Subgroups — C₃₇×#28282 #22649535

Order 9472.

860 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#477	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#476	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#124×C₃₇	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2067	C₂	1	2	yes	maximal
6	C₃₇×#2066	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1983	C₂	1	2	yes	maximal
8	C₃₇×#1949	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1842	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1802	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₃₇	—	2	1	no	—
15	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
17	C₃₇×#477	—	2	4	no	—
18	C₃₇×#476	—	2	4	no	—
19	C₂×#107×C₃₇	C₂²	1	2	yes	—
20	C₂×#106×C₃₇	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
25	C₂×#103×C₃₇	C₂²	1	2	yes	—
26	C₂×#103×C₃₇	C₂²	1	2	yes	—
27	C₂×#102×C₃₇	C₂²	1	2	yes	—
28	C₂×#102×C₃₇	C₂²	1	2	yes	—
29	C₃₇×#391	—	2	1	no	—
30	C₃₇×#391	C₂²	1	1	yes	characteristic
31	C₃₇×#390	C₂²	1	1	yes	characteristic
32	C₃₇×#389	—	2	1	no	—
33	C₃₇×#389	C₂²	1	2	yes	—
34	C₃₇×#388	—	2	1	no	—
35	C₃₇×#388	—	2	1	no	—
36	C₃₇×#384	C₂²	1	1	yes	characteristic
37	C₃₇×#382	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₃₇	—	2	1	no	—
39	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
40	C₄×C₂²⋊C₄×C₃₇	—	2	1	no	—
41	C₄×C₂²⋊C₄×C₃₇	—	2	1	no	—
42	C₄³×C₃₇	C₂²	1	1	yes	characteristic
43	C₃₇×#340	C₂²	1	2	yes	—
44	C₃₇×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₃₇	—	2	1	no	—
46	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₃₇	—	2	1	no	—
49	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
50	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₃₇	—	2	2	no	—
52	C₄⋊Q₈×C₃₇	D₄	1	4	yes	—
53	#124×C₃₇	—	2	2	no	—
54	#124×C₃₇	Q₈	1	4	yes	complemented
55	C₄×Q₈×C₃₇	—	2	2	no	—
56	C₄×Q₈×C₃₇	—	2	2	no	—
57	C₄×Q₈×C₃₇	—	4	4	no	—
58	C₄×D₄×C₃₇	—	2	2	no	—
59	C₄×D₄×C₃₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
74	C₂×C₄²×C₃₇	—	2	1	no	—
75	C₂×C₄²×C₃₇	—	2	2	no	—
76	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
83	#107×C₃₇	—	2	4	no	—
84	#106×C₃₇	—	2	4	no	—
85	C₄⋊C₈×C₃₇	—	2	2	no	—
86	C₄⋊C₈×C₃₇	—	2	2	no	—
87	C₄⋊C₈×C₃₇	—	2	4	no	—
88	C₄⋊C₈×C₃₇	—	4	2	no	—
89	#103×C₃₇	—	2	4	no	—
90	#103×C₃₇	—	4	2	no	—
91	#102×C₃₇	—	2	4	no	—
92	#102×C₃₇	—	4	2	no	—
93	#95×C₃₇	—	2	1	no	—
94	#95×C₃₇	—	2	1	no	—
95	#95×C₃₇	—	2	1	no	—
96	#95×C₃₇	—	2	1	no	—
97	#95×C₃₇	—	2	2	no	—
98	#95×C₃₇	—	2	2	no	—
99	C₂⁴×C₃₇	—	2	1	no	—
100	C₂×Q₈×C₃₇	—	2	4	no	—
101	C₂×Q₈×C₃₇	—	2	1	no	—
102	C₂×Q₈×C₃₇	—	2	1	no	—
103	C₂×Q₈×C₃₇	—	2	1	no	—
104	C₂×Q₈×C₃₇	—	2	1	no	—
105	C₂×Q₈×C₃₇	—	2	1	no	—
106	C₂×Q₈×C₃₇	—	4	2	no	—
107	C₂×Q₈×C₃₇	—	4	2	no	—
108	C₂×Q₈×C₃₇	C₂×Q₈	1	2	yes	—
109	C₂×D₄×C₃₇	—	2	1	no	—
110	C₂×D₄×C₃₇	—	2	1	no	—
