Subgroups — C₃₇×#18898 #22640151

Order 9472.

978 conjugacy classes of subgroups.

The subgroup lattice has 508 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, complemented
2	C₃₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3205	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₇×#460	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#1628	C₂	1	4	yes	maximal, complemented
6	C₃₇×#1622	C₂	1	4	yes	maximal, complemented
7	C₃₇×#1542	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1479	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₃₇	—	2	1	no	—
11	C₃₇×#559	—	2	1	no	—
12	C₃₇×#557	—	2	1	no	—
13	C₃₇×#556	—	2	2	no	—
14	C₃₇×#556	C₂²	1	2	yes	complemented
15	C₃₇×#554	C₂²	1	2	yes	complemented
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×#127×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×#493	—	2	1	no	—
26	C₃₇×#492	C₂²	1	2	yes	—
27	C₃₇×#486	—	2	1	no	—
28	C₃₇×#486	C₂²	1	2	yes	—
29	C₃₇×#460	—	2	2	no	—
30	C₃₇×#460	—	2	2	no	—
31	C₃₇×#460	C₂²	1	4	yes	—
32	C₃₇×#459	C₂²	1	4	yes	—
33	C₃₇×#450	—	2	2	no	—
34	C₃₇×#447	—	2	2	no	—
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×#102×C₃₇	—	2	1	no	—
39	C₃₇×#333	C₂²	1	2	yes	complemented
40	C₃₇×#332	C₂²	1	2	yes	complemented
41	C₃₇×Q₈⋊C₈	C₂²	1	4	yes	complemented
42	C₃₇×D₄⋊C₈	C₂²	1	4	yes	complemented
43	C₂×#41×C₃₇	—	2	1	no	—
44	C₂²×Q₈×C₃₇	D₄	1	1	yes	characteristic
45	C₂²×D₄×C₃₇	—	2	1	no	—
46	C₂²×D₄×C₃₇	—	2	1	no	—
47	C₂²×D₄×C₃₇	—	2	1	no	—
48	C₂×SD₁₆×C₃₇	—	2	4	no	—
49	C₂×SD₁₆×C₃₇	—	2	4	no	—
50	C₂×SD₁₆×C₃₇	—	4	4	no	—
51	C₂×D₈×C₃₇	—	2	4	no	—
52	C₂²×C₈×C₃₇	—	2	1	no	—
53	C₄⋊Q₈×C₃₇	—	2	2	no	—
54	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
55	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
56	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
57	#127×C₃₇	—	2	1	no	—
58	#127×C₃₇	—	2	1	no	—
59	#127×C₃₇	—	2	1	no	—
60	#127×C₃₇	D₄	1	1	yes	characteristic
61	#127×C₃₇	C₂³	1	2	yes	—
62	#126×C₃₇	—	2	4	no	—
63	#126×C₃₇	—	2	4	no	—
64	#125×C₃₇	—	2	4	no	—
65	#125×C₃₇	—	2	2	no	—
66	#125×C₃₇	—	2	1	no	—
67	#124×C₃₇	—	2	2	no	—
68	#124×C₃₇	—	2	2	no	—
69	#124×C₃₇	—	2	1	no	—
70	#123×C₃₇	—	2	4	no	—
71	#123×C₃₇	—	2	4	no	—
72	C₂²⋊Q₈×C₃₇	—	2	2	no	—
73	C₂²⋊Q₈×C₃₇	—	2	2	no	—
74	C₂²⋊Q₈×C₃₇	—	2	4	no	—
75	C₂²⋊Q₈×C₃₇	—	2	1	no	—
76	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
77	#121×C₃₇	—	2	1	no	—
78	#121×C₃₇	D₄	1	2	yes	—
79	C₄×Q₈×C₃₇	—	2	2	no	—
80	C₄×Q₈×C₃₇	—	2	2	no	—
81	C₄×Q₈×C₃₇	—	2	1	no	—
82	C₄×Q₈×C₃₇	—	2	1	no	—
83	C₄×Q₈×C₃₇	—	2	1	no	—
84	C₄×Q₈×C₃₇	D₄	1	2	yes	—
85	C₄×Q₈×C₃₇	D₄	1	2	yes	—
86	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
87	C₄×D₄×C₃₇	—	2	4	no	—
88	C₄×D₄×C₃₇	—	2	2	no	—
89	C₄×D₄×C₃₇	—	2	2	no	—
90	C₄×D₄×C₃₇	—	2	1	no	—
91	C₄×D₄×C₃₇	C₂³	1	2	yes	—
92	#117×C₃₇	—	2	4	no	—
93	#117×C₃₇	—	2	1	no	—
94	#117×C₃₇	—	2	2	no	—
95	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
