Subgroups — C₃₇×#18906 #22640159

Order 9472.

902 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3507	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#3229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3226	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#1648	C₂	1	4	yes	maximal, complemented
6	C₃₇×#1640	C₂	1	4	yes	maximal, complemented
7	C₃₇×#1540	C₂	1	1	yes	maximal, characteristic
8	C₃₇×#1481	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1479	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₃₇	—	2	1	no	—
11	C₃₇×#559	C₂²	1	2	yes	—
12	C₃₇×#557	C₂²	1	2	yes	—
13	C₃₇×#556	—	2	1	no	—
14	C₃₇×#556	—	2	2	no	—
15	C₃₇×#554	—	2	1	no	—
16	C₃₇×#552	—	2	2	no	—
17	C₃₇×#539	—	2	2	no	—
18	C₃₇×#536	—	2	1	no	—
19	C₃₇×#533	C₂²	1	1	yes	characteristic
20	C₃₇×#532	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
22	C₃₇×#529	—	2	2	no	—
23	C₃₇×#520	—	2	1	no	—
24	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
25	C₃₇×#500	C₂²	1	2	yes	—
26	C₃₇×#498	—	2	1	no	—
27	C₃₇×#487	—	2	1	no	—
28	C₃₇×#486	C₂²	1	2	yes	—
29	C₃₇×#483	—	2	2	no	—
30	C₃₇×#480	—	2	2	no	—
31	C₃₇×#475	C₂²	1	4	yes	—
32	C₃₇×#474	—	2	2	no	—
33	C₃₇×#462	—	2	2	no	—
34	C₃₇×#462	C₂²	1	4	yes	—
35	C₃₇×#431	C₂²	1	1	yes	characteristic
36	C₃₇×#431	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
38	C₂×#103×C₃₇	—	2	1	no	—
39	C₃₇×#332	C₂²	1	2	yes	—
40	C₃₇×#331	C₂²	1	2	yes	—
41	C₃₇×Q₈⋊C₈	C₂²	1	4	yes	—
42	C₃₇×Q₈⋊C₈	C₂²	1	4	yes	—
43	C₂×#41×C₃₇	—	2	1	no	—
44	C₂²×Q₈×C₃₇	—	2	1	no	—
45	C₂²×Q₈×C₃₇	D₄	1	1	yes	characteristic
46	C₂×Q₁₆×C₃₇	—	2	4	no	—
47	C₂×Q₁₆×C₃₇	—	4	4	no	—
48	C₂²×C₈×C₃₇	—	2	1	no	—
49	C₄⋊Q₈×C₃₇	—	2	2	no	—
50	C₄⋊Q₈×C₃₇	—	2	1	no	—
51	C₄⋊Q₈×C₃₇	—	2	1	no	—
52	C₄⋊Q₈×C₃₇	—	2	1	no	—
53	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
54	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
55	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
56	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
57	#127×C₃₇	C₂³	1	1	yes	characteristic
58	#126×C₃₇	—	2	4	no	—
59	#126×C₃₇	—	2	4	no	—
60	#125×C₃₇	—	2	2	no	—
61	#125×C₃₇	—	2	4	no	—
62	#125×C₃₇	—	2	1	no	—
63	#124×C₃₇	—	2	2	no	—
64	#124×C₃₇	—	2	2	no	—
65	#124×C₃₇	—	2	1	no	—
66	#123×C₃₇	—	2	4	no	—
67	#123×C₃₇	—	2	4	no	—
68	C₂²⋊Q₈×C₃₇	—	2	2	no	—
69	C₂²⋊Q₈×C₃₇	—	2	2	no	—
70	C₂²⋊Q₈×C₃₇	—	2	4	no	—
71	C₂²⋊Q₈×C₃₇	—	2	1	no	—
72	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
73	#121×C₃₇	—	2	1	no	—
74	#121×C₃₇	D₄	1	2	yes	—
75	C₄×Q₈×C₃₇	—	2	2	no	—
76	C₄×Q₈×C₃₇	—	2	2	no	—
77	C₄×Q₈×C₃₇	—	2	1	no	—
78	C₄×Q₈×C₃₇	—	2	1	no	—
79	C₄×Q₈×C₃₇	—	2	1	no	—
80	C₄×Q₈×C₃₇	D₄	1	2	yes	—
81	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
82	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
