Subgroups — C₃₇×#18946 #22640199

Order 9472.

936 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3245	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, complemented
5	C₃₇×#1654	C₂	1	2	yes	maximal, complemented
6	C₃₇×#1647	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1625	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1625	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1552	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1496	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1480	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#562	—	2	2	no	—
13	C₃₇×#554	—	2	1	no	—
14	C₃₇×#554	—	2	1	no	—
15	C₃₇×#550	—	2	1	no	—
16	C₃₇×#550	—	2	1	no	—
17	C₃₇×#547	C₂²	1	2	yes	—
18	C₃₇×#547	C₂²	1	2	yes	—
19	C₃₇×#540	—	2	2	no	—
20	C₃₇×#537	—	2	2	no	—
21	C₃₇×#537	—	2	2	no	—
22	C₃₇×#533	C₂²	1	1	yes	characteristic
23	C₃₇×#532	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×#474	—	2	1	no	—
35	C₃₇×#474	C₂²	1	2	yes	—
36	C₃₇×#466	—	2	2	no	—
37	C₃₇×#461	C₂²	1	2	yes	—
38	C₃₇×#459	—	2	1	no	—
39	C₃₇×#459	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×D₄⋊C₈	C₂²	1	2	yes	—
48	C₃₇×D₄⋊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	2	no	—
52	C₂×#41×C₃₇	—	2	2	no	—
53	C₂×#41×C₃₇	—	2	1	no	—
54	C₂×#41×C₃₇	—	2	1	no	—
55	C₂×#41×C₃₇	—	2	1	no	—
56	C₂×SD₁₆×C₃₇	—	2	2	no	—
57	C₂×D₈×C₃₇	—	2	2	no	—
58	C₂×D₈×C₃₇	—	2	2	no	—
59	C₂²×C₈×C₃₇	—	2	1	no	—
60	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
61	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
62	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
63	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
65	#127×C₃₇	—	2	2	no	—
66	#127×C₃₇	D₄	1	1	yes	characteristic
67	#127×C₃₇	D₄	1	1	yes	characteristic
68	#127×C₃₇	C₂³	1	1	yes	characteristic
69	#125×C₃₇	—	2	2	no	—
70	#125×C₃₇	D₄	1	2	yes	—
71	#124×C₃₇	—	2	1	no	—
72	#124×C₃₇	—	2	1	no	—
73	#124×C₃₇	—	2	1	no	—
74	#123×C₃₇	—	2	4	no	—
75	#123×C₃₇	—	2	4	no	—
76	C₂²⋊Q₈×C₃₇	—	2	4	no	—
77	C₂²⋊Q₈×C₃₇	—	2	4	no	—
78	C₂²⋊Q₈×C₃₇	—	2	1	no	—
79	C₂²⋊Q₈×C₃₇	—	2	1	no	—
80	C₂²⋊Q₈×C₃₇	—	2	2	no	—
81	C₂²⋊Q₈×C₃₇	—	2	2	no	—
82	#121×C₃₇	—	2	4	no	—
83	#121×C₃₇	—	2	4	no	—
84	#121×C₃₇	—	2	4	no	—
85	#121×C₃₇	—	2	4	no	—
86	#121×C₃₇	—	2	2	no	—
87	#121×C₃₇	—	2	2	no	—
88	#121×C₃₇	—	2	1	no	—
89	#121×C₃₇	—	2	1	no	—
90	#121×C₃₇	—	2	1	no	—
91	#121×C₃₇	—	2	1	no	—
92	#121×C₃₇	D₄	1	2	yes	—
93	#121×C₃₇	D₄	1	2	yes	—
94	C₄×Q₈×C₃₇	—	2	1	no	—
95	C₄×Q₈×C₃₇	—	2	1	no	—
96	C₄×D₄×C₃₇	—	2	2	no	—
97	C₄×D₄×C₃₇	—	2	2	no	—
98	C₄×D₄×C₃₇	—	2	1	no	—
99	C₄×D₄×C₃₇	—	2	1	no	—
100	C₄×D₄×C₃₇	—	2	1	no	—
101	C₄×D₄×C₃₇	—	2	1	no	—
102	C₄×D₄×C₃₇	C₂³	1	2	yes	—
103	C₄×D₄×C₃₇	C₂³	1	2	yes	—
104	#117×C₃₇	D₄	1	2	yes	—
105	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
106	C₂×C₄⋊C₄×C₃₇	—	2	2	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	#102×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	2	no	—
128	#41×C₃₇	—	8	1	no	—