96	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
97	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₃₇	—	2	1	no	—
99	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
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	#102×C₃₇	—	2	4	no	—
105	#102×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	C₂⁴×C₃₇	—	4	1	no	—
112	#41×C₃₇	—	4	2	no	—
113	#41×C₃₇	—	4	2	no	—
114	C₂×Q₈×C₃₇	—	2	1	no	—
115	C₂×Q₈×C₃₇	—	2	1	no	—
116	C₂×Q₈×C₃₇	—	2	1	no	—
117	C₂×Q₈×C₃₇	—	2	2	no	—
118	C₂×Q₈×C₃₇	—	2	2	no	—
119	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
120	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
121	C₂×D₄×C₃₇	—	2	2	no	—
122	C₂×D₄×C₃₇	—	2	1	no	—
123	C₂×D₄×C₃₇	—	2	1	no	—
124	C₂×D₄×C₃₇	—	2	2	no	—
125	C₂×D₄×C₃₇	—	2	2	no	—
126	C₂×D₄×C₃₇	—	2	2	no	—
127	C₂×D₄×C₃₇	—	4	1	no	—
128	C₂×D₄×C₃₇	—	4	1	no	—
129	C₂×D₄×C₃₇	—	4	1	no	—
130	C₂×D₄×C₃₇	—	4	2	no	—
131	C₂×D₄×C₃₇	—	4	2	no	—
132	C₂×D₄×C₃₇	—	8	2	no	—
133	C₂×D₄×C₃₇	—	8	2	no	—
134	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₃₇	—	2	1	no	—
136	C₂²×C₄×C₃₇	—	2	4	no	—
137	C₂²×C₄×C₃₇	—	2	1	no	—
138	C₂²×C₄×C₃₇	—	2	2	no	—
139	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
142	SD₁₆×C₃₇	—	4	8	no	—
143	SD₁₆×C₃₇	—	8	4	no	—
144	D₈×C₃₇	—	8	4	no	—
145	C₂×C₈×C₃₇	—	2	2	no	—
146	C₂×C₈×C₃₇	—	2	2	no	—
147	C₂×C₈×C₃₇	—	2	2	no	—
148	C₂×C₈×C₃₇	—	4	2	no	—
149	C₄⋊C₄×C₃₇	—	2	4	no	—
150	C₄⋊C₄×C₃₇	—	2	4	no	—
151	C₄⋊C₄×C₃₇	—	2	4	no	—
152	C₄⋊C₄×C₃₇	—	2	2	no	—
153	C₄⋊C₄×C₃₇	—	2	1	no	—
154	C₄⋊C₄×C₃₇	—	2	2	no	—
155	C₄⋊C₄×C₃₇	—	2	1	no	—
156	C₄⋊C₄×C₃₇	—	2	2	no	—
157	C₄⋊C₄×C₃₇	—	2	1	no	—
158	C₄⋊C₄×C₃₇	—	2	2	no	—
159	C₄⋊C₄×C₃₇	—	2	1	no	—
160	C₄⋊C₄×C₃₇	—	2	1	no	—
161	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
162	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
163	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
164	C₂²⋊C₄×C₃₇	—	2	4	no	—
165	C₂²⋊C₄×C₃₇	—	2	4	no	—
166	C₂²⋊C₄×C₃₇	—	2	4	no	—
167	C₂²⋊C₄×C₃₇	—	2	2	no	—
168	C₂²⋊C₄×C₃₇	—	2	2	no	—
169	C₂²⋊C₄×C₃₇	—	2	2	no	—
170	C₄²×C₃₇	—	2	4	no	—
171	C₄²×C₃₇	—	2	2	no	—
172	C₄²×C₃₇	—	2	2	no	—
173	C₄²×C₃₇	—	2	2	no	—
174	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
178	C₂³×C₃₇	—	2	2	no	—
179	C₂³×C₃₇	—	4	2	no	—
180	C₂³×C₃₇	—	8	2	no	—
181	C₂³×C₃₇	—	8	2	no	—
182	C₂³×C₃₇	—	8	2	no	—
183	C₂³×C₃₇	#120	1	1	yes	characteristic
184	Q₈×C₃₇	—	2	2	no	—
185	Q₈×C₃₇	—	2	2	no	—
186	Q₈×C₃₇	—	4	2	no	—
187	Q₈×C₃₇	—	4	2	no	—
188	Q₈×C₃₇	—	4	2	no	—
189	Q₈×C₃₇	—	4	2	no	—
190	D₄×C₃₇	—	2	4	no	—
191	D₄×C₃₇	—	4	4	no	—
192	D₄×C₃₇	—	4	4	no	—
193	D₄×C₃₇	—	4	2	no	—
194	D₄×C₃₇	—	4	2	no	—
195	D₄×C₃₇	—	4	4	no	—
196	D₄×C₃₇	—	4	2	no	—
197	D₄×C₃₇	—	8	1	no	—
198	D₄×C₃₇	—	8	2	no	—
199	D₄×C₃₇	—	8	2	no	—
200	D₄×C₃₇	—	8	2	no	—
201	C₂×C₄×C₃₇	—	2	2	no	—
202	C₂×C₄×C₃₇	—	2	2	no	—
203	C₂×C₄×C₃₇	—	2	2	no	—
204	C₂×C₄×C₃₇	—	2	2	no	—
205	C₂×C₄×C₃₇	—	2	2	no	—
206	C₂×C₄×C₃₇	—	2	2	no	—
207	C₂×C₄×C₃₇	—	4	1	no	—
208	C₂×C₄×C₃₇	—	4	2	no	—
