Subgroups — C₃₇×#21476 #22642729

Order 9472.

1322 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×2₋¹⁺⁴×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₇×#456	C₂	1	1	yes	maximal, characteristic
3	C₄×#137×C₃₇	C₂	1	2	yes	maximal, complemented
4	C₃₇×#2327	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#1886	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#1882	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1860	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1857	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1793	C₂	1	1	yes	maximal, characteristic
10	C₃₇×#1759	C₂	1	2	yes	maximal, complemented
11	C₄×#101×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×#137×C₃₇	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₃₇×#520	—	2	2	no	—
16	C₃₇×#520	—	2	2	no	—
17	C₃₇×#520	C₂²	1	2	yes	—
18	C₃₇×#519	—	2	2	no	—
19	C₃₇×#519	C₂²	1	1	yes	characteristic
20	C₄×#41×C₃₇	—	2	2	no	—
21	C₄×#41×C₃₇	—	2	2	no	—
22	C₄×#41×C₃₇	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₃₇	—	2	2	no	—
24	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
26	C₃₇×#456	C₄	1	8	yes	complemented
27	C₃₇×#441	—	2	2	no	—
28	C₃₇×#440	—	2	2	no	—
29	C₄×Q₁₆×C₃₇	—	2	2	no	—
30	C₄×SD₁₆×C₃₇	—	2	2	no	—
31	C₃₇×#428	C₂²	1	2	yes	—
32	C₂×#104×C₃₇	C₂²	1	2	yes	—
33	C₂×#104×C₃₇	C₂²	1	2	yes	—
34	C₃₇×#419	C₂²	1	2	yes	—
35	C₃₇×#417	C₂²	1	2	yes	—
36	C₂×#101×C₃₇	C₂²	1	1	yes	characteristic
37	C₂×#101×C₃₇	C₂²	1	1	yes	characteristic
38	C₄×M₁₆×C₃₇	C₂²	1	2	yes	—
39	C₃₇×#391	C₂²	1	1	yes	characteristic
40	C₃₇×#391	C₂²	1	1	yes	characteristic
41	C₃₇×#387	—	2	2	no	—
42	C₃₇×#387	—	2	2	no	—
43	C₃₇×#382	C₂²	1	1	yes	characteristic
44	C₃₇×#376	C₂²	1	1	yes	characteristic
45	C₃₇×#343	C₂²	1	2	yes	—
46	C₃₇×#339	C₂²	1	2	yes	—
47	C₃₇×#339	C₂²	1	2	yes	—
48	2₋¹⁺⁴×C₃₇	—	2	4	no	—
49	2₋¹⁺⁴×C₃₇	—	2	2	no	—
50	2₋¹⁺⁴×C₃₇	C₂×C₄	1	4	yes	—
51	C₂×#41×C₃₇	—	2	2	no	—
52	C₂×#41×C₃₇	—	2	2	no	—
53	C₂×#41×C₃₇	C₂³	1	2	yes	—
54	C₂²×Q₈×C₃₇	—	2	2	no	—
55	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
56	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
57	#137×C₃₇	—	2	4	no	—
58	#137×C₃₇	C₂×C₄	1	8	yes	complemented
59	C₂×Q₁₆×C₃₇	—	2	2	no	—
60	C₂×SD₁₆×C₃₇	—	2	2	no	—
61	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
62	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
63	C₄⋊Q₈×C₃₇	—	2	2	no	—
64	C₄⋊Q₈×C₃₇	C₂×C₄	1	4	yes	complemented
65	C₄×Q₈×C₃₇	—	2	2	no	—
66	C₄×Q₈×C₃₇	—	2	4	no	—
67	C₄×Q₈×C₃₇	—	2	2	no	—
68	C₄×Q₈×C₃₇	—	2	2	no	—
69	C₄×Q₈×C₃₇	—	2	2	no	—
70	C₄×Q₈×C₃₇	—	2	2	no	—
71	C₄×Q₈×C₃₇	—	2	2	no	—
72	C₄×Q₈×C₃₇	—	2	2	no	—
73	C₄×Q₈×C₃₇	—	2	2	no	—
74	C₄×Q₈×C₃₇	—	2	2	no	—
75	C₄×Q₈×C₃₇	D₄	1	2	yes	—
76	C₄×Q₈×C₃₇	D₄	1	2	yes	—
77	C₄×D₄×C₃₇	—	2	4	no	—
