Subgroups — C₃₇×#61737 #22682990

Order 9472.

2012 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3353	C₂	1	2	yes	maximal, complemented
4	C₃₇×#3343	C₂	1	4	yes	maximal, complemented
5	C₃₇×#3334	C₂	1	2	yes	maximal, complemented
6	C₃₇×#3330	C₂	1	2	yes	maximal, complemented
7	C₃₇×#3308	C₂	1	4	yes	maximal, complemented
8	C₃₇×#3298	C₂	1	2	yes	maximal, complemented
9	C₃₇×#3239	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#3230	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#3193	C₂	1	2	yes	maximal, complemented
12	C₃₇×#3188	C₂	1	2	yes	maximal, complemented
13	C₃₇×#3110	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#3105	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₇×#3092	C₂	1	2	yes	maximal, complemented
16	C₂×C₃₇×#484	C₂	1	2	yes	maximal, complemented
17	C₃₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₃₇	—	2	1	no	—
19	C₃₇×#556	C₂²	1	1	yes	characteristic, complemented
20	C₃₇×#554	—	2	1	no	—
21	C₃₇×#552	C₂²	1	2	yes	complemented
22	C₃₇×#551	—	2	2	no	—
23	D₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
24	C₃₇×#548	C₂²	1	2	yes	complemented
25	C₃₇×#547	—	2	1	no	—
26	C₃₇×#547	—	2	2	no	—
27	C₃₇×#547	—	2	1	no	—
28	C₃₇×#547	C₂²	1	2	yes	—
29	C₃₇×#547	C₂²	1	4	yes	—
30	C₃₇×#547	C₂²	1	2	yes	—
31	C₃₇×#547	C₂²	1	1	yes	characteristic, complemented
32	C₃₇×#547	C₂²	1	1	yes	characteristic, complemented
33	C₃₇×#546	—	2	1	no	—
34	C₃₇×#542	—	2	1	no	—
35	C₃₇×#539	—	2	2	no	—
36	C₃₇×#533	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
38	C₃₇×#529	C₂²	1	1	yes	characteristic
39	C₃₇×#525	C₂²	1	2	yes	—
40	C₂×#123×C₃₇	—	2	2	no	—
41	C₂×C₂²⋊Q₈×C₃₇	—	2	1	no	—
42	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	—
43	C₂×#121×C₃₇	C₂²	1	2	yes	—
44	C₃₇×#520	—	2	1	no	—
45	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
48	C₃₇×#501	C₂²	1	2	yes	complemented
49	C₃₇×#500	C₂²	1	2	yes	complemented
50	C₃₇×#489	C₂²	1	2	yes	complemented
51	C₃₇×#487	C₂²	1	2	yes	complemented
52	C₃₇×#484	C₂²	1	2	yes	—
53	C₃₇×#484	C₂²	1	2	yes	—
54	C₃₇×#484	C₂²	1	2	yes	—
55	C₃₇×#484	C₂²	1	1	yes	characteristic
56	C₃₇×#484	C₂²	1	2	yes	—
57	C₃₇×#484	C₂²	1	4	yes	complemented
58	C₃₇×#484	C₂²	1	4	yes	complemented
59	C₃₇×#483	C₂²	1	4	yes	complemented
60	C₃₇×#482	C₂²	1	4	yes	complemented
61	C₃₇×#481	C₂²	1	2	yes	—
62	C₃₇×#481	C₂²	1	1	yes	characteristic
63	C₃₇×#480	C₂²	1	4	yes	complemented
