×C₃₇	—	2	2	no	—
59	C₂²×C₈×C₃₇	—	2	1	no	—
60	C₄⋊Q₈×C₃₇	—	2	4	no	—
61	C₄⋊Q₈×C₃₇	—	2	2	no	—
62	C₄⋊Q₈×C₃₇	—	2	2	no	—
63	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
64	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
65	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
66	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
67	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
68	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
69	#127×C₃₇	C₂³	1	1	yes	characteristic
70	#127×C₃₇	C₂³	1	1	yes	characteristic
71	#126×C₃₇	—	2	4	no	—
72	#126×C₃₇	—	2	4	no	—
73	#125×C₃₇	—	2	1	no	—
74	#125×C₃₇	—	2	1	no	—
75	#124×C₃₇	—	2	4	no	—
76	#124×C₃₇	—	2	2	no	—
77	#124×C₃₇	—	2	2	no	—
78	#124×C₃₇	—	2	1	no	—
79	#124×C₃₇	D₄	1	2	yes	—
80	#123×C₃₇	—	2	4	no	—
81	#123×C₃₇	—	2	4	no	—
82	C₂²⋊Q₈×C₃₇	—	2	2	no	—
83	C₂²⋊Q₈×C₃₇	—	2	2	no	—
84	C₂²⋊Q₈×C₃₇	—	2	4	no	—
85	C₂²⋊Q₈×C₃₇	—	2	4	no	—
86	C₂²⋊Q₈×C₃₇	—	2	1	no	—
87	C₂²⋊Q₈×C₃₇	—	2	1	no	—
88	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
89	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
90	#121×C₃₇	—	2	1	no	—
91	#121×C₃₇	—	2	1	no	—
92	#121×C₃₇	—	2	1	no	—
93	#121×C₃₇	—	2	1	no	—
94	C₄×Q₈×C₃₇	—	2	2	no	—
95	C₄×Q₈×C₃₇	—	2	2	no	—
96	C₄×Q₈×C₃₇	—	2	1	no	—
97	C₄×Q₈×C₃₇	—	2	1	no	—
98	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
99	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
100	C₄×D₄×C₃₇	—	2	2	no	—
101	C₄×D₄×C₃₇	—	2	2	no	—
102	C₄×D₄×C₃₇	—	2	1	no	—
103	C₄×D₄×C₃₇	—	2	1	no	—
104	C₄×D₄×C₃₇	—	2	1	no	—
105	C₄×D₄×C₃₇	—	2	1	no	—
106	#117×C₃₇	—	2	2	no	—
107	#117×C₃₇	—	2	1	no	—
108	#117×C₃₇	—	2	1	no	—
109	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
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	#103×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	2	no	—
127	#41×C₃₇	—	8	2	no	—
128	C₂×Q₈×C₃₇	—	2	4	no	—
129	C₂×Q₈×C₃₇	—	2	1	no	—
130	C₂×Q₈×C₃₇	—	2	1	no	—
131	C₂×Q₈×C₃₇	—	2	1	no	—
132	C₂×Q₈×C₃₇	—	8	4	no	—
133	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
135	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
136	C₂×D₄×C₃₇	—	2	2	no	—
137	C₂×D₄×C₃₇	—	2	1	no	—
138	C₂×D₄×C₃₇	—	2	1	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	—	4	1	no	—
143	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₃₇	—	2	4	no	—
145	C₂²×C₄×C₃₇	—	2	2	no	—
146	C₂²×C₄×C₃₇	—	4	1	no	—
147	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
150	Q₁₆×C₃₇	—	8	2	no	—
151	SD₁₆×C₃₇	—	8	2	no	—
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	1	no	—
167	C₄⋊C₄×C₃₇	—	2	1	no	—
168	C₄⋊C₄×C₃₇	—	2	2	no	—
169	C₄⋊C₄×C₃₇	—	2	2	no	—
170	C₄⋊C₄×C₃₇	—	2	1	no	—
171	C₄⋊C₄×C₃₇	—	2	1	no	—
172	C₄⋊C₄×C₃₇	—	2	2	no	—
173	C₄⋊C₄×C₃₇	—	2	2	no	—
174	C₄⋊C₄×C₃₇	—	2	1	no	—
175	C₄⋊C₄×C₃₇	—	2	1	no	—
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	—	2	2	no	—
200	Q₈×C₃₇	—	2	2	no	—
201	Q₈×C₃₇	—	4	2	no	—
202	Q₈×C₃₇	—	4	2	no	—
203	Q₈×C₃₇	—	4	2	no	—
204	Q₈×C₃₇	—	4	2	no	—
205	Q₈×C₃₇	—	8	4	no	—
206	D₄×C₃₇	—	4	2	no	—
