Subgroups — C₃₇×#28501 #22649754

Order 9472.

1030 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3156	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3155	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₇×#495	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#471	C₂	1	2	yes	maximal, complemented
5	C₃₇×#3057	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₇×#443	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2004	C₂	1	2	yes	maximal, complemented
8	C₃₇×#2003	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1979	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1978	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₃₇	C₂²	1	2	yes	—
13	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	2	yes	—
14	C₂×#135×C₃₇	C₂²	1	1	yes	characteristic
15	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
16	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
17	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×#131×C₃₇	C₂²	1	2	yes	—
19	C₃₇×#536	C₂²	1	2	yes	—
20	C₃₇×#535	C₂²	1	2	yes	—
21	C₂×#124×C₃₇	C₂²	1	2	yes	—
22	C₃₇×#497	—	2	2	no	—
23	C₃₇×#496	—	2	2	no	—
24	C₃₇×#495	—	2	1	no	—
25	C₃₇×#495	—	2	1	no	—
26	C₃₇×#495	—	2	4	no	—
27	C₃₇×#494	—	2	1	no	—
28	C₃₇×#493	—	2	1	no	—
29	C₃₇×#471	—	2	8	no	—
30	C₃₇×#468	—	2	4	no	—
31	C₃₇×#465	—	2	4	no	—
32	C₃₇×#443	—	2	4	no	—
33	C₂×#108×C₃₇	C₂²	1	1	yes	characteristic
34	C₂×#108×C₃₇	C₂²	1	1	yes	characteristic
35	C₃₇×#427	C₂²	1	1	yes	characteristic
36	C₂×#104×C₃₇	C₂²	1	2	yes	—
37	C₃₇×#419	C₂²	1	2	yes	—
38	C₃₇×#418	C₂²	1	2	yes	—
39	C₂×#101×C₃₇	C₂²	1	2	yes	—
40	C₂×#100×C₃₇	C₂²	1	2	yes	—
41	C₃₇×#405	C₂²	1	1	yes	characteristic
42	C₃₇×#405	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
44	C₃₇×#339	C₂²	1	1	yes	characteristic
45	C₃₇×#339	C₂²	1	1	yes	characteristic
46	C₂×#41×C₃₇	C₂³	1	2	yes	—
47	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
48	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
49	#137×C₃₇	—	2	4	no	—
50	#137×C₃₇	—	4	2	no	—
51	AGL(1,ℤ/8)×C₃₇	—	2	4	no	—
52	AGL(1,ℤ/8)×C₃₇	—	4	2	no	—
53	#135×C₃₇	—	2	2	no	—
54	#135×C₃₇	—	2	2	no	—
55	C₂×Q₁₆×C₃₇	—	2	2	no	—
56	C₂×Q₁₆×C₃₇	—	2	1	no	—
57	C₂×Q₁₆×C₃₇	—	2	2	no	—
58	C₂×Q₁₆×C₃₇	—	2	1	no	—
59	C₂×Q₁₆×C₃₇	—	2	2	no	—
60	C₂×Q₁₆×C₃₇	D₄	1	1	yes	characteristic
61	C₂×SD₁₆×C₃₇	—	2	2	no	—
62	C₂×SD₁₆×C₃₇	—	2	2	no	—
63	C₂×SD₁₆×C₃₇	—	2	2	no	—
64	C₂×SD₁₆×C₃₇	—	2	2	no	—
65	C₂×SD₁₆×C₃₇	—	2	4	no	—
66	C₂×SD₁₆×C₃₇	—	2	4	no	—
67	C₂×SD₁₆×C₃₇	D₄	1	2	yes	—
