Subgroups — C₃₇×#60859 #22682112

Order 9472.

1654 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3455	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#3244	C₂	1	4	yes	maximal, complemented
4	C₃₇×#3243	C₂	1	4	yes	maximal, complemented
5	C₃₇×#3242	C₂	1	4	yes	maximal, complemented
6	C₃₇×#3241	C₂	1	4	yes	maximal, complemented
7	C₃₇×#3162	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#3160	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#3135	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#3131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#3091	C₂	1	4	yes	maximal, complemented
12	C₃₇×#3076	C₂	1	4	yes	maximal, complemented
13	C₂×C₃₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#544	—	2	2	no	—
15	C₃₇×#544	C₂²	1	4	yes	—
16	C₃₇×#544	C₂²	1	4	yes	—
17	C₃₇×#543	—	2	2	no	—
18	C₃₇×#542	C₂²	1	4	yes	—
19	C₃₇×#541	C₂²	1	2	yes	—
20	C₃₇×#540	C₂²	1	2	yes	—
21	C₃₇×#539	—	2	2	no	—
22	C₃₇×#538	—	2	2	no	—
23	C₃₇×#533	—	2	4	no	—
24	C₃₇×#533	C₂²	1	1	yes	characteristic
25	C₃₇×#533	C₂²	1	1	yes	characteristic
26	C₃₇×#533	C₂²	1	1	yes	characteristic
27	C₃₇×#533	C₂²	1	2	yes	—
28	C₃₇×#532	C₂²	1	1	yes	characteristic
29	C₃₇×#529	—	2	4	no	—
30	C₃₇×#525	C₂²	1	2	yes	—
31	C₄×#41×C₃₇	C₂²	1	2	yes	—
32	C₂×#117×C₃₇	C₂²	1	2	yes	—
33	C₂×#117×C₃₇	C₂²	1	1	yes	characteristic
34	C₃₇×#501	C₂²	1	4	yes	complemented
35	C₃₇×#501	C₂²	1	4	yes	complemented
36	C₃₇×#500	C₂²	1	2	yes	complemented
37	C₃₇×#499	C₂²	1	4	yes	complemented
38	C₃₇×#498	C₂²	1	2	yes	complemented
39	C₃₇×#491	C₂²	1	2	yes	complemented
40	C₃₇×#490	C₂²	1	2	yes	complemented
41	C₃₇×#489	C₂²	1	4	yes	complemented
42	C₃₇×#488	C₂²	1	2	yes	complemented
43	C₃₇×#488	C₂²	1	2	yes	complemented
44	C₃₇×#487	C₂²	1	2	yes	complemented
45	C₃₇×#486	C₂²	1	2	yes	complemented
46	C₃₇×#485	C₂²	1	4	yes	—
47	C₃₇×#485	C₂²	1	4	yes	—
48	C₃₇×#484	C₂²	1	4	yes	—
49	C₃₇×#483	C₂²	1	4	yes	—
50	C₃₇×#482	C₂²	1	4	yes	—
51	C₃₇×#482	C₂²	1	4	yes	—
52	C₃₇×#481	C₂²	1	4	yes	—
53	C₃₇×#480	C₂²	1	4	yes	—
54	C₃₇×#479	C₂²	1	4	yes	complemented
55	C₃₇×#479	C₂²	1	4	yes	complemented
56	C₃₇×#478	C₂²	1	4	yes	complemented
57	C₃₇×#478	C₂²	1	4	yes	complemented
58	C₃₇×#477	C₂²	1	4	yes	complemented
59	C₃₇×#476	C₂²	1	4	yes	complemented
60	C₃₇×#475	C₂²	1	4	yes	complemented
61	C₃₇×#474	C₂²	1	4	yes	complemented
62	C₃₇×#433	C₂²	1	4	yes	—
63	C₃₇×#433	C₂²	1	2	yes	—
64	C₃₇×#433	C₂²	1	2	yes	—
65	C₃₇×#427	C₂²	1	4	yes	—
66	C₃₇×#427	C₂²	1	4	yes	—
67	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