64	C₃₇×#480	C₂²	1	4	yes	complemented
65	C₃₇×#478	C₂²	1	2	yes	complemented
66	C₃₇×#477	C₂²	1	4	yes	complemented
67	C₃₇×#475	C₂²	1	2	yes	complemented
68	C₃₇×#474	C₂²	1	2	yes	complemented
69	C₃₇×#474	C₂²	1	2	yes	complemented
70	C₃₇×#468	C₂²	1	4	yes	complemented
71	C₃₇×#468	C₂²	1	4	yes	complemented
72	C₃₇×#466	C₂²	1	4	yes	complemented
73	C₃₇×#465	C₂²	1	4	yes	complemented
74	C₃₇×#463	C₂²	1	2	yes	complemented
75	C₃₇×#461	C₂²	1	2	yes	complemented
76	C₃₇×#450	C₂²	1	2	yes	—
77	C₃₇×#450	C₂²	1	1	yes	characteristic
78	C₃₇×#449	C₂²	1	4	yes	complemented
79	C₃₇×#448	C₂²	1	4	yes	complemented
80	C₃₇×#447	C₂²	1	1	yes	characteristic
81	C₃₇×#440	C₂²	1	4	yes	complemented
82	C₄×SD₁₆×C₃₇	C₂²	1	2	yes	complemented
83	C₄×D₈×C₃₇	C₂²	1	2	yes	complemented
84	C₃₇×#436	C₂²	1	2	yes	complemented
85	C₃₇×#435	C₂²	1	4	yes	complemented
86	C₈×D₄×C₃₇	C₂²	1	2	yes	complemented
87	C₃₇×#432	C₂²	1	1	yes	characteristic
88	C₃₇×#431	C₂²	1	1	yes	characteristic
89	C₃₇×#428	C₂²	1	4	yes	complemented
90	C₂×#107×C₃₇	C₂²	1	4	yes	complemented
91	C₃₇×#417	C₂²	1	4	yes	complemented
92	C₂×#103×C₃₇	C₂²	1	4	yes	complemented
93	C₃₇×#407	C₂²	1	2	yes	—
94	C₂×C₂²⋊C₈×C₃₇	C₂²	1	2	yes	—
95	C₂×#41×C₃₇	—	2	1	no	—
96	C₂×#41×C₃₇	—	2	4	no	—
97	C₂×#41×C₃₇	—	2	2	no	—
98	C₂×#41×C₃₇	—	2	2	no	—
99	C₂×#41×C₃₇	—	4	8	no	—
100	C₂×#41×C₃₇	C₂³	1	2	yes	—
101	C₂²×Q₈×C₃₇	—	2	1	no	—
102	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
103	C₂²×D₄×C₃₇	—	2	2	no	—
104	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
105	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₃₇	—	2	2	no	—
107	C₂³×C₄×C₃₇	—	2	1	no	—
108	C₂³×C₄×C₃₇	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₃₇	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₃₇	C₂³	1	4	yes	—
111	C₂×D₈×C₃₇	C₂³	1	2	yes	—
112	C₂×M₁₆×C₃₇	C₂³	1	4	yes	—
113	C₂²×C₈×C₃₇	C₂³	1	4	yes	—
114	C₄⋊Q₈×C₃₇	—	2	1	no	—
115	C₄⋊Q₈×C₃₇	—	2	1	no	—
116	C₄⋊Q₈×C₃₇	—	2	1	no	—
117	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
118	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
119	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
120	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
121	#126×C₃₇	—	2	2	no	—
122	#126×C₃₇	—	2	2	no	—
123	#126×C₃₇	—	2	1	no	—
124	#125×C₃₇	—	2	2	no	—
125	#125×C₃₇	—	2	1	no	—
126	#125×C₃₇	C₂³	1	1	yes	characteristic
127	#124×C₃₇	—	2	1	no	—
128	#124×C₃₇	—	2	2	no	—