111	C₂×D₄×C₃₇	—	2	1	no	—
112	C₂×D₄×C₃₇	—	2	1	no	—
113	C₂×D₄×C₃₇	—	2	1	no	—
114	C₂×D₄×C₃₇	C₂×Q₈	1	2	yes	—
115	C₂²×C₄×C₃₇	—	2	1	no	—
116	C₂²×C₄×C₃₇	—	2	2	no	—
117	C₂²×C₄×C₃₇	—	2	1	no	—
118	C₂²×C₄×C₃₇	—	2	1	no	—
119	C₂²×C₄×C₃₇	—	2	2	no	—
120	C₂²×C₄×C₃₇	—	4	2	no	—
121	C₂²×C₄×C₃₇	—	4	2	no	—
122	C₂²×C₄×C₃₇	—	4	2	no	—
123	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
130	C₂×C₈×C₃₇	—	2	2	no	—
131	C₂×C₈×C₃₇	—	2	2	no	—
132	C₂×C₈×C₃₇	—	2	2	no	—
133	C₂×C₈×C₃₇	—	2	2	no	—
134	C₂×C₈×C₃₇	—	2	2	no	—
135	C₂×C₈×C₃₇	—	2	2	no	—
136	C₄⋊C₄×C₃₇	—	2	4	no	—
137	C₄⋊C₄×C₃₇	—	2	2	no	—
138	C₄⋊C₄×C₃₇	—	2	1	no	—
139	C₄⋊C₄×C₃₇	—	2	1	no	—
140	C₄⋊C₄×C₃₇	—	2	1	no	—
141	C₄⋊C₄×C₃₇	—	2	1	no	—
142	C₄⋊C₄×C₃₇	—	2	2	no	—
143	C₄⋊C₄×C₃₇	—	2	2	no	—
144	C₄⋊C₄×C₃₇	—	4	2	no	—
145	C₄⋊C₄×C₃₇	—	4	2	no	—
146	C₄⋊C₄×C₃₇	—	4	2	no	—
147	C₄⋊C₄×C₃₇	—	4	4	no	—
148	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
149	C₂²⋊C₄×C₃₇	—	2	4	no	—
150	C₂²⋊C₄×C₃₇	—	2	4	no	—
151	C₂²⋊C₄×C₃₇	—	4	2	no	—
152	C₂²⋊C₄×C₃₇	—	4	2	no	—
153	C₂²⋊C₄×C₃₇	—	4	2	no	—
154	C₄²×C₃₇	—	2	2	no	—
155	C₄²×C₃₇	—	2	2	no	—
156	C₄²×C₃₇	—	2	2	no	—
157	C₄²×C₃₇	—	2	1	no	—
158	C₄²×C₃₇	—	2	1	no	—
159	C₄²×C₃₇	—	4	1	no	—
160	C₄²×C₃₇	—	4	4	no	—
161	C₄²×C₃₇	—	4	2	no	—
162	C₄²×C₃₇	C₂×D₄	1	2	yes	—
163	C₄²×C₃₇	C₂×Q₈	1	2	yes	—
164	C₄²×C₃₇	#41	1	2	yes	—
165	C₄²×C₃₇	#41	1	2	yes	—
166	C₂³×C₃₇	—	2	2	no	—
167	C₂³×C₃₇	—	4	1	no	—
168	C₂³×C₃₇	—	4	1	no	—
169	C₂³×C₃₇	—	4	1	no	—
170	C₂³×C₃₇	—	4	1	no	—
171	C₂³×C₃₇	—	4	1	no	—
172	C₂³×C₃₇	—	4	1	no	—
173	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
174	Q₈×C₃₇	—	2	2	no	—
175	Q₈×C₃₇	—	2	2	no	—
176	Q₈×C₃₇	—	4	8	no	—
177	Q₈×C₃₇	—	4	1	no	—
178	Q₈×C₃₇	—	4	1	no	—
179	D₄×C₃₇	—	2	2	no	—
180	D₄×C₃₇	—	2	2	no	—
181	D₄×C₃₇	—	4	1	no	—
182	D₄×C₃₇	—	4	1	no	—
183	C₂×C₄×C₃₇	—	2	1	no	—
184	C₂×C₄×C₃₇	—	2	1	no	—
185	C₂×C₄×C₃₇	—	2	1	no	—
186	C₂×C₄×C₃₇	—	2	1	no	—
187	C₂×C₄×C₃₇	—	2	1	no	—
188	C₂×C₄×C₃₇	—	2	1	no	—
189	C₂×C₄×C₃₇	—	2	1	no	—
190	C₂×C₄×C₃₇	—	2	1	no	—
191	C₂×C₄×C₃₇	—	2	4	no	—
192	C₂×C₄×C₃₇	—	2	2	no	—
193	C₂×C₄×C₃₇	—	2	1	no	—
194	C₂×C₄×C₃₇	—	2	1	no	—
195	C₂×C₄×C₃₇	—	2	1	no	—
196	C₂×C₄×C₃₇	—	4	1	no	—
197	C₂×C₄×C₃₇	—	4	1	no	—
198	C₂×C₄×C₃₇	—	4	2	no	—
199	C₂×C₄×C₃₇	—	4	2	no	—
200	C₂×C₄×C₃₇	—	4	1	no	—
201	C₂×C₄×C₃₇	—	4	1	no	—
202	C₂×C₄×C₃₇	—	4	2	no	—
203	C₂×C₄×C₃₇	—	4	2	no	—
204	C₂×C₄×C₃₇	—	4	1	no	—
205	C₂×C₄×C₃₇	—	4	2	no	—
206	C₂×C₄×C₃₇	—	4	1	no	—
207	C₂×C₄×C₃₇	—	4	1	no	—
208	C₂×C₄×C₃₇	—	4	1	no	—
209	C₂×C₄×C₃₇	—	8	4	no	—
210	C₂×C₄×C₃₇	#121	1	2	yes	—
211	C₂×C₄×C₃₇	#121	1	2	yes	—
212	C₂×C₄×C₃₇	C₂²⋊Q₈	1	2	yes	—
213	C₂×C₄×C₃₇	C₂²⋊Q₈	1	2	yes	—
214	C₂×C₄×C₃₇	#135	1	2	yes	—
215	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
216	C₂×C₄×C₃₇	#137	1	2	yes	—
217	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
