Subgroups — C₃₇×#28407 #22649660

Order 9472.

900 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#488	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₇×#479	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#464	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×Q₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2565	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2545	C₂	1	1	yes	maximal, characteristic
7	C₃₇×#2097	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2093	C₂	1	1	yes	maximal, characteristic
9	C₃₇×#2016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#2015	C₂	1	1	yes	maximal, characteristic
11	C₃₇×#1969	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#1968	C₂	1	1	yes	maximal, characteristic
13	C₃₇×#1958	C₂	1	1	yes	maximal, characteristic
14	C₃₇×#1956	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₄⋊C₄×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
20	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
21	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
25	C₃₇×#488	—	2	4	no	—
26	C₃₇×#479	—	2	4	no	—
27	C₃₇×#464	—	2	4	no	—
28	C₄×Q₁₆×C₃₇	—	2	4	no	—
29	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
33	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
34	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
35	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
36	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
37	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
38	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
39	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
40	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
41	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
42	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
46	C₃₇×#398	—	2	2	no	—
47	C₃₇×#396	—	2	2	no	—
48	C₃₇×#391	C₂²	1	1	yes	characteristic
49	C₃₇×#391	C₂²	1	1	yes	characteristic
50	C₃₇×#391	C₂²	1	1	yes	characteristic
51	C₃₇×#390	C₂²	1	1	yes	characteristic
52	C₃₇×#388	—	2	2	no	—
53	C₃₇×#387	—	2	2	no	—
54	C₃₇×#384	C₂²	1	1	yes	characteristic
55	C₃₇×#382	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
57	C₃₇×#336	C₂²	1	1	yes	characteristic
58	C₃₇×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
60	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
61	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
63	C₂×Q₁₆×C₃₇	—	2	2	no	—
64	C₂×Q₁₆×C₃₇	—	2	2	no	—
65	C₂×Q₁₆×C₃₇	—	2	2	no	—
66	C₂×Q₁₆×C₃₇	—	2	2	no	—
67	C₂×Q₁₆×C₃₇	—	2	2	no	—
68	C₂×Q₁₆×C₃₇	—	4	1	no	—
69	C₂×SD₁₆×C₃₇	—	2	2	no	—
70	C₂×SD₁₆×C₃₇	—	2	2	no	—
71	C₂×SD₁₆×C₃₇	—	4	1	no	—
72	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
76	C₄⋊Q₈×C₃₇	—	2	2	no	—
77	C₄⋊Q₈×C₃₇	—	4	1	no	—
78	#125×C₃₇	—	2	2	no	—
79	#125×C₃₇	—	2	2	no	—
80	#124×C₃₇	—	2	2	no	—
81	#124×C₃₇	—	2	2	no	—
82	#124×C₃₇	—	2	2	no	—
