Subgroups — C₃₇×#18702 #22639955

Order 9472.

868 conjugacy classes of subgroups.

The subgroup lattice has 534 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
2	C₃₇×#3255	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3254	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#3160	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#1652	C₂	1	2	yes	maximal, complemented
6	C₃₇×#1651	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1650	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1649	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1561	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1493	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1492	C₂	1	1	yes	maximal, characteristic
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×#533	C₂²	1	1	yes	characteristic
25	C₃₇×#532	C₂²	1	1	yes	characteristic
26	C₃₇×#500	C₂²	1	1	yes	characteristic
27	C₃₇×#500	C₂²	1	1	yes	characteristic
28	C₃₇×#499	—	2	2	no	—
29	C₃₇×#498	C₂²	1	1	yes	characteristic
30	C₃₇×#498	C₂²	1	1	yes	characteristic
31	C₃₇×#477	—	2	1	no	—
32	C₃₇×#475	—	2	1	no	—
33	C₃₇×#475	C₂²	1	2	yes	—
34	C₃₇×#474	C₂²	1	2	yes	—
35	C₃₇×#470	—	2	2	no	—
36	C₃₇×#468	—	2	2	no	—
37	C₃₇×#462	—	2	1	no	—
38	C₃₇×#462	C₂²	1	2	yes	—
39	C₃₇×#461	C₂²	1	2	yes	—
40	C₃₇×#460	—	2	1	no	—
41	C₃₇×#427	—	2	2	no	—
42	C₃₇×#423	C₂²	1	1	yes	characteristic
43	C₃₇×#423	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	C₂²×Q₈×C₃₇	—	2	2	no	—
53	C₂×Q₁₆×C₃₇	—	2	2	no	—
54	C₂×SD₁₆×C₃₇	—	2	2	no	—
55	C₂×M₁₆×C₃₇	—	2	1	no	—
56	C₂×M₁₆×C₃₇	—	2	1	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	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
68	#127×C₃₇	D₄	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	—	2	1	no	—
73	#125×C₃₇	D₄	1	2	yes	—
74	#124×C₃₇	—	2	4	no	—
75	#124×C₃₇	—	2	2	no	—
76	#124×C₃₇	—	2	2	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	—	2	1	no	—
88	C₂²⋊Q₈×C₃₇	—	2	1	no	—
89	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
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	—	2	1	no	—
98	C₄×Q₈×C₃₇	—	2	1	no	—
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	C₂³	1	2	yes	—
104	#117×C₃₇	—	2	1	no	—
105	#117×C₃₇	—	2	2	no	—
106	#117×C₃₇	—	2	1	no	—
107	#117×C₃₇	D₄	1	2	yes	—
108	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
109	#107×C₃₇	—	2	2	no	—
110	#107×C₃₇	—	2	2	no	—
111	#107×C₃₇	—	2	2	no	—
112	#106×C₃₇	—	2	2	no	—
113	#106×C₃₇	—	2	2	no	—
114	#106×C₃₇	—	2	2	no	—
115	C₄⋊C₈×C₃₇	—	2	1	no	—
116	C₄⋊C₈×C₃₇	—	2	1	no	—
117	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
118	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
119	#103×C₃₇	—	2	2	no	—
120	#103×C₃₇	—	2	2	no	—
121	#103×C₃₇	—	2	2	no	—
122	#102×C₃₇	—	2	2	no	—
123	C₄×C₈×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	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	—	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	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₃₇	—	2	4	no	—
143	C₂²×C₄×C₃₇	—	2	2	no	—
144	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
147	Q₁₆×C₃₇	—	8	2	no	—
148	SD₁₆×C₃₇	—	8	2	no	—
149	M₁₆×C₃₇	—	8	1	no	—
