Subgroups — C₃₇×#18847 #22640100

Order 9472.

902 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3501	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#3255	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3231	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#3110	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#1651	C₂	1	2	yes	maximal, complemented
6	C₃₇×#1649	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1644	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1643	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1559	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1497	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1486	C₂	1	1	yes	maximal, characteristic
12	C₃₇×#554	—	2	1	no	—
13	C₃₇×#554	—	2	2	no	—
14	C₃₇×#554	—	2	2	no	—
15	C₃₇×#554	C₂²	1	2	yes	—
16	D₄×Q₈×C₃₇	—	2	1	no	—
17	D₄×Q₈×C₃₇	C₂²	1	2	yes	—
18	C₃₇×#544	—	2	1	no	—
19	C₃₇×#543	—	2	2	no	—
20	C₃₇×#533	C₂²	1	1	yes	characteristic
21	C₃₇×#533	C₂²	1	1	yes	characteristic
22	C₃₇×#533	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₃₇	—	2	2	no	—
24	C₃₇×#518	—	2	1	no	—
25	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
26	C₃₇×#500	C₂²	1	1	yes	characteristic, complemented
27	C₃₇×#498	C₂²	1	1	yes	characteristic, complemented
28	C₃₇×#487	C₂²	1	1	yes	characteristic, complemented
29	C₃₇×#487	C₂²	1	1	yes	characteristic, complemented
30	C₃₇×#485	—	2	2	no	—
31	C₃₇×#484	—	2	1	no	—
32	C₃₇×#479	—	2	2	no	—
33	C₃₇×#475	—	2	1	no	—
34	C₃₇×#475	C₂²	1	2	yes	complemented
35	C₃₇×#474	C₂²	1	2	yes	—
36	C₃₇×#470	—	2	2	no	—
37	C₃₇×#462	—	2	1	no	—
38	C₃₇×#462	C₂²	1	2	yes	complemented
39	C₃₇×#461	C₂²	1	2	yes	—
40	C₃₇×#450	—	2	1	no	—
41	C₃₇×#440	—	2	2	no	—
42	C₃₇×#432	C₂²	1	1	yes	characteristic
43	C₃₇×#431	C₂²	1	1	yes	characteristic
44	C₃₇×#423	C₂²	1	1	yes	characteristic
45	C₃₇×#333	C₂²	1	2	yes	complemented
46	C₃₇×#332	C₂²	1	2	yes	complemented
47	C₃₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
48	C₃₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
49	C₃₇×D₄⋊C₈	C₂²	1	2	yes	—
50	C₃₇×D₄⋊C₈	C₂²	1	2	yes	—
51	C₂²×Q₈×C₃₇	—	2	2	no	—
52	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₃₇	—	2	1	no	—
54	C₂×Q₁₆×C₃₇	—	2	2	no	—
55	C₂×SD₁₆×C₃₇	—	2	2	no	—
56	C₂×M₁₆×C₃₇	—	2	1	no	—
57	C₄⋊Q₈×C₃₇	—	2	2	no	—
58	C₄⋊Q₈×C₃₇	—	2	2	no	—
59	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
60	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
61	C₄⋊Q₈×C₃₇	C₂³	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	#125×C₃₇	—	2	2	no	—
66	#125×C₃₇	—	2	2	no	—
67	#125×C₃₇	—	2	1	no	—
68	#125×C₃₇	—	2	1	no	—
69	#125×C₃₇	—	2	1	no	—
70	C₂²⋊Q₈×C₃₇	—	2	4	no	—
71	C₂²⋊Q₈×C₃₇	—	2	4	no	—
72	C₂²⋊Q₈×C₃₇	—	2	4	no	—
73	C₂²⋊Q₈×C₃₇	—	2	4	no	—
74	C₂²⋊Q₈×C₃₇	—	2	2	no	—
75	C₂²⋊Q₈×C₃₇	—	2	4	no	—
76	C₂²⋊Q₈×C₃₇	—	2	1	no	—
77	C₂²⋊Q₈×C₃₇	—	2	1	no	—
78	C₂²⋊Q₈×C₃₇	—	2	2	no	—
79	C₂²⋊Q₈×C₃₇	—	2	4	no	—
80	C₂²⋊Q₈×C₃₇	—	2	1	no	—
81	C₂²⋊Q₈×C₃₇	—	2	1	no	—
82	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
