Subgroups — C₃₇×#28503 #22649756

Order 9472.

1030 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3154	C₂	1	2	yes	maximal, complemented
2	C₂×C₃₇×#495	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#473	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#472	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#3059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#3058	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₇×#443	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2004	C₂	1	2	yes	maximal, complemented
9	C₃₇×#2003	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1977	C₂	1	2	yes	maximal, 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	1	yes	characteristic
19	C₂×#131×C₃₇	C₂²	1	1	yes	characteristic
20	C₃₇×#536	C₂²	1	2	yes	—
21	C₃₇×#535	C₂²	1	2	yes	—
22	C₂×#124×C₃₇	C₂²	1	2	yes	—
23	C₃₇×#497	—	2	2	no	—
24	C₃₇×#496	—	2	2	no	—
25	C₃₇×#495	—	2	2	no	—
26	C₃₇×#495	—	2	4	no	—
27	C₃₇×#492	—	2	2	no	—
28	C₃₇×#473	—	2	4	no	—
29	C₃₇×#472	—	2	4	no	—
30	C₃₇×#470	—	2	2	no	—
31	C₃₇×#469	—	2	2	no	—
32	C₃₇×#467	—	2	2	no	—
33	C₃₇×#466	—	2	2	no	—
34	C₃₇×#443	—	2	4	no	—
35	C₂×#108×C₃₇	C₂²	1	1	yes	characteristic
36	C₂×#108×C₃₇	C₂²	1	1	yes	characteristic
37	C₃₇×#427	C₂²	1	1	yes	characteristic
38	C₂×#104×C₃₇	C₂²	1	1	yes	characteristic
39	C₂×#104×C₃₇	C₂²	1	1	yes	characteristic
40	C₃₇×#419	C₂²	1	2	yes	—
41	C₃₇×#418	C₂²	1	2	yes	—
42	C₂×#101×C₃₇	C₂²	1	2	yes	—
43	C₂×#100×C₃₇	C₂²	1	2	yes	—
44	C₃₇×#405	C₂²	1	2	yes	—
45	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
46	C₃₇×#339	C₂²	1	2	yes	—
47	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
48	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
50	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
51	#137×C₃₇	—	2	4	no	—
52	#137×C₃₇	—	4	2	no	—
53	AGL(1,ℤ/8)×C₃₇	—	2	4	no	—
54	AGL(1,ℤ/8)×C₃₇	—	4	2	no	—
55	#135×C₃₇	—	2	2	no	—
56	#135×C₃₇	—	2	2	no	—
57	C₂×Q₁₆×C₃₇	—	2	2	no	—
58	C₂×Q₁₆×C₃₇	—	2	1	no	—
59	C₂×Q₁₆×C₃₇	—	2	1	no	—
60	C₂×Q₁₆×C₃₇	—	2	2	no	—
61	C₂×Q₁₆×C₃₇	—	2	2	no	—
62	C₂×Q₁₆×C₃₇	D₄	1	1	yes	characteristic
63	C₂×SD₁₆×C₃₇	—	2	2	no	—
64	C₂×SD₁₆×C₃₇	—	2	2	no	—
65	C₂×SD₁₆×C₃₇	—	2	2	no	—
66	C₂×SD₁₆×C₃₇	—	2	4	no	—
67	C₂×SD₁₆×C₃₇	—	2	2	no	—
68	C₂×SD₁₆×C₃₇	—	2	4	no	—
69	C₂×SD₁₆×C₃₇	D₄	1	1	yes	characteristic
70	C₂×SD₁₆×C₃₇	D₄	1	1	yes	characteristic
71	C₂×D₈×C₃₇	—	2	2	no	—
72	C₂×D₈×C₃₇	—	2	1	no	—
73	C₂×D₈×C₃₇	—	2	1	no	—
74	C₂×D₈×C₃₇	—	2	2	no	—
75	C₂×D₈×C₃₇	—	2	2	no	—
76	C₂×D₈×C₃₇	D₄	1	1	yes	characteristic
77	#131×C₃₇	—	2	2	no	—
78	#131×C₃₇	—	2	2	no	—
79	#131×C₃₇	—	2	2	no	—
80	#131×C₃₇	—	2	2	no	—
81	C₂×M₁₆×C₃₇	—	2	1	no	—
82	C₂×M₁₆×C₃₇	—	2	1	no	—
83	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
