Subgroups — C₃₇×#24630 #22645883

Order 9472.

906 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#461	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2546	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2354	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2055	C₂	1	2	yes	maximal
6	C₃₇×#2013	C₂	1	2	yes	maximal
7	C₃₇×#1981	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1927	C₂	1	2	yes	maximal, complemented
11	C₃₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
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	2	yes	—
16	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×#117×C₃₇	—	2	1	no	—
19	C₃₇×#461	—	2	4	no	—
20	C₄×SD₁₆×C₃₇	—	2	4	no	—
21	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
24	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×#103×C₃₇	C₂²	1	2	yes	—
26	C₂×#103×C₃₇	C₂²	1	2	yes	—
27	C₂×#103×C₃₇	C₂²	1	2	yes	—
28	C₂×#103×C₃₇	C₂²	1	2	yes	—
29	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
31	C₃₇×#398	—	2	2	no	—
32	C₃₇×#391	C₂²	1	2	yes	—
33	C₃₇×#390	C₂²	1	2	yes	—
34	C₃₇×#389	—	2	1	no	—
35	C₃₇×#389	—	2	1	no	—
36	C₃₇×#388	—	2	2	no	—
37	C₃₇×#384	C₂²	1	1	yes	characteristic
38	C₃₇×#380	—	2	1	no	—
39	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
40	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
41	C₃₇×#340	C₂²	1	2	yes	—
42	C₃₇×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
44	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₃₇	—	2	1	no	—
47	C₂×SD₁₆×C₃₇	—	2	2	no	—
48	C₂×SD₁₆×C₃₇	—	2	2	no	—
49	C₂×SD₁₆×C₃₇	—	2	4	no	—
50	C₂×SD₁₆×C₃₇	—	2	2	no	—
51	C₂×SD₁₆×C₃₇	—	4	2	no	—
52	C₂×SD₁₆×C₃₇	—	4	2	no	—
53	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
54	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
56	C₄⋊Q₈×C₃₇	—	2	4	no	—
57	C₄⋊Q₈×C₃₇	—	2	2	no	—
58	C₄⋊Q₈×C₃₇	—	2	2	no	—
59	C₄⋊Q₈×C₃₇	—	4	2	no	—
60	C₄×Q₈×C₃₇	—	2	2	no	—
61	C₄×Q₈×C₃₇	—	2	2	no	—
62	C₄×D₄×C₃₇	—	2	2	no	—
63	C₄×D₄×C₃₇	D₄	1	4	yes	—
64	#117×C₃₇	—	4	4	no	—
65	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
67	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
72	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
80	C₂×C₄²×C₃₇	—	2	2	no	—
81	C₂×C₄²×C₃₇	—	2	1	no	—
82	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
83	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
84	#106×C₃₇	—	2	2	no	—
85	C₄⋊C₈×C₃₇	—	2	2	no	—
86	C₄⋊C₈×C₃₇	—	4	2	no	—
87	#103×C₃₇	—	2	4	no	—
88	#103×C₃₇	—	2	2	no	—
89	#103×C₃₇	—	2	4	no	—
90	#103×C₃₇	—	4	2	no	—
91	#103×C₃₇	—	4	2	no	—
92	#102×C₃₇	—	2	2	no	—
93	C₄×C₈×C₃₇	—	2	2	no	—
94	#95×C₃₇	—	2	2	no	—
95	#95×C₃₇	—	2	2	no	—
96	#95×C₃₇	—	2	2	no	—
97	#95×C₃₇	D₄	1	2	yes	—
98	C₂⁴×C₃₇	—	2	1	no	—
99	C₂×Q₈×C₃₇	—	2	1	no	—
100	C₂×Q₈×C₃₇	—	2	1	no	—