83	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
84	C₄×Q₈×C₃₇	—	2	1	no	—
85	C₄×Q₈×C₃₇	—	2	1	no	—
86	C₄×Q₈×C₃₇	—	2	1	no	—
87	C₄×Q₈×C₃₇	—	2	1	no	—
88	C₄×Q₈×C₃₇	D₄	1	2	yes	—
89	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
90	C₄×D₄×C₃₇	—	2	2	no	—
91	C₄×D₄×C₃₇	—	2	2	no	—
92	C₄×D₄×C₃₇	—	2	2	no	—
93	C₄×D₄×C₃₇	—	2	2	no	—
94	C₄×D₄×C₃₇	—	2	1	no	—
95	C₄×D₄×C₃₇	—	2	1	no	—
96	C₄×D₄×C₃₇	D₄	1	2	yes	—
97	C₄×D₄×C₃₇	C₂³	1	2	yes	—
98	#117×C₃₇	—	2	1	no	—
99	#117×C₃₇	—	2	1	no	—
100	#117×C₃₇	—	2	1	no	—
101	C₂×C₄⋊C₄×C₃₇	—	2	4	no	—
102	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
103	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
105	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
106	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
107	#107×C₃₇	—	2	2	no	—
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	#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	C₂⁴×C₃₇	—	2	1	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	2	no	—
133	C₂×Q₈×C₃₇	—	8	2	no	—
134	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
135	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
136	C₂×D₄×C₃₇	—	2	4	no	—
137	C₂×D₄×C₃₇	—	2	1	no	—
138	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₃₇	—	2	4	no	—
140	C₂²×C₄×C₃₇	—	2	4	no	—
141	C₂²×C₄×C₃₇	—	2	1	no	—
142	C₂²×C₄×C₃₇	—	2	2	no	—
143	C₂²×C₄×C₃₇	—	2	2	no	—
144	C₂²×C₄×C₃₇	—	8	1	no	—
145	C₂²×C₄×C₃₇	—	8	1	no	—
146	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
149	Q₁₆×C₃₇	—	8	2	no	—
150	SD₁₆×C₃₇	—	4	4	no	—
151	M₁₆×C₃₇	—	8	1	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	4	no	—
159	C₄⋊C₄×C₃₇	—	2	2	no	—
160	C₄⋊C₄×C₃₇	—	2	2	no	—
161	C₄⋊C₄×C₃₇	—	2	1	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	2	no	—
166	C₄⋊C₄×C₃₇	—	2	1	no	—
167	C₄⋊C₄×C₃₇	—	2	1	no	—
168	C₄⋊C₄×C₃₇	—	2	1	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	1	no	—
173	C₄⋊C₄×C₃₇	—	2	1	no	—
174	C₄⋊C₄×C₃₇	—	4	1	no	—
175	C₄⋊C₄×C₃₇	—	4	1	no	—
176	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
177	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
178	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
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	2	no	—
187	C₄²×C₃₇	—	2	2	no	—
188	C₄²×C₃₇	—	4	1	no	—
189	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
193	C₂³×C₃₇	—	2	4	no	—
194	C₂³×C₃₇	—	2	2	no	—
195	C₂³×C₃₇	—	8	1	no	—
196	C₂³×C₃₇	—	8	1	no	—
197	C₂³×C₃₇	#120	1	1	yes	characteristic
198	Q₈×C₃₇	—	2	2	no	—
199	Q₈×C₃₇	—	2	2	no	—
200	Q₈×C₃₇	—	4	2	no	—
201	Q₈×C₃₇	—	4	1	no	—
202	Q₈×C₃₇	—	4	1	no	—
203	Q₈×C₃₇	—	4	2	no	—
204	Q₈×C₃₇	—	4	1	no	—
205	Q₈×C₃₇	—	4	1	no	—
206	Q₈×C₃₇	—	8	1	no	—
207	Q₈×C₃₇	—	8	4	no	—
208	D₄×C₃₇	—	2	4	no	—
209	D₄×C₃₇	—	2	2	no	—
210	D₄×C₃₇	#137	1	4	yes	—
211	C₂×C₄×C₃₇	—	2	2	no	—
212	C₂×C₄×C₃₇	—	2	1	no	—
213	C₂×C₄×C₃₇	—	2	1	no	—
214	C₂×C₄×C₃₇	—	2	2	no	—
215	C₂×C₄×C₃₇	—	2	2	no	—
216	C₂×C₄×C₃₇	—	2	2	no	—
217	C₂×C₄×C₃₇	—	2	2	no	—
218	C₂×C₄×C₃₇	—	2	2	no	—
219	C₂×C₄×C₃₇	—	4	1	no	—