83	C₄×D₄×C₃₇	—	2	4	no	—
84	C₄×D₄×C₃₇	—	2	2	no	—
85	C₄×D₄×C₃₇	—	2	2	no	—
86	C₄×D₄×C₃₇	—	2	1	no	—
87	C₄×D₄×C₃₇	D₄	1	2	yes	—
88	#117×C₃₇	—	2	2	no	—
89	#117×C₃₇	—	2	4	no	—
90	#117×C₃₇	—	2	1	no	—
91	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
92	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
93	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
94	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
95	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₃₇	—	2	1	no	—
97	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
98	#107×C₃₇	—	2	4	no	—
99	#106×C₃₇	—	2	4	no	—
100	C₄⋊C₈×C₃₇	—	2	1	no	—
101	C₄⋊C₈×C₃₇	—	2	1	no	—
102	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
103	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
104	#103×C₃₇	—	2	4	no	—
105	#103×C₃₇	—	2	4	no	—
106	#102×C₃₇	—	2	4	no	—
107	C₂²⋊C₈×C₃₇	—	2	1	no	—
108	C₂²⋊C₈×C₃₇	—	2	1	no	—
109	C₄×C₈×C₃₇	—	2	1	no	—
110	C₄×C₈×C₃₇	C₂³	1	2	yes	—
111	#41×C₃₇	—	4	2	no	—
112	#41×C₃₇	—	4	2	no	—
113	C₂×Q₈×C₃₇	—	2	1	no	—
114	C₂×Q₈×C₃₇	—	2	1	no	—
115	C₂×Q₈×C₃₇	—	2	1	no	—
116	C₂×Q₈×C₃₇	—	2	2	no	—
117	C₂×Q₈×C₃₇	—	2	2	no	—
118	C₂×Q₈×C₃₇	—	2	2	no	—
119	C₂×Q₈×C₃₇	—	4	1	no	—
120	C₂×Q₈×C₃₇	—	4	2	no	—
121	C₂×Q₈×C₃₇	—	4	2	no	—
122	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
123	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
124	C₂×D₄×C₃₇	—	2	2	no	—
125	C₂×D₄×C₃₇	—	2	1	no	—
126	C₂×D₄×C₃₇	—	2	1	no	—
127	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₃₇	—	2	1	no	—
129	C₂²×C₄×C₃₇	—	2	4	no	—
130	C₂²×C₄×C₃₇	—	2	1	no	—
131	C₂²×C₄×C₃₇	—	2	2	no	—
132	C₂²×C₄×C₃₇	—	4	1	no	—
133	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
136	Q₁₆×C₃₇	—	4	8	no	—
137	C₂×C₈×C₃₇	—	2	2	no	—
138	C₂×C₈×C₃₇	—	2	2	no	—
139	C₂×C₈×C₃₇	—	2	2	no	—
140	C₂×C₈×C₃₇	—	4	2	no	—
141	C₄⋊C₄×C₃₇	—	2	4	no	—
142	C₄⋊C₄×C₃₇	—	2	4	no	—
143	C₄⋊C₄×C₃₇	—	2	4	no	—
144	C₄⋊C₄×C₃₇	—	2	1	no	—
145	C₄⋊C₄×C₃₇	—	2	1	no	—
146	C₄⋊C₄×C₃₇	—	2	2	no	—
147	C₄⋊C₄×C₃₇	—	2	1	no	—
148	C₄⋊C₄×C₃₇	—	2	2	no	—
149	C₄⋊C₄×C₃₇	—	2	1	no	—
150	C₄⋊C₄×C₃₇	—	2	2	no	—
151	C₄⋊C₄×C₃₇	—	2	1	no	—
152	C₄⋊C₄×C₃₇	—	2	2	no	—
153	C₄⋊C₄×C₃₇	—	2	2	no	—
154	C₄⋊C₄×C₃₇	—	2	2	no	—
155	C₄⋊C₄×C₃₇	—	4	1	no	—
156	C₄⋊C₄×C₃₇	—	4	1	no	—
157	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
158	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
159	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
160	C₂²⋊C₄×C₃₇	—	2	4	no	—
161	C₂²⋊C₄×C₃₇	—	2	4	no	—
162	C₂²⋊C₄×C₃₇	—	2	4	no	—
163	C₂²⋊C₄×C₃₇	—	2	2	no	—
164	C₂²⋊C₄×C₃₇	—	2	2	no	—
165	C₂²⋊C₄×C₃₇	—	2	2	no	—
166	C₄²×C₃₇	—	2	4	no	—
167	C₄²×C₃₇	—	2	2	no	—
168	C₄²×C₃₇	—	2	2	no	—
169	C₄²×C₃₇	—	2	2	no	—
170	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
