Subgroups — C₃₇×#60725 #22681978

Order 9472.

1962 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3180	C₂	1	4	yes	maximal, complemented
4	C₃₇×#3176	C₂	1	4	yes	maximal, complemented
5	C₃₇×#3174	C₂	1	4	yes	maximal, complemented
6	C₃₇×#3171	C₂	1	4	yes	maximal, complemented
7	C₃₇×#3166	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#3151	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#3135	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₇×#490	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#3062	C₂	1	4	yes	maximal, complemented
12	C₃₇×#2946	C₂	1	4	yes	maximal, complemented
13	C₃₇×#2875	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	4	yes	—
15	C₂×#131×C₃₇	C₂²	1	2	yes	—
16	C₃₇×#559	—	2	2	no	—
17	C₃₇×#553	—	2	4	no	—
18	C₃₇×#553	—	2	2	no	—
19	C₃₇×#552	—	2	2	no	—
20	C₃₇×#550	—	2	2	no	—
21	C₃₇×#546	—	2	4	no	—
22	C₃₇×#541	C₂²	1	2	yes	complemented
23	C₃₇×#540	C₂²	1	4	yes	—
24	C₃₇×#540	C₂²	1	2	yes	complemented
25	C₃₇×#537	C₂²	1	2	yes	—
26	C₃₇×#535	C₂²	1	2	yes	—
27	C₃₇×#533	C₂²	1	1	yes	characteristic
28	C₃₇×#532	C₂²	1	1	yes	characteristic
29	C₃₇×#532	C₂²	1	4	yes	—
30	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
31	C₃₇×#529	C₂²	1	4	yes	complemented
32	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
33	C₃₇×#520	C₂²	1	2	yes	—
34	C₃₇×#518	C₂²	1	2	yes	—
35	C₄×#41×C₃₇	C₂²	1	1	yes	characteristic
36	C₃₇×#501	C₂²	1	4	yes	complemented
37	C₃₇×#499	C₂²	1	4	yes	complemented
38	C₃₇×#496	C₂²	1	4	yes	—
39	C₃₇×#493	C₂²	1	2	yes	—
40	C₃₇×#492	C₂²	1	2	yes	—
41	C₃₇×#491	C₂²	1	2	yes	complemented
42	C₃₇×#490	C₂²	1	2	yes	—
43	C₃₇×#490	C₂²	1	4	yes	—
44	C₃₇×#490	C₂²	1	2	yes	—
45	C₃₇×#490	C₂²	1	2	yes	complemented
46	C₃₇×#489	C₂²	1	2	yes	complemented
47	C₃₇×#489	C₂²	1	2	yes	complemented
48	C₃₇×#469	C₂²	1	8	yes	complemented
49	C₃₇×#468	C₂²	1	8	yes	complemented
50	C₃₇×#466	C₂²	1	8	yes	complemented
51	C₃₇×#465	C₂²	1	8	yes	complemented
52	C₃₇×#442	C₂²	1	8	yes	complemented
53	C₃₇×#440	C₂²	1	8	yes	complemented
54	C₄×SD₁₆×C₃₇	C₂²	1	8	yes	complemented
55	C₄×D₈×C₃₇	C₂²	1	8	yes	complemented
56	C₃₇×#428	C₂²	1	4	yes	—
57	C₃₇×#416	C₂²	1	4	yes	—
58	C₂×#102×C₃₇	C₂²	1	4	yes	—
59	C₃₇×#405	C₂²	1	2	yes	—
60	C₃₇×#405	C₂²	1	4	yes	complemented
61	C₄×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
62	C₄×M₁₆×C₃₇	C₂²	1	2	yes	complemented
63	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
64	C₂×#97×C₃₇	C₂²	1	2	yes	complemented
65	C₂×#41×C₃₇	—	2	4	no	—