129	#41×C₃₇	—	8	2	no	—
130	#41×C₃₇	—	8	2	no	—
131	#41×C₃₇	—	8	2	no	—
132	#41×C₃₇	—	8	2	no	—
133	#41×C₃₇	—	8	2	no	—
134	C₂×Q₈×C₃₇	—	2	1	no	—
135	C₂×Q₈×C₃₇	—	2	1	no	—
136	C₂×Q₈×C₃₇	—	2	1	no	—
137	C₂×Q₈×C₃₇	—	2	1	no	—
138	C₂×Q₈×C₃₇	—	2	1	no	—
139	C₂×D₄×C₃₇	—	2	4	no	—
140	C₂×D₄×C₃₇	—	2	4	no	—
141	C₂×D₄×C₃₇	—	2	2	no	—
142	C₂×D₄×C₃₇	—	2	2	no	—
143	C₂×D₄×C₃₇	—	2	1	no	—
144	C₂×D₄×C₃₇	—	2	1	no	—
145	C₂×D₄×C₃₇	—	2	1	no	—
146	C₂×D₄×C₃₇	—	2	1	no	—
147	C₂×D₄×C₃₇	—	2	1	no	—
148	C₂×D₄×C₃₇	—	2	1	no	—
149	C₂×D₄×C₃₇	—	2	1	no	—
150	C₂×D₄×C₃₇	—	4	1	no	—
151	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
152	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₃₇	—	2	4	no	—
154	C₂²×C₄×C₃₇	—	2	4	no	—
155	C₂²×C₄×C₃₇	—	2	2	no	—
156	C₂²×C₄×C₃₇	—	2	2	no	—
157	C₂²×C₄×C₃₇	—	4	1	no	—
158	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
161	SD₁₆×C₃₇	—	8	2	no	—
162	D₈×C₃₇	—	8	2	no	—
163	D₈×C₃₇	—	8	2	no	—
164	C₂×C₈×C₃₇	—	2	1	no	—
165	C₂×C₈×C₃₇	—	2	1	no	—
166	C₂×C₈×C₃₇	—	2	2	no	—
167	C₂×C₈×C₃₇	—	2	2	no	—
168	C₂×C₈×C₃₇	—	8	1	no	—
169	C₄⋊C₄×C₃₇	—	2	4	no	—
170	C₄⋊C₄×C₃₇	—	2	4	no	—
171	C₄⋊C₄×C₃₇	—	2	1	no	—
172	C₄⋊C₄×C₃₇	—	2	1	no	—
173	C₄⋊C₄×C₃₇	—	2	2	no	—
174	C₄⋊C₄×C₃₇	—	2	2	no	—
175	C₄⋊C₄×C₃₇	—	2	1	no	—
176	C₄⋊C₄×C₃₇	—	2	1	no	—
177	C₄⋊C₄×C₃₇	—	2	1	no	—
178	C₄⋊C₄×C₃₇	—	2	1	no	—
179	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
180	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
181	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
182	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
183	C₂²⋊C₄×C₃₇	—	2	4	no	—
184	C₂²⋊C₄×C₃₇	—	2	4	no	—
185	C₂²⋊C₄×C₃₇	—	2	2	no	—
186	C₂²⋊C₄×C₃₇	—	2	2	no	—
187	C₂²⋊C₄×C₃₇	—	2	2	no	—
188	C₂²⋊C₄×C₃₇	—	2	2	no	—
189	C₂²⋊C₄×C₃₇	—	2	2	no	—
190	C₂²⋊C₄×C₃₇	—	4	1	no	—
191	C₂²⋊C₄×C₃₇	—	4	1	no	—
192	C₄²×C₃₇	—	2	2	no	—
193	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
197	C₂³×C₃₇	—	2	2	no	—
198	C₂³×C₃₇	—	2	2	no	—
199	C₂³×C₃₇	—	4	1	no	—
200	C₂³×C₃₇	#120	1	1	yes	characteristic
201	Q₈×C₃₇	—	4	2	no	—
202	Q₈×C₃₇	—	4	1	no	—
203	Q₈×C₃₇	—	4	1	no	—
204	Q₈×C₃₇	—	4	2	no	—
205	Q₈×C₃₇	—	8	1	no	—
206	Q₈×C₃₇	—	8	1	no	—
207	D₄×C₃₇	—	2	2	no	—
208	D₄×C₃₇	—	2	2	no	—
209	D₄×C₃₇	—	2	2	no	—
210	D₄×C₃₇	—	2	2	no	—
211	D₄×C₃₇	—	4	2	no	—
212	D₄×C₃₇	—	4	2	no	—
213	D₄×C₃₇	—	4	2	no	—
214	D₄×C₃₇	—	4	1	no	—
215	D₄×C₃₇	—	4	2	no	—
216	D₄×C₃₇	—	4	1	no	—
217	D₄×C₃₇	—	8	1	no	—
218	D₄×C₃₇	—	8	1	no	—
219	D₄×C₃₇	—	8	2	no	—
220	D₄×C₃₇	—	8	2	no	—
221	D₄×C₃₇	—	8	4	no	—
222	D₄×C₃₇	—	8	4	no	—
223	D₄×C₃₇	—	8	2	no	—
224	C₂×C₄×C₃₇	—	2	1	no	—
225	C₂×C₄×C₃₇	—	2	2	no	—
226	C₂×C₄×C₃₇	—	2	1	no	—
227	C₂×C₄×C₃₇	—	2	2	no	—
228	C₂×C₄×C₃₇	—	2	2	no	—
229	C₂×C₄×C₃₇	—	2	2	no	—
230	C₂×C₄×C₃₇	—	2	2	no	—
231	C₂×C₄×C₃₇	—	4	1	no	—
232	C₂×C₄×C₃₇	—	4	2	no	—
233	C₂×C₄×C₃₇	—	4	2	no	—
234	C₂×C₄×C₃₇	—	4	2	no	—
235	C₂×C₄×C₃₇	—	4	2	no	—
236	C₂×C₄×C₃₇	—	4	1	no	—
237	C₂×C₄×C₃₇	—	8	2	no	—
238	C₂×C₄×C₃₇	—	8	4	no	—
239	C₂×C₄×C₃₇	—	8	4	no	—