78	C₄×D₄×C₃₇	—	2	2	no	—
79	C₄×D₄×C₃₇	—	2	2	no	—
80	C₄×D₄×C₃₇	—	2	2	no	—
81	C₄×D₄×C₃₇	—	2	2	no	—
82	C₄×D₄×C₃₇	—	2	4	no	—
83	C₄×D₄×C₃₇	—	2	2	no	—
84	C₄×D₄×C₃₇	D₄	1	2	yes	—
85	C₄×D₄×C₃₇	D₄	1	2	yes	—
86	#117×C₃₇	—	2	4	no	—
87	#117×C₃₇	—	2	4	no	—
88	#117×C₃₇	—	2	2	no	—
89	#117×C₃₇	—	2	2	no	—
90	#117×C₃₇	—	2	2	no	—
91	#117×C₃₇	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₃₇	—	2	4	no	—
93	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
94	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
95	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
96	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
97	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₃₇	—	2	4	no	—
100	C₂×C₄²×C₃₇	—	2	2	no	—
101	C₂×C₄²×C₃₇	—	2	1	no	—
102	C₂×C₄²×C₃₇	D₄	1	2	yes	—
103	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
106	#107×C₃₇	—	2	2	no	—
107	#106×C₃₇	—	2	2	no	—
108	#104×C₃₇	—	2	4	no	—
109	#104×C₃₇	C₂×C₄	1	8	yes	complemented
110	#103×C₃₇	—	2	2	no	—
111	#103×C₃₇	—	2	2	no	—
112	#103×C₃₇	—	2	2	no	—
113	#102×C₃₇	—	2	2	no	—
114	#101×C₃₇	—	2	2	no	—
115	#101×C₃₇	C₂×C₄	1	4	yes	complemented
116	#97×C₃₇	—	2	2	no	—
117	C₄×C₈×C₃₇	—	2	2	no	—
118	#95×C₃₇	—	2	1	no	—
119	#95×C₃₇	—	2	1	no	—
120	#95×C₃₇	—	2	2	no	—
121	#95×C₃₇	—	2	2	no	—
122	#95×C₃₇	—	2	2	no	—
123	#41×C₃₇	—	2	8	no	—
124	#41×C₃₇	—	2	8	no	—
125	#41×C₃₇	—	2	8	no	—
126	#41×C₃₇	—	2	8	no	—
127	#41×C₃₇	—	2	2	no	—
128	#41×C₃₇	—	2	2	no	—
129	#41×C₃₇	C₂²×C₄	1	4	yes	—
130	#41×C₃₇	#41	1	4	yes	—
131	C₂×Q₈×C₃₇	—	2	2	no	—
132	C₂×Q₈×C₃₇	—	2	8	no	—
133	C₂×Q₈×C₃₇	—	2	8	no	—
134	C₂×Q₈×C₃₇	—	2	2	no	—
135	C₂×Q₈×C₃₇	—	2	2	no	—
136	C₂×Q₈×C₃₇	—	2	1	no	—
137	C₂×Q₈×C₃₇	—	2	2	no	—
138	C₂×Q₈×C₃₇	—	2	2	no	—
139	C₂×Q₈×C₃₇	C₂²×C₄	1	2	yes	—
140	C₂×Q₈×C₃₇	C₂²×C₄	1	2	yes	—
141	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
142	C₂×Q₈×C₃₇	#41	1	2	yes	—
143	C₂×D₄×C₃₇	—	2	2	no	—
144	C₂×D₄×C₃₇	—	2	2	no	—
145	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₃₇	—	2	4	no	—
147	C₂²×C₄×C₃₇	—	2	2	no	—
148	C₂²×C₄×C₃₇	—	2	1	no	—
149	C₂²×C₄×C₃₇	—	2	1	no	—
150	C₂²×C₄×C₃₇	—	2	4	no	—
151	C₂²×C₄×C₃₇	—	2	2	no	—
152	C₂²×C₄×C₃₇	—	2	2	no	—
153	C₂²×C₄×C₃₇	—	2	1	no	—
154	C₂²×C₄×C₃₇	—	2	1	no	—
155	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
160	Q₁₆×C₃₇	—	2	8	no	—
161	SD₁₆×C₃₇	—	2	8	no	—
162	M₁₆×C₃₇	—	2	2	no	—
163	M₁₆×C₃₇	—	2	2	no	—
164	M₁₆×C₃₇	—	2	2	no	—
165	M₁₆×C₃₇	C₂²×C₄	1	4	yes	—
166	C₂×C₈×C₃₇	—	2	2	no	—
167	C₂×C₈×C₃₇	—	2	2	no	—
168	C₄⋊C₄×C₃₇	—	2	4	no	—
169	C₄⋊C₄×C₃₇	—	2	2	no	—
170	C₄⋊C₄×C₃₇	—	2	2	no	—
171	C₄⋊C₄×C₃₇	—	2	8	no	—
172	C₄⋊C₄×C₃₇	—	2	2	no	—
173	C₄⋊C₄×C₃₇	—	2	4	no	—
174	C₄⋊C₄×C₃₇	—	2	2	no	—
175	C₄⋊C₄×C₃₇	—	2	2	no	—
176	C₄⋊C₄×C₃₇	—	2	2	no	—
177	C₄⋊C₄×C₃₇	—	4	1	no	—