101	C₂×Q₈×C₃₇	—	2	2	no	—
102	C₂×Q₈×C₃₇	—	2	1	no	—
103	C₂×Q₈×C₃₇	—	2	1	no	—
104	C₂×Q₈×C₃₇	—	2	2	no	—
105	C₂×Q₈×C₃₇	—	2	2	no	—
106	C₂×Q₈×C₃₇	—	2	2	no	—
107	C₂×Q₈×C₃₇	—	2	1	no	—
108	C₂×Q₈×C₃₇	—	2	2	no	—
109	C₂×Q₈×C₃₇	—	2	2	no	—
110	C₂×Q₈×C₃₇	#41	1	2	yes	—
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	—	2	1	no	—
116	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₃₇	—	2	1	no	—
118	C₂²×C₄×C₃₇	—	2	1	no	—
119	C₂²×C₄×C₃₇	—	2	4	no	—
120	C₂²×C₄×C₃₇	—	2	1	no	—
121	C₂²×C₄×C₃₇	—	2	2	no	—
122	C₂²×C₄×C₃₇	—	2	2	no	—
123	C₂²×C₄×C₃₇	—	4	2	no	—
124	C₂²×C₄×C₃₇	—	4	2	no	—
125	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
130	SD₁₆×C₃₇	—	2	8	no	—
131	SD₁₆×C₃₇	—	4	8	no	—
132	C₂×C₈×C₃₇	—	2	1	no	—
133	C₂×C₈×C₃₇	—	2	1	no	—
134	C₂×C₈×C₃₇	—	2	1	no	—
135	C₂×C₈×C₃₇	—	2	2	no	—
136	C₂×C₈×C₃₇	—	2	1	no	—
137	C₂×C₈×C₃₇	—	2	2	no	—
138	C₂×C₈×C₃₇	—	2	1	no	—
139	C₂×C₈×C₃₇	—	2	2	no	—
140	C₂×C₈×C₃₇	#41	1	2	yes	—
141	C₄⋊C₄×C₃₇	—	2	2	no	—
142	C₄⋊C₄×C₃₇	—	2	1	no	—
143	C₄⋊C₄×C₃₇	—	2	1	no	—
144	C₄⋊C₄×C₃₇	—	2	2	no	—
145	C₄⋊C₄×C₃₇	—	2	1	no	—
146	C₄⋊C₄×C₃₇	—	2	2	no	—
147	C₄⋊C₄×C₃₇	—	4	4	no	—
148	C₄⋊C₄×C₃₇	—	4	4	no	—
149	C₄⋊C₄×C₃₇	—	4	2	no	—
150	C₄⋊C₄×C₃₇	—	4	2	no	—
151	C₄⋊C₄×C₃₇	—	4	2	no	—
152	C₄⋊C₄×C₃₇	—	4	2	no	—
153	C₄⋊C₄×C₃₇	—	8	1	no	—
154	C₄⋊C₄×C₃₇	SD₁₆	1	4	yes	complemented
155	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
156	C₂²⋊C₄×C₃₇	—	2	4	no	—
157	C₂²⋊C₄×C₃₇	—	4	4	no	—
158	C₂²⋊C₄×C₃₇	—	8	2	no	—
159	C₄²×C₃₇	—	2	2	no	—
160	C₄²×C₃₇	—	2	2	no	—
161	C₄²×C₃₇	—	4	2	no	—
162	C₄²×C₃₇	—	4	4	no	—
163	C₄²×C₃₇	C₂×D₄	1	2	yes	—
164	C₄²×C₃₇	#41	1	2	yes	—
165	C₂³×C₃₇	—	2	2	no	—
166	C₂³×C₃₇	—	4	1	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	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₃₇	—	2	2	no	—
174	Q₈×C₃₇	—	2	2	no	—
175	Q₈×C₃₇	—	4	1	no	—
176	Q₈×C₃₇	—	4	1	no	—
177	Q₈×C₃₇	—	4	2	no	—
178	Q₈×C₃₇	—	4	2	no	—
179	Q₈×C₃₇	—	4	2	no	—
180	Q₈×C₃₇	—	4	2	no	—
181	D₄×C₃₇	—	2	2	no	—
182	D₄×C₃₇	—	2	2	no	—
183	D₄×C₃₇	—	4	1	no	—
184	D₄×C₃₇	—	4	1	no	—
185	C₂×C₄×C₃₇	—	2	2	no	—
186	C₂×C₄×C₃₇	—	2	1	no	—
187	C₂×C₄×C₃₇	—	2	2	no	—
188	C₂×C₄×C₃₇	—	2	1	no	—
189	C₂×C₄×C₃₇	—	2	2	no	—
190	C₂×C₄×C₃₇	—	2	2	no	—
191	C₂×C₄×C₃₇	—	2	2	no	—
192	C₂×C₄×C₃₇	—	2	2	no	—
193	C₂×C₄×C₃₇	—	2	2	no	—
194	C₂×C₄×C₃₇	—	4	1	no	—
195	C₂×C₄×C₃₇	—	4	1	no	—
196	C₂×C₄×C₃₇	—	4	1	no	—
197	C₂×C₄×C₃₇	—	4	1	no	—
198	C₂×C₄×C₃₇	—	4	8	no	—
199	C₂×C₄×C₃₇	—	4	1	no	—
200	C₂×C₄×C₃₇	—	4	2	no	—
201	C₂×C₄×C₃₇	—	4	2	no	—
202	C₂×C₄×C₃₇	—	4	2	no	—
203	C₂×C₄×C₃₇	—	4	2	no	—
204	C₂×C₄×C₃₇	—	4	2	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	#121	1	2	yes	—
209	C₂×C₄×C₃₇	#121	1	2	yes	—
210	C₂×C₄×C₃₇	C₂×SD₁₆	1	4	yes	—
211	C₂×C₄×C₃₇	C₂×SD₁₆	1	2	yes	—
212	C₂×C₄×C₃₇	#137	1	2	yes	—