83	#124×C₃₇	—	4	1	no	—
84	C₄×Q₈×C₃₇	—	2	2	no	—
85	C₄×Q₈×C₃₇	—	2	2	no	—
86	C₄×Q₈×C₃₇	—	2	2	no	—
87	C₄×Q₈×C₃₇	—	2	2	no	—
88	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
89	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
90	C₂×C₄⋊C₄×C₃₇	—	2	2	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	D₄	1	2	yes	—
95	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
103	C₂×C₄²×C₃₇	—	2	1	no	—
104	C₂×C₄²×C₃₇	—	2	1	no	—
105	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
108	#107×C₃₇	—	2	2	no	—
109	#107×C₃₇	—	2	2	no	—
110	#106×C₃₇	—	2	2	no	—
111	C₄⋊C₈×C₃₇	D₄	1	4	yes	—
112	#103×C₃₇	—	2	2	no	—
113	#103×C₃₇	—	2	2	no	—
114	#103×C₃₇	—	2	2	no	—
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	#102×C₃₇	—	2	2	no	—
120	#102×C₃₇	—	2	2	no	—
121	#102×C₃₇	—	2	2	no	—
122	C₄×C₈×C₃₇	—	4	1	no	—
123	C₄×C₈×C₃₇	—	4	1	no	—
124	C₄×C₈×C₃₇	D₄	1	4	yes	—
125	#95×C₃₇	—	2	2	no	—
126	#95×C₃₇	—	2	2	no	—
127	#95×C₃₇	—	2	2	no	—
128	#95×C₃₇	—	2	2	no	—
129	#95×C₃₇	D₄	1	2	yes	—
130	C₂⁴×C₃₇	—	2	1	no	—
131	C₂×Q₈×C₃₇	—	2	1	no	—
132	C₂×Q₈×C₃₇	—	2	1	no	—
133	C₂×Q₈×C₃₇	—	2	1	no	—
134	C₂×Q₈×C₃₇	—	2	1	no	—
135	C₂×Q₈×C₃₇	—	2	1	no	—
136	C₂×Q₈×C₃₇	—	2	1	no	—
137	C₂×Q₈×C₃₇	—	2	1	no	—
138	C₂×Q₈×C₃₇	—	2	1	no	—
139	C₂×Q₈×C₃₇	—	2	1	no	—
140	C₂×Q₈×C₃₇	—	2	1	no	—
141	C₂×Q₈×C₃₇	—	2	1	no	—
142	C₂×Q₈×C₃₇	—	2	1	no	—
143	C₂×Q₈×C₃₇	—	2	1	no	—
144	C₂×Q₈×C₃₇	—	2	1	no	—
145	C₂×Q₈×C₃₇	—	2	1	no	—
146	C₂×Q₈×C₃₇	—	2	1	no	—
147	C₂×Q₈×C₃₇	#41	1	2	yes	—
148	C₂×Q₈×C₃₇	#41	1	2	yes	—
149	C₂×D₄×C₃₇	—	2	1	no	—
150	C₂×D₄×C₃₇	—	2	1	no	—
151	C₂×D₄×C₃₇	—	2	1	no	—
152	C₂×D₄×C₃₇	—	2	1	no	—
153	C₂×D₄×C₃₇	—	2	1	no	—
154	C₂×D₄×C₃₇	—	2	1	no	—
155	C₂²×C₄×C₃₇	—	2	1	no	—
156	C₂²×C₄×C₃₇	—	2	1	no	—
157	C₂²×C₄×C₃₇	—	2	1	no	—
158	C₂²×C₄×C₃₇	—	2	1	no	—
159	C₂²×C₄×C₃₇	—	2	1	no	—
160	C₂²×C₄×C₃₇	—	2	1	no	—
161	C₂²×C₄×C₃₇	—	2	1	no	—
162	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
167	Q₁₆×C₃₇	—	2	8	no	—
168	Q₁₆×C₃₇	—	4	4	no	—
169	SD₁₆×C₃₇	—	4	4	no	—
170	C₂×C₈×C₃₇	—	2	1	no	—
171	C₂×C₈×C₃₇	—	2	1	no	—
172	C₂×C₈×C₃₇	—	2	1	no	—
173	C₂×C₈×C₃₇	—	2	1	no	—
174	C₂×C₈×C₃₇	—	2	1	no	—
175	C₂×C₈×C₃₇	—	2	1	no	—
176	C₂×C₈×C₃₇	—	2	1	no	—
177	C₂×C₈×C₃₇	—	2	1	no	—
178	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
179	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
180	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
181	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
182	C₄⋊C₄×C₃₇	—	2	4	no	—
183	C₄⋊C₄×C₃₇	—	2	1	no	—
184	C₄⋊C₄×C₃₇	—	2	1	no	—
185	C₄⋊C₄×C₃₇	—	2	1	no	—
186	C₄⋊C₄×C₃₇	—	2	1	no	—
187	C₄⋊C₄×C₃₇	—	2	1	no	—
188	C₄⋊C₄×C₃₇	—	2	1	no	—
189	C₄⋊C₄×C₃₇	—	2	1	no	—
190	C₄⋊C₄×C₃₇	—	2	1	no	—
191	C₄⋊C₄×C₃₇	—	4	4	no	—
192	C₄⋊C₄×C₃₇	—	4	2	no	—
193	C₄⋊C₄×C₃₇	—	4	2	no	—
194	C₄⋊C₄×C₃₇	—	4	2	no	—
195	C₄⋊C₄×C₃₇	—	4	2	no	—
196	C₄⋊C₄×C₃₇	—	4	4	no	—
197	C₂²⋊C₄×C₃₇	—	4	4	no	—
198	C₂²⋊C₄×C₃₇	—	4	2	no	—