174	C₂³×C₃₇	—	2	2	no	—
175	C₂³×C₃₇	#120	1	1	yes	characteristic
176	Q₈×C₃₇	—	2	2	no	—
177	Q₈×C₃₇	—	2	2	no	—
178	Q₈×C₃₇	—	2	4	no	—
179	Q₈×C₃₇	—	4	1	no	—
180	Q₈×C₃₇	—	4	1	no	—
181	Q₈×C₃₇	—	4	2	no	—
182	Q₈×C₃₇	—	4	2	no	—
183	Q₈×C₃₇	—	4	2	no	—
184	Q₈×C₃₇	—	8	1	no	—
185	Q₈×C₃₇	—	8	2	no	—
186	D₄×C₃₇	—	4	2	no	—
187	D₄×C₃₇	—	4	4	no	—
188	D₄×C₃₇	—	4	1	no	—
189	D₄×C₃₇	—	4	1	no	—
190	D₄×C₃₇	—	4	2	no	—
191	C₂×C₄×C₃₇	—	2	2	no	—
192	C₂×C₄×C₃₇	—	2	2	no	—
193	C₂×C₄×C₃₇	—	2	2	no	—
194	C₂×C₄×C₃₇	—	2	2	no	—
195	C₂×C₄×C₃₇	—	2	2	no	—
196	C₂×C₄×C₃₇	—	2	2	no	—
197	C₂×C₄×C₃₇	—	4	1	no	—
198	C₂×C₄×C₃₇	—	4	2	no	—
199	C₂×C₄×C₃₇	—	4	4	no	—
200	C₂×C₄×C₃₇	—	4	2	no	—
201	C₂×C₄×C₃₇	—	8	1	no	—
202	C₂×C₄×C₃₇	—	8	4	no	—
203	C₂×C₄×C₃₇	—	8	2	no	—
204	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
205	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
206	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
207	C₂×C₄×C₃₇	#135	1	2	yes	—
208	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
209	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
212	C₈×C₃₇	—	4	2	no	—
213	C₈×C₃₇	—	4	2	no	—
214	C₈×C₃₇	—	4	2	no	—
215	#18906	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂²×C₃₇	—	2	1	no	—
217	C₂²×C₃₇	—	2	1	no	—
218	C₂²×C₃₇	—	4	2	no	—
219	C₂²×C₃₇	—	4	2	no	—
220	C₂²×C₃₇	—	4	2	no	—
221	C₂²×C₃₇	#449	1	2	yes	—
222	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
223	C₄×C₃₇	—	2	1	no	—
224	C₄×C₃₇	—	2	1	no	—
225	C₄×C₃₇	—	2	1	no	—
226	C₄×C₃₇	—	4	2	no	—
227	C₄×C₃₇	—	4	2	no	—
228	C₄×C₃₇	—	4	2	no	—
229	C₄×C₃₇	—	4	2	no	—
230	C₄×C₃₇	—	4	2	no	—
231	C₄×C₃₇	—	8	2	no	—
232	C₄×C₃₇	#449	1	2	yes	—
233	C₄×C₃₇	C₂×#135	1	1	yes	characteristic
234	C₄×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
235	C₄×C₃₇	#578	1	2	yes	—
236	#3507	C₂×C₃₇	1	1	yes	characteristic
237	#3229	C₂×C₃₇	1	1	yes	characteristic, complemented
238	#3226	C₂×C₃₇	1	1	yes	characteristic
239	C₂×#462	C₂×C₃₇	1	1	yes	characteristic, complemented
240	#1648	C₂×C₃₇	1	4	yes	complemented
241	#1640	C₂×C₃₇	1	4	yes	complemented
242	#1540	C₂×C₃₇	1	1	yes	characteristic
243	#1481	C₂×C₃₇	1	1	yes	characteristic, complemented
244	#1479	C₂×C₃₇	1	1	yes	characteristic, complemented
245	C₂×C₃₇	—	2	2	no	—
246	C₂×C₃₇	—	8	2	no	—
247	C₂×C₃₇	C₂×#449	1	1	yes	characteristic
248	C₂×C₃₇	#3011	1	1	yes	characteristic
249	C₂×C₃₇	#3022	1	1	yes	characteristic
250	C₂²×Q₁₆	—	2	1	no	—
251	#559	C₂²×C₃₇	1	2	yes	—
252	#557	C₂²×C₃₇	1	2	yes	—
253	#556	—	2	1	no	—
254	#556	—	2	2	no	—
255	#554	—	2	1	no	—
256	#552	—	2	2	no	—
257	#539	—	2	2	no	—
258	#536	—	2	1	no	—
259	#533	C₂²×C₃₇	1	1	yes	characteristic
260	#532	C₂²×C₃₇	1	1	yes	characteristic
261	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
262	#529	—	2	2	no	—