129	#124×C₃₇	C₂³	1	1	yes	characteristic
130	#123×C₃₇	—	2	2	no	—
131	#123×C₃₇	—	2	2	no	—
132	#123×C₃₇	—	2	1	no	—
133	#123×C₃₇	—	2	4	no	—
134	#123×C₃₇	—	2	4	no	—
135	#123×C₃₇	—	2	4	no	—
136	#123×C₃₇	—	2	4	no	—
137	#123×C₃₇	—	2	2	no	—
138	#123×C₃₇	—	2	2	no	—
139	C₂²⋊Q₈×C₃₇	—	2	2	no	—
140	C₂²⋊Q₈×C₃₇	—	2	2	no	—
141	C₂²⋊Q₈×C₃₇	—	2	1	no	—
142	C₂²⋊Q₈×C₃₇	—	2	2	no	—
143	C₂²⋊Q₈×C₃₇	—	2	4	no	—
144	C₂²⋊Q₈×C₃₇	—	2	2	no	—
145	C₂²⋊Q₈×C₃₇	—	2	2	no	—
146	C₂²⋊Q₈×C₃₇	—	2	1	no	—
147	C₂²⋊Q₈×C₃₇	—	2	2	no	—
148	C₂²⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
149	C₂²⋊Q₈×C₃₇	C₂³	1	2	yes	—
150	C₂²⋊Q₈×C₃₇	C₂³	1	2	yes	—
151	C₂²⋊Q₈×C₃₇	C₂³	1	2	yes	—
152	C₂²⋊Q₈×C₃₇	C₂³	1	2	yes	—
153	#121×C₃₇	—	2	2	no	—
154	#121×C₃₇	—	2	1	no	—
155	#121×C₃₇	—	2	2	no	—
156	#121×C₃₇	—	2	2	no	—
157	#121×C₃₇	C₂³	1	4	yes	—
158	#121×C₃₇	C₂³	1	4	yes	—
159	#121×C₃₇	C₂³	1	1	yes	characteristic
160	#121×C₃₇	C₂³	1	2	yes	—
161	#120×C₃₇	—	2	2	no	—
162	C₄×Q₈×C₃₇	—	2	1	no	—
163	C₄×Q₈×C₃₇	—	2	1	no	—
164	C₄×Q₈×C₃₇	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
166	C₄×D₄×C₃₇	—	2	1	no	—
167	C₄×D₄×C₃₇	—	2	2	no	—
168	C₄×D₄×C₃₇	—	2	2	no	—
169	C₄×D₄×C₃₇	—	2	1	no	—
170	C₄×D₄×C₃₇	—	2	2	no	—
171	C₄×D₄×C₃₇	—	2	1	no	—
172	C₄×D₄×C₃₇	—	2	1	no	—
173	C₄×D₄×C₃₇	D₄	1	1	yes	characteristic
174	C₄×D₄×C₃₇	D₄	1	2	yes	—
175	C₄×D₄×C₃₇	D₄	1	1	yes	characteristic
176	C₄×D₄×C₃₇	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₃₇	C₂³	1	2	yes	—
178	C₄×D₄×C₃₇	C₂³	1	2	yes	—
179	C₄×D₄×C₃₇	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₃₇	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₃₇	C₂³	1	2	yes	—
182	#117×C₃₇	—	2	1	no	—
183	#117×C₃₇	—	2	2	no	—
184	#117×C₃₇	—	2	1	no	—
185	#117×C₃₇	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
187	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
188	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
189	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
190	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
191	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
192	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
196	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
197	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
201	C₂×C₂²⋊C₄×C₃₇	D₄	1	2	yes	—
202	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
203	#107×C₃₇	C₂³	1	2	yes	—
204	#107×C₃₇	C₂³	1	4	yes	—