209	C₂×C₄×C₃₇	—	4	2	no	—
210	C₂×C₄×C₃₇	—	4	2	no	—
211	C₂×C₄×C₃₇	—	8	1	no	—
212	C₂×C₄×C₃₇	—	8	4	no	—
213	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
214	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
215	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
216	C₂×C₄×C₃₇	#135	1	2	yes	—
217	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
218	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
221	C₈×C₃₇	—	4	2	no	—
222	C₈×C₃₇	—	4	2	no	—
223	C₈×C₃₇	—	4	2	no	—
224	#18898	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂²×C₃₇	—	2	1	no	—
226	C₂²×C₃₇	—	2	1	no	—
227	C₂²×C₃₇	—	4	2	no	—
228	C₂²×C₃₇	—	4	2	no	—
229	C₂²×C₃₇	—	4	2	no	—
230	C₂²×C₃₇	—	8	2	no	—
231	C₂²×C₃₇	—	8	2	no	—
232	C₂²×C₃₇	—	8	2	no	—
233	C₂²×C₃₇	—	16	4	no	—
234	C₂²×C₃₇	#449	1	2	yes	—
235	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
236	C₄×C₃₇	—	2	1	no	—
237	C₄×C₃₇	—	2	1	no	—
238	C₄×C₃₇	—	2	1	no	—
239	C₄×C₃₇	—	4	2	no	—
240	C₄×C₃₇	—	4	2	no	—
241	C₄×C₃₇	—	4	2	no	—
242	C₄×C₃₇	—	4	2	no	—
243	C₄×C₃₇	—	4	2	no	—
244	C₄×C₃₇	#449	1	2	yes	—
245	C₄×C₃₇	C₂×#135	1	1	yes	characteristic
246	C₄×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
247	C₄×C₃₇	#577	1	2	yes	—
248	#3507	C₂×C₃₇	1	1	yes	characteristic, complemented
249	#3208	C₂×C₃₇	1	1	yes	characteristic, complemented
250	#3205	C₂×C₃₇	1	1	yes	characteristic
251	C₂×#460	C₂×C₃₇	1	1	yes	characteristic, complemented
252	#1628	C₂×C₃₇	1	4	yes	complemented
253	#1622	C₂×C₃₇	1	4	yes	complemented
254	#1542	C₂×C₃₇	1	1	yes	characteristic, complemented
255	#1480	C₂×C₃₇	1	1	yes	characteristic, complemented
256	#1479	C₂×C₃₇	1	1	yes	characteristic, complemented
257	C₂×C₃₇	—	2	2	no	—
258	C₂×C₃₇	—	8	2	no	—
259	C₂×C₃₇	—	16	2	no	—
260	C₂×C₃₇	C₂×#449	1	1	yes	characteristic
261	C₂×C₃₇	#3010	1	1	yes	characteristic
262	C₂×C₃₇	#3021	1	1	yes	characteristic
263	C₂²×SD₁₆	—	2	1	no	—
264	#559	—	2	1	no	—
265	#557	—	2	1	no	—
266	#556	—	2	2	no	—
267	#556	C₂²×C₃₇	1	2	yes	complemented
268	#554	C₂²×C₃₇	1	2	yes	complemented
269	#552	—	2	2	no	—
270	#539	—	2	2	no	—
271	#536	—	2	1	no	—
272	#533	C₂²×C₃₇	1	1	yes	characteristic
273	#532	C₂²×C₃₇	1	1	yes	characteristic
274	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
275	#529	—	2	2	no	—
276	#520	—	2	1	no	—
277	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
278	#493	—	2	1	no	—
279	#492	C₂²×C₃₇	1	2	yes	—
280	#486	—	2	1	no	—
281	#486	C₂²×C₃₇	1	2	yes	—
282	#460	—	2	2	no	—
283	#460	—	2	2	no	—
284	#460	C₂²×C₃₇	1	4	yes	—
285	#459	C₂²×C₃₇	1	4	yes	—
286	#450	—	2	2	no	—
287	#447	—	2	2	no	—
288	#431	C₂²×C₃₇	1	1	yes	characteristic
289	#431	C₂²×C₃₇	1	1	yes	characteristic
290	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
291	C₂×#102	—	2	1	no	—
292	#333	C₂²×C₃₇	1	2	yes	complemented
293	#332	C₂²×C₃₇	1	2	yes	complemented
294	Q₈⋊C₈	C₂²×C₃₇	1	4	yes	complemented
295	D₄⋊C₈	C₂²×C₃₇	1	4	yes	complemented