178	C₄⋊C₄×C₃₇	—	4	1	no	—
179	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
180	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
181	C₂²⋊C₄×C₃₇	—	2	4	no	—
182	C₂²⋊C₄×C₃₇	—	2	2	no	—
183	C₂²⋊C₄×C₃₇	—	2	2	no	—
184	C₂²⋊C₄×C₃₇	—	2	2	no	—
185	C₄²×C₃₇	—	2	4	no	—
186	C₄²×C₃₇	—	2	4	no	—
187	C₄²×C₃₇	—	2	2	no	—
188	C₄²×C₃₇	—	2	2	no	—
189	C₄²×C₃₇	—	2	2	no	—
190	C₄²×C₃₇	—	2	2	no	—
191	C₄²×C₃₇	—	2	2	no	—
192	C₄²×C₃₇	—	2	1	no	—
193	C₄²×C₃₇	—	2	2	no	—
194	C₄²×C₃₇	—	4	2	no	—
195	C₄²×C₃₇	C₂²×C₄	1	2	yes	—
196	C₄²×C₃₇	C₂×D₄	1	2	yes	—
197	C₄²×C₃₇	C₂×D₄	1	2	yes	—
198	C₂³×C₃₇	—	2	2	no	—
199	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
200	Q₈×C₃₇	—	2	8	no	—
201	Q₈×C₃₇	—	2	4	no	—
202	Q₈×C₃₇	—	2	2	no	—
203	Q₈×C₃₇	—	2	4	no	—
204	Q₈×C₃₇	—	2	4	no	—
205	Q₈×C₃₇	—	4	2	no	—
206	Q₈×C₃₇	C₄×D₄	1	4	yes	—
207	D₄×C₃₇	—	2	8	no	—
208	D₄×C₃₇	—	2	4	no	—
209	D₄×C₃₇	—	2	4	no	—
210	D₄×C₃₇	—	2	2	no	—
211	D₄×C₃₇	C₄×D₄	1	4	yes	—
212	C₂×C₄×C₃₇	—	2	16	no	—
213	C₂×C₄×C₃₇	—	2	2	no	—
214	C₂×C₄×C₃₇	—	2	2	no	—
215	C₂×C₄×C₃₇	—	2	2	no	—
216	C₂×C₄×C₃₇	—	2	4	no	—
217	C₂×C₄×C₃₇	—	2	4	no	—
218	C₂×C₄×C₃₇	—	2	2	no	—
219	C₂×C₄×C₃₇	—	2	2	no	—
220	C₂×C₄×C₃₇	—	2	2	no	—
221	C₂×C₄×C₃₇	—	2	2	no	—
222	C₂×C₄×C₃₇	—	2	2	no	—
223	C₂×C₄×C₃₇	—	4	1	no	—
224	C₂×C₄×C₃₇	—	4	1	no	—
225	C₂×C₄×C₃₇	—	4	4	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	1	no	—
232	C₂×C₄×C₃₇	—	4	1	no	—
233	C₂×C₄×C₃₇	—	4	2	no	—
234	C₂×C₄×C₃₇	—	4	1	no	—
235	C₂×C₄×C₃₇	—	4	1	no	—
236	C₂×C₄×C₃₇	—	8	2	no	—
237	C₂×C₄×C₃₇	—	8	4	no	—
238	C₂×C₄×C₃₇	C₄×D₄	1	4	yes	—
239	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
240	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
241	C₂×C₄×C₃₇	#120	1	2	yes	—
242	C₂×C₄×C₃₇	C₂³×C₄	1	1	yes	characteristic
243	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
244	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
245	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
246	C₈×C₃₇	—	2	4	no	—
247	C₈×C₃₇	—	4	2	no	—
248	#21476	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
249	C₂²×C₃₇	—	2	1	no	—
250	C₂²×C₃₇	—	2	1	no	—
251	C₂²×C₃₇	—	2	4	no	—
252	C₂²×C₃₇	—	4	2	no	—
253	C₂²×C₃₇	—	4	2	no	—
254	C₂²×C₃₇	C₂×C₄×D₄	1	1	yes	characteristic
255	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
256	C₂²×C₃₇	#525	1	1	yes	characteristic
257	C₄×C₃₇	—	2	1	no	—
258	C₄×C₃₇	—	2	1	no	—
259	C₄×C₃₇	—	2	2	no	—
260	C₄×C₃₇	—	2	4	no	—
261	C₄×C₃₇	—	2	4	no	—
262	C₄×C₃₇	—	4	2	no	—
263	C₄×C₃₇	—	4	2	no	—
264	C₄×C₃₇	—	4	2	no	—
265	C₄×C₃₇	—	4	2	no	—
266	C₄×C₃₇	—	4	2	no	—
267	C₄×C₃₇	—	8	1	no	—
268	C₄×C₃₇	—	8	1	no	—
269	C₄×C₃₇	C₂×C₄×D₄	1	2	yes	—
270	C₄×C₃₇	#525	1	2	yes	—
271	C₄×2₋¹⁺⁴	C₂×C₃₇	1	1	yes	characteristic
272	C₂×#456	C₂×C₃₇	1	1	yes	characteristic