86	C₂²×C₈×C₃₇	—	2	1	no	—
87	C₂²×C₈×C₃₇	—	2	1	no	—
88	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
90	C₄⋊Q₈×C₃₇	—	2	2	no	—
91	#127×C₃₇	—	2	2	no	—
92	#124×C₃₇	—	2	2	no	—
93	#124×C₃₇	—	2	2	no	—
94	#124×C₃₇	—	2	4	no	—
95	#124×C₃₇	—	4	2	no	—
96	#123×C₃₇	—	4	2	no	—
97	C₂²⋊Q₈×C₃₇	—	2	4	no	—
98	#121×C₃₇	—	2	4	no	—
99	#120×C₃₇	—	4	2	no	—
100	#117×C₃₇	C₂³	1	2	yes	—
101	C₂×C₂²⋊C₄×C₃₇	—	4	2	no	—
102	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
103	#108×C₃₇	—	2	2	no	—
104	#108×C₃₇	D₄	1	4	yes	complemented
105	#107×C₃₇	D₄	1	2	yes	—
106	#106×C₃₇	D₄	1	2	yes	—
107	#104×C₃₇	—	2	2	no	—
108	#104×C₃₇	—	2	2	no	—
109	#103×C₃₇	—	2	4	no	—
110	#102×C₃₇	—	2	4	no	—
111	#101×C₃₇	—	2	4	no	—
112	#100×C₃₇	—	2	4	no	—
113	#97×C₃₇	—	2	2	no	—
114	C₄×C₈×C₃₇	—	2	2	no	—
115	C₄×C₈×C₃₇	D₄	1	4	yes	complemented
116	C₂⁴×C₃₇	—	2	2	no	—
117	#41×C₃₇	—	2	1	no	—
118	#41×C₃₇	—	2	1	no	—
119	#41×C₃₇	—	2	1	no	—
120	#41×C₃₇	—	2	1	no	—
121	#41×C₃₇	—	2	1	no	—
122	#41×C₃₇	—	2	1	no	—
123	#41×C₃₇	—	2	1	no	—
124	#41×C₃₇	—	2	1	no	—
125	C₂×Q₈×C₃₇	—	2	2	no	—
126	C₂×Q₈×C₃₇	—	2	2	no	—
127	C₂×Q₈×C₃₇	—	2	2	no	—
128	C₂×Q₈×C₃₇	—	2	2	no	—
129	C₂×Q₈×C₃₇	—	2	2	no	—
130	C₂×Q₈×C₃₇	—	2	2	no	—
131	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
132	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
133	C₂×D₄×C₃₇	—	2	1	no	—
134	C₂×D₄×C₃₇	—	2	1	no	—
135	C₂×D₄×C₃₇	—	2	2	no	—
136	C₂×D₄×C₃₇	—	2	2	no	—
137	C₂×D₄×C₃₇	—	2	2	no	—
138	C₂×D₄×C₃₇	—	2	2	no	—
139	C₂×D₄×C₃₇	—	2	2	no	—
140	C₂×D₄×C₃₇	—	2	2	no	—
141	C₂×D₄×C₃₇	—	4	4	no	—
142	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
143	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₃₇	—	2	1	no	—
145	C₂²×C₄×C₃₇	—	2	1	no	—
146	C₂²×C₄×C₃₇	—	2	1	no	—
147	C₂²×C₄×C₃₇	—	2	2	no	—
148	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
149	Q₁₆×C₃₇	—	2	2	no	—
150	Q₁₆×C₃₇	—	4	4	no	—
151	Q₁₆×C₃₇	—	4	2	no	—
152	Q₁₆×C₃₇	—	4	2	no	—
153	SD₁₆×C₃₇	—	2	2	no	—
154	SD₁₆×C₃₇	—	2	2	no	—
155	SD₁₆×C₃₇	—	4	4	no	—
156	SD₁₆×C₃₇	—	4	4	no	—
157	SD₁₆×C₃₇	—	4	4	no	—
158	SD₁₆×C₃₇	—	4	4	no	—
159	D₈×C₃₇	—	2	2	no	—
160	D₈×C₃₇	—	4	4	no	—
161	D₈×C₃₇	—	4	2	no	—
162	D₈×C₃₇	—	4	2	no	—
163	M₁₆×C₃₇	—	2	2	no	—
164	M₁₆×C₃₇	—	2	1	no	—
165	M₁₆×C₃₇	—	2	1	no	—
166	M₁₆×C₃₇	—	2	1	no	—
167	M₁₆×C₃₇	—	2	1	no	—
168	M₁₆×C₃₇	—	4	2	no	—
169	M₁₆×C₃₇	—	4	2	no	—
170	M₁₆×C₃₇	C₂×D₄	1	4	yes	—
171	C₂×C₈×C₃₇	—	2	2	no	—
172	C₂×C₈×C₃₇	—	2	1	no	—
173	C₂×C₈×C₃₇	—	2	1	no	—
174	C₂×C₈×C₃₇	—	4	2	no	—
175	C₂×C₈×C₃₇	—	4	2	no	—
176	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
178	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
179	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
