Subgroups — C₃₇×#28384 #22649637

Order 9472.

934 conjugacy classes of subgroups.

The subgroup lattice has 476 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	C₂×C₃₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#461	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2862	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#124×C₃₇	C₂	1	1	yes	maximal, characteristic
7	C₃₇×#2097	C₂	1	2	yes	maximal, complemented
8	C₃₇×#2015	C₂	1	2	yes	maximal
9	C₃₇×#1973	C₂	1	2	yes	maximal
10	C₃₇×#1971	C₂	1	2	yes	maximal, complemented
11	C₃₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₃₇	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
16	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
19	C₃₇×#477	—	2	4	no	—
20	C₃₇×#476	—	2	4	no	—
21	C₃₇×#462	—	2	4	no	—
22	C₃₇×#461	—	2	4	no	—
23	C₂×#107×C₃₇	C₂²	1	2	yes	—
24	C₂×#106×C₃₇	C₂²	1	2	yes	—
25	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
27	C₂×#103×C₃₇	C₂²	1	2	yes	—
28	C₂×#103×C₃₇	C₂²	1	2	yes	—
29	C₂×#103×C₃₇	C₂²	1	2	yes	—
30	C₂×#102×C₃₇	C₂²	1	2	yes	—
31	C₂×#97×C₃₇	C₂²	1	2	yes	—
32	C₃₇×#391	—	2	2	no	—
33	C₃₇×#391	C₂²	1	2	yes	—
34	C₃₇×#391	C₂²	1	2	yes	—
35	C₃₇×#391	C₂²	1	1	yes	characteristic
36	C₃₇×#390	C₂²	1	1	yes	characteristic
37	C₃₇×#388	—	2	2	no	—
38	C₃₇×#382	—	2	2	no	—
39	C₃₇×#382	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₃₇	—	2	2	no	—
41	C₄³×C₃₇	C₂²	1	1	yes	characteristic
42	C₃₇×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₃₇	—	2	1	no	—
44	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
45	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₃₇	—	2	1	no	—
48	C₂×Q₁₆×C₃₇	—	2	4	no	—
49	C₂×Q₁₆×C₃₇	—	2	4	no	—
50	C₂×Q₁₆×C₃₇	—	4	2	no	—
51	C₂×SD₁₆×C₃₇	—	2	4	no	—
52	C₂×SD₁₆×C₃₇	—	2	4	no	—
53	C₂×SD₁₆×C₃₇	—	4	2	no	—
54	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
55	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
56	C₄⋊Q₈×C₃₇	—	2	2	no	—
57	C₄⋊Q₈×C₃₇	—	2	2	no	—
58	C₄⋊Q₈×C₃₇	—	2	2	no	—
59	C₄⋊Q₈×C₃₇	—	2	2	no	—
60	#124×C₃₇	—	2	2	no	—
61	#124×C₃₇	—	2	2	no	—
62	C₄×Q₈×C₃₇	—	2	2	no	—
63	C₄×Q₈×C₃₇	—	2	2	no	—
64	C₄×D₄×C₃₇	—	2	2	no	—
65	C₄×D₄×C₃₇	—	2	2	no	—
66	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
68	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
76	C₂×C₄²×C₃₇	—	2	1	no	—
77	C₂×C₄²×C₃₇	D₄	1	2	yes	—
78	C₂×C₄²×C₃₇	D₄	1	2	yes	—
79	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
82	#107×C₃₇	—	2	4	no	—
83	#106×C₃₇	—	2	4	no	—
84	C₄⋊C₈×C₃₇	D₄	1	4	yes	—