199	C₂²⋊C₄×C₃₇	—	4	2	no	—
200	C₂²⋊C₄×C₃₇	—	4	4	no	—
201	C₄²×C₃₇	—	2	1	no	—
202	C₄²×C₃₇	—	2	1	no	—
203	C₄²×C₃₇	—	2	1	no	—
204	C₄²×C₃₇	—	2	1	no	—
205	C₄²×C₃₇	—	4	2	no	—
206	C₄²×C₃₇	—	4	2	no	—
207	C₄²×C₃₇	C₂×D₄	1	2	yes	—
208	C₄²×C₃₇	C₂×D₄	1	2	yes	—
209	C₂³×C₃₇	—	4	1	no	—
210	C₂³×C₃₇	—	4	1	no	—
211	C₂³×C₃₇	—	4	1	no	—
212	C₂³×C₃₇	—	4	2	no	—
213	C₂³×C₃₇	—	4	2	no	—
214	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
215	Q₈×C₃₇	—	2	2	no	—
216	Q₈×C₃₇	—	2	2	no	—
217	Q₈×C₃₇	—	2	2	no	—
218	Q₈×C₃₇	—	2	2	no	—
219	Q₈×C₃₇	—	4	1	no	—
220	Q₈×C₃₇	—	4	1	no	—
221	Q₈×C₃₇	—	4	1	no	—
222	Q₈×C₃₇	—	4	1	no	—
223	Q₈×C₃₇	—	4	1	no	—
224	Q₈×C₃₇	—	4	1	no	—
225	Q₈×C₃₇	—	4	1	no	—
226	Q₈×C₃₇	—	4	1	no	—
227	D₄×C₃₇	—	4	1	no	—
228	D₄×C₃₇	—	4	1	no	—
229	D₄×C₃₇	—	4	1	no	—
230	D₄×C₃₇	—	4	1	no	—
231	C₂×C₄×C₃₇	—	2	2	no	—
232	C₂×C₄×C₃₇	—	2	2	no	—
233	C₂×C₄×C₃₇	—	2	2	no	—
234	C₂×C₄×C₃₇	—	2	2	no	—
235	C₂×C₄×C₃₇	—	2	2	no	—
236	C₂×C₄×C₃₇	—	2	2	no	—
237	C₂×C₄×C₃₇	—	2	2	no	—
238	C₂×C₄×C₃₇	—	2	2	no	—
239	C₂×C₄×C₃₇	—	2	2	no	—
240	C₂×C₄×C₃₇	—	4	1	no	—
241	C₂×C₄×C₃₇	—	4	1	no	—
242	C₂×C₄×C₃₇	—	4	1	no	—
243	C₂×C₄×C₃₇	—	4	1	no	—
244	C₂×C₄×C₃₇	—	4	1	no	—
245	C₂×C₄×C₃₇	—	4	1	no	—
246	C₂×C₄×C₃₇	—	4	1	no	—
247	C₂×C₄×C₃₇	—	4	1	no	—
248	C₂×C₄×C₃₇	—	4	1	no	—
249	C₂×C₄×C₃₇	—	4	1	no	—
250	C₂×C₄×C₃₇	—	4	1	no	—
251	C₂×C₄×C₃₇	—	4	2	no	—
252	C₂×C₄×C₃₇	—	4	2	no	—
253	C₂×C₄×C₃₇	—	4	2	no	—
254	C₂×C₄×C₃₇	—	4	2	no	—
255	C₂×C₄×C₃₇	#127	1	2	yes	—
256	C₂×C₄×C₃₇	#127	1	2	yes	—
257	C₂×C₄×C₃₇	#135	1	4	yes	—
258	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
261	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
263	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
264	C₈×C₃₇	—	2	2	no	—
265	C₈×C₃₇	—	2	2	no	—
266	C₈×C₃₇	—	2	2	no	—
267	C₈×C₃₇	—	2	2	no	—
268	#28407	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₂²×C₃₇	—	8	2	no	—
270	C₂²×C₃₇	—	8	1	no	—
271	C₂²×C₃₇	—	8	1	no	—
272	C₂²×C₃₇	—	8	2	no	—
273	C₂²×C₃₇	—	8	1	no	—
274	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
275	C₂²×C₃₇	#546	1	1	yes	characteristic
276	C₂²×C₃₇	#548	1	1	yes	characteristic
277	C₂²×C₃₇	C₂×#135	1	2	yes	—
278	C₂²×C₃₇	#578	1	2	yes	—
279	C₄×C₃₇	—	2	2	no	—
280	C₄×C₃₇	—	2	2	no	—
281	C₄×C₃₇	—	2	4	no	—
282	C₄×C₃₇	—	4	2	no	—
283	C₄×C₃₇	—	4	2	no	—
284	C₄×C₃₇	—	4	2	no	—
285	C₄×C₃₇	—	8	1	no	—
286	C₄×C₃₇	—	8	1	no	—
287	C₄×C₃₇	—	8	1	no	—
288	C₄×C₃₇	—	8	1	no	—
289	C₄×C₃₇	—	8	1	no	—
290	C₄×C₃₇	#525	1	1	yes	characteristic
291	C₄×C₃₇	#537	1	1	yes	characteristic
292	C₄×C₃₇	#546	1	1	yes	characteristic
293	C₄×C₃₇	#548	1	1	yes	characteristic
294	C₂×#488	C₂×C₃₇	1	1	yes	characteristic
295	C₂×#479	C₂×C₃₇	1	1	yes	characteristic, complemented
296	C₂×#464	C₂×C₃₇	1	1	yes	characteristic
297	C₂×C₄×Q₁₆	C₂×C₃₇	1	1	yes	characteristic, complemented
298	#2565	C₂×C₃₇	1	1	yes	characteristic, complemented
299	#2545	C₂×C₃₇	1	1	yes	characteristic