180	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
183	C₂×C₈×C₃₇	#41	1	2	yes	—
184	C₄⋊C₄×C₃₇	—	4	4	no	—
185	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
186	C₂²⋊C₄×C₃₇	—	2	2	no	—
187	C₂²⋊C₄×C₃₇	—	4	4	no	—
188	C₂²⋊C₄×C₃₇	—	4	4	no	—
189	C₂²⋊C₄×C₃₇	—	4	8	no	—
190	C₄²×C₃₇	—	2	2	no	—
191	C₄²×C₃₇	—	2	1	no	—
192	C₄²×C₃₇	C₂×D₄	1	2	yes	—
193	C₂³×C₃₇	—	2	1	no	—
194	C₂³×C₃₇	—	2	1	no	—
195	C₂³×C₃₇	—	4	2	no	—
196	C₂³×C₃₇	—	4	2	no	—
197	C₂³×C₃₇	—	4	2	no	—
198	C₂³×C₃₇	—	8	4	no	—
199	C₂³×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
200	Q₈×C₃₇	—	2	1	no	—
201	Q₈×C₃₇	—	2	1	no	—
202	Q₈×C₃₇	—	2	1	no	—
203	Q₈×C₃₇	—	2	1	no	—
204	Q₈×C₃₇	—	4	2	no	—
205	Q₈×C₃₇	—	4	2	no	—
206	Q₈×C₃₇	—	4	2	no	—
207	Q₈×C₃₇	—	4	2	no	—
208	D₄×C₃₇	—	2	1	no	—
209	D₄×C₃₇	—	2	1	no	—
210	D₄×C₃₇	—	2	1	no	—
211	D₄×C₃₇	—	2	1	no	—
212	D₄×C₃₇	—	4	1	no	—
213	D₄×C₃₇	—	4	1	no	—
214	D₄×C₃₇	—	4	1	no	—
215	D₄×C₃₇	—	4	1	no	—
216	D₄×C₃₇	—	4	2	no	—
217	D₄×C₃₇	—	4	2	no	—
218	D₄×C₃₇	—	4	2	no	—
219	D₄×C₃₇	—	4	2	no	—
220	D₄×C₃₇	—	16	4	no	—
221	C₂×C₄×C₃₇	—	2	2	no	—
222	C₂×C₄×C₃₇	—	2	4	no	—
223	C₂×C₄×C₃₇	—	2	1	no	—
224	C₂×C₄×C₃₇	—	2	1	no	—
225	C₂×C₄×C₃₇	—	4	2	no	—
226	C₂×C₄×C₃₇	—	4	1	no	—
227	C₂×C₄×C₃₇	—	4	1	no	—
228	C₂×C₄×C₃₇	—	4	1	no	—
229	C₂×C₄×C₃₇	—	4	1	no	—
230	C₂×C₄×C₃₇	—	4	2	no	—
231	C₂×C₄×C₃₇	—	4	2	no	—
232	C₂×C₄×C₃₇	—	4	2	no	—
233	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
239	C₈×C₃₇	—	2	4	no	—
240	C₈×C₃₇	—	4	1	no	—
241	C₈×C₃₇	—	4	1	no	—
242	C₈×C₃₇	#121	1	2	yes	—
243	C₈×C₃₇	#121	1	2	yes	—
244	C₈×C₃₇	#127	1	2	yes	—
245	C₈×C₃₇	#127	1	2	yes	—
246	#28503	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₂²×C₃₇	—	2	2	no	—
248	C₂²×C₃₇	—	4	2	no	—
249	C₂²×C₃₇	—	4	2	no	—
250	C₂²×C₃₇	—	4	1	no	—
251	C₂²×C₃₇	—	4	1	no	—
252	C₂²×C₃₇	—	8	4	no	—
253	C₂²×C₃₇	—	8	4	no	—
254	C₂²×C₃₇	—	8	2	no	—
255	C₂²×C₃₇	—	16	2	no	—
256	C₂²×C₃₇	#535	1	1	yes	characteristic
257	C₂²×C₃₇	D₄²	1	1	yes	characteristic
258	C₂²×C₃₇	#550	1	1	yes	characteristic
259	C₄×C₃₇	—	4	2	no	—
260	C₄×C₃₇	—	4	4	no	—
261	C₄×C₃₇	—	4	1	no	—
262	C₄×C₃₇	—	4	1	no	—
263	C₄×C₃₇	—	8	2	no	—
264	C₄×C₃₇	C₂×#121	1	1	yes	characteristic
265	C₄×C₃₇	C₂×#127	1	1	yes	characteristic
266	C₄×C₃₇	D₄²	1	1	yes	characteristic
267	C₄×C₃₇	#550	1	1	yes	characteristic
268	#3154	C₂×C₃₇	1	2	yes	complemented
269	C₂×#495	C₂×C₃₇	1	1	yes	characteristic, complemented
270	C₂×#473	C₂×C₃₇	1	1	yes	characteristic, complemented
271	C₂×#472	C₂×C₃₇	1	1	yes	characteristic, complemented
272	#3059	C₂×C₃₇	1	1	yes	characteristic, complemented
273	#3058	C₂×C₃₇	1	1	yes	characteristic, complemented
274	C₂×#443	C₂×C₃₇	1	1	yes	characteristic, complemented
275	#2004	C₂×C₃₇	1	2	yes	complemented
276	#2003	C₂×C₃₇	1	2	yes	complemented