213	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
219	C₈×C₃₇	—	2	2	no	—
220	C₈×C₃₇	—	4	1	no	—
221	C₈×C₃₇	—	4	2	no	—
222	#24630	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂²×C₃₇	—	4	2	no	—
224	C₂²×C₃₇	—	4	2	no	—
225	C₂²×C₃₇	—	4	2	no	—
226	C₂²×C₃₇	—	8	1	no	—
227	C₂²×C₃₇	—	8	1	no	—
228	C₂²×C₃₇	—	8	1	no	—
229	C₂²×C₃₇	—	8	1	no	—
230	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
231	C₂²×C₃₇	#546	1	1	yes	characteristic
232	C₂²×C₃₇	#550	1	1	yes	characteristic
233	C₂²×C₃₇	C₂²×SD₁₆	1	1	yes	characteristic
234	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
235	C₂²×C₃₇	#577	1	1	yes	characteristic
236	C₂²×C₃₇	#578	1	1	yes	characteristic
237	C₄×C₃₇	—	2	4	no	—
238	C₄×C₃₇	—	2	2	no	—
239	C₄×C₃₇	—	4	2	no	—
240	C₄×C₃₇	—	4	2	no	—
241	C₄×C₃₇	—	4	2	no	—
242	C₄×C₃₇	—	8	2	no	—
243	C₄×C₃₇	—	8	2	no	—
244	C₄×C₃₇	—	8	1	no	—
245	C₄×C₃₇	#461	1	4	yes	—
246	C₄×C₃₇	#525	1	1	yes	characteristic
247	C₄×C₃₇	#535	1	1	yes	characteristic
248	C₄×C₃₇	#553	1	1	yes	characteristic
249	C₄×C₃₇	#555	1	1	yes	characteristic
250	C₂×#461	C₂×C₃₇	1	1	yes	characteristic
251	C₂×C₄×SD₁₆	C₂×C₃₇	1	1	yes	characteristic
252	#2546	C₂×C₃₇	1	1	yes	characteristic, complemented
253	#2354	C₂×C₃₇	1	1	yes	characteristic
254	#2055	C₂×C₃₇	1	2	yes	—
255	#2013	C₂×C₃₇	1	2	yes	—
256	#1981	C₂×C₃₇	1	2	yes	complemented
257	#1956	C₂×C₃₇	1	1	yes	characteristic, complemented
258	#1939	C₂×C₃₇	1	1	yes	characteristic, complemented
259	#1927	C₂×C₃₇	1	2	yes	complemented
260	#1803	C₂×C₃₇	1	1	yes	characteristic, complemented
261	C₂×C₃₇	—	8	2	no	—
262	C₂×C₃₇	#2414	1	1	yes	characteristic
263	C₂×C₃₇	C₂×#461	1	1	yes	characteristic
264	C₂×C₃₇	#3046	1	1	yes	characteristic
265	C₂×C₃₇	#3298	1	1	yes	characteristic
266	C₂×C₃₇	#3329	1	1	yes	characteristic
267	C₂×C₃₇	#3392	1	1	yes	characteristic
268	C₂×C₃₇	#3398	1	1	yes	characteristic
269	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
270	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
271	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
272	C₂×C₄⋊Q₈	C₂²×C₃₇	1	2	yes	—
273	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
274	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
275	C₂×#117	—	2	1	no	—
276	#461	—	2	4	no	—
277	C₄×SD₁₆	—	2	4	no	—
278	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
279	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
281	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
282	C₂×#103	C₂²×C₃₇	1	2	yes	—
283	C₂×#103	C₂²×C₃₇	1	2	yes	—
284	C₂×#103	C₂²×C₃₇	1	2	yes	—
285	C₂×#103	C₂²×C₃₇	1	2	yes	—
286	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
287	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
288	#398	—	2	2	no	—
289	#391	C₂²×C₃₇	1	2	yes	—
290	#390	C₂²×C₃₇	1	2	yes	—