85	C₄⋊C₈×C₃₇	D₄	1	4	yes	—
86	#103×C₃₇	—	2	4	no	—
87	#103×C₃₇	—	2	4	no	—
88	#103×C₃₇	—	2	4	no	—
89	#102×C₃₇	—	2	4	no	—
90	#97×C₃₇	—	4	2	no	—
91	#95×C₃₇	—	2	2	no	—
92	#95×C₃₇	—	2	2	no	—
93	#95×C₃₇	—	2	4	no	—
94	#95×C₃₇	—	2	4	no	—
95	C₂⁴×C₃₇	—	2	1	no	—
96	C₂×Q₈×C₃₇	—	2	1	no	—
97	C₂×Q₈×C₃₇	—	2	1	no	—
98	C₂×Q₈×C₃₇	—	2	1	no	—
99	C₂×Q₈×C₃₇	—	2	2	no	—
100	C₂×Q₈×C₃₇	—	2	2	no	—
101	C₂×Q₈×C₃₇	—	2	2	no	—
102	C₂×Q₈×C₃₇	—	2	2	no	—
103	C₂×Q₈×C₃₇	—	2	1	no	—
104	C₂×Q₈×C₃₇	—	2	2	no	—
105	C₂×Q₈×C₃₇	—	2	1	no	—
106	C₂×Q₈×C₃₇	—	2	2	no	—
107	C₂×Q₈×C₃₇	—	4	4	no	—
108	C₂×Q₈×C₃₇	—	4	2	no	—
109	C₂×Q₈×C₃₇	#41	1	2	yes	—
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	—	2	1	no	—
115	C₂×D₄×C₃₇	#41	1	2	yes	—
116	C₂²×C₄×C₃₇	—	2	1	no	—
117	C₂²×C₄×C₃₇	—	2	1	no	—
118	C₂²×C₄×C₃₇	—	2	2	no	—
119	C₂²×C₄×C₃₇	—	2	2	no	—
120	C₂²×C₄×C₃₇	—	2	1	no	—
121	C₂²×C₄×C₃₇	—	4	2	no	—
122	C₂²×C₄×C₃₇	—	4	4	no	—
123	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
128	Q₁₆×C₃₇	—	4	8	no	—
129	SD₁₆×C₃₇	—	4	8	no	—
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	C₂×D₄	1	4	yes	—
135	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
136	C₄⋊C₄×C₃₇	—	2	2	no	—
137	C₄⋊C₄×C₃₇	—	2	1	no	—
138	C₄⋊C₄×C₃₇	—	2	1	no	—
139	C₄⋊C₄×C₃₇	—	2	2	no	—
140	C₄⋊C₄×C₃₇	—	2	1	no	—
141	C₄⋊C₄×C₃₇	—	2	1	no	—
142	C₄⋊C₄×C₃₇	—	4	2	no	—
143	C₄⋊C₄×C₃₇	—	4	2	no	—
144	C₄⋊C₄×C₃₇	—	4	2	no	—
145	C₄⋊C₄×C₃₇	—	4	2	no	—
146	C₂²⋊C₄×C₃₇	—	2	8	no	—
147	C₂²⋊C₄×C₃₇	—	4	4	no	—
148	C₂²⋊C₄×C₃₇	—	4	2	no	—
149	C₄²×C₃₇	—	2	4	no	—
150	C₄²×C₃₇	—	2	1	no	—
151	C₄²×C₃₇	—	2	1	no	—
152	C₄²×C₃₇	—	2	1	no	—
153	C₄²×C₃₇	—	2	1	no	—
154	C₄²×C₃₇	—	4	2	no	—
155	C₄²×C₃₇	—	4	2	no	—
156	C₄²×C₃₇	C₂×D₄	1	2	yes	—
157	C₄²×C₃₇	C₂×D₄	1	2	yes	—
158	C₂³×C₃₇	—	2	2	no	—
159	C₂³×C₃₇	—	4	1	no	—
160	C₂³×C₃₇	—	4	1	no	—
161	C₂³×C₃₇	—	4	2	no	—
162	C₂³×C₃₇	—	4	2	no	—
163	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₃₇	—	2	2	no	—
165	Q₈×C₃₇	—	2	2	no	—
166	Q₈×C₃₇	—	4	1	no	—
167	Q₈×C₃₇	—	4	1	no	—
168	Q₈×C₃₇	—	4	2	no	—
169	Q₈×C₃₇	—	4	2	no	—
170	Q₈×C₃₇	—	4	2	no	—
171	Q₈×C₃₇	—	4	2	no	—
172	Q₈×C₃₇	—	8	4	no	—
173	D₄×C₃₇	—	2	2	no	—
174	D₄×C₃₇	—	2	2	no	—
175	D₄×C₃₇	—	4	1	no	—
176	D₄×C₃₇	—	4	1	no	—
177	C₂×C₄×C₃₇	—	2	2	no	—
178	C₂×C₄×C₃₇	—	2	2	no	—
179	C₂×C₄×C₃₇	—	2	2	no	—
180	C₂×C₄×C₃₇	—	2	2	no	—
181	C₂×C₄×C₃₇	—	2	2	no	—
182	C₂×C₄×C₃₇	—	2	2	no	—
183	C₂×C₄×C₃₇	—	2	2	no	—
184	C₂×C₄×C₃₇	—	2	2	no	—
185	C₂×C₄×C₃₇	—	4	1	no	—
186	C₂×C₄×C₃₇	—	4	1	no	—
187	C₂×C₄×C₃₇	—	4	2	no	—
188	C₂×C₄×C₃₇	—	4	1	no	—