66	C₂×#41×C₃₇	C₂³	1	2	yes	—
67	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₃₇	—	2	2	no	—
69	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
70	AGL(1,ℤ/8)×C₃₇	—	2	16	no	—
71	C₂×SD₁₆×C₃₇	C₂³	1	8	yes	—
72	C₂×D₈×C₃₇	C₂³	1	8	yes	—
73	#131×C₃₇	—	2	8	no	—
74	C₂×M₁₆×C₃₇	C₂³	1	4	yes	—
75	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
76	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
77	C₂²×C₈×C₃₇	C₂³	1	4	yes	—
78	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
79	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
80	#127×C₃₇	—	2	2	no	—
81	#127×C₃₇	—	2	2	no	—
82	#127×C₃₇	C₂³	1	2	yes	—
83	#127×C₃₇	C₂³	1	2	yes	—
84	#127×C₃₇	C₂³	1	1	yes	characteristic
85	#126×C₃₇	—	2	4	no	—
86	#126×C₃₇	—	2	4	no	—
87	#125×C₃₇	—	2	4	no	—
88	#125×C₃₇	—	2	2	no	—
89	#125×C₃₇	C₂³	1	2	yes	—
90	#125×C₃₇	C₂³	1	2	yes	—
91	#125×C₃₇	C₂³	1	2	yes	—
92	#124×C₃₇	—	2	2	no	—
93	#124×C₃₇	—	2	4	no	—
94	#124×C₃₇	C₂³	1	2	yes	—
95	#123×C₃₇	—	2	4	no	—
96	#123×C₃₇	—	2	8	no	—
97	#123×C₃₇	—	2	4	no	—
98	C₂²⋊Q₈×C₃₇	—	2	2	no	—
99	C₂²⋊Q₈×C₃₇	—	2	2	no	—
100	C₂²⋊Q₈×C₃₇	C₂³	1	4	yes	—
101	#121×C₃₇	—	2	2	no	—
102	#121×C₃₇	—	2	4	no	—
103	#121×C₃₇	—	2	4	no	—
104	#121×C₃₇	—	2	2	no	—
105	#121×C₃₇	—	2	8	no	—
106	#121×C₃₇	—	2	4	no	—
107	#121×C₃₇	C₂³	1	4	yes	—
108	#121×C₃₇	C₂³	1	8	yes	—
109	#120×C₃₇	—	2	4	no	—
110	C₄×Q₈×C₃₇	—	2	2	no	—
111	C₄×Q₈×C₃₇	D₄	1	2	yes	—
112	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
113	C₄×D₄×C₃₇	—	2	4	no	—
114	C₄×D₄×C₃₇	—	2	4	no	—
115	C₄×D₄×C₃₇	—	2	4	no	—
116	C₄×D₄×C₃₇	—	2	4	no	—
117	C₄×D₄×C₃₇	—	2	2	no	—
118	C₄×D₄×C₃₇	D₄	1	4	yes	—
119	C₄×D₄×C₃₇	D₄	1	2	yes	—
120	C₄×D₄×C₃₇	C₂³	1	4	yes	—
121	C₄×D₄×C₃₇	C₂³	1	8	yes	—
122	#117×C₃₇	—	2	2	no	—
123	#117×C₃₇	—	2	4	no	—
124	#117×C₃₇	C₂³	1	2	yes	—
125	#117×C₃₇	C₂³	1	1	yes	characteristic
126	#117×C₃₇	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
128	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
129	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
131	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
133	#107×C₃₇	C₂³	1	8	yes	—
134	#106×C₃₇	C₂³	1	8	yes	—
135	#103×C₃₇	C₂³	1	4	yes	—
136	#103×C₃₇	C₂³	1	4	yes	—
137	#102×C₃₇	C₂³	1	8	yes	—
138	#102×C₃₇	C₂³	1	8	yes	—
139	#102×C₃₇	C₂³	1	4	yes	—
140	#102×C₃₇	C₂³	1	4	yes	—
141	#97×C₃₇	C₂³	1	1	yes	characteristic
142	#97×C₃₇	C₂³	1	1	yes	characteristic
143	#97×C₃₇	C₂³	1	2	yes	—
144	#97×C₃₇	C₂³	1	2	yes	—
145	#97×C₃₇	C₂³	1	4	yes	—
146	C₄×C₈×C₃₇	C₂³	1	2	yes	—
147	C₄×C₈×C₃₇	C₂³	1	4	yes	—