240	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
241	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
242	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
243	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
246	C₈×C₃₇	—	4	1	no	—
247	C₈×C₃₇	—	4	1	no	—
248	C₈×C₃₇	—	4	2	no	—
249	C₈×C₃₇	—	4	2	no	—
250	#18946	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
251	C₂²×C₃₇	—	2	1	no	—
252	C₂²×C₃₇	—	2	1	no	—
253	C₂²×C₃₇	—	2	1	no	—
254	C₂²×C₃₇	—	4	2	no	—
255	C₂²×C₃₇	—	4	2	no	—
256	C₂²×C₃₇	—	4	2	no	—
257	C₂²×C₃₇	—	4	2	no	—
258	C₂²×C₃₇	—	4	2	no	—
259	C₂²×C₃₇	—	4	2	no	—
260	C₂²×C₃₇	—	8	1	no	—
261	C₂²×C₃₇	—	8	1	no	—
262	C₂²×C₃₇	—	8	1	no	—
263	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
264	C₄×C₃₇	—	2	1	no	—
265	C₄×C₃₇	—	2	1	no	—
266	C₄×C₃₇	—	2	1	no	—
267	C₄×C₃₇	—	2	1	no	—
268	C₄×C₃₇	—	4	2	no	—
269	C₄×C₃₇	—	4	2	no	—
270	C₄×C₃₇	—	4	2	no	—
271	C₄×C₃₇	—	4	2	no	—
272	C₄×C₃₇	—	8	1	no	—
273	C₄×C₃₇	#576	1	2	yes	—
274	C₄×C₃₇	#576	1	1	yes	characteristic
275	C₄×C₃₇	#577	1	1	yes	characteristic
276	#3548	C₂×C₃₇	1	1	yes	characteristic, complemented
277	#3245	C₂×C₃₇	1	1	yes	characteristic, complemented
278	#3228	C₂×C₃₇	1	1	yes	characteristic, complemented
279	#3214	C₂×C₃₇	1	1	yes	characteristic, complemented
280	#1654	C₂×C₃₇	1	2	yes	complemented
281	#1647	C₂×C₃₇	1	2	yes	complemented
282	#1625	C₂×C₃₇	1	2	yes	complemented
283	#1625	C₂×C₃₇	1	2	yes	complemented
284	#1552	C₂×C₃₇	1	1	yes	characteristic, complemented
285	#1496	C₂×C₃₇	1	1	yes	characteristic, complemented
286	#1480	C₂×C₃₇	1	1	yes	characteristic, complemented
287	C₂×C₃₇	—	4	1	no	—
288	C₂×C₃₇	—	8	2	no	—
289	C₂×C₃₇	—	8	2	no	—
290	C₂×C₃₇	—	16	1	no	—
291	C₂×C₃₇	#3008	1	1	yes	characteristic
292	C₂×C₃₇	#3012	1	1	yes	characteristic
293	C₂×C₃₇	#3020	1	1	yes	characteristic
294	#562	—	2	2	no	—
295	#554	—	2	1	no	—
296	#554	—	2	1	no	—
297	#550	—	2	1	no	—
298	#550	—	2	1	no	—
299	#547	C₂²×C₃₇	1	2	yes	—
300	#547	C₂²×C₃₇	1	2	yes	—
301	#540	—	2	2	no	—
302	#537	—	2	2	no	—
303	#537	—	2	2	no	—
304	#533	C₂²×C₃₇	1	1	yes	characteristic
305	#532	C₂²×C₃₇	1	1	yes	characteristic
306	#532	C₂²×C₃₇	1	1	yes	characteristic
307	#532	C₂²×C₃₇	1	1	yes	characteristic
308	#500	C₂²×C₃₇	1	1	yes	characteristic
309	#498	C₂²×C₃₇	1	1	yes	characteristic
310	#496	—	2	1	no	—
311	#489	—	2	1	no	—
312	#486	C₂²×C₃₇	1	1	yes	characteristic
313	#486	C₂²×C₃₇	1	1	yes	characteristic
314	#482	—	2	2	no	—
315	#478	—	2	2	no	—
316	#474	—	2	1	no	—
317	#474	C₂²×C₃₇	1	2	yes	—
318	#466	—	2	2	no	—
319	#461	C₂²×C₃₇	1	2	yes	—
320	#459	—	2	1	no	—
321	#459	C₂²×C₃₇	1	2	yes	—
322	#459	C₂²×C₃₇	1	2	yes	—
323	#449	—	2	2	no	—
324	#432	C₂²×C₃₇	1	1	yes	characteristic
325	#431	C₂²×C₃₇	1	1	yes	characteristic
326	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
327	#332	C₂²×C₃₇	1	2	yes	—
328	#332	C₂²×C₃₇	1	2	yes	—
329	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
330	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