68	C₃₇×#416	C₂²	1	4	yes	—
69	C₃₇×#416	C₂²	1	4	yes	—
70	C₂×C₂²⋊C₈×C₃₇	C₂²	1	2	yes	—
71	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
72	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
73	C₂×#41×C₃₇	C₂³	1	2	yes	—
74	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
76	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
77	C₄⋊Q₈×C₃₇	—	2	4	no	—
78	C₄⋊Q₈×C₃₇	—	2	4	no	—
79	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
80	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
81	C₄⋊Q₈×C₃₇	C₂³	1	4	yes	—
82	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
83	C₄⋊Q₈×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	4	no	—
89	#125×C₃₇	—	2	4	no	—
90	#125×C₃₇	C₂³	1	2	yes	—
91	#125×C₃₇	C₂³	1	4	yes	—
92	#125×C₃₇	C₂³	1	2	yes	—
93	#125×C₃₇	C₂³	1	2	yes	—
94	#124×C₃₇	—	2	4	no	—
95	#124×C₃₇	C₂³	1	2	yes	—
96	#123×C₃₇	—	2	2	no	—
97	#123×C₃₇	—	2	4	no	—
98	#123×C₃₇	—	2	4	no	—
99	C₂²⋊Q₈×C₃₇	—	2	2	no	—
100	C₂²⋊Q₈×C₃₇	—	2	4	no	—
101	C₂²⋊Q₈×C₃₇	—	2	2	no	—
102	C₂²⋊Q₈×C₃₇	—	2	2	no	—
103	C₂²⋊Q₈×C₃₇	—	2	4	no	—
104	C₂²⋊Q₈×C₃₇	—	2	4	no	—
105	C₂²⋊Q₈×C₃₇	—	2	4	no	—
106	C₂²⋊Q₈×C₃₇	—	2	4	no	—
107	C₂²⋊Q₈×C₃₇	—	2	4	no	—
108	C₂²⋊Q₈×C₃₇	C₂³	1	4	yes	—
109	#121×C₃₇	—	2	2	no	—
110	#121×C₃₇	—	2	4	no	—
111	#121×C₃₇	C₂³	1	4	yes	—
112	#120×C₃₇	—	2	2	no	—
113	C₄×Q₈×C₃₇	—	2	2	no	—
114	C₄×Q₈×C₃₇	—	2	4	no	—
115	C₄×Q₈×C₃₇	—	2	2	no	—
116	C₄×Q₈×C₃₇	—	2	2	no	—
117	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
118	C₄×D₄×C₃₇	—	2	4	no	—
119	C₄×D₄×C₃₇	—	2	4	no	—
120	C₄×D₄×C₃₇	—	2	2	no	—
121	C₄×D₄×C₃₇	C₂³	1	4	yes	—
122	#117×C₃₇	—	2	2	no	—
123	#117×C₃₇	—	2	2	no	—
124	#117×C₃₇	—	2	2	no	—
125	#117×C₃₇	D₄	1	4	yes	—
126	#117×C₃₇	C₂³	1	2	yes	—
127	#117×C₃₇	C₂³	1	2	yes	—
128	#117×C₃₇	C₂³	1	2	yes	—
129	#117×C₃₇	C₂³	1	4	yes	—
130	#117×C₃₇	C₂³	1	2	yes	—
131	#117×C₃₇	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
133	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
135	C₂×C₂²⋊C₄×C₃₇	D₄	1	2	yes	—
136	C₂×C₄²×C₃₇	—	2	2	no	—
137	C₂×C₄²×C₃₇	—	2	2	no	—
138	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
140	#107×C₃₇	C₂³	1	4	yes	—
141	#107×C₃₇	C₂³	1	4	yes	—
142	#107×C₃₇	C₂³	1	4	yes	—
143	#107×C₃₇	C₂³	1	4	yes	—
144	#106×C₃₇	C₂³	1	4	yes	—
145	#106×C₃₇	C₂³	1	4	yes	—
146	#106×C₃₇	C₂³	1	4	yes	—
147	#106×C₃₇	C₂³	1	4	yes	—
148	C₄⋊C₈×C₃₇	C₂³	1	4	yes	—
149	C₄⋊C₈×C₃₇	C₂³	1	4	yes	—
150	#103×C₃₇	C₂³	1	4	yes	—
151	#103×C₃₇	C₂³	1	4	yes	—
152	#103×C₃₇	C₂³	1	4	yes	—
153	#103×C₃₇	C₂³	1	4	yes	—
154	#102×C₃₇	C₂³	1	4	yes	—