148	C₂⁴×C₃₇	—	2	2	no	—
149	#41×C₃₇	—	2	4	no	—
150	#41×C₃₇	—	2	8	no	—
151	#41×C₃₇	—	8	8	no	—
152	C₂×Q₈×C₃₇	—	2	2	no	—
153	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₃₇	C₂⁴	1	2	yes	—
155	C₂×D₄×C₃₇	—	2	2	no	—
156	C₂×D₄×C₃₇	—	2	4	no	—
157	C₂×D₄×C₃₇	—	2	8	no	—
158	C₂×D₄×C₃₇	—	2	2	no	—
159	C₂×D₄×C₃₇	—	2	4	no	—
160	C₂×D₄×C₃₇	—	2	2	no	—
161	C₂×D₄×C₃₇	—	2	4	no	—
162	C₂×D₄×C₃₇	—	2	8	no	—
163	C₂×D₄×C₃₇	—	8	4	no	—
164	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
165	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
166	C₂×D₄×C₃₇	C₂⁴	1	2	yes	—
167	C₂×D₄×C₃₇	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₃₇	—	2	2	no	—
169	C₂²×C₄×C₃₇	—	2	2	no	—
170	C₂²×C₄×C₃₇	—	2	8	no	—
171	C₂²×C₄×C₃₇	—	2	4	no	—
172	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₃₇	C₂×D₄	1	4	yes	—
174	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
176	SD₁₆×C₃₇	—	2	16	no	—
177	D₈×C₃₇	—	2	16	no	—
178	M₁₆×C₃₇	—	2	8	no	—
179	M₁₆×C₃₇	#41	1	8	yes	complemented
180	C₂×C₈×C₃₇	—	2	4	no	—
181	C₂×C₈×C₃₇	—	2	8	no	—
182	C₂×C₈×C₃₇	C₂⁴	1	2	yes	—
183	C₂×C₈×C₃₇	C₂⁴	1	2	yes	—
184	C₂×C₈×C₃₇	C₂⁴	1	4	yes	—
185	C₄⋊C₄×C₃₇	—	2	2	no	—
186	C₄⋊C₄×C₃₇	—	2	4	no	—
187	C₄⋊C₄×C₃₇	—	2	4	no	—
188	C₄⋊C₄×C₃₇	—	2	4	no	—
189	C₄⋊C₄×C₃₇	—	2	4	no	—
190	C₄⋊C₄×C₃₇	—	2	2	no	—
191	C₄⋊C₄×C₃₇	—	2	2	no	—
192	C₄⋊C₄×C₃₇	—	2	4	no	—
193	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
194	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
195	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
196	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
197	C₂²⋊C₄×C₃₇	—	2	2	no	—
198	C₂²⋊C₄×C₃₇	—	2	4	no	—
199	C₂²⋊C₄×C₃₇	—	2	8	no	—
200	C₂²⋊C₄×C₃₇	—	2	2	no	—
201	C₂²⋊C₄×C₃₇	—	2	4	no	—
202	C₂²⋊C₄×C₃₇	—	2	4	no	—
203	C₂²⋊C₄×C₃₇	—	2	2	no	—
204	C₂²⋊C₄×C₃₇	—	2	8	no	—
205	C₂²⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
206	C₂²⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
207	C₄²×C₃₇	—	2	4	no	—
208	C₄²×C₃₇	—	2	2	no	—
209	C₄²×C₃₇	C₂×D₄	1	4	yes	—
210	C₄²×C₃₇	C₂×D₄	1	2	yes	—
211	C₄²×C₃₇	C₂⁴	1	2	yes	—
212	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
213	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
214	C₂³×C₃₇	—	2	2	no	—
215	C₂³×C₃₇	—	2	4	no	—
216	C₂³×C₃₇	—	4	4	no	—
217	C₂³×C₃₇	—	8	4	no	—
218	C₂³×C₃₇	C₂²×D₄	1	2	yes	—
219	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
220	Q₈×C₃₇	—	2	2	no	—
221	Q₈×C₃₇	—	2	4	no	—
222	Q₈×C₃₇	—	4	4	no	—
223	D₄×C₃₇	—	2	4	no	—
224	D₄×C₃₇	—	2	2	no	—