300	#2097	C₂×C₃₇	1	1	yes	characteristic, complemented
301	#2093	C₂×C₃₇	1	1	yes	characteristic
302	#2016	C₂×C₃₇	1	1	yes	characteristic, complemented
303	#2015	C₂×C₃₇	1	1	yes	characteristic
304	#1969	C₂×C₃₇	1	1	yes	characteristic, complemented
305	#1968	C₂×C₃₇	1	1	yes	characteristic
306	#1958	C₂×C₃₇	1	1	yes	characteristic
307	#1956	C₂×C₃₇	1	1	yes	characteristic, complemented
308	C₈×C₄⋊C₄	C₂×C₃₇	1	1	yes	characteristic, complemented
309	C₂×C₃₇	—	16	1	no	—
310	C₂×C₃₇	#2540	1	1	yes	characteristic
311	C₂×C₃₇	#3147	1	1	yes	characteristic
312	C₂×C₃₇	#3156	1	1	yes	characteristic
313	C₂×C₃₇	#3300	1	2	yes	—
314	C₂×C₃₇	#3364	1	2	yes	—
315	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
316	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
317	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
318	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
319	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
320	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
321	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
322	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
323	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
324	#488	—	2	4	no	—
325	#479	—	2	4	no	—
326	#464	—	2	4	no	—
327	C₄×Q₁₆	—	2	4	no	—
328	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
329	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
330	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
331	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
332	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
333	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
334	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
335	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
336	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
337	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
338	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
339	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
340	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
341	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
342	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
343	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
344	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
345	#398	—	2	2	no	—
346	#396	—	2	2	no	—
347	#391	C₂²×C₃₇	1	1	yes	characteristic
348	#391	C₂²×C₃₇	1	1	yes	characteristic
349	#391	C₂²×C₃₇	1	1	yes	characteristic
350	#390	C₂²×C₃₇	1	1	yes	characteristic
351	#388	—	2	2	no	—
352	#387	—	2	2	no	—
353	#384	C₂²×C₃₇	1	1	yes	characteristic
354	#382	C₂²×C₃₇	1	1	yes	characteristic
355	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
356	#336	C₂²×C₃₇	1	1	yes	characteristic
357	#336	C₂²×C₃₇	1	1	yes	characteristic
358	C₃₇	#28407	1	1	yes	characteristic, direct product factor, Sylow
359	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