155	#102×C₃₇	C₂³	1	4	yes	—
156	#102×C₃₇	C₂³	1	4	yes	—
157	#102×C₃₇	C₂³	1	4	yes	—
158	C₂²⋊C₈×C₃₇	C₂³	1	4	yes	—
159	C₂²⋊C₈×C₃₇	C₂³	1	4	yes	—
160	#97×C₃₇	C₂³	1	2	yes	—
161	#97×C₃₇	C₂³	1	2	yes	—
162	C₄×C₈×C₃₇	C₂³	1	2	yes	—
163	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
164	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
165	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
166	#41×C₃₇	—	2	8	no	—
167	C₂×Q₈×C₃₇	—	2	2	no	—
168	C₂×Q₈×C₃₇	—	2	4	no	—
169	C₂×Q₈×C₃₇	—	2	2	no	—
170	C₂×Q₈×C₃₇	—	2	2	no	—
171	C₂×Q₈×C₃₇	C₂⁴	1	2	yes	—
172	C₂×D₄×C₃₇	—	2	2	no	—
173	C₂×D₄×C₃₇	—	2	4	no	—
174	C₂×D₄×C₃₇	—	2	2	no	—
175	C₂×D₄×C₃₇	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₃₇	—	2	4	no	—
177	C₂²×C₄×C₃₇	—	2	4	no	—
178	C₂²×C₄×C₃₇	—	2	2	no	—
179	C₂²×C₄×C₃₇	—	2	4	no	—
180	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
183	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
186	C₂×C₈×C₃₇	—	2	4	no	—
187	C₂×C₈×C₃₇	—	2	4	no	—
188	C₂×C₈×C₃₇	C₂⁴	1	2	yes	—
189	C₂×C₈×C₃₇	C₂⁴	1	2	yes	—
190	C₂×C₈×C₃₇	C₂⁴	1	4	yes	—
191	C₄⋊C₄×C₃₇	—	2	4	no	—
192	C₄⋊C₄×C₃₇	—	2	4	no	—
193	C₄⋊C₄×C₃₇	—	2	2	no	—
194	C₄⋊C₄×C₃₇	—	2	4	no	—
195	C₄⋊C₄×C₃₇	—	2	4	no	—
196	C₄⋊C₄×C₃₇	—	2	4	no	—
197	C₄⋊C₄×C₃₇	—	2	2	no	—
198	C₄⋊C₄×C₃₇	—	2	2	no	—
199	C₄⋊C₄×C₃₇	—	2	4	no	—
200	C₄⋊C₄×C₃₇	—	2	4	no	—
201	C₄⋊C₄×C₃₇	—	2	4	no	—
202	C₄⋊C₄×C₃₇	—	2	4	no	—
203	C₄⋊C₄×C₃₇	—	2	2	no	—
204	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
205	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
206	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
207	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
208	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
209	C₂²⋊C₄×C₃₇	—	2	4	no	—
210	C₂²⋊C₄×C₃₇	—	2	2	no	—
211	C₂²⋊C₄×C₃₇	—	2	2	no	—
212	C₂²⋊C₄×C₃₇	—	2	2	no	—
213	C₂²⋊C₄×C₃₇	—	2	4	no	—
214	C₂²⋊C₄×C₃₇	—	2	4	no	—
215	C₂²⋊C₄×C₃₇	—	2	4	no	—
216	C₂²⋊C₄×C₃₇	—	2	4	no	—
217	C₂²⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
218	C₂²⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
219	C₄²×C₃₇	—	2	4	no	—
220	C₄²×C₃₇	—	2	4	no	—
221	C₄²×C₃₇	—	2	2	no	—
222	C₄²×C₃₇	—	2	2	no	—
223	C₄²×C₃₇	—	2	2	no	—
224	C₄²×C₃₇	C₂×D₄	1	2	yes	—
225	C₄²×C₃₇	C₂×D₄	1	2	yes	—
226	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
227	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
228	C₄²×C₃₇	C₂⁴	1	2	yes	—
229	C₂³×C₃₇	—	2	2	no	—
230	C₂³×C₃₇	—	2	2	no	—
231	C₂³×C₃₇	—	4	2	no	—
232	C₂³×C₃₇	C₂²×D₄	1	2	yes	—