207	D₄×C₃₇	—	4	2	no	—
208	D₄×C₃₇	—	4	2	no	—
209	D₄×C₃₇	—	4	1	no	—
210	D₄×C₃₇	—	4	1	no	—
211	D₄×C₃₇	—	4	2	no	—
212	D₄×C₃₇	—	4	1	no	—
213	D₄×C₃₇	—	4	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	4	no	—
226	C₂×C₄×C₃₇	—	4	1	no	—
227	C₂×C₄×C₃₇	—	8	2	no	—
228	C₂×C₄×C₃₇	—	8	4	no	—
229	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
230	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
231	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
232	C₂×C₄×C₃₇	C₂²×D₄	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	C₈×C₃₇	—	4	1	no	—
236	C₈×C₃₇	—	4	1	no	—
237	C₈×C₃₇	—	4	2	no	—
238	C₈×C₃₇	—	4	2	no	—
239	#18938	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂²×C₃₇	—	2	1	no	—
241	C₂²×C₃₇	—	2	1	no	—
242	C₂²×C₃₇	—	2	1	no	—
243	C₂²×C₃₇	—	4	2	no	—
244	C₂²×C₃₇	—	4	2	no	—
245	C₂²×C₃₇	—	4	2	no	—
246	C₂²×C₃₇	—	8	1	no	—
247	C₂²×C₃₇	—	8	1	no	—
248	C₂²×C₃₇	—	8	1	no	—
249	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
250	C₄×C₃₇	—	2	1	no	—
251	C₄×C₃₇	—	2	1	no	—
252	C₄×C₃₇	—	2	1	no	—
253	C₄×C₃₇	—	2	1	no	—
254	C₄×C₃₇	—	4	2	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	—	8	1	no	—
260	C₄×C₃₇	#577	1	2	yes	—
261	C₄×C₃₇	#577	1	1	yes	characteristic
262	C₄×C₃₇	#578	1	1	yes	characteristic
263	#3550	C₂×C₃₇	1	1	yes	characteristic, complemented
264	#3246	C₂×C₃₇	1	1	yes	characteristic, complemented
265	#3216	C₂×C₃₇	1	1	yes	characteristic, complemented
266	#3207	C₂×C₃₇	1	1	yes	characteristic
267	#1645	C₂×C₃₇	1	2	yes	complemented
268	#1640	C₂×C₃₇	1	2	yes	complemented
269	#1623	C₂×C₃₇	1	2	yes	complemented
270	#1620	C₂×C₃₇	1	2	yes	complemented
271	#1551	C₂×C₃₇	1	1	yes	characteristic, complemented
272	#1497	C₂×C₃₇	1	1	yes	characteristic, complemented
273	#1481	C₂×C₃₇	1	1	yes	characteristic, complemented
274	C₂×C₃₇	—	4	1	no	—
275	C₂×C₃₇	—	8	2	no	—
276	C₂×C₃₇	—	16	1	no	—
277	C₂×C₃₇	#3010	1	1	yes	characteristic
278	C₂×C₃₇	#3013	1	1	yes	characteristic
279	C₂×C₃₇	#3019	1	1	yes	characteristic
280	#563	—	2	2	no	—
281	#559	C₂²×C₃₇	1	2	yes	—
282	Q₈²	C₂²×C₃₇	1	2	yes	—
283	#556	—	2	1	no	—
284	#556	—	2	1	no	—
285	D₄×Q₈	—	2	1	no	—
286	D₄×Q₈	—	2	1	no	—
287	#542	—	2	2	no	—
288	#542	—	2	2	no	—
289	#536	—	2	2	no	—
290	#533	C₂²×C₃₇	1	1	yes	characteristic
291	#533	C₂²×C₃₇	1	1	yes	characteristic
292	#532	C₂²×C₃₇	1	1	yes	characteristic
293	#532	C₂²×C₃₇	1	1	yes	characteristic
294	#497	—	2	1	no	—
295	#493	C₂²×C₃₇	1	1	yes	characteristic
296	#492	C₂²×C₃₇	1	1	yes	characteristic
297	#489	—	2	1	no	—
298	#487	C₂²×C₃₇	1	1	yes	characteristic
299	#486	C₂²×C₃₇	1	1	yes	characteristic
300	#476	—	2	1	no	—
301	#475	C₂²×C₃₇	1	2	yes	—
302	#465	—	2	2	no	—
303	#463	—	2	2	no	—
304	#462	C₂²×C₃₇	1	2	yes	—
305	#461	—	2	1	no	—
306	#460	C₂²×C₃₇	1	2	yes	—
307	#460	C₂²×C₃₇	1	2	yes	—
308	#452	—	2	2	no	—
309	#449	—	2	2	no	—
310	#432	C₂²×C₃₇	1	1	yes	characteristic
311	#431	C₂²×C₃₇	1	1	yes	characteristic
312	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
313	#333	C₂²×C₃₇	1	2	yes	—