360	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
361	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
362	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
363	C₂×Q₁₆	—	2	2	no	—
364	C₂×Q₁₆	—	2	2	no	—
365	C₂×Q₁₆	—	2	2	no	—
366	C₂×Q₁₆	—	2	2	no	—
367	C₂×Q₁₆	—	2	2	no	—
368	C₂×Q₁₆	—	4	1	no	—
369	C₂×SD₁₆	—	2	2	no	—
370	C₂×SD₁₆	—	2	2	no	—
371	C₂×SD₁₆	—	4	1	no	—
372	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
373	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
374	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
375	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
376	C₄⋊Q₈	—	2	2	no	—
377	C₄⋊Q₈	—	4	1	no	—
378	#125	—	2	2	no	—
379	#125	—	2	2	no	—
380	#124	—	2	2	no	—
381	#124	—	2	2	no	—
382	#124	—	2	2	no	—
383	#124	—	4	1	no	—
384	C₄×Q₈	—	2	2	no	—
385	C₄×Q₈	—	2	2	no	—
386	C₄×Q₈	—	2	2	no	—
387	C₄×Q₈	—	2	2	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	2	no	—
393	C₂×C₄⋊C₄	—	2	2	no	—
394	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
395	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₂²⋊C₄	—	2	2	no	—
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	2	no	—
403	C₂×C₄²	—	2	1	no	—
404	C₂×C₄²	—	2	1	no	—
405	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
407	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
408	#107	—	2	2	no	—
409	#107	—	2	2	no	—
410	#106	—	2	2	no	—
411	C₄⋊C₈	D₄×C₃₇	1	4	yes	—
412	#103	—	2	2	no	—
413	#103	—	2	2	no	—
414	#103	—	2	2	no	—
415	#103	—	2	2	no	—
416	#103	—	2	2	no	—
417	#103	—	2	2	no	—
418	#103	—	2	2	no	—
419	#102	—	2	2	no	—
420	#102	—	2	2	no	—
421	#102	—	2	2	no	—
422	C₄×C₈	—	4	1	no	—
423	C₄×C₈	—	4	1	no	—
424	C₄×C₈	D₄×C₃₇	1	4	yes	—
425	#95	—	2	2	no	—
426	#95	—	2	2	no	—
427	#95	—	2	2	no	—
428	#95	—	2	2	no	—
429	#95	D₄×C₃₇	1	2	yes	—
430	C₂⁴	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	#41×C₃₇	1	2	yes	—
448	C₂×Q₈	#41×C₃₇	1	2	yes	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
463	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
466	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
467	Q₁₆	—	2	8	no	—
468	Q₁₆	—	4	4	no	—
469	SD₁₆	—	4	4	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
479	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
480	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
481	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	4	4	no	—
492	C₄⋊C₄	—	4	2	no	—
493	C₄⋊C₄	—	4	2	no	—
494	C₄⋊C₄	—	4	2	no	—
495	C₄⋊C₄	—	4	2	no	—
496	C₄⋊C₄	—	4	4	no	—
497	C₂²⋊C₄	—	4	4	no	—
498	C₂²⋊C₄	—	4	2	no	—
499	C₂²⋊C₄	—	4	2	no	—
500	C₂²⋊C₄	—	4	4	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	4	2	no	—
506	C₄²	—	4	2	no	—
507	C₄²	C₂×D₄×C₃₇	1	2	yes	—
508	C₄²	C₂×D₄×C₃₇	1	2	yes	—
509	C₂³	—	4	1	no	—
510	C₂³	—	4	1	no	—
511	C₂³	—	4	1	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	4	2	no	—