273	C₄×#137	C₂×C₃₇	1	2	yes	complemented
274	#2327	C₂×C₃₇	1	1	yes	characteristic, complemented
275	#1886	C₂×C₃₇	1	1	yes	characteristic, complemented
276	#1882	C₂×C₃₇	1	2	yes	complemented
277	#1860	C₂×C₃₇	1	2	yes	complemented
278	#1857	C₂×C₃₇	1	1	yes	characteristic, complemented
279	#1793	C₂×C₃₇	1	1	yes	characteristic
280	#1759	C₂×C₃₇	1	2	yes	complemented
281	C₄×#101	C₂×C₃₇	1	1	yes	characteristic, complemented
282	C₂×C₃₇	—	2	1	no	—
283	C₂×C₃₇	—	2	1	no	—
284	C₂×C₃₇	—	4	4	no	—
285	C₂×C₃₇	C₄×#120	1	1	yes	characteristic
286	C₂×C₃₇	#3020	1	1	yes	characteristic
287	C₂×C₃₇	#3022	1	1	yes	characteristic
288	C₂×2₋¹⁺⁴	C₂²×C₃₇	1	1	yes	characteristic
289	C₂×#137	C₂²×C₃₇	1	2	yes	—
290	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
291	#520	—	2	2	no	—
292	#520	—	2	2	no	—
293	#520	C₂²×C₃₇	1	2	yes	—
294	#519	—	2	2	no	—
295	#519	C₂²×C₃₇	1	1	yes	characteristic
296	C₄×#41	—	2	2	no	—
297	C₄×#41	—	2	2	no	—
298	C₄×#41	C₂²×C₃₇	1	2	yes	—
299	C₂×C₄×Q₈	—	2	2	no	—
300	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
301	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
302	#456	C₄×C₃₇	1	8	yes	complemented
303	#441	—	2	2	no	—
304	#440	—	2	2	no	—
305	C₄×Q₁₆	—	2	2	no	—
306	C₄×SD₁₆	—	2	2	no	—
307	#428	C₂²×C₃₇	1	2	yes	—
308	C₂×#104	C₂²×C₃₇	1	2	yes	—
309	C₂×#104	C₂²×C₃₇	1	2	yes	—
310	#419	C₂²×C₃₇	1	2	yes	—
311	#417	C₂²×C₃₇	1	2	yes	—
312	C₂×#101	C₂²×C₃₇	1	1	yes	characteristic
313	C₂×#101	C₂²×C₃₇	1	1	yes	characteristic
314	C₄×M₁₆	C₂²×C₃₇	1	2	yes	—
315	#391	C₂²×C₃₇	1	1	yes	characteristic
316	#391	C₂²×C₃₇	1	1	yes	characteristic
317	#387	—	2	2	no	—
318	#387	—	2	2	no	—
319	#382	C₂²×C₃₇	1	1	yes	characteristic
320	#376	C₂²×C₃₇	1	1	yes	characteristic
321	#343	C₂²×C₃₇	1	2	yes	—
322	#339	C₂²×C₃₇	1	2	yes	—
323	#339	C₂²×C₃₇	1	2	yes	—
324	C₃₇	#21476	1	1	yes	characteristic, direct product factor, Sylow
325	2₋¹⁺⁴	—	2	4	no	—
326	2₋¹⁺⁴	—	2	2	no	—
327	2₋¹⁺⁴	C₂×C₄×C₃₇	1	4	yes	—
328	C₂×#41	—	2	2	no	—
329	C₂×#41	—	2	2	no	—
330	C₂×#41	C₂³×C₃₇	1	2	yes	—
331	C₂²×Q₈	—	2	2	no	—
332	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
333	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
334	#137	—	2	4	no	—
335	#137	C₂×C₄×C₃₇	1	8	yes	complemented
336	C₂×Q₁₆	—	2	2	no	—
337	C₂×SD₁₆	—	2	2	no	—
338	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
339	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
340	C₄⋊Q₈	—	2	2	no	—
341	C₄⋊Q₈	C₂×C₄×C₃₇	1	4	yes	complemented
342	C₄×Q₈	—	2	2	no	—
343	C₄×Q₈	—	2	4	no	—
344	C₄×Q₈	—	2	2	no	—
345	C₄×Q₈	—	2	2	no	—
346	C₄×Q₈	—	2	2	no	—
347	C₄×Q₈	—	2	2	no	—
348	C₄×Q₈	—	2	2	no	—
349	C₄×Q₈	—	2	2	no	—
350	C₄×Q₈	—	2	2	no	—
351	C₄×Q₈	—	2	2	no	—
352	C₄×Q₈	D₄×C₃₇	1	2	yes	—