314	#331	C₂²×C₃₇	1	2	yes	—
315	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
316	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
317	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
318	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
319	C₃₇	#18938	1	1	yes	characteristic, direct product factor, Sylow
320	C₂×#41	—	2	1	no	—
321	C₂×#41	D₄×C₃₇	1	2	yes	—
322	C₂²×Q₈	—	2	2	no	—
323	C₂×Q₁₆	—	2	2	no	—
324	C₂×SD₁₆	—	2	2	no	—
325	C₂×SD₁₆	—	2	2	no	—
326	C₂×SD₁₆	—	2	2	no	—
327	C₂×D₈	—	2	2	no	—
328	C₂²×C₈	—	2	1	no	—
329	C₄⋊Q₈	—	2	4	no	—
330	C₄⋊Q₈	—	2	2	no	—
331	C₄⋊Q₈	—	2	2	no	—
332	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
333	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
334	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
335	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
336	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
337	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
338	#127	C₂³×C₃₇	1	1	yes	characteristic
339	#127	C₂³×C₃₇	1	1	yes	characteristic
340	#126	—	2	4	no	—
341	#126	—	2	4	no	—
342	#125	—	2	1	no	—
343	#125	—	2	1	no	—
344	#124	—	2	4	no	—
345	#124	—	2	2	no	—
346	#124	—	2	2	no	—
347	#124	—	2	1	no	—
348	#124	D₄×C₃₇	1	2	yes	—
349	#123	—	2	4	no	—
350	#123	—	2	4	no	—
351	C₂²⋊Q₈	—	2	2	no	—
352	C₂²⋊Q₈	—	2	2	no	—
353	C₂²⋊Q₈	—	2	4	no	—
354	C₂²⋊Q₈	—	2	4	no	—
355	C₂²⋊Q₈	—	2	1	no	—
356	C₂²⋊Q₈	—	2	1	no	—
357	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
358	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
359	#121	—	2	1	no	—
360	#121	—	2	1	no	—
361	#121	—	2	1	no	—
362	#121	—	2	1	no	—
363	C₄×Q₈	—	2	2	no	—
364	C₄×Q₈	—	2	2	no	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
368	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
369	C₄×D₄	—	2	2	no	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	—	2	1	no	—
375	#117	—	2	2	no	—
376	#117	—	2	1	no	—
377	#117	—	2	1	no	—
378	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
379	#106	—	2	2	no	—
380	C₄⋊C₈	—	2	1	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
383	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
384	#103	—	2	2	no	—
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	C₂²⋊C₈	—	2	1	no	—
391	C₂²⋊C₈	—	2	1	no	—
392	#97	—	2	1	no	—
393	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
394	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
395	#41	—	8	2	no	—
396	#41	—	8	2	no	—
397	C₂×Q₈	—	2	4	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	8	4	no	—
402	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
403	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
404	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	4	1	no	—
412	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	4	1	no	—
416	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
419	Q₁₆	—	8	2	no	—
420	SD₁₆	—	8	2	no	—
421	SD₁₆	—	8	2	no	—
422	SD₁₆	—	8	2	no	—