514	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
515	Q₈	—	2	2	no	—
516	Q₈	—	2	2	no	—
517	Q₈	—	2	2	no	—
518	Q₈	—	2	2	no	—
519	Q₈	—	4	1	no	—
520	Q₈	—	4	1	no	—
521	Q₈	—	4	1	no	—
522	Q₈	—	4	1	no	—
523	Q₈	—	4	1	no	—
524	Q₈	—	4	1	no	—
525	Q₈	—	4	1	no	—
526	Q₈	—	4	1	no	—
527	D₄	—	4	1	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	1	no	—
530	D₄	—	4	1	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	#127×C₃₇	1	2	yes	—
556	C₂×C₄	#127×C₃₇	1	2	yes	—
557	C₂×C₄	#135×C₃₇	1	4	yes	—
558	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
559	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
560	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
561	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
562	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
563	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
564	C₈	—	2	2	no	—
565	C₈	—	2	2	no	—
566	C₈	—	2	2	no	—
567	C₈	—	2	2	no	—
568	C₂²	—	8	1	no	—
569	C₂²	—	8	1	no	—
570	C₂²	—	8	2	no	—
571	C₂²	—	8	1	no	—
572	C₂²	—	8	2	no	—
573	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
574	C₂²	C₃₇×#546	1	1	yes	characteristic
575	C₂²	C₃₇×#548	1	1	yes	characteristic
576	C₂²	C₂×#135×C₃₇	1	2	yes	—
577	C₂²	C₃₇×#578	1	2	yes	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	4	no	—
581	C₄	—	4	2	no	—
582	C₄	—	4	2	no	—
583	C₄	—	4	2	no	—
584	C₄	—	8	1	no	—
585	C₄	—	8	1	no	—
586	C₄	—	8	1	no	—
587	C₄	—	8	1	no	—
588	C₄	—	8	1	no	—
589	C₄	C₃₇×#525	1	1	yes	characteristic
590	C₄	C₃₇×#537	1	1	yes	characteristic
591	C₄	C₃₇×#546	1	1	yes	characteristic
592	C₄	C₃₇×#548	1	1	yes	characteristic
593	C₂	—	16	1	no	—
594	C₂	C₃₇×#2540	1	1	yes	characteristic
595	C₂	C₃₇×#3147	1	1	yes	characteristic
596	C₂	C₃₇×#3156	1	1	yes	characteristic
597	C₂	C₃₇×#3300	1	2	yes	—
598	C₂	C₃₇×#3364	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂²×D₄×C₃₇	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₄×C₄⋊C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₇×#479	C₂	semidirect
4. C₂×C₄×Q₁₆×C₃₇	C₂	semidirect
5. C₃₇×#2565	C₂	semidirect
7. C₃₇×#2097	C₂	semidirect
9. C₃₇×#2016	C₂	semidirect
11. C₃₇×#1969	C₂	semidirect
14. C₃₇×#1956	C₂	semidirect
15. C₈×C₄⋊C₄×C₃₇	C₂	semidirect
268. #28407	C₃₇	direct (N × H)
295. C₂×#479	C₂×C₃₇	semidirect
297. C₂×C₄×Q₁₆	C₂×C₃₇	semidirect
298. #2565	C₂×C₃₇	semidirect
300. #2097	C₂×C₃₇	semidirect
302. #2016	C₂×C₃₇	semidirect
304. #1969	C₂×C₃₇	semidirect
307. #1956	C₂×C₃₇	semidirect
308. C₈×C₄⋊C₄	C₂×C₃₇	semidirect
358. C₃₇	#28407	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#488	2
C₂×C₃₇×#479	2
C₂×C₃₇×#464	2
C₂×C₄×Q₁₆×C₃₇	2
C₃₇×#2565	2
C₃₇×#2545	2
C₃₇×#2097	2
C₃₇×#2093	2
C₃₇×#2016	2
C₃₇×#2015	2
C₃₇×#1969	2
C₃₇×#1968	2
C₃₇×#1958	2
C₃₇×#1956	2
C₈×C₄⋊C₄×C₃₇	2
#28407	37

Subgroups — C37×#28407 #22649660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28407 #22649660