219	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
222	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
223	C₈×C₃₇	—	4	2	no	—
224	C₈×C₃₇	—	4	2	no	—
225	#28282	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₂²×C₃₇	—	4	2	no	—
227	C₂²×C₃₇	—	4	2	no	—
228	C₂²×C₃₇	—	4	2	no	—
229	C₂²×C₃₇	—	8	1	no	—
230	C₂²×C₃₇	—	8	1	no	—
231	C₂²×C₃₇	—	8	1	no	—
232	C₂²×C₃₇	—	8	1	no	—
233	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
234	C₂²×C₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
235	C₂²×C₃₇	#537	1	1	yes	characteristic
236	C₂²×C₃₇	C₂×#135	1	1	yes	characteristic
237	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
238	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
239	C₂²×C₃₇	#575	1	1	yes	characteristic
240	C₄×C₃₇	—	2	2	no	—
241	C₄×C₃₇	—	2	2	no	—
242	C₄×C₃₇	—	2	2	no	—
243	C₄×C₃₇	—	2	2	no	—
244	C₄×C₃₇	—	4	1	no	—
245	C₄×C₃₇	—	4	4	no	—
246	C₄×C₃₇	—	4	2	no	—
247	C₄×C₃₇	—	8	2	no	—
248	C₄×C₃₇	—	8	1	no	—
249	C₄×C₃₇	—	8	1	no	—
250	C₄×C₃₇	#464	1	4	yes	—
251	C₄×C₃₇	D₄×Q₈	1	1	yes	characteristic
252	C₄×C₃₇	#550	1	1	yes	characteristic
253	C₄×C₃₇	#554	1	1	yes	characteristic
254	C₄×C₃₇	#556	1	1	yes	characteristic
255	C₂×#477	C₂×C₃₇	1	1	yes	characteristic, complemented
256	C₂×#476	C₂×C₃₇	1	1	yes	characteristic
257	C₄×C₄⋊Q₈	C₂×C₃₇	1	1	yes	characteristic, complemented
258	C₄×#124	C₂×C₃₇	1	1	yes	characteristic
259	#2067	C₂×C₃₇	1	2	yes	—
260	#2066	C₂×C₃₇	1	2	yes	complemented
261	#1983	C₂×C₃₇	1	2	yes	—
262	#1949	C₂×C₃₇	1	2	yes	complemented
263	#1842	C₂×C₃₇	1	1	yes	characteristic, complemented
264	#1803	C₂×C₃₇	1	1	yes	characteristic, complemented
265	#1802	C₂×C₃₇	1	1	yes	characteristic
266	C₂×C₃₇	—	8	2	no	—
267	C₂×C₃₇	#2538	1	1	yes	characteristic
268	C₂×C₃₇	C₂×#464	1	1	yes	characteristic
269	C₂×C₃₇	#3036	1	1	yes	characteristic
270	C₂×C₃₇	#3076	1	1	yes	characteristic
271	C₂×C₃₇	#3079	1	1	yes	characteristic
272	C₂×C₃₇	#3247	1	1	yes	characteristic
273	C₂×C₃₇	#3252	1	1	yes	characteristic
274	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
275	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
276	C₂×C₄×Q₈	—	2	1	no	—
277	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
278	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
279	#477	—	2	4	no	—
280	#476	—	2	4	no	—
281	C₂×#107	C₂²×C₃₇	1	2	yes	—
282	C₂×#106	C₂²×C₃₇	1	2	yes	—
283	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
284	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
285	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
286	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
287	C₂×#103	C₂²×C₃₇	1	2	yes	—
288	C₂×#103	C₂²×C₃₇	1	2	yes	—
289	C₂×#102	C₂²×C₃₇	1	2	yes	—
290	C₂×#102	C₂²×C₃₇	1	2	yes	—
291	#391	—	2	1	no	—
292	#391	C₂²×C₃₇	1	1	yes	characteristic