225	D₄×C₃₇	—	2	4	no	—
226	D₄×C₃₇	—	2	8	no	—
227	D₄×C₃₇	—	4	8	no	—
228	D₄×C₃₇	—	4	4	no	—
229	D₄×C₃₇	—	4	4	no	—
230	D₄×C₃₇	—	8	2	no	—
231	D₄×C₃₇	—	8	4	no	—
232	D₄×C₃₇	—	8	4	no	—
233	D₄×C₃₇	—	8	8	no	—
234	C₂×C₄×C₃₇	—	2	4	no	—
235	C₂×C₄×C₃₇	—	2	2	no	—
236	C₂×C₄×C₃₇	—	2	4	no	—
237	C₂×C₄×C₃₇	—	2	4	no	—
238	C₂×C₄×C₃₇	—	4	2	no	—
239	C₂×C₄×C₃₇	—	4	4	no	—
240	C₂×C₄×C₃₇	—	4	4	no	—
241	C₂×C₄×C₃₇	—	8	4	no	—
242	C₂×C₄×C₃₇	—	8	8	no	—
243	C₂×C₄×C₃₇	—	8	2	no	—
244	C₂×C₄×C₃₇	C₂²×D₄	1	4	yes	—
245	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₃₇	C₂×#41	1	4	yes	—
250	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
251	C₈×C₃₇	—	2	2	no	—
252	C₈×C₃₇	—	2	2	no	—
253	C₈×C₃₇	C₂×#41	1	8	yes	—
254	#60725	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂²×C₃₇	—	2	2	no	—
256	C₂²×C₃₇	—	2	4	no	—
257	C₂²×C₃₇	—	2	2	no	—
258	C₂²×C₃₇	—	4	2	no	—
259	C₂²×C₃₇	—	4	8	no	—
260	C₂²×C₃₇	—	4	2	no	—
261	C₂²×C₃₇	—	4	2	no	—
262	C₂²×C₃₇	—	4	4	no	—
263	C₂²×C₃₇	—	16	4	no	—
264	C₂²×C₃₇	#532	1	2	yes	—
265	C₂²×C₃₇	C₂³×D₄	1	1	yes	characteristic
266	C₄×C₃₇	—	2	2	no	—
267	C₄×C₃₇	—	2	4	no	—
268	C₄×C₃₇	—	2	2	no	—
269	C₄×C₃₇	—	2	2	no	—
270	C₄×C₃₇	—	4	4	no	—
271	C₄×C₃₇	—	4	4	no	—
272	C₄×C₃₇	—	4	2	no	—
273	C₄×C₃₇	#532	1	2	yes	—
274	C₄×C₃₇	C₂²×#41	1	2	yes	—
275	#3512	C₂×C₃₇	1	1	yes	characteristic, complemented
276	#3508	C₂×C₃₇	1	1	yes	characteristic, complemented
277	#3180	C₂×C₃₇	1	4	yes	complemented
278	#3176	C₂×C₃₇	1	4	yes	complemented
279	#3174	C₂×C₃₇	1	4	yes	complemented
280	#3171	C₂×C₃₇	1	4	yes	complemented
281	#3166	C₂×C₃₇	1	1	yes	characteristic, complemented
282	#3151	C₂×C₃₇	1	1	yes	characteristic, complemented
283	#3135	C₂×C₃₇	1	1	yes	characteristic, complemented
284	C₂×#490	C₂×C₃₇	1	1	yes	characteristic, complemented
285	#3062	C₂×C₃₇	1	4	yes	complemented
286	#2946	C₂×C₃₇	1	4	yes	complemented
287	#2875	C₂×C₃₇	1	1	yes	characteristic, complemented
288	C₂×C₃₇	—	2	2	no	—
289	C₂×C₃₇	—	4	2	no	—
290	C₂×C₃₇	—	8	2	no	—
291	C₂×C₃₇	—	8	4	no	—
292	C₂×C₃₇	C₂×#532	1	1	yes	characteristic
293	C₂×C₃₇	#3585	1	2	yes	—
294	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	4	yes	—
295	C₂×#131	C₂²×C₃₇	1	2	yes	—
296	#559	—	2	2	no	—
297	#553	—	2	4	no	—
298	#553	—	2	2	no	—
299	#552	—	2	2	no	—
300	#550	—	2	2	no	—
301	#546	—	2	4	no	—
302	#541	C₂²×C₃₇	1	2	yes	complemented
303	#540	C₂²×C₃₇	1	4	yes	—
304	#540	C₂²×C₃₇	1	2	yes	complemented
305	#537	C₂²×C₃₇	1	2	yes	—
306	#535	C₂²×C₃₇	1	2	yes	—
307	#533	C₂²×C₃₇	1	1	yes	characteristic