233	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
234	Q₈×C₃₇	—	2	4	no	—
235	Q₈×C₃₇	—	8	4	no	—
236	Q₈×C₃₇	—	8	2	no	—
237	Q₈×C₃₇	—	8	2	no	—
238	Q₈×C₃₇	—	8	2	no	—
239	D₄×C₃₇	—	2	4	no	—
240	D₄×C₃₇	—	4	4	no	—
241	D₄×C₃₇	—	8	2	no	—
242	D₄×C₃₇	—	8	4	no	—
243	C₂×C₄×C₃₇	—	2	2	no	—
244	C₂×C₄×C₃₇	—	2	4	no	—
245	C₂×C₄×C₃₇	—	2	4	no	—
246	C₂×C₄×C₃₇	—	2	2	no	—
247	C₂×C₄×C₃₇	—	2	4	no	—
248	C₂×C₄×C₃₇	—	2	4	no	—
249	C₂×C₄×C₃₇	—	2	4	no	—
250	C₂×C₄×C₃₇	—	4	2	no	—
251	C₂×C₄×C₃₇	—	4	2	no	—
252	C₂×C₄×C₃₇	—	4	4	no	—
253	C₂×C₄×C₃₇	—	8	4	no	—
254	C₂×C₄×C₃₇	—	8	4	no	—
255	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₃₇	C₂²×D₄	1	4	yes	—
257	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₃₇	2₋¹⁺⁴	1	4	yes	—
261	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
262	C₈×C₃₇	—	2	2	no	—
263	C₈×C₃₇	—	2	2	no	—
264	C₈×C₃₇	—	2	4	no	—
265	#60859	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
266	C₂²×C₃₇	—	2	2	no	—
267	C₂²×C₃₇	—	2	4	no	—
268	C₂²×C₃₇	—	2	2	no	—
269	C₂²×C₃₇	—	4	4	no	—
270	C₂²×C₃₇	—	4	2	no	—
271	C₂²×C₃₇	—	8	2	no	—
272	C₂²×C₃₇	#536	1	2	yes	—
273	C₂²×C₃₇	C₂³×D₄	1	1	yes	characteristic
274	C₄×C₃₇	—	2	4	no	—
275	C₄×C₃₇	—	2	2	no	—
276	C₄×C₃₇	—	2	2	no	—
277	C₄×C₃₇	—	2	2	no	—
278	C₄×C₃₇	—	4	4	no	—
279	C₄×C₃₇	—	4	4	no	—
280	C₄×C₃₇	—	4	4	no	—
281	C₄×C₃₇	—	4	2	no	—
282	C₄×C₃₇	#536	1	2	yes	—
283	C₄×C₃₇	C₂×2₋¹⁺⁴	1	2	yes	—
284	#3458	C₂×C₃₇	1	1	yes	characteristic, complemented
285	#3455	C₂×C₃₇	1	1	yes	characteristic
286	#3244	C₂×C₃₇	1	4	yes	complemented
287	#3243	C₂×C₃₇	1	4	yes	complemented
288	#3242	C₂×C₃₇	1	4	yes	complemented
289	#3241	C₂×C₃₇	1	4	yes	complemented
290	#3162	C₂×C₃₇	1	1	yes	characteristic, complemented
291	#3160	C₂×C₃₇	1	1	yes	characteristic, complemented
292	#3135	C₂×C₃₇	1	1	yes	characteristic, complemented
293	#3131	C₂×C₃₇	1	1	yes	characteristic, complemented
294	#3091	C₂×C₃₇	1	4	yes	complemented
295	#3076	C₂×C₃₇	1	4	yes	complemented
296	C₂×#433	C₂×C₃₇	1	1	yes	characteristic, complemented
297	C₂×C₃₇	—	2	2	no	—
298	C₂×C₃₇	—	4	2	no	—
299	C₂×C₃₇	—	8	2	no	—
300	C₂×C₃₇	C₂×#536	1	1	yes	characteristic
301	C₂×C₃₇	#3584	1	2	yes	—
302	#544	—	2	2	no	—
303	#544	C₂²×C₃₇	1	4	yes	—
304	#544	C₂²×C₃₇	1	4	yes	—
305	#543	—	2	2	no	—
306	#542	C₂²×C₃₇	1	4	yes	—
307	#541	C₂²×C₃₇	1	2	yes	—
308	#540	C₂²×C₃₇	1	2	yes	—
309	#539	—	2	2	no	—
310	#538	—	2	2	no	—
311	#533	—	2	4	no	—
312	#533	C₂²×C₃₇	1	2	yes	—
313	#533	C₂²×C₃₇	1	1	yes	characteristic
314	#533	C₂²×C₃₇	1	1	yes	characteristic
315	#533	C₂²×C₃₇	1	1	yes	characteristic