263	#520	—	2	1	no	—
264	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
265	#500	C₂²×C₃₇	1	2	yes	—
266	#498	—	2	1	no	—
267	#487	—	2	1	no	—
268	#486	C₂²×C₃₇	1	2	yes	—
269	#483	—	2	2	no	—
270	#480	—	2	2	no	—
271	#475	C₂²×C₃₇	1	4	yes	—
272	#474	—	2	2	no	—
273	#462	—	2	2	no	—
274	#462	C₂²×C₃₇	1	4	yes	—
275	#431	C₂²×C₃₇	1	1	yes	characteristic
276	#431	C₂²×C₃₇	1	1	yes	characteristic
277	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
278	C₂×#103	—	2	1	no	—
279	#332	C₂²×C₃₇	1	2	yes	—
280	#331	C₂²×C₃₇	1	2	yes	—
281	Q₈⋊C₈	C₂²×C₃₇	1	4	yes	—
282	Q₈⋊C₈	C₂²×C₃₇	1	4	yes	—
283	C₃₇	#18906	1	1	yes	characteristic, direct product factor, Sylow
284	C₂×#41	—	2	1	no	—
285	C₂²×Q₈	—	2	1	no	—
286	C₂²×Q₈	D₄×C₃₇	1	1	yes	characteristic
287	C₂×Q₁₆	—	2	4	no	—
288	C₂×Q₁₆	—	4	4	no	—
289	C₂²×C₈	—	2	1	no	—
290	C₄⋊Q₈	—	2	2	no	—
291	C₄⋊Q₈	—	2	1	no	—
292	C₄⋊Q₈	—	2	1	no	—
293	C₄⋊Q₈	—	2	1	no	—
294	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
295	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
296	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
297	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
298	#127	C₂³×C₃₇	1	1	yes	characteristic
299	#126	—	2	4	no	—
300	#126	—	2	4	no	—
301	#125	—	2	2	no	—
302	#125	—	2	4	no	—
303	#125	—	2	1	no	—
304	#124	—	2	2	no	—
305	#124	—	2	2	no	—
306	#124	—	2	1	no	—
307	#123	—	2	4	no	—
308	#123	—	2	4	no	—
309	C₂²⋊Q₈	—	2	2	no	—
310	C₂²⋊Q₈	—	2	2	no	—
311	C₂²⋊Q₈	—	2	4	no	—
312	C₂²⋊Q₈	—	2	1	no	—
313	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
314	#121	—	2	1	no	—
315	#121	D₄×C₃₇	1	2	yes	—
316	C₄×Q₈	—	2	2	no	—
317	C₄×Q₈	—	2	2	no	—
318	C₄×Q₈	—	2	1	no	—
319	C₄×Q₈	—	2	1	no	—
320	C₄×Q₈	—	2	1	no	—
321	C₄×Q₈	D₄×C₃₇	1	2	yes	—
322	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
323	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
324	C₄×D₄	—	2	4	no	—
325	C₄×D₄	—	2	2	no	—
326	C₄×D₄	—	2	2	no	—
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	D₄×C₃₇	1	2	yes	—
329	#117	—	2	2	no	—
330	#117	—	2	4	no	—
331	#117	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
337	C₂×C₄²	—	2	1	no	—
338	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
339	#107	—	2	4	no	—
340	#106	—	2	4	no	—
341	C₄⋊C₈	—	2	1	no	—
342	C₄⋊C₈	—	2	1	no	—
343	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
344	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
345	#103	—	2	4	no	—
346	#103	—	2	4	no	—
347	#102	—	2	4	no	—
348	C₂²⋊C₈	—	2	1	no	—
349	C₂²⋊C₈	—	2	1	no	—
350	C₄×C₈	—	2	1	no	—
351	C₄×C₈	C₂³×C₃₇	1	2	yes	—
352	#41	—	4	2	no	—
353	#41	—	4	2	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	4	1	no	—
361	C₂×Q₈	—	4	2	no	—
362	C₂×Q₈	—	4	2	no	—
363	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