308	#532	C₂²×C₃₇	1	1	yes	characteristic
309	#532	C₂²×C₃₇	1	4	yes	—
310	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
311	#529	C₂²×C₃₇	1	4	yes	complemented
312	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
313	#520	C₂²×C₃₇	1	2	yes	—
314	#518	C₂²×C₃₇	1	2	yes	—
315	C₄×#41	C₂²×C₃₇	1	1	yes	characteristic
316	#501	C₂²×C₃₇	1	4	yes	complemented
317	#499	C₂²×C₃₇	1	4	yes	complemented
318	#496	C₂²×C₃₇	1	4	yes	—
319	#493	C₂²×C₃₇	1	2	yes	—
320	#492	C₂²×C₃₇	1	2	yes	—
321	#491	C₂²×C₃₇	1	2	yes	complemented
322	#490	C₂²×C₃₇	1	2	yes	—
323	#490	C₂²×C₃₇	1	4	yes	—
324	#490	C₂²×C₃₇	1	2	yes	—
325	#490	C₂²×C₃₇	1	2	yes	complemented
326	#489	C₂²×C₃₇	1	2	yes	complemented
327	#489	C₂²×C₃₇	1	2	yes	complemented
328	#469	C₂²×C₃₇	1	8	yes	complemented
329	#468	C₂²×C₃₇	1	8	yes	complemented
330	#466	C₂²×C₃₇	1	8	yes	complemented
331	#465	C₂²×C₃₇	1	8	yes	complemented
332	#442	C₂²×C₃₇	1	8	yes	complemented
333	#440	C₂²×C₃₇	1	8	yes	complemented
334	C₄×SD₁₆	C₂²×C₃₇	1	8	yes	complemented
335	C₄×D₈	C₂²×C₃₇	1	8	yes	complemented
336	#428	C₂²×C₃₇	1	4	yes	—
337	#416	C₂²×C₃₇	1	4	yes	—
338	C₂×#102	C₂²×C₃₇	1	4	yes	—
339	#405	C₂²×C₃₇	1	2	yes	—
340	#405	C₂²×C₃₇	1	4	yes	complemented
341	C₄×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
342	C₄×M₁₆	C₂²×C₃₇	1	2	yes	complemented
343	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
344	C₂×#97	C₂²×C₃₇	1	2	yes	complemented
345	C₃₇	#60725	1	1	yes	characteristic, direct product factor, Sylow
346	C₂×#41	—	2	4	no	—
347	C₂×#41	C₂³×C₃₇	1	2	yes	—
348	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
349	C₂²×D₄	—	2	2	no	—
350	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
351	AGL(1,ℤ/8)	—	2	16	no	—
352	C₂×SD₁₆	C₂³×C₃₇	1	8	yes	—
353	C₂×D₈	C₂³×C₃₇	1	8	yes	—
354	#131	—	2	8	no	—
355	C₂×M₁₆	C₂³×C₃₇	1	4	yes	—
356	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
357	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
358	C₂²×C₈	C₂³×C₃₇	1	4	yes	—
359	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
360	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
361	#127	—	2	2	no	—
362	#127	—	2	2	no	—
363	#127	C₂³×C₃₇	1	2	yes	—
364	#127	C₂³×C₃₇	1	2	yes	—
365	#127	C₂³×C₃₇	1	1	yes	characteristic
366	#126	—	2	4	no	—
367	#126	—	2	4	no	—
368	#125	—	2	4	no	—
369	#125	—	2	2	no	—
370	#125	C₂³×C₃₇	1	2	yes	—
371	#125	C₂³×C₃₇	1	2	yes	—
372	#125	C₂³×C₃₇	1	2	yes	—
373	#124	—	2	2	no	—
374	#124	—	2	4	no	—
375	#124	C₂³×C₃₇	1	2	yes	—
376	#123	—	2	4	no	—