316	#532	C₂²×C₃₇	1	1	yes	characteristic
317	#529	—	2	4	no	—
318	#525	C₂²×C₃₇	1	2	yes	—
319	C₄×#41	C₂²×C₃₇	1	2	yes	—
320	C₂×#117	C₂²×C₃₇	1	2	yes	—
321	C₂×#117	C₂²×C₃₇	1	1	yes	characteristic
322	#501	C₂²×C₃₇	1	4	yes	complemented
323	#501	C₂²×C₃₇	1	4	yes	complemented
324	#500	C₂²×C₃₇	1	2	yes	complemented
325	#499	C₂²×C₃₇	1	4	yes	complemented
326	#498	C₂²×C₃₇	1	2	yes	complemented
327	#491	C₂²×C₃₇	1	2	yes	complemented
328	#490	C₂²×C₃₇	1	2	yes	complemented
329	#489	C₂²×C₃₇	1	4	yes	complemented
330	#488	C₂²×C₃₇	1	2	yes	complemented
331	#488	C₂²×C₃₇	1	2	yes	complemented
332	#487	C₂²×C₃₇	1	2	yes	complemented
333	#486	C₂²×C₃₇	1	2	yes	complemented
334	#485	C₂²×C₃₇	1	4	yes	—
335	#485	C₂²×C₃₇	1	4	yes	—
336	#484	C₂²×C₃₇	1	4	yes	—
337	#483	C₂²×C₃₇	1	4	yes	—
338	#482	C₂²×C₃₇	1	4	yes	—
339	#482	C₂²×C₃₇	1	4	yes	—
340	#481	C₂²×C₃₇	1	4	yes	—
341	#480	C₂²×C₃₇	1	4	yes	—
342	#479	C₂²×C₃₇	1	4	yes	complemented
343	#479	C₂²×C₃₇	1	4	yes	complemented
344	#478	C₂²×C₃₇	1	4	yes	complemented
345	#478	C₂²×C₃₇	1	4	yes	complemented
346	#477	C₂²×C₃₇	1	4	yes	complemented
347	#476	C₂²×C₃₇	1	4	yes	complemented
348	#475	C₂²×C₃₇	1	4	yes	complemented
349	#474	C₂²×C₃₇	1	4	yes	complemented
350	#433	C₂²×C₃₇	1	4	yes	—
351	#433	C₂²×C₃₇	1	2	yes	—
352	#433	C₂²×C₃₇	1	2	yes	—
353	#427	C₂²×C₃₇	1	4	yes	—
354	#427	C₂²×C₃₇	1	4	yes	—
355	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
356	#416	C₂²×C₃₇	1	4	yes	—
357	#416	C₂²×C₃₇	1	4	yes	—
358	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	—
359	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
360	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
361	C₃₇	#60859	1	1	yes	characteristic, direct product factor, Sylow
362	C₂×#41	C₂³×C₃₇	1	2	yes	—
363	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
365	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
366	C₄⋊Q₈	—	2	4	no	—
367	C₄⋊Q₈	—	2	4	no	—
368	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
369	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
370	C₄⋊Q₈	C₂³×C₃₇	1	4	yes	—
371	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
372	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
373	#127	C₂³×C₃₇	1	1	yes	characteristic
374	#126	—	2	4	no	—
375	#126	—	2	4	no	—
376	#125	—	2	4	no	—
377	#125	—	2	4	no	—
378	#125	—	2	4	no	—
379	#125	C₂³×C₃₇	1	2	yes	—
380	#125	C₂³×C₃₇	1	4	yes	—
381	#125	C₂³×C₃₇	1	2	yes	—
382	#125	C₂³×C₃₇	1	2	yes	—
383	#124	—	2	4	no	—
384	#124	C₂³×C₃₇	1	2	yes	—
385	#123	—	2	2	no	—