150	M₁₆×C₃₇	—	8	1	no	—
151	C₂×C₈×C₃₇	—	2	4	no	—
152	C₂×C₈×C₃₇	—	2	1	no	—
153	C₂×C₈×C₃₇	—	2	1	no	—
154	C₂×C₈×C₃₇	—	2	2	no	—
155	C₂×C₈×C₃₇	—	2	2	no	—
156	C₄⋊C₄×C₃₇	—	2	4	no	—
157	C₄⋊C₄×C₃₇	—	2	4	no	—
158	C₄⋊C₄×C₃₇	—	2	1	no	—
159	C₄⋊C₄×C₃₇	—	2	1	no	—
160	C₄⋊C₄×C₃₇	—	2	1	no	—
161	C₄⋊C₄×C₃₇	—	2	1	no	—
162	C₄⋊C₄×C₃₇	—	2	2	no	—
163	C₄⋊C₄×C₃₇	—	2	2	no	—
164	C₄⋊C₄×C₃₇	—	2	2	no	—
165	C₄⋊C₄×C₃₇	—	2	1	no	—
166	C₄⋊C₄×C₃₇	—	2	1	no	—
167	C₄⋊C₄×C₃₇	—	2	2	no	—
168	C₄⋊C₄×C₃₇	—	2	1	no	—
169	C₄⋊C₄×C₃₇	—	2	1	no	—
170	C₄⋊C₄×C₃₇	—	2	1	no	—
171	C₄⋊C₄×C₃₇	—	2	1	no	—
172	C₄⋊C₄×C₃₇	—	4	1	no	—
173	C₄⋊C₄×C₃₇	—	4	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	C₄²×C₃₇	—	2	4	no	—
187	C₄²×C₃₇	—	2	2	no	—
188	C₄²×C₃₇	—	2	2	no	—
189	C₄²×C₃₇	—	4	1	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	#120	1	1	yes	characteristic
196	Q₈×C₃₇	—	2	2	no	—
197	Q₈×C₃₇	—	2	2	no	—
198	Q₈×C₃₇	—	4	1	no	—
199	Q₈×C₃₇	—	4	1	no	—
200	Q₈×C₃₇	—	4	1	no	—
201	Q₈×C₃₇	—	4	1	no	—
202	Q₈×C₃₇	—	4	2	no	—
203	Q₈×C₃₇	—	4	1	no	—
204	Q₈×C₃₇	—	4	1	no	—
205	Q₈×C₃₇	—	4	1	no	—
206	Q₈×C₃₇	—	4	1	no	—
207	Q₈×C₃₇	—	8	1	no	—
208	Q₈×C₃₇	—	8	4	no	—
209	D₄×C₃₇	—	2	2	no	—
210	D₄×C₃₇	—	2	2	no	—
211	D₄×C₃₇	—	4	2	no	—
212	D₄×C₃₇	—	8	1	no	—
213	D₄×C₃₇	—	8	2	no	—
214	C₂×C₄×C₃₇	—	2	1	no	—
215	C₂×C₄×C₃₇	—	2	1	no	—
216	C₂×C₄×C₃₇	—	2	1	no	—
217	C₂×C₄×C₃₇	—	2	1	no	—
218	C₂×C₄×C₃₇	—	2	2	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	2	no	—
225	C₂×C₄×C₃₇	—	4	2	no	—
226	C₂×C₄×C₃₇	—	4	1	no	—
227	C₂×C₄×C₃₇	—	4	1	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	—	2	2	no	—
236	C₈×C₃₇	—	2	2	no	—
237	C₈×C₃₇	—	4	2	no	—
238	C₈×C₃₇	—	4	2	no	—
239	#18702	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	C₂×#120	1	1	yes	characteristic
247	C₄×C₃₇	—	2	1	no	—
248	C₄×C₃₇	—	2	1	no	—
249	C₄×C₃₇	—	2	1	no	—
250	C₄×C₃₇	—	4	2	no	—
251	C₄×C₃₇	—	4	2	no	—
252	C₄×C₃₇	—	4	2	no	—
253	C₄×C₃₇	—	4	2	no	—
254	C₄×C₃₇	—	4	2	no	—
255	C₄×C₃₇	—	8	1	no	—
256	C₄×C₃₇	—	8	1	no	—
257	C₄×C₃₇	#456	1	2	yes	—
258	C₄×C₃₇	#576	1	1	yes	characteristic
259	C₄×C₃₇	#577	1	1	yes	characteristic
260	C₄×C₃₇	#577	1	1	yes	characteristic
261	C₄×C₃₇	#578	1	1	yes	characteristic
262	#3550	C₂×C₃₇	1	1	yes	characteristic
263	#3255	C₂×C₃₇	1	1	yes	characteristic, complemented
264	#3254	C₂×C₃₇	1	1	yes	characteristic
265	#3160	C₂×C₃₇	1	1	yes	characteristic, complemented
266	#1652	C₂×C₃₇	1	2	yes	complemented
267	#1651	C₂×C₃₇	1	2	yes	complemented
268	#1650	C₂×C₃₇	1	2	yes	complemented
269	#1649	C₂×C₃₇	1	2	yes	complemented
270	#1561	C₂×C₃₇	1	1	yes	characteristic, complemented
271	#1493	C₂×C₃₇	1	1	yes	characteristic, complemented
272	#1492	C₂×C₃₇	1	1	yes	characteristic
273	C₂×C₃₇	—	4	1	no	—
274	C₂×C₃₇	—	8	2	no	—
275	C₂×C₃₇	#3012	1	1	yes	characteristic
276	C₂×C₃₇	#3013	1	1	yes	characteristic
277	C₂×C₃₇	C₂×#456	1	1	yes	characteristic
278	#563	—	2	2	no	—
279	#559	—	2	1	no	—
280	Q₈²	—	2	1	no	—
281	#556	—	2	1	no	—
282	#556	C₂²×C₃₇	1	2	yes	—
283	D₄×Q₈	—	2	1	no	—
284	D₄×Q₈	C₂²×C₃₇	1	2	yes	—
285	#542	—	2	2	no	—
286	#542	—	2	2	no	—
287	#536	—	2	2	no	—
288	#533	C₂²×C₃₇	1	1	yes	characteristic
289	#533	C₂²×C₃₇	1	1	yes	characteristic