364	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	4	1	no	—
374	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
377	Q₁₆	—	4	8	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	4	2	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	4	1	no	—
397	C₄⋊C₄	—	4	1	no	—
398	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
399	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
400	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₄²	—	2	4	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
412	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
413	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
414	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
415	C₂³	—	2	2	no	—
416	C₂³	#120×C₃₇	1	1	yes	characteristic
417	Q₈	—	2	2	no	—
418	Q₈	—	2	2	no	—
419	Q₈	—	2	4	no	—
420	Q₈	—	4	1	no	—
421	Q₈	—	4	1	no	—
422	Q₈	—	4	2	no	—
423	Q₈	—	4	2	no	—
424	Q₈	—	4	2	no	—
425	Q₈	—	8	1	no	—
426	Q₈	—	8	2	no	—
427	D₄	—	4	2	no	—
428	D₄	—	4	4	no	—
429	D₄	—	4	1	no	—
430	D₄	—	4	1	no	—
431	D₄	—	4	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	8	1	no	—
443	C₂×C₄	—	8	4	no	—
444	C₂×C₄	—	8	2	no	—
445	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
446	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
447	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
448	C₂×C₄	#135×C₃₇	1	2	yes	—
449	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
450	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
453	C₈	—	4	2	no	—
454	C₈	—	4	2	no	—
455	C₈	—	4	2	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	C₃₇×#449	1	2	yes	—
462	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	8	2	no	—
472	C₄	C₃₇×#449	1	2	yes	—
473	C₄	C₂×#135×C₃₇	1	1	yes	characteristic
474	C₄	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
475	C₄	C₃₇×#578	1	2	yes	—
476	C₂	—	2	2	no	—
477	C₂	—	8	2	no	—
478	C₂	C₂×C₃₇×#449	1	1	yes	characteristic
479	C₂	C₃₇×#3011	1	1	yes	characteristic
480	C₂	C₃₇×#3022	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×#3229	C₂	semidirect
4. C₂×C₃₇×#462	C₂	semidirect
5. C₃₇×#1648	C₂	semidirect
6. C₃₇×#1640	C₂	semidirect
8. C₃₇×#1481	C₂	semidirect
9. C₃₇×#1479	C₂	semidirect
215. #18906	C₃₇	direct (N × H)
237. #3229	C₂×C₃₇	semidirect
239. C₂×#462	C₂×C₃₇	semidirect
240. #1648	C₂×C₃₇	semidirect
241. #1640	C₂×C₃₇	semidirect
243. #1481	C₂×C₃₇	semidirect
244. #1479	C₂×C₃₇	semidirect
283. C₃₇	#18906	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×#3507	2
C₃₇×#3229	2
C₃₇×#3226	2
C₂×C₃₇×#462	2
C₃₇×#1648	2
C₃₇×#1640	2
C₃₇×#1540	2
C₃₇×#1481	2
C₃₇×#1479	2
#18906	37

Subgroups — C37×#18906 #22640159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18906 #22640159