68	C₂×D₈×C₃₇	—	2	2	no	—
69	C₂×D₈×C₃₇	—	2	1	no	—
70	C₂×D₈×C₃₇	—	2	2	no	—
71	C₂×D₈×C₃₇	—	2	1	no	—
72	C₂×D₈×C₃₇	—	2	2	no	—
73	C₂×D₈×C₃₇	D₄	1	1	yes	characteristic
74	#131×C₃₇	—	2	4	no	—
75	#131×C₃₇	—	2	4	no	—
76	C₂×M₁₆×C₃₇	—	2	2	no	—
77	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
78	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
79	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₃₇	—	2	2	no	—
81	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
83	C₄⋊Q₈×C₃₇	—	2	2	no	—
84	#127×C₃₇	—	2	2	no	—
85	#124×C₃₇	—	2	2	no	—
86	#124×C₃₇	—	2	2	no	—
87	#124×C₃₇	—	2	4	no	—
88	#124×C₃₇	—	4	2	no	—
89	#123×C₃₇	—	4	2	no	—
90	C₂²⋊Q₈×C₃₇	—	2	4	no	—
91	#121×C₃₇	—	2	4	no	—
92	#120×C₃₇	—	4	2	no	—
93	#117×C₃₇	C₂³	1	1	yes	characteristic
94	#117×C₃₇	C₂³	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₃₇	—	4	2	no	—
96	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
97	#108×C₃₇	—	2	2	no	—
98	#108×C₃₇	D₄	1	4	yes	complemented
99	#107×C₃₇	D₄	1	2	yes	—
100	#106×C₃₇	D₄	1	2	yes	—
101	#104×C₃₇	—	2	4	no	—
102	#103×C₃₇	—	2	4	no	—
103	#102×C₃₇	—	2	4	no	—
104	#101×C₃₇	—	2	4	no	—
105	#100×C₃₇	—	2	4	no	—
106	#97×C₃₇	—	2	1	no	—
107	#97×C₃₇	—	2	1	no	—
108	C₄×C₈×C₃₇	—	2	1	no	—
109	C₄×C₈×C₃₇	—	2	1	no	—
110	C₄×C₈×C₃₇	D₄	1	4	yes	complemented
111	C₂⁴×C₃₇	—	2	2	no	—
112	#41×C₃₇	—	2	2	no	—
113	#41×C₃₇	—	2	2	no	—
114	#41×C₃₇	—	2	2	no	—
115	#41×C₃₇	—	2	2	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	—	2	2	no	—
120	C₂×Q₈×C₃₇	—	2	2	no	—
121	C₂×Q₈×C₃₇	—	2	2	no	—
122	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
123	C₂×D₄×C₃₇	—	2	2	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	—	2	2	no	—
128	C₂×D₄×C₃₇	—	2	2	no	—
129	C₂×D₄×C₃₇	—	2	2	no	—
130	C₂×D₄×C₃₇	—	4	4	no	—
131	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₃₇	—	2	1	no	—
133	C₂²×C₄×C₃₇	—	2	2	no	—
134	C₂²×C₄×C₃₇	—	2	2	no	—
135	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
136	Q₁₆×C₃₇	—	2	2	no	—
137	Q₁₆×C₃₇	—	4	4	no	—
138	Q₁₆×C₃₇	—	4	2	no	—
139	Q₁₆×C₃₇	—	4	2	no	—
140	SD₁₆×C₃₇	—	2	4	no	—
141	SD₁₆×C₃₇	—	4	4	no	—
142	SD₁₆×C₃₇	—	4	4	no	—
143	SD₁₆×C₃₇	—	4	4	no	—
144	SD₁₆×C₃₇	—	4	4	no	—
145	D₈×C₃₇	—	2	2	no	—
146	D₈×C₃₇	—	4	4	no	—
147	D₈×C₃₇	—	4	2	no	—
148	D₈×C₃₇	—	4	2	no	—
149	M₁₆×C₃₇	—	2	1	no	—
150	M₁₆×C₃₇	—	2	1	no	—
151	M₁₆×C₃₇	—	2	2	no	—
152	M₁₆×C₃₇	—	2	2	no	—
153	M₁₆×C₃₇	—	4	4	no	—
154	M₁₆×C₃₇	C₂×D₄	1	2	yes	—
155	M₁₆×C₃₇	C₂×D₄	1	2	yes	—
156	C₂×C₈×C₃₇	—	2	1	no	—
157	C₂×C₈×C₃₇	—	2	1	no	—
158	C₂×C₈×C₃₇	—	2	2	no	—