290	#533	C₂²×C₃₇	1	1	yes	characteristic
291	#532	C₂²×C₃₇	1	1	yes	characteristic
292	#500	C₂²×C₃₇	1	1	yes	characteristic
293	#500	C₂²×C₃₇	1	1	yes	characteristic
294	#499	—	2	2	no	—
295	#498	C₂²×C₃₇	1	1	yes	characteristic
296	#498	C₂²×C₃₇	1	1	yes	characteristic
297	#477	—	2	1	no	—
298	#475	—	2	1	no	—
299	#475	C₂²×C₃₇	1	2	yes	—
300	#474	C₂²×C₃₇	1	2	yes	—
301	#470	—	2	2	no	—
302	#468	—	2	2	no	—
303	#462	—	2	1	no	—
304	#462	C₂²×C₃₇	1	2	yes	—
305	#461	C₂²×C₃₇	1	2	yes	—
306	#460	—	2	1	no	—
307	#427	—	2	2	no	—
308	#423	C₂²×C₃₇	1	1	yes	characteristic
309	#423	C₂²×C₃₇	1	1	yes	characteristic
310	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
311	#332	C₂²×C₃₇	1	2	yes	—
312	#332	C₂²×C₃₇	1	2	yes	—
313	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
314	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
315	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
316	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
317	C₃₇	#18702	1	1	yes	characteristic, direct product factor, Sylow
318	C₂×#41	—	2	1	no	—
319	C₂²×Q₈	—	2	2	no	—
320	C₂×Q₁₆	—	2	2	no	—
321	C₂×SD₁₆	—	2	2	no	—
322	C₂×M₁₆	—	2	1	no	—
323	C₂×M₁₆	—	2	1	no	—
324	C₂²×C₈	—	2	1	no	—
325	C₄⋊Q₈	—	2	4	no	—
326	C₄⋊Q₈	—	2	2	no	—
327	C₄⋊Q₈	—	2	2	no	—
328	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
329	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
330	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
331	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
332	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
333	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
334	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
335	#127	D₄×C₃₇	1	1	yes	characteristic
336	#126	—	2	4	no	—
337	#126	—	2	4	no	—
338	#125	—	2	1	no	—
339	#125	—	2	1	no	—
340	#125	D₄×C₃₇	1	2	yes	—
341	#124	—	2	4	no	—
342	#124	—	2	2	no	—
343	#124	—	2	2	no	—
344	#124	—	2	1	no	—
345	#123	—	2	4	no	—
346	#123	—	2	4	no	—
347	C₂²⋊Q₈	—	2	4	no	—
348	C₂²⋊Q₈	—	2	2	no	—
349	C₂²⋊Q₈	—	2	1	no	—
350	C₂²⋊Q₈	—	2	1	no	—
351	C₂²⋊Q₈	—	2	1	no	—
352	C₂²⋊Q₈	—	2	2	no	—
353	C₂²⋊Q₈	—	2	4	no	—
354	C₂²⋊Q₈	—	2	1	no	—
355	C₂²⋊Q₈	—	2	1	no	—
356	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
357	#121	—	2	1	no	—
358	#121	D₄×C₃₇	1	2	yes	—
359	C₄×Q₈	—	2	2	no	—
360	C₄×Q₈	—	2	2	no	—
361	C₄×Q₈	—	2	1	no	—
362	C₄×Q₈	—	2	1	no	—
363	C₄×Q₈	—	2	1	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	C₂³×C₃₇	1	2	yes	—
371	#117	—	2	1	no	—
372	#117	—	2	2	no	—
373	#117	—	2	1	no	—
374	#117	D₄×C₃₇	1	2	yes	—
375	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
376	#107	—	2	2	no	—
377	#107	—	2	2	no	—
378	#107	—	2	2	no	—
379	#106	—	2	2	no	—
380	#106	—	2	2	no	—
381	#106	—	2	2	no	—
382	C₄⋊C₈	—	2	1	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
385	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
386	#103	—	2	2	no	—
387	#103	—	2	2	no	—
388	#103	—	2	2	no	—
389	#102	—	2	2	no	—
390	C₄×C₈	—	2	1	no	—
391	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
392	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
393	#41	—	8	1	no	—
394	#41	—	8	1	no	—
395	C₂×Q₈	—	2	4	no	—