220	C₂×C₄×C₃₇	—	4	2	no	—
221	C₂×C₄×C₃₇	—	4	2	no	—
222	C₂×C₄×C₃₇	—	4	1	no	—
223	C₂×C₄×C₃₇	—	4	1	no	—
224	C₂×C₄×C₃₇	—	8	2	no	—
225	C₂×C₄×C₃₇	—	8	1	no	—
226	C₂×C₄×C₃₇	—	8	4	no	—
227	C₂×C₄×C₃₇	—	8	4	no	—
228	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
229	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
230	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
231	C₂×C₄×C₃₇	C₂²×D₄	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	C₈×C₃₇	—	4	1	no	—
235	C₈×C₃₇	—	4	1	no	—
236	C₈×C₃₇	—	4	2	no	—
237	C₈×C₃₇	—	4	2	no	—
238	#18847	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂²×C₃₇	—	2	1	no	—
240	C₂²×C₃₇	—	2	4	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	—	8	4	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	—	2	1	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	—	4	2	no	—
256	C₄×C₃₇	—	8	1	no	—
257	C₄×C₃₇	—	8	1	no	—
258	C₄×C₃₇	C₂×#137	1	2	yes	—
259	C₄×C₃₇	#576	1	1	yes	characteristic
260	C₄×C₃₇	#577	1	1	yes	characteristic
261	#3501	C₂×C₃₇	1	1	yes	characteristic
262	#3255	C₂×C₃₇	1	1	yes	characteristic, complemented
263	#3231	C₂×C₃₇	1	1	yes	characteristic, complemented
264	#3110	C₂×C₃₇	1	1	yes	characteristic
265	#1651	C₂×C₃₇	1	2	yes	complemented
266	#1649	C₂×C₃₇	1	2	yes	complemented
267	#1644	C₂×C₃₇	1	2	yes	complemented
268	#1643	C₂×C₃₇	1	2	yes	complemented
269	#1559	C₂×C₃₇	1	1	yes	characteristic, complemented
270	#1497	C₂×C₃₇	1	1	yes	characteristic, complemented
271	#1486	C₂×C₃₇	1	1	yes	characteristic
272	C₂×C₃₇	—	4	1	no	—
273	C₂×C₃₇	—	4	4	no	—
274	C₂×C₃₇	#3004	1	1	yes	characteristic
275	C₂×C₃₇	#3012	1	1	yes	characteristic
276	C₂×C₃₇	#3022	1	1	yes	characteristic
277	#554	—	2	1	no	—
278	#554	—	2	2	no	—
279	#554	—	2	2	no	—
280	#554	C₂²×C₃₇	1	2	yes	—
281	D₄×Q₈	—	2	1	no	—
282	D₄×Q₈	C₂²×C₃₇	1	2	yes	—
283	#544	—	2	1	no	—
284	#543	—	2	2	no	—
285	#533	C₂²×C₃₇	1	1	yes	characteristic
286	#533	C₂²×C₃₇	1	1	yes	characteristic
287	#533	C₂²×C₃₇	1	1	yes	characteristic
288	C₂×C₂²⋊Q₈	—	2	2	no	—
289	#518	—	2	1	no	—
290	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
291	#500	C₂²×C₃₇	1	1	yes	characteristic, complemented
292	#498	C₂²×C₃₇	1	1	yes	characteristic, complemented
293	#487	C₂²×C₃₇	1	1	yes	characteristic, complemented
294	#487	C₂²×C₃₇	1	1	yes	characteristic, complemented
295	#485	—	2	2	no	—
296	#484	—	2	1	no	—
297	#479	—	2	2	no	—
298	#475	—	2	1	no	—
299	#475	C₂²×C₃₇	1	2	yes	complemented
300	#474	C₂²×C₃₇	1	2	yes	—
301	#470	—	2	2	no	—
302	#462	—	2	1	no	—
303	#462	C₂²×C₃₇	1	2	yes	complemented
304	#461	C₂²×C₃₇	1	2	yes	—
305	#450	—	2	1	no	—
306	#440	—	2	2	no	—
307	#432	C₂²×C₃₇	1	1	yes	characteristic
308	#431	C₂²×C₃₇	1	1	yes	characteristic
309	#423	C₂²×C₃₇	1	1	yes	characteristic
310	#333	C₂²×C₃₇	1	2	yes	complemented
311	#332	C₂²×C₃₇	1	2	yes	complemented
312	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	complemented
313	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	complemented
314	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