277	#1977	C₂×C₃₇	1	2	yes	complemented
278	#1772	C₂×C₃₇	1	1	yes	characteristic, complemented
279	C₂×C₃₇	—	2	1	no	—
280	C₂×C₃₇	—	2	1	no	—
281	C₂×C₃₇	—	8	1	no	—
282	C₂×C₃₇	—	8	1	no	—
283	C₂×C₃₇	—	16	2	no	—
284	C₂×C₃₇	#2541	1	1	yes	characteristic
285	C₂×C₃₇	#3290	1	2	yes	—
286	C₂×#137	C₂²×C₃₇	1	2	yes	—
287	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	2	yes	—
288	C₂×#135	C₂²×C₃₇	1	1	yes	characteristic
289	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
290	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
291	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
292	C₂×#131	C₂²×C₃₇	1	1	yes	characteristic
293	C₂×#131	C₂²×C₃₇	1	1	yes	characteristic
294	#536	C₂²×C₃₇	1	2	yes	—
295	#535	C₂²×C₃₇	1	2	yes	—
296	C₂×#124	C₂²×C₃₇	1	2	yes	—
297	#497	—	2	2	no	—
298	#496	—	2	2	no	—
299	#495	—	2	2	no	—
300	#495	—	2	4	no	—
301	#492	—	2	2	no	—
302	#473	—	2	4	no	—
303	#472	—	2	4	no	—
304	#470	—	2	2	no	—
305	#469	—	2	2	no	—
306	#467	—	2	2	no	—
307	#466	—	2	2	no	—
308	#443	—	2	4	no	—
309	C₂×#108	C₂²×C₃₇	1	1	yes	characteristic
310	C₂×#108	C₂²×C₃₇	1	1	yes	characteristic
311	#427	C₂²×C₃₇	1	1	yes	characteristic
312	C₂×#104	C₂²×C₃₇	1	1	yes	characteristic
313	C₂×#104	C₂²×C₃₇	1	1	yes	characteristic
314	#419	C₂²×C₃₇	1	2	yes	—
315	#418	C₂²×C₃₇	1	2	yes	—
316	C₂×#101	C₂²×C₃₇	1	2	yes	—
317	C₂×#100	C₂²×C₃₇	1	2	yes	—
318	#405	C₂²×C₃₇	1	2	yes	—
319	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
320	#339	C₂²×C₃₇	1	2	yes	—
321	C₃₇	#28503	1	1	yes	characteristic, direct product factor, Sylow
322	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
323	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
324	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
325	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
326	#137	—	2	4	no	—
327	#137	—	4	2	no	—
328	AGL(1,ℤ/8)	—	2	4	no	—
329	AGL(1,ℤ/8)	—	4	2	no	—
330	#135	—	2	2	no	—
331	#135	—	2	2	no	—
332	C₂×Q₁₆	—	2	2	no	—
333	C₂×Q₁₆	—	2	1	no	—
334	C₂×Q₁₆	—	2	1	no	—
335	C₂×Q₁₆	—	2	2	no	—
336	C₂×Q₁₆	—	2	2	no	—
337	C₂×Q₁₆	D₄×C₃₇	1	1	yes	characteristic
338	C₂×SD₁₆	—	2	2	no	—
339	C₂×SD₁₆	—	2	2	no	—
340	C₂×SD₁₆	—	2	2	no	—
341	C₂×SD₁₆	—	2	4	no	—
342	C₂×SD₁₆	—	2	2	no	—
343	C₂×SD₁₆	—	2	4	no	—
344	C₂×SD₁₆	D₄×C₃₇	1	1	yes	characteristic
345	C₂×SD₁₆	D₄×C₃₇	1	1	yes	characteristic
346	C₂×D₈	—	2	2	no	—
347	C₂×D₈	—	2	1	no	—
348	C₂×D₈	—	2	1	no	—
349	C₂×D₈	—	2	2	no	—
350	C₂×D₈	—	2	2	no	—
351	C₂×D₈	D₄×C₃₇	1	1	yes	characteristic
352	#131	—	2	2	no	—
353	#131	—	2	2	no	—
354	#131	—	2	2	no	—
355	#131	—	2	2	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
359	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
360	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