423	D₈	—	8	2	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	8	1	no	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	1	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	1	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	2	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
446	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	4	1	no	—
455	C₂²⋊C₄	—	4	1	no	—
456	C₄²	—	2	4	no	—
457	C₄²	—	2	2	no	—
458	C₄²	—	2	2	no	—
459	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
460	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
461	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
462	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
463	C₂³	—	2	2	no	—
464	C₂³	—	4	1	no	—
465	C₂³	#120×C₃₇	1	1	yes	characteristic
466	Q₈	—	2	2	no	—
467	Q₈	—	2	2	no	—
468	Q₈	—	2	2	no	—
469	Q₈	—	2	2	no	—
470	Q₈	—	4	2	no	—
471	Q₈	—	4	2	no	—
472	Q₈	—	4	2	no	—
473	Q₈	—	4	2	no	—
474	Q₈	—	8	4	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	1	no	—
479	D₄	—	4	1	no	—
480	D₄	—	4	2	no	—
481	D₄	—	4	1	no	—
482	D₄	—	4	1	no	—
483	D₄	—	8	2	no	—
484	D₄	—	8	2	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	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	—	4	1	no	—
494	C₂×C₄	—	4	4	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	8	2	no	—
497	C₂×C₄	—	8	4	no	—
498	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
499	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
500	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
502	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
504	C₈	—	4	1	no	—
505	C₈	—	4	1	no	—
506	C₈	—	4	2	no	—
507	C₈	—	4	2	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	8	1	no	—
515	C₂²	—	8	1	no	—
516	C₂²	—	8	1	no	—
517	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	8	1	no	—
528	C₄	C₃₇×#577	1	2	yes	—
529	C₄	C₃₇×#577	1	1	yes	characteristic
530	C₄	C₃₇×#578	1	1	yes	characteristic
531	C₂	—	4	1	no	—
532	C₂	—	8	2	no	—
533	C₂	—	16	1	no	—
534	C₂	C₃₇×#3010	1	1	yes	characteristic
535	C₂	C₃₇×#3013	1	1	yes	characteristic
536	C₂	C₃₇×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
prime radical	C₃₇×#3207	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×#3216	C₂	semidirect
5. C₃₇×#1645	C₂	semidirect
6. C₃₇×#1640	C₂	semidirect
7. C₃₇×#1623	C₂	semidirect
8. C₃₇×#1620	C₂	semidirect
9. C₃₇×#1551	C₂	semidirect
10. C₃₇×#1497	C₂	semidirect
11. C₃₇×#1481	C₂	semidirect
239. #18938	C₃₇	direct (N × H)
263. #3550	C₂×C₃₇	semidirect
264. #3246	C₂×C₃₇	semidirect
265. #3216	C₂×C₃₇	semidirect
267. #1645	C₂×C₃₇	semidirect
268. #1640	C₂×C₃₇	semidirect
269. #1623	C₂×C₃₇	semidirect
270. #1620	C₂×C₃₇	semidirect
271. #1551	C₂×C₃₇	semidirect
272. #1497	C₂×C₃₇	semidirect
273. #1481	C₂×C₃₇	semidirect
319. C₃₇	#18938	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×#3216	2
C₃₇×#3207	2
C₃₇×#1645	2
C₃₇×#1640	2
C₃₇×#1623	2
C₃₇×#1620	2
C₃₇×#1551	2
C₃₇×#1497	2
C₃₇×#1481	2
#18938	37

Subgroups — C37×#18938 #22640191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18938 #22640191