377	#123	—	2	8	no	—
378	#123	—	2	4	no	—
379	C₂²⋊Q₈	—	2	2	no	—
380	C₂²⋊Q₈	—	2	2	no	—
381	C₂²⋊Q₈	C₂³×C₃₇	1	4	yes	—
382	#121	—	2	2	no	—
383	#121	—	2	4	no	—
384	#121	—	2	4	no	—
385	#121	—	2	2	no	—
386	#121	—	2	8	no	—
387	#121	—	2	4	no	—
388	#121	C₂³×C₃₇	1	4	yes	—
389	#121	C₂³×C₃₇	1	8	yes	—
390	#120	—	2	4	no	—
391	C₄×Q₈	—	2	2	no	—
392	C₄×Q₈	D₄×C₃₇	1	2	yes	—
393	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
394	C₄×D₄	—	2	4	no	—
395	C₄×D₄	—	2	4	no	—
396	C₄×D₄	—	2	4	no	—
397	C₄×D₄	—	2	4	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	D₄×C₃₇	1	4	yes	—
400	C₄×D₄	D₄×C₃₇	1	2	yes	—
401	C₄×D₄	C₂³×C₃₇	1	8	yes	—
402	C₄×D₄	C₂³×C₃₇	1	4	yes	—
403	#117	—	2	2	no	—
404	#117	—	2	4	no	—
405	#117	C₂³×C₃₇	1	2	yes	—
406	#117	C₂³×C₃₇	1	1	yes	characteristic
407	#117	C₂³×C₃₇	1	2	yes	—
408	C₂×C₄⋊C₄	—	2	2	no	—
409	C₂×C₄⋊C₄	—	2	2	no	—
410	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
411	C₂×C₂²⋊C₄	—	2	4	no	—
412	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
413	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
414	#107	C₂³×C₃₇	1	8	yes	—
415	#106	C₂³×C₃₇	1	8	yes	—
416	#103	C₂³×C₃₇	1	4	yes	—
417	#103	C₂³×C₃₇	1	4	yes	—
418	#102	C₂³×C₃₇	1	8	yes	—
419	#102	C₂³×C₃₇	1	8	yes	—
420	#102	C₂³×C₃₇	1	4	yes	—
421	#102	C₂³×C₃₇	1	4	yes	—
422	#97	C₂³×C₃₇	1	1	yes	characteristic
423	#97	C₂³×C₃₇	1	1	yes	characteristic
424	#97	C₂³×C₃₇	1	2	yes	—
425	#97	C₂³×C₃₇	1	2	yes	—
426	#97	C₂³×C₃₇	1	4	yes	—
427	C₄×C₈	C₂³×C₃₇	1	2	yes	—
428	C₄×C₈	C₂³×C₃₇	1	4	yes	—
429	C₂⁴	—	2	2	no	—
430	#41	—	2	4	no	—
431	#41	—	2	8	no	—
432	#41	—	8	8	no	—
433	C₂×Q₈	—	2	2	no	—
434	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
435	C₂×Q₈	C₂⁴×C₃₇	1	2	yes	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	8	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	4	no	—
443	C₂×D₄	—	2	8	no	—
444	C₂×D₄	—	8	4	no	—
445	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
446	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
447	C₂×D₄	C₂⁴×C₃₇	1	2	yes	—
448	C₂×D₄	C₂⁴×C₃₇	1	4	yes	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	8	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
454	C₂²×C₄	C₂×D₄×C₃₇	1	4	yes	—
455	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
456	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
457	SD₁₆	—	2	16	no	—
458	D₈	—	2	16	no	—
459	M₁₆	—	2	8	no	—
460	M₁₆	#41×C₃₇	1	8	yes	complemented
461	C₂×C₈	—	2	4	no	—
462	C₂×C₈	—	2	8	no	—
463	C₂×C₈	C₂⁴×C₃₇	1	2	yes	—