315	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
316	C₃₇	#18847	1	1	yes	characteristic, direct product factor, Sylow
317	C₂²×Q₈	—	2	2	no	—
318	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
319	C₂³×C₄	—	2	1	no	—
320	C₂×Q₁₆	—	2	2	no	—
321	C₂×SD₁₆	—	2	2	no	—
322	C₂×M₁₆	—	2	1	no	—
323	C₄⋊Q₈	—	2	2	no	—
324	C₄⋊Q₈	—	2	2	no	—
325	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
326	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
327	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
328	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
329	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
330	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
331	#125	—	2	2	no	—
332	#125	—	2	2	no	—
333	#125	—	2	1	no	—
334	#125	—	2	1	no	—
335	#125	—	2	1	no	—
336	C₂²⋊Q₈	—	2	4	no	—
337	C₂²⋊Q₈	—	2	4	no	—
338	C₂²⋊Q₈	—	2	4	no	—
339	C₂²⋊Q₈	—	2	4	no	—
340	C₂²⋊Q₈	—	2	2	no	—
341	C₂²⋊Q₈	—	2	4	no	—
342	C₂²⋊Q₈	—	2	1	no	—
343	C₂²⋊Q₈	—	2	1	no	—
344	C₂²⋊Q₈	—	2	2	no	—
345	C₂²⋊Q₈	—	2	4	no	—
346	C₂²⋊Q₈	—	2	1	no	—
347	C₂²⋊Q₈	—	2	1	no	—
348	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
349	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
350	C₄×Q₈	—	2	1	no	—
351	C₄×Q₈	—	2	1	no	—
352	C₄×Q₈	—	2	1	no	—
353	C₄×Q₈	—	2	1	no	—
354	C₄×Q₈	D₄×C₃₇	1	2	yes	—
355	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	—	2	1	no	—
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	D₄×C₃₇	1	2	yes	—
363	C₄×D₄	C₂³×C₃₇	1	2	yes	—
364	#117	—	2	1	no	—
365	#117	—	2	1	no	—
366	#117	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	4	no	—
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
370	C₂×C₂²⋊C₄	—	2	4	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
373	#107	—	2	2	no	—
374	#107	—	2	2	no	—
375	#106	—	2	2	no	—
376	#106	—	2	2	no	—
377	C₄⋊C₈	—	2	1	no	—
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
380	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
381	#103	—	2	2	no	—
382	#103	—	2	2	no	—
383	#103	—	2	2	no	—
384	#103	—	2	2	no	—
385	#103	—	2	2	no	—
386	#102	—	2	2	no	—
387	C₂²⋊C₈	—	2	1	no	—
388	C₂²⋊C₈	—	2	1	no	—
389	#97	—	2	1	no	—
390	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
391	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
392	C₂⁴	—	2	1	no	—
393	C₂×Q₈	—	2	4	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	—	2	1	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	8	2	no	—
399	C₂×Q₈	—	8	2	no	—
400	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
401	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	8	1	no	—
411	C₂²×C₄	—	8	1	no	—
412	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
415	Q₁₆	—	8	2	no	—
416	SD₁₆	—	4	4	no	—
417	M₁₆	—	8	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	4	1	no	—
441	C₄⋊C₄	—	4	1	no	—
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	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	4	1	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	2	2	no	—