386	#123	—	2	4	no	—
387	#123	—	2	4	no	—
388	C₂²⋊Q₈	—	2	2	no	—
389	C₂²⋊Q₈	—	2	4	no	—
390	C₂²⋊Q₈	—	2	2	no	—
391	C₂²⋊Q₈	—	2	2	no	—
392	C₂²⋊Q₈	—	2	4	no	—
393	C₂²⋊Q₈	—	2	4	no	—
394	C₂²⋊Q₈	—	2	4	no	—
395	C₂²⋊Q₈	—	2	4	no	—
396	C₂²⋊Q₈	—	2	4	no	—
397	C₂²⋊Q₈	C₂³×C₃₇	1	4	yes	—
398	#121	—	2	2	no	—
399	#121	—	2	4	no	—
400	#121	C₂³×C₃₇	1	4	yes	—
401	#120	—	2	2	no	—
402	C₄×Q₈	—	2	2	no	—
403	C₄×Q₈	—	2	4	no	—
404	C₄×Q₈	—	2	2	no	—
405	C₄×Q₈	—	2	2	no	—
406	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
407	C₄×D₄	—	2	4	no	—
408	C₄×D₄	—	2	4	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	C₂³×C₃₇	1	4	yes	—
411	#117	—	2	2	no	—
412	#117	—	2	2	no	—
413	#117	—	2	2	no	—
414	#117	D₄×C₃₇	1	4	yes	—
415	#117	C₂³×C₃₇	1	2	yes	—
416	#117	C₂³×C₃₇	1	2	yes	—
417	#117	C₂³×C₃₇	1	4	yes	—
418	#117	C₂³×C₃₇	1	2	yes	—
419	#117	C₂³×C₃₇	1	2	yes	—
420	#117	C₂³×C₃₇	1	2	yes	—
421	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
423	C₂×C₂²⋊C₄	—	2	2	no	—
424	C₂×C₂²⋊C₄	D₄×C₃₇	1	2	yes	—
425	C₂×C₄²	—	2	2	no	—
426	C₂×C₄²	—	2	2	no	—
427	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
429	#107	C₂³×C₃₇	1	4	yes	—
430	#107	C₂³×C₃₇	1	4	yes	—
431	#107	C₂³×C₃₇	1	4	yes	—
432	#107	C₂³×C₃₇	1	4	yes	—
433	#106	C₂³×C₃₇	1	4	yes	—
434	#106	C₂³×C₃₇	1	4	yes	—
435	#106	C₂³×C₃₇	1	4	yes	—
436	#106	C₂³×C₃₇	1	4	yes	—
437	C₄⋊C₈	C₂³×C₃₇	1	4	yes	—
438	C₄⋊C₈	C₂³×C₃₇	1	4	yes	—
439	#103	C₂³×C₃₇	1	4	yes	—
440	#103	C₂³×C₃₇	1	4	yes	—
441	#103	C₂³×C₃₇	1	4	yes	—
442	#103	C₂³×C₃₇	1	4	yes	—
443	#102	C₂³×C₃₇	1	4	yes	—
444	#102	C₂³×C₃₇	1	4	yes	—
445	#102	C₂³×C₃₇	1	4	yes	—
446	#102	C₂³×C₃₇	1	4	yes	—
447	C₂²⋊C₈	C₂³×C₃₇	1	4	yes	—
448	C₂²⋊C₈	C₂³×C₃₇	1	4	yes	—
449	#97	C₂³×C₃₇	1	2	yes	—
450	#97	C₂³×C₃₇	1	2	yes	—
451	C₄×C₈	C₂³×C₃₇	1	2	yes	—
452	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
453	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
454	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
455	#41	—	2	8	no	—
456	C₂×Q₈	—	2	2	no	—
457	C₂×Q₈	—	2	4	no	—
458	C₂×Q₈	—	2	2	no	—
459	C₂×Q₈	—	2	2	no	—
460	C₂×Q₈	C₂⁴×C₃₇	1	2	yes	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	4	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	C₂⁴×C₃₇	1	2	yes	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
470	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
472	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
473	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
474	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
475	C₂×C₈	—	2	4	no	—
