Subgroups — C₃₇×#18939 #22640192

Order 9472.

858 conjugacy classes of subgroups.

The subgroup lattice has 516 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×#3249	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3237	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#3210	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×#1633	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1630	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1551	C₂	1	1	yes	maximal, characteristic
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×#533	C₂²	1	1	yes	characteristic
25	C₃₇×#532	C₂²	1	1	yes	characteristic
26	C₃₇×#501	—	2	1	no	—
27	C₃₇×#494	C₂²	1	1	yes	characteristic
28	C₃₇×#492	C₂²	1	1	yes	characteristic
29	C₃₇×#491	—	2	1	no	—
30	C₃₇×#487	C₂²	1	1	yes	characteristic
31	C₃₇×#486	C₂²	1	1	yes	characteristic
32	C₃₇×#485	—	2	2	no	—
33	C₃₇×#477	—	2	1	no	—
34	C₃₇×#477	C₂²	1	2	yes	—
35	C₃₇×#477	C₂²	1	2	yes	—
36	C₃₇×#475	C₂²	1	2	yes	—
37	C₃₇×#467	—	2	2	no	—
38	C₃₇×#464	—	2	2	no	—
39	C₃₇×#462	—	2	1	no	—
40	C₃₇×#462	C₂²	1	2	yes	—
41	C₃₇×#452	—	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	D₄	1	2	yes	—
52	C₂²×Q₈×C₃₇	—	2	2	no	—
53	C₂×Q₁₆×C₃₇	—	2	2	no	—
54	C₂×Q₁₆×C₃₇	—	2	2	no	—
55	C₂×SD₁₆×C₃₇	—	2	2	no	—
56	C₂²×C₈×C₃₇	—	2	1	no	—
57	C₄⋊Q₈×C₃₇	—	2	4	no	—
58	C₄⋊Q₈×C₃₇	—	2	2	no	—
59	C₄⋊Q₈×C₃₇	—	2	2	no	—
60	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
68	#126×C₃₇	—	2	4	no	—
69	#126×C₃₇	—	2	4	no	—
70	#125×C₃₇	—	2	1	no	—
71	#125×C₃₇	—	2	1	no	—
72	#125×C₃₇	—	2	1	no	—
73	#124×C₃₇	—	2	4	no	—
74	#124×C₃₇	—	2	2	no	—
75	#124×C₃₇	—	2	2	no	—
76	#124×C₃₇	D₄	1	2	yes	—
77	#123×C₃₇	—	2	4	no	—
78	#123×C₃₇	—	2	4	no	—
79	C₂²⋊Q₈×C₃₇	—	2	2	no	—
80	C₂²⋊Q₈×C₃₇	—	2	2	no	—
81	C₂²⋊Q₈×C₃₇	—	2	4	no	—
82	C₂²⋊Q₈×C₃₇	—	2	4	no	—
83	C₂²⋊Q₈×C₃₇	—	2	1	no	—
84	C₂²⋊Q₈×C₃₇	—	2	1	no	—
85	C₂²⋊Q₈×C₃₇	—	2	1	no	—
86	C₂²⋊Q₈×C₃₇	—	2	1	no	—
87	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
88	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
89	#121×C₃₇	—	2	1	no	—
90	#121×C₃₇	—	2	1	no	—
91	C₄×Q₈×C₃₇	—	2	2	no	—
92	C₄×Q₈×C₃₇	—	2	2	no	—
93	C₄×Q₈×C₃₇	—	2	1	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×Q₈×C₃₇	C₂³	1	2	yes	—
99	C₄×D₄×C₃₇	—	2	2	no	—
100	C₄×D₄×C₃₇	—	2	2	no	—
101	C₄×D₄×C₃₇	—	2	1	no	—
102	C₄×D₄×C₃₇	—	2	1	no	—
103	#117×C₃₇	—	2	2	no	—
104	#117×C₃₇	—	2	1	no	—
105	#117×C₃₇	—	2	1	no	—
106	#117×C₃₇	—	2	1	no	—
107	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
108	#107×C₃₇	—	2	2	no	—
109	#107×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	#103×C₃₇	—	2	2	no	—
118	#103×C₃₇	—	2	2	no	—
119	#103×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	C₂×Q₈×C₃₇	—	2	4	no	—
128	C₂×Q₈×C₃₇	—	2	1	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	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₃₇	—	2	4	no	—
141	C₂²×C₄×C₃₇	—	2	2	no	—
142	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
145	Q₁₆×C₃₇	—	8	2	no	—
146	Q₁₆×C₃₇	—	8	2	no	—
147	SD₁₆×C₃₇	—	8	2	no	—
148	C₂×C₈×C₃₇	—	2	1	no	—
149	C₂×C₈×C₃₇	—	2	1	no	—
150	C₂×C₈×C₃₇	—	2	2	no	—
151	C₂×C₈×C₃₇	—	2	2	no	—
152	C₂×C₈×C₃₇	—	8	1	no	—
153	C₄⋊C₄×C₃₇	—	2	4	no	—
154	C₄⋊C₄×C₃₇	—	2	4	no	—
155	C₄⋊C₄×C₃₇	—	2	1	no	—
156	C₄⋊C₄×C₃₇	—	2	1	no	—