396	C₂×Q₈	—	2	1	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	8	2	no	—
403	C₂×Q₈	—	8	2	no	—
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	C₂×D₄×C₃₇	1	2	yes	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
414	Q₁₆	—	8	2	no	—
415	SD₁₆	—	8	2	no	—
416	M₁₆	—	8	1	no	—
417	M₁₆	—	8	1	no	—
418	C₂×C₈	—	2	4	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	4	1	no	—
440	C₄⋊C₄	—	4	1	no	—
441	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
442	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
443	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
444	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
445	C₂²⋊C₄	—	2	4	no	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	4	1	no	—
453	C₄²	—	2	4	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	2	2	no	—
456	C₄²	—	4	1	no	—
457	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
458	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
459	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
460	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
461	C₂³	—	2	2	no	—
462	C₂³	#120×C₃₇	1	1	yes	characteristic
463	Q₈	—	2	2	no	—
464	Q₈	—	2	2	no	—
465	Q₈	—	4	1	no	—
466	Q₈	—	4	1	no	—
467	Q₈	—	4	1	no	—
468	Q₈	—	4	1	no	—
469	Q₈	—	4	2	no	—
470	Q₈	—	4	1	no	—
471	Q₈	—	4	1	no	—
472	Q₈	—	4	1	no	—
473	Q₈	—	4	1	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	—	8	1	no	—
480	D₄	—	8	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	8	4	no	—
496	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
497	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
498	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
500	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
502	C₈	—	2	2	no	—
503	C₈	—	2	2	no	—
504	C₈	—	4	2	no	—
505	C₈	—	4	2	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	2	no	—
521	C₄	—	8	1	no	—
522	C₄	—	8	1	no	—
523	C₄	C₃₇×#456	1	2	yes	—
524	C₄	C₃₇×#576	1	1	yes	characteristic
525	C₄	C₃₇×#577	1	1	yes	characteristic
526	C₄	C₃₇×#577	1	1	yes	characteristic
527	C₄	C₃₇×#578	1	1	yes	characteristic
528	C₂	—	4	1	no	—
529	C₂	—	8	2	no	—
530	C₂	C₃₇×#3012	1	1	yes	characteristic
531	C₂	C₃₇×#3013	1	1	yes	characteristic
532	C₂	C₂×C₃₇×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
prime radical	C₃₇×#532	C₂²
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
2. C₃₇×#3255	C₂	semidirect
4. C₃₇×#3160	C₂	semidirect
5. C₃₇×#1652	C₂	semidirect
6. C₃₇×#1651	C₂	semidirect
7. C₃₇×#1650	C₂	semidirect
8. C₃₇×#1649	C₂	semidirect
9. C₃₇×#1561	C₂	semidirect
10. C₃₇×#1493	C₂	semidirect
239. #18702	C₃₇	direct (N × H)
263. #3255	C₂×C₃₇	semidirect
265. #3160	C₂×C₃₇	semidirect
266. #1652	C₂×C₃₇	semidirect
267. #1651	C₂×C₃₇	semidirect
268. #1650	C₂×C₃₇	semidirect
269. #1649	C₂×C₃₇	semidirect
270. #1561	C₂×C₃₇	semidirect
271. #1493	C₂×C₃₇	semidirect
317. C₃₇	#18702	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×#3255	2
C₃₇×#3254	2
C₃₇×#3160	2
C₃₇×#1652	2
C₃₇×#1651	2
C₃₇×#1650	2
C₃₇×#1649	2
C₃₇×#1561	2
C₃₇×#1493	2
C₃₇×#1492	2
#18702	37

Subgroups — C37×#18702 #22639955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18702 #22639955