293	#390	C₂²×C₃₇	1	1	yes	characteristic
294	#389	—	2	1	no	—
295	#389	C₂²×C₃₇	1	2	yes	—
296	#388	—	2	1	no	—
297	#388	—	2	1	no	—
298	#384	C₂²×C₃₇	1	1	yes	characteristic
299	#382	C₂²×C₃₇	1	1	yes	characteristic
300	C₄×C₄⋊C₄	—	2	1	no	—
301	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
302	C₄×C₂²⋊C₄	—	2	1	no	—
303	C₄×C₂²⋊C₄	—	2	1	no	—
304	C₄³	C₂²×C₃₇	1	1	yes	characteristic
305	#340	C₂²×C₃₇	1	2	yes	—
306	#340	C₂²×C₃₇	1	2	yes	—
307	C₃₇	#28282	1	1	yes	characteristic, direct product factor, Sylow
308	C₂²×Q₈	—	2	1	no	—
309	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
310	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
311	C₂³×C₄	—	2	1	no	—
312	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
313	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
314	C₄⋊Q₈	—	2	2	no	—
315	C₄⋊Q₈	D₄×C₃₇	1	4	yes	—
316	#124	—	2	2	no	—
317	#124	Q₈×C₃₇	1	4	yes	complemented
318	C₄×Q₈	—	2	2	no	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	—	4	4	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	2	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
331	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₄²	—	2	2	no	—
338	C₂×C₄²	—	2	1	no	—
339	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
340	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
341	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
342	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
345	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
346	#107	—	2	4	no	—
347	#106	—	2	4	no	—
348	C₄⋊C₈	—	2	2	no	—
349	C₄⋊C₈	—	2	2	no	—
350	C₄⋊C₈	—	2	4	no	—
351	C₄⋊C₈	—	4	2	no	—
352	#103	—	2	4	no	—
353	#103	—	4	2	no	—
354	#102	—	2	4	no	—
355	#102	—	4	2	no	—
356	#95	—	2	1	no	—
357	#95	—	2	1	no	—
358	#95	—	2	1	no	—
359	#95	—	2	1	no	—
360	#95	—	2	2	no	—
361	#95	—	2	2	no	—
362	C₂⁴	—	2	1	no	—
363	C₂×Q₈	—	2	4	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	4	2	no	—
370	C₂×Q₈	—	4	2	no	—
371	C₂×Q₈	C₂×Q₈×C₃₇	1	2	yes	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	C₂×Q₈×C₃₇	1	2	yes	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
392	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	4	2	no	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	—	4	4	no	—
411	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	4	2	no	—
415	C₂²⋊C₄	—	4	2	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	4	1	no	—
423	C₄²	—	4	4	no	—
424	C₄²	—	4	2	no	—
425	C₄²	C₂×D₄×C₃₇	1	2	yes	—
426	C₄²	C₂×Q₈×C₃₇	1	2	yes	—
427	C₄²	#41×C₃₇	1	2	yes	—
428	C₄²	#41×C₃₇	1	2	yes	—
429	C₂³	—	2	2	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
437	Q₈	—	2	2	no	—
438	Q₈	—	2	2	no	—
439	Q₈	—	4	8	no	—
440	Q₈	—	4	1	no	—
441	Q₈	—	4	1	no	—
442	D₄	—	2	2	no	—
443	D₄	—	2	2	no	—
444	D₄	—	4	1	no	—