189	C₂×C₄×C₃₇	—	4	1	no	—
190	C₂×C₄×C₃₇	—	4	2	no	—
191	C₂×C₄×C₃₇	—	4	2	no	—
192	C₂×C₄×C₃₇	—	4	2	no	—
193	C₂×C₄×C₃₇	—	4	2	no	—
194	C₂×C₄×C₃₇	—	4	2	no	—
195	C₂×C₄×C₃₇	—	4	4	no	—
196	C₂×C₄×C₃₇	—	8	4	no	—
197	C₂×C₄×C₃₇	#127	1	2	yes	—
198	C₂×C₄×C₃₇	#127	1	2	yes	—
199	C₂×C₄×C₃₇	#137	1	4	yes	—
200	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
205	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
206	C₈×C₃₇	—	2	4	no	—
207	C₈×C₃₇	—	2	4	no	—
208	#28384	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂²×C₃₇	—	4	4	no	—
210	C₂²×C₃₇	—	4	2	no	—
211	C₂²×C₃₇	—	8	1	no	—
212	C₂²×C₃₇	—	8	1	no	—
213	C₂²×C₃₇	—	8	2	no	—
214	C₂²×C₃₇	#525	1	1	yes	characteristic
215	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
216	C₂²×C₃₇	#537	1	1	yes	characteristic
217	C₂²×C₃₇	C₂×#137	1	2	yes	—
218	C₂²×C₃₇	#575	1	2	yes	—
219	C₄×C₃₇	—	2	2	no	—
220	C₄×C₃₇	—	4	2	no	—
221	C₄×C₃₇	—	4	2	no	—
222	C₄×C₃₇	—	4	2	no	—
223	C₄×C₃₇	—	8	1	no	—
224	C₄×C₃₇	—	8	1	no	—
225	C₄×C₃₇	—	8	2	no	—
226	C₄×C₃₇	—	8	2	no	—
227	C₄×C₃₇	#497	1	4	yes	—
228	C₄×C₃₇	#546	1	1	yes	characteristic
229	C₄×C₃₇	#546	1	1	yes	characteristic
230	C₄×C₃₇	#548	1	1	yes	characteristic
231	C₄×C₃₇	#548	1	1	yes	characteristic
232	C₂×#477	C₂×C₃₇	1	1	yes	characteristic, complemented
233	C₂×#476	C₂×C₃₇	1	1	yes	characteristic
234	C₂×#462	C₂×C₃₇	1	1	yes	characteristic, complemented
235	C₂×#461	C₂×C₃₇	1	1	yes	characteristic
236	#2862	C₂×C₃₇	1	1	yes	characteristic, complemented
237	C₄×#124	C₂×C₃₇	1	1	yes	characteristic
238	#2097	C₂×C₃₇	1	2	yes	complemented
239	#2015	C₂×C₃₇	1	2	yes	—
240	#1973	C₂×C₃₇	1	2	yes	—
241	#1971	C₂×C₃₇	1	2	yes	complemented
242	#1767	C₂×C₃₇	1	1	yes	characteristic, complemented
243	C₂×C₃₇	—	8	2	no	—
244	C₂×C₃₇	#2540	1	1	yes	characteristic
245	C₂×C₃₇	#3116	1	2	yes	—
246	C₂×C₃₇	C₂×#497	1	1	yes	characteristic
247	C₂×C₃₇	#3153	1	1	yes	characteristic
248	C₂×C₃₇	#3252	1	2	yes	—
249	C₂²×Q₁₆	C₂²×C₃₇	1	2	yes	—
250	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
251	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
252	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
253	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
254	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
255	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
256	#477	—	2	4	no	—
257	#476	—	2	4	no	—
258	#462	—	2	4	no	—
259	#461	—	2	4	no	—
260	C₂×#107	C₂²×C₃₇	1	2	yes	—
261	C₂×#106	C₂²×C₃₇	1	2	yes	—
262	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