353	C₄×Q₈	D₄×C₃₇	1	2	yes	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	—	2	4	no	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	4	no	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	D₄×C₃₇	1	2	yes	—
362	C₄×D₄	D₄×C₃₇	1	2	yes	—
363	#117	—	2	4	no	—
364	#117	—	2	4	no	—
365	#117	—	2	2	no	—
366	#117	—	2	2	no	—
367	#117	—	2	2	no	—
368	#117	C₂³×C₃₇	1	2	yes	—
369	C₂×C₄⋊C₄	—	2	4	no	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	—	2	2	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
374	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
376	C₂×C₄²	—	2	4	no	—
377	C₂×C₄²	—	2	2	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	D₄×C₃₇	1	2	yes	—
380	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
383	#107	—	2	2	no	—
384	#106	—	2	2	no	—
385	#104	—	2	4	no	—
386	#104	C₂×C₄×C₃₇	1	8	yes	complemented
387	#103	—	2	2	no	—
388	#103	—	2	2	no	—
389	#103	—	2	2	no	—
390	#102	—	2	2	no	—
391	#101	—	2	2	no	—
392	#101	C₂×C₄×C₃₇	1	4	yes	complemented
393	#97	—	2	2	no	—
394	C₄×C₈	—	2	2	no	—
395	#95	—	2	1	no	—
396	#95	—	2	1	no	—
397	#95	—	2	2	no	—
398	#95	—	2	2	no	—
399	#95	—	2	2	no	—
400	#41	—	2	8	no	—
401	#41	—	2	8	no	—
402	#41	—	2	8	no	—
403	#41	—	2	8	no	—
404	#41	—	2	2	no	—
405	#41	—	2	2	no	—
406	#41	C₂²×C₄×C₃₇	1	4	yes	—
407	#41	#41×C₃₇	1	4	yes	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	8	no	—
410	C₂×Q₈	—	2	8	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	C₂²×C₄×C₃₇	1	2	yes	—
417	C₂×Q₈	C₂²×C₄×C₃₇	1	2	yes	—
418	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
419	C₂×Q₈	#41×C₃₇	1	2	yes	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
433	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
434	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
436	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
437	Q₁₆	—	2	8	no	—
438	SD₁₆	—	2	8	no	—
439	M₁₆	—	2	2	no	—
440	M₁₆	—	2	2	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	C₂²×C₄×C₃₇	1	4	yes	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	8	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	4	1	no	—
455	C₄⋊C₄	—	4	1	no	—
456	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
457	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
458	C₂²⋊C₄	—	2	4	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₄²	—	2	4	no	—
463	C₄²	—	2	4	no	—
464	C₄²	—	2	2	no	—
465	C₄²	—	2	2	no	—
466	C₄²	—	2	2	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	4	2	no	—
472	C₄²	C₂²×C₄×C₃₇	1	2	yes	—
473	C₄²	C₂×D₄×C₃₇	1	2	yes	—
474	C₄²	C₂×D₄×C₃₇	1	2	yes	—
475	C₂³	—	2	2	no	—
476	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
477	Q₈	—	2	8	no	—
478	Q₈	—	2	2	no	—
479	Q₈	—	2	4	no	—
480	Q₈	—	2	4	no	—
481	Q₈	—	2	4	no	—
482	Q₈	—	4	2	no	—