157	C₄⋊C₄×C₃₇	—	2	1	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	2	no	—
162	C₄⋊C₄×C₃₇	—	2	2	no	—
163	C₄⋊C₄×C₃₇	—	2	1	no	—
164	C₄⋊C₄×C₃₇	—	2	1	no	—
165	C₄⋊C₄×C₃₇	—	2	2	no	—
166	C₄⋊C₄×C₃₇	—	2	2	no	—
167	C₄⋊C₄×C₃₇	—	2	1	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	—	4	1	no	—
172	C₄⋊C₄×C₃₇	—	4	1	no	—
173	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
174	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
175	C₂²⋊C₄×C₃₇	—	2	4	no	—
176	C₂²⋊C₄×C₃₇	—	2	4	no	—
177	C₂²⋊C₄×C₃₇	—	2	4	no	—
178	C₂²⋊C₄×C₃₇	—	2	2	no	—
179	C₂²⋊C₄×C₃₇	—	2	2	no	—
180	C₂²⋊C₄×C₃₇	—	2	2	no	—
181	C₂²⋊C₄×C₃₇	—	2	2	no	—
182	C₂²⋊C₄×C₃₇	—	4	1	no	—
183	C₄²×C₃₇	—	2	4	no	—
184	C₄²×C₃₇	—	2	2	no	—
185	C₄²×C₃₇	—	2	2	no	—
186	C₄²×C₃₇	—	4	1	no	—
187	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
191	C₂³×C₃₇	—	2	2	no	—
192	C₂³×C₃₇	#120	1	1	yes	characteristic
193	Q₈×C₃₇	—	2	2	no	—
194	Q₈×C₃₇	—	2	4	no	—
195	Q₈×C₃₇	—	2	2	no	—
196	Q₈×C₃₇	—	4	2	no	—
197	Q₈×C₃₇	—	4	2	no	—
198	Q₈×C₃₇	—	4	2	no	—
199	Q₈×C₃₇	—	4	2	no	—
200	Q₈×C₃₇	—	4	1	no	—
201	Q₈×C₃₇	—	4	1	no	—
202	Q₈×C₃₇	—	8	4	no	—
203	D₄×C₃₇	—	4	2	no	—
204	D₄×C₃₇	—	4	1	no	—
205	D₄×C₃₇	—	4	2	no	—
206	D₄×C₃₇	—	4	1	no	—
207	D₄×C₃₇	—	8	2	no	—
208	C₂×C₄×C₃₇	—	2	1	no	—
209	C₂×C₄×C₃₇	—	2	2	no	—
210	C₂×C₄×C₃₇	—	2	1	no	—
211	C₂×C₄×C₃₇	—	2	2	no	—
212	C₂×C₄×C₃₇	—	2	2	no	—
213	C₂×C₄×C₃₇	—	2	2	no	—
214	C₂×C₄×C₃₇	—	2	2	no	—
215	C₂×C₄×C₃₇	—	2	2	no	—
216	C₂×C₄×C₃₇	—	4	1	no	—
217	C₂×C₄×C₃₇	—	4	4	no	—
218	C₂×C₄×C₃₇	—	4	1	no	—
219	C₂×C₄×C₃₇	—	4	1	no	—
220	C₂×C₄×C₃₇	—	8	4	no	—
221	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
222	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
223	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
224	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
227	C₈×C₃₇	—	4	1	no	—
228	C₈×C₃₇	—	4	1	no	—
229	C₈×C₃₇	—	4	2	no	—
230	C₈×C₃₇	—	4	2	no	—
231	#18939	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂²×C₃₇	—	2	1	no	—
233	C₂²×C₃₇	—	2	1	no	—
234	C₂²×C₃₇	—	2	1	no	—
235	C₂²×C₃₇	—	4	2	no	—
236	C₂²×C₃₇	—	4	2	no	—
237	C₂²×C₃₇	—	4	2	no	—
238	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
239	C₄×C₃₇	—	2	1	no	—
240	C₄×C₃₇	—	2	1	no	—
241	C₄×C₃₇	—	2	1	no	—
242	C₄×C₃₇	—	2	1	no	—
243	C₄×C₃₇	—	4	2	no	—
244	C₄×C₃₇	—	4	2	no	—
245	C₄×C₃₇	—	4	2	no	—
246	C₄×C₃₇	—	4	2	no	—
247	C₄×C₃₇	—	4	2	no	—
248	C₄×C₃₇	—	8	1	no	—
249	C₄×C₃₇	—	8	1	no	—
250	C₄×C₃₇	#577	1	1	yes	characteristic
251	C₄×C₃₇	#578	1	2	yes	—
252	C₄×C₃₇	#578	1	1	yes	characteristic
253	#3550	C₂×C₃₇	1	1	yes	characteristic
254	#3249	C₂×C₃₇	1	1	yes	characteristic, complemented
255	#3237	C₂×C₃₇	1	1	yes	characteristic, complemented
256	#3210	C₂×C₃₇	1	1	yes	characteristic
257	#1645	C₂×C₃₇	1	2	yes	complemented
258	#1640	C₂×C₃₇	1	2	yes	complemented
259	#1633	C₂×C₃₇	1	2	yes	complemented
260	#1630	C₂×C₃₇	1	2	yes	complemented
261	#1551	C₂×C₃₇	1	1	yes	characteristic
262	#1497	C₂×C₃₇	1	1	yes	characteristic, complemented
263	#1481	C₂×C₃₇	1	1	yes	characteristic, complemented
264	C₂×C₃₇	—	4	1	no	—
265	C₂×C₃₇	—	8	2	no	—
266	C₂×C₃₇	#3011	1	1	yes	characteristic
267	C₂×C₃₇	#3013	1	1	yes	characteristic
268	C₂×C₃₇	#3019	1	1	yes	characteristic
269	#563	—	2	2	no	—
270	#559	C₂²×C₃₇	1	2	yes	—
271	Q₈²	C₂²×C₃₇	1	2	yes	—
272	#556	—	2	1	no	—
273	#556	—	2	1	no	—