291	#389	—	2	1	no	—
292	#389	—	2	1	no	—
293	#388	—	2	2	no	—
294	#384	C₂²×C₃₇	1	1	yes	characteristic
295	#380	—	2	1	no	—
296	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
297	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
298	#340	C₂²×C₃₇	1	2	yes	—
299	#336	C₂²×C₃₇	1	2	yes	—
300	C₃₇	#24630	1	1	yes	characteristic, direct product factor, Sylow
301	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
302	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
303	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
304	C₂³×C₄	—	2	1	no	—
305	C₂×SD₁₆	—	2	2	no	—
306	C₂×SD₁₆	—	2	2	no	—
307	C₂×SD₁₆	—	2	4	no	—
308	C₂×SD₁₆	—	2	2	no	—
309	C₂×SD₁₆	—	4	2	no	—
310	C₂×SD₁₆	—	4	2	no	—
311	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
312	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
314	C₄⋊Q₈	—	2	4	no	—
315	C₄⋊Q₈	—	2	2	no	—
316	C₄⋊Q₈	—	2	2	no	—
317	C₄⋊Q₈	—	4	2	no	—
318	C₄×Q₈	—	2	2	no	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	D₄×C₃₇	1	4	yes	—
322	#117	—	4	4	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
331	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₄²	—	2	2	no	—
339	C₂×C₄²	—	2	1	no	—
340	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
341	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
342	#106	—	2	2	no	—
343	C₄⋊C₈	—	2	2	no	—
344	C₄⋊C₈	—	4	2	no	—
345	#103	—	2	4	no	—
346	#103	—	2	2	no	—
347	#103	—	2	4	no	—
348	#103	—	4	2	no	—
349	#103	—	4	2	no	—
350	#102	—	2	2	no	—
351	C₄×C₈	—	2	2	no	—
352	#95	—	2	2	no	—
353	#95	—	2	2	no	—
354	#95	—	2	2	no	—
355	#95	D₄×C₃₇	1	2	yes	—
356	C₂⁴	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	#41×C₃₇	1	2	yes	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
384	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
386	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
387	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
388	SD₁₆	—	2	8	no	—
389	SD₁₆	—	4	8	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	#41×C₃₇	1	2	yes	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	4	4	no	—
406	C₄⋊C₄	—	4	4	no	—
407	C₄⋊C₄	—	4	2	no	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	—	8	1	no	—
412	C₄⋊C₄	SD₁₆×C₃₇	1	4	yes	complemented
413	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	4	4	no	—
416	C₂²⋊C₄	—	8	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	4	2	no	—
420	C₄²	—	4	4	no	—
421	C₄²	C₂×D₄×C₃₇	1	2	yes	—
422	C₄²	#41×C₃₇	1	2	yes	—
423	C₂³	—	2	2	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	1	no	—
430	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
431	Q₈	—	2	2	no	—
432	Q₈	—	2	2	no	—
433	Q₈	—	4	1	no	—
434	Q₈	—	4	1	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	4	2	no	—