361	C₂²×C₈	—	2	1	no	—
362	C₂²×C₈	—	2	1	no	—
363	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
365	C₄⋊Q₈	—	2	2	no	—
366	#127	—	2	2	no	—
367	#124	—	2	2	no	—
368	#124	—	2	2	no	—
369	#124	—	2	4	no	—
370	#124	—	4	2	no	—
371	#123	—	4	2	no	—
372	C₂²⋊Q₈	—	2	4	no	—
373	#121	—	2	4	no	—
374	#120	—	4	2	no	—
375	#117	C₂³×C₃₇	1	2	yes	—
376	C₂×C₂²⋊C₄	—	4	2	no	—
377	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
378	#108	—	2	2	no	—
379	#108	D₄×C₃₇	1	4	yes	complemented
380	#107	D₄×C₃₇	1	2	yes	—
381	#106	D₄×C₃₇	1	2	yes	—
382	#104	—	2	2	no	—
383	#104	—	2	2	no	—
384	#103	—	2	4	no	—
385	#102	—	2	4	no	—
386	#101	—	2	4	no	—
387	#100	—	2	4	no	—
388	#97	—	2	2	no	—
389	C₄×C₈	—	2	2	no	—
390	C₄×C₈	D₄×C₃₇	1	4	yes	complemented
391	C₂⁴	—	2	2	no	—
392	#41	—	2	1	no	—
393	#41	—	2	1	no	—
394	#41	—	2	1	no	—
395	#41	—	2	1	no	—
396	#41	—	2	1	no	—
397	#41	—	2	1	no	—
398	#41	—	2	1	no	—
399	#41	—	2	1	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
407	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	4	4	no	—
417	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
418	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
424	Q₁₆	—	2	2	no	—
425	Q₁₆	—	4	4	no	—
426	Q₁₆	—	4	2	no	—
427	Q₁₆	—	4	2	no	—
428	SD₁₆	—	2	2	no	—
429	SD₁₆	—	2	2	no	—
430	SD₁₆	—	4	4	no	—
431	SD₁₆	—	4	4	no	—
432	SD₁₆	—	4	4	no	—
433	SD₁₆	—	4	4	no	—
434	D₈	—	2	2	no	—
435	D₈	—	4	4	no	—
436	D₈	—	4	2	no	—
437	D₈	—	4	2	no	—
438	M₁₆	—	2	2	no	—
439	M₁₆	—	2	1	no	—
440	M₁₆	—	2	1	no	—
441	M₁₆	—	2	1	no	—
442	M₁₆	—	2	1	no	—
443	M₁₆	—	4	2	no	—
444	M₁₆	—	4	2	no	—
445	M₁₆	C₂×D₄×C₃₇	1	4	yes	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	4	2	no	—
450	C₂×C₈	—	4	2	no	—
451	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
452	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
453	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
454	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
455	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
456	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
457	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
458	C₂×C₈	#41×C₃₇	1	2	yes	—
459	C₄⋊C₄	—	4	4	no	—
460	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	4	4	no	—
463	C₂²⋊C₄	—	4	4	no	—
464	C₂²⋊C₄	—	4	8	no	—
465	C₄²	—	2	2	no	—
466	C₄²	—	2	1	no	—
467	C₄²	C₂×D₄×C₃₇	1	2	yes	—
468	C₂³	—	2	1	no	—
469	C₂³	—	2	1	no	—
470	C₂³	—	4	2	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	8	4	no	—
474	C₂³	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
475	Q₈	—	2	1	no	—
476	Q₈	—	2	1	no	—
477	Q₈	—	2	1	no	—
478	Q₈	—	2	1	no	—
479	Q₈	—	4	2	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	4	2	no	—