331	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
332	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
333	C₃₇	#18946	1	1	yes	characteristic, direct product factor, Sylow
334	C₂×#41	—	2	2	no	—
335	C₂×#41	—	2	2	no	—
336	C₂×#41	—	2	1	no	—
337	C₂×#41	—	2	1	no	—
338	C₂×#41	—	2	1	no	—
339	C₂×SD₁₆	—	2	2	no	—
340	C₂×D₈	—	2	2	no	—
341	C₂×D₈	—	2	2	no	—
342	C₂²×C₈	—	2	1	no	—
343	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
344	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
345	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
346	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
347	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
348	#127	—	2	2	no	—
349	#127	D₄×C₃₇	1	1	yes	characteristic
350	#127	D₄×C₃₇	1	1	yes	characteristic
351	#127	C₂³×C₃₇	1	1	yes	characteristic
352	#125	—	2	2	no	—
353	#125	D₄×C₃₇	1	2	yes	—
354	#124	—	2	1	no	—
355	#124	—	2	1	no	—
356	#124	—	2	1	no	—
357	#123	—	2	4	no	—
358	#123	—	2	4	no	—
359	C₂²⋊Q₈	—	2	4	no	—
360	C₂²⋊Q₈	—	2	4	no	—
361	C₂²⋊Q₈	—	2	1	no	—
362	C₂²⋊Q₈	—	2	1	no	—
363	C₂²⋊Q₈	—	2	2	no	—
364	C₂²⋊Q₈	—	2	2	no	—
365	#121	—	2	4	no	—
366	#121	—	2	4	no	—
367	#121	—	2	4	no	—
368	#121	—	2	4	no	—
369	#121	—	2	2	no	—
370	#121	—	2	2	no	—
371	#121	—	2	1	no	—
372	#121	—	2	1	no	—
373	#121	—	2	1	no	—
374	#121	—	2	1	no	—
375	#121	D₄×C₃₇	1	2	yes	—
376	#121	D₄×C₃₇	1	2	yes	—
377	C₄×Q₈	—	2	1	no	—
378	C₄×Q₈	—	2	1	no	—
379	C₄×D₄	—	2	2	no	—
380	C₄×D₄	—	2	2	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	—	2	1	no	—
385	C₄×D₄	C₂³×C₃₇	1	2	yes	—
386	C₄×D₄	C₂³×C₃₇	1	2	yes	—
387	#117	D₄×C₃₇	1	2	yes	—
388	C₂×C₄⋊C₄	—	2	2	no	—
389	C₂×C₄⋊C₄	—	2	2	no	—
390	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
391	#107	—	2	2	no	—
392	#107	—	2	2	no	—
393	#106	—	2	2	no	—
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
397	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
398	#103	—	2	2	no	—
399	#102	—	2	2	no	—
400	#102	—	2	2	no	—
401	#102	—	2	2	no	—
402	#102	—	2	2	no	—
403	#102	—	2	2	no	—
404	C₂²⋊C₈	—	2	1	no	—
405	C₂²⋊C₈	—	2	1	no	—
406	#97	—	2	1	no	—
407	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
408	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
409	#41	—	8	1	no	—
410	#41	—	8	2	no	—
411	#41	—	8	1	no	—
412	#41	—	8	2	no	—
413	#41	—	8	2	no	—
414	#41	—	8	2	no	—
415	#41	—	8	2	no	—
416	#41	—	8	2	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	2	1	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	4	1	no	—
434	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
435	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	4	1	no	—
441	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
444	SD₁₆	—	8	2	no	—
445	D₈	—	8	2	no	—
446	D₈	—	8	2	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	8	1	no	—
452	C₄⋊C₄	—	2	4	no	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
463	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