159	C₂×C₈×C₃₇	—	4	4	no	—
160	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
162	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
164	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
167	C₂×C₈×C₃₇	#41	1	2	yes	—
168	C₄⋊C₄×C₃₇	—	4	4	no	—
169	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
170	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
171	C₂²⋊C₄×C₃₇	—	2	1	no	—
172	C₂²⋊C₄×C₃₇	—	2	1	no	—
173	C₂²⋊C₄×C₃₇	—	4	4	no	—
174	C₂²⋊C₄×C₃₇	—	4	4	no	—
175	C₂²⋊C₄×C₃₇	—	4	8	no	—
176	C₄²×C₃₇	—	2	1	no	—
177	C₄²×C₃₇	—	2	1	no	—
178	C₄²×C₃₇	—	2	1	no	—
179	C₄²×C₃₇	C₂×D₄	1	2	yes	—
180	C₂³×C₃₇	—	2	2	no	—
181	C₂³×C₃₇	—	4	2	no	—
182	C₂³×C₃₇	—	4	2	no	—
183	C₂³×C₃₇	—	4	2	no	—
184	C₂³×C₃₇	—	8	4	no	—
185	C₂³×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
186	Q₈×C₃₇	—	2	2	no	—
187	Q₈×C₃₇	—	2	2	no	—
188	Q₈×C₃₇	—	4	2	no	—
189	Q₈×C₃₇	—	4	2	no	—
190	Q₈×C₃₇	—	4	2	no	—
191	Q₈×C₃₇	—	4	2	no	—
192	D₄×C₃₇	—	2	2	no	—
193	D₄×C₃₇	—	2	2	no	—
194	D₄×C₃₇	—	4	2	no	—
195	D₄×C₃₇	—	4	2	no	—
196	D₄×C₃₇	—	4	2	no	—
197	D₄×C₃₇	—	4	2	no	—
198	D₄×C₃₇	—	4	2	no	—
199	D₄×C₃₇	—	4	2	no	—
200	D₄×C₃₇	—	16	4	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	—	4	2	no	—
206	C₂×C₄×C₃₇	—	4	2	no	—
207	C₂×C₄×C₃₇	—	4	2	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	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
217	C₈×C₃₇	—	2	2	no	—
218	C₈×C₃₇	—	2	2	no	—
219	C₈×C₃₇	—	4	2	no	—
220	C₈×C₃₇	#121	1	2	yes	—
221	C₈×C₃₇	#121	1	2	yes	—
222	C₈×C₃₇	#127	1	2	yes	—
223	C₈×C₃₇	#127	1	2	yes	—
224	#28501	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂²×C₃₇	—	2	2	no	—
226	C₂²×C₃₇	—	4	4	no	—
227	C₂²×C₃₇	—	4	2	no	—
228	C₂²×C₃₇	—	8	4	no	—
229	C₂²×C₃₇	—	8	4	no	—
230	C₂²×C₃₇	—	8	2	no	—
231	C₂²×C₃₇	—	16	2	no	—
232	C₂²×C₃₇	#535	1	1	yes	characteristic
233	C₂²×C₃₇	D₄²	1	1	yes	characteristic
234	C₂²×C₃₇	#550	1	1	yes	characteristic
235	C₄×C₃₇	—	4	2	no	—
236	C₄×C₃₇	—	4	2	no	—
237	C₄×C₃₇	—	4	2	no	—
238	C₄×C₃₇	—	4	2	no	—
239	C₄×C₃₇	—	8	2	no	—
240	C₄×C₃₇	C₂×#121	1	1	yes	characteristic
241	C₄×C₃₇	C₂×#127	1	1	yes	characteristic
242	C₄×C₃₇	D₄²	1	1	yes	characteristic
243	C₄×C₃₇	#550	1	1	yes	characteristic
244	#3156	C₂×C₃₇	1	1	yes	characteristic, complemented
245	#3155	C₂×C₃₇	1	1	yes	characteristic
246	C₂×#495	C₂×C₃₇	1	1	yes	characteristic, complemented
247	C₂×#471	C₂×C₃₇	1	2	yes	complemented
248	#3057	C₂×C₃₇	1	2	yes	complemented
249	C₂×#443	C₂×C₃₇	1	1	yes	characteristic, complemented
250	#2004	C₂×C₃₇	1	2	yes	complemented