264	C₂×#103	C₂²×C₃₇	1	2	yes	—
265	C₂×#103	C₂²×C₃₇	1	2	yes	—
266	C₂×#103	C₂²×C₃₇	1	2	yes	—
267	C₂×#102	C₂²×C₃₇	1	2	yes	—
268	C₂×#97	C₂²×C₃₇	1	2	yes	—
269	#391	—	2	2	no	—
270	#391	C₂²×C₃₇	1	2	yes	—
271	#391	C₂²×C₃₇	1	2	yes	—
272	#391	C₂²×C₃₇	1	1	yes	characteristic
273	#390	C₂²×C₃₇	1	1	yes	characteristic
274	#388	—	2	2	no	—
275	#382	—	2	2	no	—
276	#382	C₂²×C₃₇	1	1	yes	characteristic
277	C₄×C₂²⋊C₄	—	2	2	no	—
278	C₄³	C₂²×C₃₇	1	1	yes	characteristic
279	#336	C₂²×C₃₇	1	2	yes	—
280	C₃₇	#28384	1	1	yes	characteristic, direct product factor, Sylow
281	C₂²×Q₈	—	2	1	no	—
282	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
283	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
284	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
285	C₂³×C₄	—	2	1	no	—
286	C₂×Q₁₆	—	2	4	no	—
287	C₂×Q₁₆	—	2	4	no	—
288	C₂×Q₁₆	—	4	2	no	—
289	C₂×SD₁₆	—	2	4	no	—
290	C₂×SD₁₆	—	2	4	no	—
291	C₂×SD₁₆	—	4	2	no	—
292	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
293	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
294	C₄⋊Q₈	—	2	2	no	—
295	C₄⋊Q₈	—	2	2	no	—
296	C₄⋊Q₈	—	2	2	no	—
297	C₄⋊Q₈	—	2	2	no	—
298	#124	—	2	2	no	—
299	#124	—	2	2	no	—
300	C₄×Q₈	—	2	2	no	—
301	C₄×Q₈	—	2	2	no	—
302	C₄×D₄	—	2	2	no	—
303	C₄×D₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₄²	—	2	1	no	—
315	C₂×C₄²	D₄×C₃₇	1	2	yes	—
316	C₂×C₄²	D₄×C₃₇	1	2	yes	—
317	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
318	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
320	#107	—	2	4	no	—
321	#106	—	2	4	no	—
322	C₄⋊C₈	D₄×C₃₇	1	4	yes	—
323	C₄⋊C₈	D₄×C₃₇	1	4	yes	—
324	#103	—	2	4	no	—
325	#103	—	2	4	no	—
326	#103	—	2	4	no	—
327	#102	—	2	4	no	—
328	#97	—	4	2	no	—
329	#95	—	2	2	no	—
330	#95	—	2	2	no	—
331	#95	—	2	4	no	—
332	#95	—	2	4	no	—
333	C₂⁴	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	4	4	no	—
346	C₂×Q₈	—	4	2	no	—
347	C₂×Q₈	#41×C₃₇	1	2	yes	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	#41×C₃₇	1	2	yes	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	4	no	—
361	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
365	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
366	Q₁₆	—	4	8	no	—
367	SD₁₆	—	4	8	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
373	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	—	4	4	no	—
386	C₂²⋊C₄	—	4	2	no	—
387	C₄²	—	2	4	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	4	2	no	—
393	C₄²	—	4	2	no	—
394	C₄²	C₂×D₄×C₃₇	1	2	yes	—