476	C₂×C₈	—	2	4	no	—
477	C₂×C₈	C₂⁴×C₃₇	1	2	yes	—
478	C₂×C₈	C₂⁴×C₃₇	1	2	yes	—
479	C₂×C₈	C₂⁴×C₃₇	1	4	yes	—
480	C₄⋊C₄	—	2	4	no	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	2	4	no	—
485	C₄⋊C₄	—	2	4	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	4	no	—
491	C₄⋊C₄	—	2	4	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
494	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
495	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
496	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
497	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
498	C₂²⋊C₄	—	2	4	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	4	no	—
503	C₂²⋊C₄	—	2	4	no	—
504	C₂²⋊C₄	—	2	4	no	—
505	C₂²⋊C₄	—	2	4	no	—
506	C₂²⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
507	C₂²⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
508	C₄²	—	2	2	no	—
509	C₄²	—	2	2	no	—
510	C₄²	—	2	2	no	—
511	C₄²	—	2	4	no	—
512	C₄²	—	2	4	no	—
513	C₄²	C₂×D₄×C₃₇	1	2	yes	—
514	C₄²	C₂×D₄×C₃₇	1	2	yes	—
515	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
516	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
517	C₄²	C₂⁴×C₃₇	1	2	yes	—
518	C₂³	—	2	2	no	—
519	C₂³	—	2	2	no	—
520	C₂³	—	4	2	no	—
521	C₂³	C₂²×D₄×C₃₇	1	2	yes	—
522	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
523	Q₈	—	2	4	no	—
524	Q₈	—	8	4	no	—
525	Q₈	—	8	2	no	—
526	Q₈	—	8	2	no	—
527	Q₈	—	8	2	no	—
528	D₄	—	2	4	no	—
529	D₄	—	4	4	no	—
530	D₄	—	8	2	no	—
531	D₄	—	8	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	4	no	—
542	C₂×C₄	—	8	4	no	—
543	C₂×C₄	—	8	4	no	—
544	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
545	C₂×C₄	C₂²×D₄×C₃₇	1	4	yes	—
546	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
547	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
548	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
549	C₂×C₄	2₋¹⁺⁴×C₃₇	1	4	yes	—
550	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
551	C₈	—	2	2	no	—
552	C₈	—	2	2	no	—
553	C₈	—	2	4	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	4	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	8	2	no	—
560	C₂²	C₃₇×#536	1	2	yes	—
561	C₂²	C₂³×D₄×C₃₇	1	1	yes	characteristic
562	C₄	—	2	2	no	—
563	C₄	—	2	4	no	—
564	C₄	—	2	2	no	—
565	C₄	—	2	2	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	4	no	—
568	C₄	—	4	4	no	—
569	C₄	—	4	4	no	—
570	C₄	C₃₇×#536	1	2	yes	—
571	C₄	C₂×2₋¹⁺⁴×C₃₇	1	2	yes	—
572	C₂	—	2	2	no	—
573	C₂	—	4	2	no	—
574	C₂	—	8	2	no	—
575	C₂	C₂×C₃₇×#536	1	1	yes	characteristic