464	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
465	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₄²	—	2	2	no	—
476	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
477	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
478	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
479	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
480	C₂³	—	2	2	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	4	1	no	—
483	C₂³	#120×C₃₇	1	1	yes	characteristic
484	Q₈	—	4	2	no	—
485	Q₈	—	4	1	no	—
486	Q₈	—	4	1	no	—
487	Q₈	—	4	2	no	—
488	Q₈	—	8	1	no	—
489	Q₈	—	8	1	no	—
490	D₄	—	2	2	no	—
491	D₄	—	2	2	no	—
492	D₄	—	2	2	no	—
493	D₄	—	2	2	no	—
494	D₄	—	4	2	no	—
495	D₄	—	4	2	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	1	no	—
498	D₄	—	4	2	no	—
499	D₄	—	4	1	no	—
500	D₄	—	8	1	no	—
501	D₄	—	8	1	no	—
502	D₄	—	8	2	no	—
503	D₄	—	8	2	no	—
504	D₄	—	8	4	no	—
505	D₄	—	8	4	no	—
506	D₄	—	8	2	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	8	2	no	—
521	C₂×C₄	—	8	4	no	—
522	C₂×C₄	—	8	4	no	—
523	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
524	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
525	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
526	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	2	no	—
532	C₈	—	4	2	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	8	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	1	no	—
545	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	2	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	2	no	—
554	C₄	—	8	1	no	—
555	C₄	C₃₇×#576	1	2	yes	—
556	C₄	C₃₇×#576	1	1	yes	characteristic
557	C₄	C₃₇×#577	1	1	yes	characteristic
558	C₂	—	4	1	no	—
559	C₂	—	8	2	no	—
560	C₂	—	8	2	no	—
561	C₂	—	16	1	no	—
562	C₂	C₃₇×#3008	1	1	yes	characteristic
563	C₂	C₃₇×#3012	1	1	yes	characteristic
564	C₂	C₃₇×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
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×#3548	C₂	semidirect
2. C₃₇×#3245	C₂	semidirect
3. C₃₇×#3228	C₂	semidirect
4. C₃₇×#3214	C₂	semidirect
5. C₃₇×#1654	C₂	semidirect
6. C₃₇×#1647	C₂	semidirect
7. C₃₇×#1625	C₂	semidirect
8. C₃₇×#1625	C₂	semidirect
9. C₃₇×#1552	C₂	semidirect
10. C₃₇×#1496	C₂	semidirect
11. C₃₇×#1480	C₂	semidirect
250. #18946	C₃₇	direct (N × H)
276. #3548	C₂×C₃₇	semidirect
277. #3245	C₂×C₃₇	semidirect
278. #3228	C₂×C₃₇	semidirect
279. #3214	C₂×C₃₇	semidirect
280. #1654	C₂×C₃₇	semidirect
281. #1647	C₂×C₃₇	semidirect
282. #1625	C₂×C₃₇	semidirect
283. #1625	C₂×C₃₇	semidirect
284. #1552	C₂×C₃₇	semidirect
285. #1496	C₂×C₃₇	semidirect
286. #1480	C₂×C₃₇	semidirect
333. C₃₇	#18946	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×#3548	2
C₃₇×#3245	2
C₃₇×#3228	2
C₃₇×#3214	2
C₃₇×#1654	2
C₃₇×#1647	2
C₃₇×#1625	2
C₃₇×#1552	2
C₃₇×#1496	2
C₃₇×#1480	2
#18946	37

Subgroups — C37×#18946 #22640199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18946 #22640199