395	C₄²	C₂×D₄×C₃₇	1	2	yes	—
396	C₂³	—	2	2	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
402	Q₈	—	2	2	no	—
403	Q₈	—	2	2	no	—
404	Q₈	—	4	1	no	—
405	Q₈	—	4	1	no	—
406	Q₈	—	4	2	no	—
407	Q₈	—	4	2	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	8	4	no	—
411	D₄	—	2	2	no	—
412	D₄	—	2	2	no	—
413	D₄	—	4	1	no	—
414	D₄	—	4	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	8	4	no	—
435	C₂×C₄	#127×C₃₇	1	2	yes	—
436	C₂×C₄	#127×C₃₇	1	2	yes	—
437	C₂×C₄	#137×C₃₇	1	4	yes	—
438	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
439	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
440	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
441	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
442	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
443	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
444	C₈	—	2	4	no	—
445	C₈	—	2	4	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	1	no	—
450	C₂²	—	8	2	no	—
451	C₂²	C₃₇×#525	1	1	yes	characteristic
452	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
453	C₂²	C₃₇×#537	1	1	yes	characteristic
454	C₂²	C₂×#137×C₃₇	1	2	yes	—
455	C₂²	C₃₇×#575	1	2	yes	—
456	C₄	—	2	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	8	1	no	—
461	C₄	—	8	2	no	—
462	C₄	—	8	1	no	—
463	C₄	—	8	2	no	—
464	C₄	C₃₇×#497	1	4	yes	—
465	C₄	C₃₇×#546	1	1	yes	characteristic
466	C₄	C₃₇×#546	1	1	yes	characteristic
467	C₄	C₃₇×#548	1	1	yes	characteristic
468	C₄	C₃₇×#548	1	1	yes	characteristic
469	C₂	—	8	2	no	—
470	C₂	C₃₇×#2540	1	1	yes	characteristic
471	C₂	C₃₇×#3116	1	2	yes	—
472	C₂	C₂×C₃₇×#497	1	1	yes	characteristic
473	C₂	C₃₇×#3153	1	1	yes	characteristic
474	C₂	C₃₇×#3252	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 ◁ 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. C₂×C₃₇×#462	C₂	semidirect
5. C₃₇×#2862	C₂	semidirect
7. C₃₇×#2097	C₂	semidirect
10. C₃₇×#1971	C₂	semidirect
11. C₃₇×#1767	C₂	semidirect
208. #28384	C₃₇	direct (N × H)
232. C₂×#477	C₂×C₃₇	semidirect
234. C₂×#462	C₂×C₃₇	semidirect
236. #2862	C₂×C₃₇	semidirect
238. #2097	C₂×C₃₇	semidirect
241. #1971	C₂×C₃₇	semidirect
242. #1767	C₂×C₃₇	semidirect
280. C₃₇	#28384	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×#477	2
C₂×C₃₇×#476	2
C₂×C₃₇×#462	2
C₂×C₃₇×#461	2
C₃₇×#2862	2
C₄×#124×C₃₇	2
C₃₇×#2097	2
C₃₇×#2015	2
C₃₇×#1973	2
C₃₇×#1971	2
C₃₇×#1767	2
#28384	37

Subgroups — C37×#28384 #22649637

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28384 #22649637