205	#107×C₃₇	C₂³	1	4	yes	—
206	#107×C₃₇	C₂³	1	4	yes	—
207	#107×C₃₇	C₂³	1	4	yes	—
208	#106×C₃₇	C₂³	1	2	yes	—
209	#106×C₃₇	C₂³	1	4	yes	—
210	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
211	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
212	#103×C₃₇	C₂³	1	2	yes	—
213	#103×C₃₇	C₂³	1	4	yes	—
214	#103×C₃₇	C₂³	1	4	yes	—
215	#103×C₃₇	C₂³	1	4	yes	—
216	#103×C₃₇	C₂³	1	4	yes	—
217	#102×C₃₇	C₂³	1	2	yes	—
218	#102×C₃₇	C₂³	1	4	yes	—
219	#102×C₃₇	C₂³	1	2	yes	—
220	#102×C₃₇	C₂³	1	2	yes	—
221	#102×C₃₇	C₂³	1	4	yes	—
222	C₂²⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
223	C₂²⋊C₈×C₃₇	C₂³	1	2	yes	—
224	C₂²⋊C₈×C₃₇	C₂³	1	4	yes	—
225	C₂²⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
226	C₂²⋊C₈×C₃₇	C₂³	1	4	yes	—
227	#97×C₃₇	C₂³	1	2	yes	—
228	C₄×C₈×C₃₇	C₂³	1	2	yes	—
229	C₂⁴×C₃₇	—	2	1	no	—
230	C₂⁴×C₃₇	C₂×D₄	1	2	yes	—
231	#41×C₃₇	—	4	4	no	—
232	#41×C₃₇	—	4	16	no	—
233	#41×C₃₇	—	4	8	no	—
234	#41×C₃₇	—	4	4	no	—
235	#41×C₃₇	—	4	8	no	—
236	C₂×Q₈×C₃₇	—	2	1	no	—
237	C₂×Q₈×C₃₇	—	2	2	no	—
238	C₂×Q₈×C₃₇	—	2	2	no	—
239	C₂×Q₈×C₃₇	—	2	2	no	—
240	C₂×Q₈×C₃₇	—	4	4	no	—
241	C₂×Q₈×C₃₇	—	4	4	no	—
242	C₂×Q₈×C₃₇	C₂⁴	1	1	yes	characteristic
243	C₂×Q₈×C₃₇	C₂⁴	1	2	yes	—
244	C₂×D₄×C₃₇	—	2	4	no	—
245	C₂×D₄×C₃₇	—	2	1	no	—
246	C₂×D₄×C₃₇	—	2	2	no	—
247	C₂×D₄×C₃₇	—	2	4	no	—
248	C₂×D₄×C₃₇	—	2	4	no	—
249	C₂×D₄×C₃₇	—	2	2	no	—
250	C₂×D₄×C₃₇	—	2	1	no	—
251	C₂×D₄×C₃₇	—	4	2	no	—
252	C₂×D₄×C₃₇	—	4	8	no	—
253	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
254	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
255	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₃₇	C₂⁴	1	1	yes	characteristic
257	C₂×D₄×C₃₇	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₃₇	—	2	1	no	—
259	C₂²×C₄×C₃₇	—	2	2	no	—
260	C₂²×C₄×C₃₇	—	2	2	no	—
261	C₂²×C₄×C₃₇	—	2	4	no	—
262	C₂²×C₄×C₃₇	—	2	4	no	—
263	C₂²×C₄×C₃₇	—	2	2	no	—
264	C₂²×C₄×C₃₇	—	2	1	no	—
265	C₂²×C₄×C₃₇	—	2	2	no	—
266	C₂²×C₄×C₃₇	—	2	2	no	—
267	C₂²×C₄×C₃₇	—	2	2	no	—
268	C₂²×C₄×C₃₇	—	4	4	no	—
269	C₂²×C₄×C₃₇	—	4	4	no	—
270	C₂²×C₄×C₃₇	—	4	8	no	—
271	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
279	SD₁₆×C₃₇	—	4	4	no	—
280	SD₁₆×C₃₇	—	4	2	no	—
281	D₈×C₃₇	—	4	2	no	—
282	M₁₆×C₃₇	—	4	4	no	—
283	C₂×C₈×C₃₇	—	4	4	no	—
284	C₂×C₈×C₃₇	C₂⁴	1	2	yes	—
285	C₂×C₈×C₃₇	C₂⁴	1	2	yes	—
286	C₂×C₈×C₃₇	C₂⁴	1	4	yes	—
287	C₄⋊C₄×C₃₇	—	2	1	no	—
288	C₄⋊C₄×C₃₇	—	2	2	no	—
289	C₄⋊C₄×C₃₇	—	2	4	no	—