251	#2003	C₂×C₃₇	1	2	yes	complemented
252	#1979	C₂×C₃₇	1	1	yes	characteristic, complemented
253	#1978	C₂×C₃₇	1	1	yes	characteristic, complemented
254	#1772	C₂×C₃₇	1	1	yes	characteristic, complemented
255	C₂×C₃₇	—	2	1	no	—
256	C₂×C₃₇	—	2	1	no	—
257	C₂×C₃₇	—	8	2	no	—
258	C₂×C₃₇	—	16	2	no	—
259	C₂×C₃₇	#2541	1	1	yes	characteristic
260	C₂×C₃₇	#3290	1	2	yes	—
261	C₂×#137	C₂²×C₃₇	1	2	yes	—
262	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	2	yes	—
263	C₂×#135	C₂²×C₃₇	1	1	yes	characteristic
264	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
265	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
266	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
267	C₂×#131	C₂²×C₃₇	1	2	yes	—
268	#536	C₂²×C₃₇	1	2	yes	—
269	#535	C₂²×C₃₇	1	2	yes	—
270	C₂×#124	C₂²×C₃₇	1	2	yes	—
271	#497	—	2	2	no	—
272	#496	—	2	2	no	—
273	#495	—	2	1	no	—
274	#495	—	2	1	no	—
275	#495	—	2	4	no	—
276	#494	—	2	1	no	—
277	#493	—	2	1	no	—
278	#471	—	2	8	no	—
279	#468	—	2	4	no	—
280	#465	—	2	4	no	—
281	#443	—	2	4	no	—
282	C₂×#108	C₂²×C₃₇	1	1	yes	characteristic
283	C₂×#108	C₂²×C₃₇	1	1	yes	characteristic
284	#427	C₂²×C₃₇	1	1	yes	characteristic
285	C₂×#104	C₂²×C₃₇	1	2	yes	—
286	#419	C₂²×C₃₇	1	2	yes	—
287	#418	C₂²×C₃₇	1	2	yes	—
288	C₂×#101	C₂²×C₃₇	1	2	yes	—
289	C₂×#100	C₂²×C₃₇	1	2	yes	—
290	#405	C₂²×C₃₇	1	1	yes	characteristic
291	#405	C₂²×C₃₇	1	1	yes	characteristic
292	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
293	#339	C₂²×C₃₇	1	1	yes	characteristic
294	#339	C₂²×C₃₇	1	1	yes	characteristic
295	C₃₇	#28501	1	1	yes	characteristic, direct product factor, Sylow
296	C₂×#41	C₂³×C₃₇	1	2	yes	—
297	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
298	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
299	#137	—	2	4	no	—
300	#137	—	4	2	no	—
301	AGL(1,ℤ/8)	—	2	4	no	—
302	AGL(1,ℤ/8)	—	4	2	no	—
303	#135	—	2	2	no	—
304	#135	—	2	2	no	—
305	C₂×Q₁₆	—	2	2	no	—
306	C₂×Q₁₆	—	2	1	no	—
307	C₂×Q₁₆	—	2	2	no	—
308	C₂×Q₁₆	—	2	1	no	—
309	C₂×Q₁₆	—	2	2	no	—
310	C₂×Q₁₆	D₄×C₃₇	1	1	yes	characteristic
311	C₂×SD₁₆	—	2	2	no	—
312	C₂×SD₁₆	—	2	2	no	—
313	C₂×SD₁₆	—	2	2	no	—
314	C₂×SD₁₆	—	2	2	no	—
315	C₂×SD₁₆	—	2	4	no	—
316	C₂×SD₁₆	—	2	4	no	—
317	C₂×SD₁₆	D₄×C₃₇	1	2	yes	—
318	C₂×D₈	—	2	2	no	—
319	C₂×D₈	—	2	1	no	—
320	C₂×D₈	—	2	2	no	—
321	C₂×D₈	—	2	1	no	—
322	C₂×D₈	—	2	2	no	—
323	C₂×D₈	D₄×C₃₇	1	1	yes	characteristic
324	#131	—	2	4	no	—
325	#131	—	2	4	no	—
326	C₂×M₁₆	—	2	2	no	—
327	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