437	Q₈	—	4	2	no	—
438	Q₈	—	4	2	no	—
439	D₄	—	2	2	no	—
440	D₄	—	2	2	no	—
441	D₄	—	4	1	no	—
442	D₄	—	4	1	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	8	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	#121×C₃₇	1	2	yes	—
467	C₂×C₄	#121×C₃₇	1	2	yes	—
468	C₂×C₄	C₂×SD₁₆×C₃₇	1	4	yes	—
469	C₂×C₄	C₂×SD₁₆×C₃₇	1	2	yes	—
470	C₂×C₄	#137×C₃₇	1	2	yes	—
471	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
472	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
473	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
474	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
475	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
476	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
477	C₈	—	2	2	no	—
478	C₈	—	4	2	no	—
479	C₈	—	4	1	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	8	1	no	—
484	C₂²	—	8	1	no	—
485	C₂²	—	8	1	no	—
486	C₂²	—	8	1	no	—
487	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
488	C₂²	C₃₇×#546	1	1	yes	characteristic
489	C₂²	C₃₇×#550	1	1	yes	characteristic
490	C₂²	C₂²×SD₁₆×C₃₇	1	1	yes	characteristic
491	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
492	C₂²	C₃₇×#577	1	1	yes	characteristic
493	C₂²	C₃₇×#578	1	1	yes	characteristic
494	C₄	—	2	4	no	—
495	C₄	—	2	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	2	no	—
499	C₄	—	8	2	no	—
500	C₄	—	8	2	no	—
501	C₄	—	8	1	no	—
502	C₄	C₃₇×#461	1	4	yes	—
503	C₄	C₃₇×#525	1	1	yes	characteristic
504	C₄	C₃₇×#535	1	1	yes	characteristic
505	C₄	C₃₇×#553	1	1	yes	characteristic
506	C₄	C₃₇×#555	1	1	yes	characteristic
507	C₂	—	8	2	no	—
508	C₂	C₃₇×#2414	1	1	yes	characteristic
509	C₂	C₂×C₃₇×#461	1	1	yes	characteristic
510	C₂	C₃₇×#3046	1	1	yes	characteristic
511	C₂	C₃₇×#3298	1	1	yes	characteristic
512	C₂	C₃₇×#3329	1	1	yes	characteristic
513	C₂	C₃₇×#3392	1	1	yes	characteristic
514	C₂	C₃₇×#3398	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 ◁ C₄×C₄⋊C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₇×#2546	C₂	semidirect
7. C₃₇×#1981	C₂	semidirect
8. C₃₇×#1956	C₂	semidirect
9. C₃₇×#1939	C₂	semidirect
10. C₃₇×#1927	C₂	semidirect
11. C₃₇×#1803	C₂	semidirect
154. C₄⋊C₄×C₃₇	SD₁₆	semidirect
222. #24630	C₃₇	direct (N × H)
252. #2546	C₂×C₃₇	semidirect
256. #1981	C₂×C₃₇	semidirect
257. #1956	C₂×C₃₇	semidirect
258. #1939	C₂×C₃₇	semidirect
259. #1927	C₂×C₃₇	semidirect
260. #1803	C₂×C₃₇	semidirect
300. C₃₇	#24630	direct (N × H)
412. C₄⋊C₄	SD₁₆×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×#461	2
C₂×C₄×SD₁₆×C₃₇	2
C₃₇×#2546	2
C₃₇×#2354	2
C₃₇×#2055	2
C₃₇×#2013	2
C₃₇×#1981	2
C₃₇×#1956	2
C₃₇×#1939	2
C₃₇×#1927	2
C₃₇×#1803	2
#24630	37

Subgroups — C37×#24630 #22645883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#24630 #22645883