296	C₃₇	#18898	1	1	yes	characteristic, direct product factor, Sylow
297	C₂×#41	—	2	1	no	—
298	C₂²×Q₈	D₄×C₃₇	1	1	yes	characteristic
299	C₂²×D₄	—	2	1	no	—
300	C₂²×D₄	—	2	1	no	—
301	C₂²×D₄	—	2	1	no	—
302	C₂×SD₁₆	—	2	4	no	—
303	C₂×SD₁₆	—	2	4	no	—
304	C₂×SD₁₆	—	4	4	no	—
305	C₂×D₈	—	2	4	no	—
306	C₂²×C₈	—	2	1	no	—
307	C₄⋊Q₈	—	2	2	no	—
308	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
309	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
310	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
311	#127	—	2	1	no	—
312	#127	—	2	1	no	—
313	#127	—	2	1	no	—
314	#127	D₄×C₃₇	1	1	yes	characteristic
315	#127	C₂³×C₃₇	1	2	yes	—
316	#126	—	2	4	no	—
317	#126	—	2	4	no	—
318	#125	—	2	4	no	—
319	#125	—	2	2	no	—
320	#125	—	2	1	no	—
321	#124	—	2	2	no	—
322	#124	—	2	2	no	—
323	#124	—	2	1	no	—
324	#123	—	2	4	no	—
325	#123	—	2	4	no	—
326	C₂²⋊Q₈	—	2	2	no	—
327	C₂²⋊Q₈	—	2	2	no	—
328	C₂²⋊Q₈	—	2	4	no	—
329	C₂²⋊Q₈	—	2	1	no	—
330	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
331	#121	—	2	1	no	—
332	#121	D₄×C₃₇	1	2	yes	—
333	C₄×Q₈	—	2	2	no	—
334	C₄×Q₈	—	2	2	no	—
335	C₄×Q₈	—	2	1	no	—
336	C₄×Q₈	—	2	1	no	—
337	C₄×Q₈	—	2	1	no	—
338	C₄×Q₈	D₄×C₃₇	1	2	yes	—
339	C₄×Q₈	D₄×C₃₇	1	2	yes	—
340	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
341	C₄×D₄	—	2	4	no	—
342	C₄×D₄	—	2	2	no	—
343	C₄×D₄	—	2	2	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	C₂³×C₃₇	1	2	yes	—
346	#117	—	2	4	no	—
347	#117	—	2	1	no	—
348	#117	—	2	2	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
352	C₂×C₄²	—	2	1	no	—
353	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
354	C₄⋊C₈	—	2	1	no	—
355	C₄⋊C₈	—	2	1	no	—
356	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
357	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
358	#102	—	2	4	no	—
359	#102	—	2	4	no	—
360	#102	—	2	4	no	—
361	C₂²⋊C₈	—	2	1	no	—
362	C₂²⋊C₈	—	2	1	no	—
363	C₄×C₈	—	2	1	no	—
364	C₄×C₈	C₂³×C₃₇	1	2	yes	—
365	C₂⁴	—	4	1	no	—
366	#41	—	4	2	no	—
367	#41	—	4	2	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
374	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	4	1	no	—
382	C₂×D₄	—	4	1	no	—
383	C₂×D₄	—	4	1	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	4	2	no	—
386	C₂×D₄	—	8	2	no	—
387	C₂×D₄	—	8	2	no	—
388	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
396	SD₁₆	—	4	8	no	—
397	SD₁₆	—	8	4	no	—
398	D₈	—	8	4	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	4	2	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
416	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
417	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
418	C₂²⋊C₄	—	2	4	no	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	2	4	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₄²	—	2	4	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
429	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
430	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