328	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
329	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
330	C₂²×C₈	—	2	2	no	—
331	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
332	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
333	C₄⋊Q₈	—	2	2	no	—
334	#127	—	2	2	no	—
335	#124	—	2	2	no	—
336	#124	—	2	2	no	—
337	#124	—	2	4	no	—
338	#124	—	4	2	no	—
339	#123	—	4	2	no	—
340	C₂²⋊Q₈	—	2	4	no	—
341	#121	—	2	4	no	—
342	#120	—	4	2	no	—
343	#117	C₂³×C₃₇	1	1	yes	characteristic
344	#117	C₂³×C₃₇	1	1	yes	characteristic
345	C₂×C₂²⋊C₄	—	4	2	no	—
346	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
347	#108	—	2	2	no	—
348	#108	D₄×C₃₇	1	4	yes	complemented
349	#107	D₄×C₃₇	1	2	yes	—
350	#106	D₄×C₃₇	1	2	yes	—
351	#104	—	2	4	no	—
352	#103	—	2	4	no	—
353	#102	—	2	4	no	—
354	#101	—	2	4	no	—
355	#100	—	2	4	no	—
356	#97	—	2	1	no	—
357	#97	—	2	1	no	—
358	C₄×C₈	—	2	1	no	—
359	C₄×C₈	—	2	1	no	—
360	C₄×C₈	D₄×C₃₇	1	4	yes	complemented
361	C₂⁴	—	2	2	no	—
362	#41	—	2	2	no	—
363	#41	—	2	2	no	—
364	#41	—	2	2	no	—
365	#41	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	4	4	no	—
381	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
386	Q₁₆	—	2	2	no	—
387	Q₁₆	—	4	4	no	—
388	Q₁₆	—	4	2	no	—
389	Q₁₆	—	4	2	no	—
390	SD₁₆	—	2	4	no	—
391	SD₁₆	—	4	4	no	—
392	SD₁₆	—	4	4	no	—
393	SD₁₆	—	4	4	no	—
394	SD₁₆	—	4	4	no	—
395	D₈	—	2	2	no	—
396	D₈	—	4	4	no	—
397	D₈	—	4	2	no	—
398	D₈	—	4	2	no	—
399	M₁₆	—	2	1	no	—
400	M₁₆	—	2	1	no	—
401	M₁₆	—	2	2	no	—
402	M₁₆	—	2	2	no	—
403	M₁₆	—	4	4	no	—
404	M₁₆	C₂×D₄×C₃₇	1	2	yes	—
405	M₁₆	C₂×D₄×C₃₇	1	2	yes	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	4	4	no	—
410	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
411	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
412	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
413	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
414	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
415	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
416	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
417	C₂×C₈	#41×C₃₇	1	2	yes	—
418	C₄⋊C₄	—	4	4	no	—
419	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
420	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	4	4	no	—
424	C₂²⋊C₄	—	4	4	no	—
425	C₂²⋊C₄	—	4	8	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	1	no	—
429	C₄²	C₂×D₄×C₃₇	1	2	yes	—
430	C₂³	—	2	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	8	4	no	—