464	C₂×C₈	C₂⁴×C₃₇	1	2	yes	—
465	C₂×C₈	C₂⁴×C₃₇	1	4	yes	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
475	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
476	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
477	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	8	no	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	4	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	8	no	—
486	C₂²⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
487	C₂²⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
488	C₄²	—	2	4	no	—
489	C₄²	—	2	2	no	—
490	C₄²	C₂×D₄×C₃₇	1	4	yes	—
491	C₄²	C₂×D₄×C₃₇	1	2	yes	—
492	C₄²	C₂⁴×C₃₇	1	2	yes	—
493	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
494	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
495	C₂³	—	2	2	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	4	4	no	—
498	C₂³	—	8	4	no	—
499	C₂³	C₂²×D₄×C₃₇	1	2	yes	—
500	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
501	Q₈	—	2	2	no	—
502	Q₈	—	2	4	no	—
503	Q₈	—	4	4	no	—
504	D₄	—	2	4	no	—
505	D₄	—	2	2	no	—
506	D₄	—	2	4	no	—
507	D₄	—	2	8	no	—
508	D₄	—	4	8	no	—
509	D₄	—	4	4	no	—
510	D₄	—	4	4	no	—
511	D₄	—	8	4	no	—
512	D₄	—	8	2	no	—
513	D₄	—	8	8	no	—
514	D₄	—	8	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	4	no	—
522	C₂×C₄	—	8	8	no	—
523	C₂×C₄	—	8	4	no	—
524	C₂×C₄	—	8	2	no	—
525	C₂×C₄	C₂²×D₄×C₃₇	1	4	yes	—
526	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
527	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
528	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
529	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
530	C₂×C₄	C₂×#41×C₃₇	1	4	yes	—
531	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
532	C₈	—	2	2	no	—
533	C₈	—	2	2	no	—
534	C₈	C₂×#41×C₃₇	1	8	yes	—
535	C₂²	—	2	2	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	4	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	4	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	8	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	16	4	no	—
544	C₂²	C₃₇×#532	1	2	yes	—
545	C₂²	C₂³×D₄×C₃₇	1	1	yes	characteristic
546	C₄	—	2	2	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	4	no	—
549	C₄	—	2	2	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	4	no	—
552	C₄	—	4	4	no	—
553	C₄	C₃₇×#532	1	2	yes	—
554	C₄	C₂²×#41×C₃₇	1	2	yes	—
555	C₂	—	2	2	no	—
556	C₂	—	4	2	no	—
557	C₂	—	8	4	no	—
558	C₂	—	8	2	no	—
559	C₂	C₂×C₃₇×#532	1	1	yes	characteristic