274	D₄×Q₈	—	2	1	no	—
275	D₄×Q₈	—	2	1	no	—
276	#542	—	2	2	no	—
277	#542	—	2	2	no	—
278	#536	—	2	2	no	—
279	#533	C₂²×C₃₇	1	1	yes	characteristic
280	#533	C₂²×C₃₇	1	1	yes	characteristic
281	#533	C₂²×C₃₇	1	1	yes	characteristic
282	#532	C₂²×C₃₇	1	1	yes	characteristic
283	#501	—	2	1	no	—
284	#494	C₂²×C₃₇	1	1	yes	characteristic
285	#492	C₂²×C₃₇	1	1	yes	characteristic
286	#491	—	2	1	no	—
287	#487	C₂²×C₃₇	1	1	yes	characteristic
288	#486	C₂²×C₃₇	1	1	yes	characteristic
289	#485	—	2	2	no	—
290	#477	—	2	1	no	—
291	#477	C₂²×C₃₇	1	2	yes	—
292	#477	C₂²×C₃₇	1	2	yes	—
293	#475	C₂²×C₃₇	1	2	yes	—
294	#467	—	2	2	no	—
295	#464	—	2	2	no	—
296	#462	—	2	1	no	—
297	#462	C₂²×C₃₇	1	2	yes	—
298	#452	—	2	2	no	—
299	#432	C₂²×C₃₇	1	1	yes	characteristic
300	#431	C₂²×C₃₇	1	1	yes	characteristic
301	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
302	#333	C₂²×C₃₇	1	2	yes	—
303	#331	C₂²×C₃₇	1	2	yes	—
304	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
305	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
306	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
307	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
308	C₃₇	#18939	1	1	yes	characteristic, direct product factor, Sylow
309	C₂×#41	D₄×C₃₇	1	2	yes	—
310	C₂²×Q₈	—	2	2	no	—
311	C₂×Q₁₆	—	2	2	no	—
312	C₂×Q₁₆	—	2	2	no	—
313	C₂×SD₁₆	—	2	2	no	—
314	C₂²×C₈	—	2	1	no	—
315	C₄⋊Q₈	—	2	4	no	—
316	C₄⋊Q₈	—	2	2	no	—
317	C₄⋊Q₈	—	2	2	no	—
318	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
319	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
320	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
321	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
322	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
323	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
324	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
325	#127	C₂³×C₃₇	1	1	yes	characteristic
326	#126	—	2	4	no	—
327	#126	—	2	4	no	—
328	#125	—	2	1	no	—
329	#125	—	2	1	no	—
330	#125	—	2	1	no	—
331	#124	—	2	4	no	—
332	#124	—	2	2	no	—
333	#124	—	2	2	no	—
334	#124	D₄×C₃₇	1	2	yes	—
335	#123	—	2	4	no	—
336	#123	—	2	4	no	—
337	C₂²⋊Q₈	—	2	2	no	—
338	C₂²⋊Q₈	—	2	2	no	—
339	C₂²⋊Q₈	—	2	4	no	—
340	C₂²⋊Q₈	—	2	4	no	—
341	C₂²⋊Q₈	—	2	1	no	—
342	C₂²⋊Q₈	—	2	1	no	—
343	C₂²⋊Q₈	—	2	1	no	—
344	C₂²⋊Q₈	—	2	1	no	—
345	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
346	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
347	#121	—	2	1	no	—
348	#121	—	2	1	no	—
349	C₄×Q₈	—	2	2	no	—
350	C₄×Q₈	—	2	2	no	—
351	C₄×Q₈	—	2	1	no	—
352	C₄×Q₈	—	2	1	no	—
353	C₄×Q₈	—	2	1	no	—
354	C₄×Q₈	—	2	1	no	—
355	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
356	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	1	no	—
360	C₄×D₄	—	2	1	no	—
361	#117	—	2	2	no	—
362	#117	—	2	1	no	—
363	#117	—	2	1	no	—
364	#117	—	2	1	no	—
365	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
366	#107	—	2	2	no	—
367	#107	—	2	2	no	—
368	#106	—	2	2	no	—
369	C₄⋊C₈	—	2	1	no	—
370	C₄⋊C₈	—	2	1	no	—
371	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
372	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
373	#103	—	2	2	no	—
374	#103	—	2	2	no	—
375	#103	—	2	2	no	—
376	#103	—	2	2	no	—
377	#103	—	2	2	no	—
378	#102	—	2	2	no	—
379	C₂²⋊C₈	—	2	1	no	—