435	C₂³	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
436	Q₈	—	2	2	no	—
437	Q₈	—	2	2	no	—
438	Q₈	—	4	2	no	—
439	Q₈	—	4	2	no	—
440	Q₈	—	4	2	no	—
441	Q₈	—	4	2	no	—
442	D₄	—	2	2	no	—
443	D₄	—	2	2	no	—
444	D₄	—	4	2	no	—
445	D₄	—	4	2	no	—
446	D₄	—	4	2	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	4	2	no	—
450	D₄	—	16	4	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
465	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
466	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	—	4	2	no	—
470	C₈	#121×C₃₇	1	2	yes	—
471	C₈	#121×C₃₇	1	2	yes	—
472	C₈	#127×C₃₇	1	2	yes	—
473	C₈	#127×C₃₇	1	2	yes	—
474	C₂²	—	2	2	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	8	4	no	—
478	C₂²	—	8	4	no	—
479	C₂²	—	8	2	no	—
480	C₂²	—	16	2	no	—
481	C₂²	C₃₇×#535	1	1	yes	characteristic
482	C₂²	D₄²×C₃₇	1	1	yes	characteristic
483	C₂²	C₃₇×#550	1	1	yes	characteristic
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	8	2	no	—
489	C₄	C₂×#121×C₃₇	1	1	yes	characteristic
490	C₄	C₂×#127×C₃₇	1	1	yes	characteristic
491	C₄	D₄²×C₃₇	1	1	yes	characteristic
492	C₄	C₃₇×#550	1	1	yes	characteristic
493	C₂	—	2	1	no	—
494	C₂	—	2	1	no	—
495	C₂	—	8	2	no	—
496	C₂	—	16	2	no	—
497	C₂	C₃₇×#2541	1	1	yes	characteristic
498	C₂	C₃₇×#3290	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₇	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#3155	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃₇×#3156	C₂	semidirect
3. C₂×C₃₇×#495	C₂	semidirect
4. C₂×C₃₇×#471	C₂	semidirect
5. C₃₇×#3057	C₂	semidirect
6. C₂×C₃₇×#443	C₂	semidirect
7. C₃₇×#2004	C₂	semidirect
8. C₃₇×#2003	C₂	semidirect
9. C₃₇×#1979	C₂	semidirect
10. C₃₇×#1978	C₂	semidirect
11. C₃₇×#1772	C₂	semidirect
98. #108×C₃₇	D₄	semidirect
110. C₄×C₈×C₃₇	D₄	semidirect
224. #28501	C₃₇	direct (N × H)
244. #3156	C₂×C₃₇	semidirect
246. C₂×#495	C₂×C₃₇	semidirect
247. C₂×#471	C₂×C₃₇	semidirect
248. #3057	C₂×C₃₇	semidirect
249. C₂×#443	C₂×C₃₇	semidirect
250. #2004	C₂×C₃₇	semidirect
251. #2003	C₂×C₃₇	semidirect
252. #1979	C₂×C₃₇	semidirect
253. #1978	C₂×C₃₇	semidirect
254. #1772	C₂×C₃₇	semidirect
295. C₃₇	#28501	direct (N × H)
348. #108	D₄×C₃₇	semidirect
360. C₄×C₈	D₄×C₃₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₇×#3156	2
C₃₇×#3155	2
C₂×C₃₇×#495	2
C₂×C₃₇×#471	2
C₃₇×#3057	2
C₂×C₃₇×#443	2
C₃₇×#2004	2
C₃₇×#2003	2
C₃₇×#1979	2
C₃₇×#1978	2
C₃₇×#1772	2
#28501	37

Subgroups — C37×#28501 #22649754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28501 #22649754