483	Q₈	C₄×D₄×C₃₇	1	4	yes	—
484	D₄	—	2	8	no	—
485	D₄	—	2	4	no	—
486	D₄	—	2	4	no	—
487	D₄	—	2	2	no	—
488	D₄	C₄×D₄×C₃₇	1	4	yes	—
489	C₂×C₄	—	2	16	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	4	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	8	2	no	—
514	C₂×C₄	—	8	4	no	—
515	C₂×C₄	C₄×D₄×C₃₇	1	4	yes	—
516	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
517	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
518	C₂×C₄	#120×C₃₇	1	2	yes	—
519	C₂×C₄	C₂³×C₄×C₃₇	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
521	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
522	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
523	C₈	—	2	4	no	—
524	C₈	—	4	2	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	C₂×C₄×D₄×C₃₇	1	1	yes	characteristic
531	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
532	C₂²	C₃₇×#525	1	1	yes	characteristic
533	C₄	—	2	1	no	—
534	C₄	—	2	1	no	—
535	C₄	—	2	2	no	—
536	C₄	—	2	4	no	—
537	C₄	—	2	4	no	—
538	C₄	—	4	2	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	2	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	2	no	—
543	C₄	—	8	1	no	—
544	C₄	—	8	1	no	—
545	C₄	C₂×C₄×D₄×C₃₇	1	2	yes	—
546	C₄	C₃₇×#525	1	2	yes	—
547	C₂	—	2	1	no	—
548	C₂	—	2	1	no	—
549	C₂	—	4	4	no	—
550	C₂	C₄×#120×C₃₇	1	1	yes	characteristic
551	C₂	C₃₇×#3020	1	1	yes	characteristic
552	C₂	C₃₇×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#120
commutator	C₂×C₄	C₂³×C₄×C₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×2₋¹⁺⁴×C₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×#137×C₃₇	C₂	semidirect
4. C₃₇×#2327	C₂	semidirect
5. C₃₇×#1886	C₂	semidirect
6. C₃₇×#1882	C₂	semidirect
7. C₃₇×#1860	C₂	semidirect
8. C₃₇×#1857	C₂	semidirect
10. C₃₇×#1759	C₂	semidirect
11. C₄×#101×C₃₇	C₂	semidirect
26. C₃₇×#456	C₄	semidirect
58. #137×C₃₇	C₂×C₄	semidirect
64. C₄⋊Q₈×C₃₇	C₂×C₄	semidirect
109. #104×C₃₇	C₂×C₄	semidirect
115. #101×C₃₇	C₂×C₄	semidirect
248. #21476	C₃₇	direct (N × H)
273. C₄×#137	C₂×C₃₇	semidirect
274. #2327	C₂×C₃₇	semidirect
275. #1886	C₂×C₃₇	semidirect
276. #1882	C₂×C₃₇	semidirect
277. #1860	C₂×C₃₇	semidirect
278. #1857	C₂×C₃₇	semidirect
280. #1759	C₂×C₃₇	semidirect
281. C₄×#101	C₂×C₃₇	semidirect
302. #456	C₄×C₃₇	semidirect
324. C₃₇	#21476	direct (N × H)
335. #137	C₂×C₄×C₃₇	semidirect
341. C₄⋊Q₈	C₂×C₄×C₃₇	semidirect
386. #104	C₂×C₄×C₃₇	semidirect
392. #101	C₂×C₄×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₄×2₋¹⁺⁴×C₃₇	2
C₂×C₃₇×#456	2
C₄×#137×C₃₇	2
C₃₇×#2327	2
C₃₇×#1886	2
C₃₇×#1882	2
C₃₇×#1860	2
C₃₇×#1857	2
C₃₇×#1793	2
C₃₇×#1759	2
C₄×#101×C₃₇	2
#21476	37

Subgroups — C37×#21476 #22642729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#21476 #22642729