482	Q₈	—	4	2	no	—
483	D₄	—	2	1	no	—
484	D₄	—	2	1	no	—
485	D₄	—	2	1	no	—
486	D₄	—	2	1	no	—
487	D₄	—	4	1	no	—
488	D₄	—	4	1	no	—
489	D₄	—	4	1	no	—
490	D₄	—	4	1	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	2	no	—
494	D₄	—	4	2	no	—
495	D₄	—	16	4	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
509	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
510	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
512	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
513	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
514	C₈	—	2	4	no	—
515	C₈	—	4	1	no	—
516	C₈	—	4	1	no	—
517	C₈	#121×C₃₇	1	2	yes	—
518	C₈	#121×C₃₇	1	2	yes	—
519	C₈	#127×C₃₇	1	2	yes	—
520	C₈	#127×C₃₇	1	2	yes	—
521	C₂²	—	2	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	8	4	no	—
527	C₂²	—	8	4	no	—
528	C₂²	—	8	2	no	—
529	C₂²	—	16	2	no	—
530	C₂²	C₃₇×#535	1	1	yes	characteristic
531	C₂²	D₄²×C₃₇	1	1	yes	characteristic
532	C₂²	C₃₇×#550	1	1	yes	characteristic
533	C₄	—	4	2	no	—
534	C₄	—	4	4	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	8	2	no	—
538	C₄	C₂×#121×C₃₇	1	1	yes	characteristic
539	C₄	C₂×#127×C₃₇	1	1	yes	characteristic
540	C₄	D₄²×C₃₇	1	1	yes	characteristic
541	C₄	C₃₇×#550	1	1	yes	characteristic
542	C₂	—	2	1	no	—
543	C₂	—	2	1	no	—
544	C₂	—	8	1	no	—
545	C₂	—	8	1	no	—
546	C₂	—	16	2	no	—
547	C₂	C₃₇×#2541	1	1	yes	characteristic
548	C₂	C₃₇×#3290	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₇	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
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×#3154	C₂	semidirect
2. C₂×C₃₇×#495	C₂	semidirect
3. C₂×C₃₇×#473	C₂	semidirect
4. C₂×C₃₇×#472	C₂	semidirect
5. C₃₇×#3059	C₂	semidirect
6. C₃₇×#3058	C₂	semidirect
7. C₂×C₃₇×#443	C₂	semidirect
8. C₃₇×#2004	C₂	semidirect
9. C₃₇×#2003	C₂	semidirect
10. C₃₇×#1977	C₂	semidirect
11. C₃₇×#1772	C₂	semidirect
104. #108×C₃₇	D₄	semidirect
115. C₄×C₈×C₃₇	D₄	semidirect
246. #28503	C₃₇	direct (N × H)
268. #3154	C₂×C₃₇	semidirect
269. C₂×#495	C₂×C₃₇	semidirect
270. C₂×#473	C₂×C₃₇	semidirect
271. C₂×#472	C₂×C₃₇	semidirect
272. #3059	C₂×C₃₇	semidirect
273. #3058	C₂×C₃₇	semidirect
274. C₂×#443	C₂×C₃₇	semidirect
275. #2004	C₂×C₃₇	semidirect
276. #2003	C₂×C₃₇	semidirect
277. #1977	C₂×C₃₇	semidirect
278. #1772	C₂×C₃₇	semidirect
321. C₃₇	#28503	direct (N × H)
379. #108	D₄×C₃₇	semidirect
390. 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×#3154	2
C₂×C₃₇×#495	2
C₂×C₃₇×#473	2
C₂×C₃₇×#472	2
C₃₇×#3059	2
C₃₇×#3058	2
C₂×C₃₇×#443	2
C₃₇×#2004	2
C₃₇×#2003	2
C₃₇×#1977	2
C₃₇×#1772	2
#28503	37

Subgroups — C37×#28503 #22649756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28503 #22649756