380	C₂²⋊C₈	—	2	1	no	—
381	#97	—	2	1	no	—
382	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
383	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
384	#41	—	8	2	no	—
385	C₂×Q₈	—	2	4	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	2	1	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	8	4	no	—
391	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
392	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
393	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
403	Q₁₆	—	8	2	no	—
404	Q₁₆	—	8	2	no	—
405	SD₁₆	—	8	2	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	8	1	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	—	2	4	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	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	—	4	1	no	—
430	C₄⋊C₄	—	4	1	no	—
431	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
432	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	4	1	no	—
441	C₄²	—	2	4	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	4	1	no	—
445	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
446	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
447	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
448	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
449	C₂³	—	2	2	no	—
450	C₂³	#120×C₃₇	1	1	yes	characteristic
451	Q₈	—	2	2	no	—
452	Q₈	—	2	4	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	4	2	no	—
455	Q₈	—	4	2	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	4	1	no	—
459	Q₈	—	4	1	no	—
460	Q₈	—	8	4	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	1	no	—
463	D₄	—	4	2	no	—
464	D₄	—	4	1	no	—
465	D₄	—	8	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	8	4	no	—
479	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
480	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
481	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
485	C₈	—	4	1	no	—
486	C₈	—	4	1	no	—
487	C₈	—	4	2	no	—
488	C₈	—	4	2	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	—	4	2	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	8	1	no	—
506	C₄	—	8	1	no	—
507	C₄	C₃₇×#577	1	1	yes	characteristic
508	C₄	C₃₇×#578	1	2	yes	—
509	C₄	C₃₇×#578	1	1	yes	characteristic
510	C₂	—	4	1	no	—
511	C₂	—	8	2	no	—
512	C₂	C₃₇×#3011	1	1	yes	characteristic
513	C₂	C₃₇×#3013	1	1	yes	characteristic
514	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×#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×#3249	C₂	semidirect
3. C₃₇×#3237	C₂	semidirect
5. C₃₇×#1645	C₂	semidirect
6. C₃₇×#1640	C₂	semidirect
7. C₃₇×#1633	C₂	semidirect
8. C₃₇×#1630	C₂	semidirect
10. C₃₇×#1497	C₂	semidirect
11. C₃₇×#1481	C₂	semidirect
231. #18939	C₃₇	direct (N × H)
254. #3249	C₂×C₃₇	semidirect
255. #3237	C₂×C₃₇	semidirect
257. #1645	C₂×C₃₇	semidirect
258. #1640	C₂×C₃₇	semidirect
259. #1633	C₂×C₃₇	semidirect
260. #1630	C₂×C₃₇	semidirect
262. #1497	C₂×C₃₇	semidirect
263. #1481	C₂×C₃₇	semidirect
308. C₃₇	#18939	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×#3249	2
C₃₇×#3237	2
C₃₇×#3210	2
C₃₇×#1645	2
C₃₇×#1640	2
C₃₇×#1633	2
C₃₇×#1630	2
C₃₇×#1551	2
C₃₇×#1497	2
C₃₇×#1481	2
#18939	37

Subgroups — C37×#18939 #22640192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18939 #22640192