454	C₄²	—	4	1	no	—
455	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
456	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
457	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
458	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
459	C₂³	—	2	4	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	8	1	no	—
462	C₂³	—	8	1	no	—
463	C₂³	#120×C₃₇	1	1	yes	characteristic
464	Q₈	—	2	2	no	—
465	Q₈	—	2	2	no	—
466	Q₈	—	4	2	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	—	8	1	no	—
473	Q₈	—	8	4	no	—
474	D₄	—	2	4	no	—
475	D₄	—	2	2	no	—
476	D₄	#137×C₃₇	1	4	yes	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	8	2	no	—
491	C₂×C₄	—	8	1	no	—
492	C₂×C₄	—	8	4	no	—
493	C₂×C₄	—	8	4	no	—
494	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
495	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
496	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
498	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
500	C₈	—	4	1	no	—
501	C₈	—	4	1	no	—
502	C₈	—	4	2	no	—
503	C₈	—	4	2	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	8	4	no	—
511	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
512	C₄	—	2	1	no	—
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	C₂×#137×C₃₇	1	2	yes	—
524	C₄	C₃₇×#576	1	1	yes	characteristic
525	C₄	C₃₇×#577	1	1	yes	characteristic
526	C₂	—	4	1	no	—
527	C₂	—	4	4	no	—
528	C₂	C₃₇×#3004	1	1	yes	characteristic
529	C₂	C₃₇×#3012	1	1	yes	characteristic
530	C₂	C₃₇×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
prime radical	C₂²×D₄×C₃₇	D₄
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
3. C₃₇×#3231	C₂	semidirect
5. C₃₇×#1651	C₂	semidirect
6. C₃₇×#1649	C₂	semidirect
7. C₃₇×#1644	C₂	semidirect
8. C₃₇×#1643	C₂	semidirect
9. C₃₇×#1559	C₂	semidirect
10. C₃₇×#1497	C₂	semidirect
26. C₃₇×#500	C₂²	semidirect
27. C₃₇×#498	C₂²	semidirect
28. C₃₇×#487	C₂²	semidirect
29. C₃₇×#487	C₂²	semidirect
34. C₃₇×#475	C₂²	semidirect
38. C₃₇×#462	C₂²	semidirect
45. C₃₇×#333	C₂²	semidirect
46. C₃₇×#332	C₂²	semidirect
47. C₃₇×Q₈⋊C₈	C₂²	semidirect
48. C₃₇×Q₈⋊C₈	C₂²	semidirect
238. #18847	C₃₇	direct (N × H)
262. #3255	C₂×C₃₇	semidirect
263. #3231	C₂×C₃₇	semidirect
265. #1651	C₂×C₃₇	semidirect
266. #1649	C₂×C₃₇	semidirect
267. #1644	C₂×C₃₇	semidirect
268. #1643	C₂×C₃₇	semidirect
269. #1559	C₂×C₃₇	semidirect
270. #1497	C₂×C₃₇	semidirect
291. #500	C₂²×C₃₇	semidirect
292. #498	C₂²×C₃₇	semidirect
293. #487	C₂²×C₃₇	semidirect
294. #487	C₂²×C₃₇	semidirect
299. #475	C₂²×C₃₇	semidirect
303. #462	C₂²×C₃₇	semidirect
310. #333	C₂²×C₃₇	semidirect
311. #332	C₂²×C₃₇	semidirect
312. Q₈⋊C₈	C₂²×C₃₇	semidirect
313. Q₈⋊C₈	C₂²×C₃₇	semidirect
316. C₃₇	#18847	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×#3501	2
C₃₇×#3255	2
C₃₇×#3231	2
C₃₇×#3110	2
C₃₇×#1651	2
C₃₇×#1649	2
C₃₇×#1644	2
C₃₇×#1643	2
C₃₇×#1559	2
C₃₇×#1497	2
C₃₇×#1486	2
#18847	37

Subgroups — C37×#18847 #22640100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18847 #22640100