560	C₂	C₃₇×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₄×#41×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3512	C₂	semidirect
2. C₃₇×#3508	C₂	semidirect
3. C₃₇×#3180	C₂	semidirect
4. C₃₇×#3176	C₂	semidirect
5. C₃₇×#3174	C₂	semidirect
6. C₃₇×#3171	C₂	semidirect
7. C₃₇×#3166	C₂	semidirect
8. C₃₇×#3151	C₂	semidirect
9. C₃₇×#3135	C₂	semidirect
10. C₂×C₃₇×#490	C₂	semidirect
11. C₃₇×#3062	C₂	semidirect
12. C₃₇×#2946	C₂	semidirect
13. C₃₇×#2875	C₂	semidirect
22. C₃₇×#541	C₂²	semidirect
24. C₃₇×#540	C₂²	semidirect
31. C₃₇×#529	C₂²	semidirect
36. C₃₇×#501	C₂²	semidirect
37. C₃₇×#499	C₂²	semidirect
41. C₃₇×#491	C₂²	semidirect
45. C₃₇×#490	C₂²	semidirect
46. C₃₇×#489	C₂²	semidirect
47. C₃₇×#489	C₂²	semidirect
48. C₃₇×#469	C₂²	semidirect
49. C₃₇×#468	C₂²	semidirect
50. C₃₇×#466	C₂²	semidirect
51. C₃₇×#465	C₂²	semidirect
52. C₃₇×#442	C₂²	semidirect
53. C₃₇×#440	C₂²	semidirect
54. C₄×SD₁₆×C₃₇	C₂²	semidirect
55. C₄×D₈×C₃₇	C₂²	semidirect
60. C₃₇×#405	C₂²	semidirect
62. C₄×M₁₆×C₃₇	C₂²	semidirect
64. C₂×#97×C₃₇	C₂²	semidirect
179. M₁₆×C₃₇	#41	semidirect
254. #60725	C₃₇	direct (N × H)
275. #3512	C₂×C₃₇	semidirect
276. #3508	C₂×C₃₇	semidirect
277. #3180	C₂×C₃₇	semidirect
278. #3176	C₂×C₃₇	semidirect
279. #3174	C₂×C₃₇	semidirect
280. #3171	C₂×C₃₇	semidirect
281. #3166	C₂×C₃₇	semidirect
282. #3151	C₂×C₃₇	semidirect
283. #3135	C₂×C₃₇	semidirect
284. C₂×#490	C₂×C₃₇	semidirect
285. #3062	C₂×C₃₇	semidirect
286. #2946	C₂×C₃₇	semidirect
287. #2875	C₂×C₃₇	semidirect
302. #541	C₂²×C₃₇	semidirect
304. #540	C₂²×C₃₇	semidirect
311. #529	C₂²×C₃₇	semidirect
316. #501	C₂²×C₃₇	semidirect
317. #499	C₂²×C₃₇	semidirect
321. #491	C₂²×C₃₇	semidirect
325. #490	C₂²×C₃₇	semidirect
326. #489	C₂²×C₃₇	semidirect
327. #489	C₂²×C₃₇	semidirect
328. #469	C₂²×C₃₇	semidirect
329. #468	C₂²×C₃₇	semidirect
330. #466	C₂²×C₃₇	semidirect
331. #465	C₂²×C₃₇	semidirect
332. #442	C₂²×C₃₇	semidirect
333. #440	C₂²×C₃₇	semidirect
334. C₄×SD₁₆	C₂²×C₃₇	semidirect
335. C₄×D₈	C₂²×C₃₇	semidirect
340. #405	C₂²×C₃₇	semidirect
342. C₄×M₁₆	C₂²×C₃₇	semidirect
344. C₂×#97	C₂²×C₃₇	semidirect
345. C₃₇	#60725	direct (N × H)
460. M₁₆	#41×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#3512	2
C₃₇×#3508	2
C₃₇×#3180	2
C₃₇×#3176	2
C₃₇×#3174	2
C₃₇×#3171	2
C₃₇×#3166	2
C₃₇×#3151	2
C₃₇×#3135	2
C₂×C₃₇×#490	2
C₃₇×#3062	2
C₃₇×#2946	2
C₃₇×#2875	2
#60725	37

Subgroups — C37×#60725 #22681978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#60725 #22681978