431	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
432	C₂³	—	2	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	8	2	no	—
435	C₂³	—	8	2	no	—
436	C₂³	—	8	2	no	—
437	C₂³	#120×C₃₇	1	1	yes	characteristic
438	Q₈	—	2	2	no	—
439	Q₈	—	2	2	no	—
440	Q₈	—	4	2	no	—
441	Q₈	—	4	2	no	—
442	Q₈	—	4	2	no	—
443	Q₈	—	4	2	no	—
444	D₄	—	2	4	no	—
445	D₄	—	4	4	no	—
446	D₄	—	4	4	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	4	4	no	—
450	D₄	—	4	2	no	—
451	D₄	—	8	1	no	—
452	D₄	—	8	2	no	—
453	D₄	—	8	2	no	—
454	D₄	—	8	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	8	1	no	—
466	C₂×C₄	—	8	4	no	—
467	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
468	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
469	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
470	C₂×C₄	#135×C₃₇	1	2	yes	—
471	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
472	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
473	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
474	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
475	C₈	—	4	2	no	—
476	C₈	—	4	2	no	—
477	C₈	—	4	2	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	8	2	no	—
484	C₂²	—	8	2	no	—
485	C₂²	—	8	2	no	—
486	C₂²	—	16	4	no	—
487	C₂²	C₃₇×#449	1	2	yes	—
488	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	C₃₇×#449	1	2	yes	—
498	C₄	C₂×#135×C₃₇	1	1	yes	characteristic
499	C₄	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
500	C₄	C₃₇×#577	1	2	yes	—
501	C₂	—	2	2	no	—
502	C₂	—	8	2	no	—
503	C₂	—	16	2	no	—
504	C₂	C₂×C₃₇×#449	1	1	yes	characteristic
505	C₂	C₃₇×#3010	1	1	yes	characteristic
506	C₂	C₃₇×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
prime radical	C₃₇×#3205	C₂
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×#3507	C₂	semidirect
2. C₃₇×#3208	C₂	semidirect
4. C₂×C₃₇×#460	C₂	semidirect
5. C₃₇×#1628	C₂	semidirect
6. C₃₇×#1622	C₂	semidirect
7. C₃₇×#1542	C₂	semidirect
8. C₃₇×#1480	C₂	semidirect
9. C₃₇×#1479	C₂	semidirect
14. C₃₇×#556	C₂²	semidirect
15. C₃₇×#554	C₂²	semidirect
39. C₃₇×#333	C₂²	semidirect
40. C₃₇×#332	C₂²	semidirect
41. C₃₇×Q₈⋊C₈	C₂²	semidirect
42. C₃₇×D₄⋊C₈	C₂²	semidirect
224. #18898	C₃₇	direct (N × H)
248. #3507	C₂×C₃₇	semidirect
249. #3208	C₂×C₃₇	semidirect
251. C₂×#460	C₂×C₃₇	semidirect
252. #1628	C₂×C₃₇	semidirect
253. #1622	C₂×C₃₇	semidirect
254. #1542	C₂×C₃₇	semidirect
255. #1480	C₂×C₃₇	semidirect
256. #1479	C₂×C₃₇	semidirect
267. #556	C₂²×C₃₇	semidirect
268. #554	C₂²×C₃₇	semidirect
292. #333	C₂²×C₃₇	semidirect
293. #332	C₂²×C₃₇	semidirect
294. Q₈⋊C₈	C₂²×C₃₇	semidirect
295. D₄⋊C₈	C₂²×C₃₇	semidirect
296. C₃₇	#18898	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×#3208	2
C₃₇×#3205	2
C₂×C₃₇×#460	2
C₃₇×#1628	2
C₃₇×#1622	2
C₃₇×#1542	2
C₃₇×#1480	2
C₃₇×#1479	2
#18898	37

Subgroups — C37×#18898 #22640151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18898 #22640151