445	D₄	—	4	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	8	4	no	—
473	C₂×C₄	#121×C₃₇	1	2	yes	—
474	C₂×C₄	#121×C₃₇	1	2	yes	—
475	C₂×C₄	C₂²⋊Q₈×C₃₇	1	2	yes	—
476	C₂×C₄	C₂²⋊Q₈×C₃₇	1	2	yes	—
477	C₂×C₄	#135×C₃₇	1	2	yes	—
478	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
479	C₂×C₄	#137×C₃₇	1	2	yes	—
480	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
481	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
482	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
483	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
484	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
485	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
486	C₈	—	4	2	no	—
487	C₈	—	4	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	8	1	no	—
492	C₂²	—	8	1	no	—
493	C₂²	—	8	1	no	—
494	C₂²	—	8	1	no	—
495	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
496	C₂²	C₂×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
497	C₂²	C₃₇×#537	1	1	yes	characteristic
498	C₂²	C₂×#135×C₃₇	1	1	yes	characteristic
499	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
500	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
501	C₂²	C₃₇×#575	1	1	yes	characteristic
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	2	2	no	—
505	C₄	—	2	2	no	—
506	C₄	—	4	1	no	—
507	C₄	—	4	4	no	—
508	C₄	—	4	2	no	—
509	C₄	—	8	2	no	—
510	C₄	—	8	1	no	—
511	C₄	—	8	1	no	—
512	C₄	C₃₇×#464	1	4	yes	—
513	C₄	D₄×Q₈×C₃₇	1	1	yes	characteristic
514	C₄	C₃₇×#550	1	1	yes	characteristic
515	C₄	C₃₇×#554	1	1	yes	characteristic
516	C₄	C₃₇×#556	1	1	yes	characteristic
517	C₂	—	8	2	no	—
518	C₂	C₃₇×#2538	1	1	yes	characteristic
519	C₂	C₂×C₃₇×#464	1	1	yes	characteristic
520	C₂	C₃₇×#3036	1	1	yes	characteristic
521	C₂	C₃₇×#3076	1	1	yes	characteristic
522	C₂	C₃₇×#3079	1	1	yes	characteristic
523	C₂	C₃₇×#3247	1	1	yes	characteristic
524	C₂	C₃₇×#3252	1	1	yes	characteristic

	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 ◁ C₄³×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#477	C₂	semidirect
3. C₄×C₄⋊Q₈×C₃₇	C₂	semidirect
6. C₃₇×#2066	C₂	semidirect
8. C₃₇×#1949	C₂	semidirect
9. C₃₇×#1842	C₂	semidirect
10. C₃₇×#1803	C₂	semidirect
54. #124×C₃₇	Q₈	semidirect
225. #28282	C₃₇	direct (N × H)
255. C₂×#477	C₂×C₃₇	semidirect
257. C₄×C₄⋊Q₈	C₂×C₃₇	semidirect
260. #2066	C₂×C₃₇	semidirect
262. #1949	C₂×C₃₇	semidirect
263. #1842	C₂×C₃₇	semidirect
264. #1803	C₂×C₃₇	semidirect
307. C₃₇	#28282	direct (N × H)
317. #124	Q₈×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#477	2
C₂×C₃₇×#476	2
C₄×C₄⋊Q₈×C₃₇	2
C₄×#124×C₃₇	2
C₃₇×#2067	2
C₃₇×#2066	2
C₃₇×#1983	2
C₃₇×#1949	2
C₃₇×#1842	2
C₃₇×#1803	2
C₃₇×#1802	2
#28282	37

Subgroups — C37×#28282 #22649535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28282 #22649535