576	C₂	C₃₇×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₇
socle	C₂²×C₃₇	C₂³×D₄
prime radical	C₃₇×#3455	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ C₂×#117×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3458	C₂	semidirect
3. C₃₇×#3244	C₂	semidirect
4. C₃₇×#3243	C₂	semidirect
5. C₃₇×#3242	C₂	semidirect
6. C₃₇×#3241	C₂	semidirect
7. C₃₇×#3162	C₂	semidirect
8. C₃₇×#3160	C₂	semidirect
9. C₃₇×#3135	C₂	semidirect
10. C₃₇×#3131	C₂	semidirect
11. C₃₇×#3091	C₂	semidirect
12. C₃₇×#3076	C₂	semidirect
13. C₂×C₃₇×#433	C₂	semidirect
34. C₃₇×#501	C₂²	semidirect
35. C₃₇×#501	C₂²	semidirect
36. C₃₇×#500	C₂²	semidirect
37. C₃₇×#499	C₂²	semidirect
38. C₃₇×#498	C₂²	semidirect
39. C₃₇×#491	C₂²	semidirect
40. C₃₇×#490	C₂²	semidirect
41. C₃₇×#489	C₂²	semidirect
42. C₃₇×#488	C₂²	semidirect
43. C₃₇×#488	C₂²	semidirect
44. C₃₇×#487	C₂²	semidirect
45. C₃₇×#486	C₂²	semidirect
54. C₃₇×#479	C₂²	semidirect
55. C₃₇×#479	C₂²	semidirect
56. C₃₇×#478	C₂²	semidirect
57. C₃₇×#478	C₂²	semidirect
58. C₃₇×#477	C₂²	semidirect
59. C₃₇×#476	C₂²	semidirect
60. C₃₇×#475	C₂²	semidirect
61. C₃₇×#474	C₂²	semidirect
265. #60859	C₃₇	direct (N × H)
284. #3458	C₂×C₃₇	semidirect
286. #3244	C₂×C₃₇	semidirect
287. #3243	C₂×C₃₇	semidirect
288. #3242	C₂×C₃₇	semidirect
289. #3241	C₂×C₃₇	semidirect
290. #3162	C₂×C₃₇	semidirect
291. #3160	C₂×C₃₇	semidirect
292. #3135	C₂×C₃₇	semidirect
293. #3131	C₂×C₃₇	semidirect
294. #3091	C₂×C₃₇	semidirect
295. #3076	C₂×C₃₇	semidirect
296. C₂×#433	C₂×C₃₇	semidirect
322. #501	C₂²×C₃₇	semidirect
323. #501	C₂²×C₃₇	semidirect
324. #500	C₂²×C₃₇	semidirect
325. #499	C₂²×C₃₇	semidirect
326. #498	C₂²×C₃₇	semidirect
327. #491	C₂²×C₃₇	semidirect
328. #490	C₂²×C₃₇	semidirect
329. #489	C₂²×C₃₇	semidirect
330. #488	C₂²×C₃₇	semidirect
331. #488	C₂²×C₃₇	semidirect
332. #487	C₂²×C₃₇	semidirect
333. #486	C₂²×C₃₇	semidirect
342. #479	C₂²×C₃₇	semidirect
343. #479	C₂²×C₃₇	semidirect
344. #478	C₂²×C₃₇	semidirect
345. #478	C₂²×C₃₇	semidirect
346. #477	C₂²×C₃₇	semidirect
347. #476	C₂²×C₃₇	semidirect
348. #475	C₂²×C₃₇	semidirect
349. #474	C₂²×C₃₇	semidirect
361. C₃₇	#60859	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₇×#3458	2
C₃₇×#3455	2
C₃₇×#3244	2
C₃₇×#3243	2
C₃₇×#3242	2
C₃₇×#3241	2
C₃₇×#3162	2
C₃₇×#3160	2
C₃₇×#3135	2
C₃₇×#3131	2
C₃₇×#3091	2
C₃₇×#3076	2
C₂×C₃₇×#433	2
#60859	37

Subgroups — C37×#60859 #22682112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#60859 #22682112