290	C₄⋊C₄×C₃₇	—	2	4	no	—
291	C₄⋊C₄×C₃₇	—	2	1	no	—
292	C₄⋊C₄×C₃₇	—	2	2	no	—
293	C₄⋊C₄×C₃₇	—	2	1	no	—
294	C₄⋊C₄×C₃₇	—	2	2	no	—
295	C₄⋊C₄×C₃₇	—	2	2	no	—
296	C₄⋊C₄×C₃₇	—	2	2	no	—
297	C₄⋊C₄×C₃₇	—	2	2	no	—
298	C₄⋊C₄×C₃₇	—	2	2	no	—
299	C₄⋊C₄×C₃₇	—	2	1	no	—
300	C₄⋊C₄×C₃₇	—	2	1	no	—
301	C₄⋊C₄×C₃₇	—	2	1	no	—
302	C₄⋊C₄×C₃₇	—	2	2	no	—
303	C₄⋊C₄×C₃₇	—	2	1	no	—
304	C₄⋊C₄×C₃₇	—	2	2	no	—
305	C₄⋊C₄×C₃₇	—	2	1	no	—
306	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
307	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
308	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
309	C₄⋊C₄×C₃₇	C₂⁴	1	1	yes	characteristic
310	C₄⋊C₄×C₃₇	C₂⁴	1	1	yes	characteristic
311	C₄⋊C₄×C₃₇	C₂⁴	1	2	yes	—
312	C₄⋊C₄×C₃₇	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
314	C₂²⋊C₄×C₃₇	—	2	1	no	—
315	C₂²⋊C₄×C₃₇	—	2	2	no	—
316	C₂²⋊C₄×C₃₇	—	2	2	no	—
317	C₂²⋊C₄×C₃₇	—	2	2	no	—
318	C₂²⋊C₄×C₃₇	—	2	2	no	—
319	C₂²⋊C₄×C₃₇	—	2	2	no	—
320	C₂²⋊C₄×C₃₇	—	2	2	no	—
321	C₂²⋊C₄×C₃₇	—	2	2	no	—
322	C₂²⋊C₄×C₃₇	—	2	4	no	—
323	C₂²⋊C₄×C₃₇	—	2	4	no	—
324	C₂²⋊C₄×C₃₇	—	2	1	no	—
325	C₂²⋊C₄×C₃₇	—	2	1	no	—
326	C₂²⋊C₄×C₃₇	—	2	1	no	—
327	C₂²⋊C₄×C₃₇	—	2	2	no	—
328	C₂²⋊C₄×C₃₇	—	2	1	no	—
329	C₂²⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
333	C₄²×C₃₇	—	2	2	no	—
334	C₄²×C₃₇	—	2	2	no	—
335	C₄²×C₃₇	—	2	1	no	—
336	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
339	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
340	C₂³×C₃₇	—	2	4	no	—
341	C₂³×C₃₇	—	2	4	no	—
342	C₂³×C₃₇	—	2	1	no	—
343	C₂³×C₃₇	—	2	2	no	—
344	C₂³×C₃₇	—	4	2	no	—
345	C₂³×C₃₇	—	4	2	no	—
346	C₂³×C₃₇	—	4	2	no	—
347	C₂³×C₃₇	—	4	2	no	—
348	C₂³×C₃₇	C₂²×D₄	1	2	yes	—
349	C₂³×C₃₇	C₂²×D₄	1	2	yes	—
350	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
351	Q₈×C₃₇	—	2	2	no	—
352	Q₈×C₃₇	—	2	4	no	—
353	Q₈×C₃₇	—	4	4	no	—
354	Q₈×C₃₇	—	4	4	no	—
355	Q₈×C₃₇	—	4	2	no	—
356	Q₈×C₃₇	—	8	2	no	—
357	D₄×C₃₇	—	2	4	no	—
358	D₄×C₃₇	—	2	2	no	—
359	D₄×C₃₇	—	2	2	no	—
360	D₄×C₃₇	—	2	2	no	—
361	D₄×C₃₇	—	2	2	no	—
362	D₄×C₃₇	—	4	2	no	—
363	D₄×C₃₇	—	4	8	no	—
364	D₄×C₃₇	—	4	8	no	—
365	D₄×C₃₇	—	4	4	no	—
366	D₄×C₃₇	—	4	2	no	—
367	D₄×C₃₇	—	8	2	no	—
368	D₄×C₃₇	AGL(1,ℤ/8)	1	4	yes	—
369	C₂×C₄×C₃₇	—	2	2	no	—
370	C₂×C₄×C₃₇	—	2	2	no	—
371	C₂×C₄×C₃₇	—	2	4	no	—
372	C₂×C₄×C₃₇	—	2	4	no	—
373	C₂×C₄×C₃₇	—	2	2	no	—
374	C₂×C₄×C₃₇	—	2	1	no	—
375	C₂×C₄×C₃₇	—	2	2	no	—
376	C₂×C₄×C₃₇	—	2	1	no	—
377	C₂×C₄×C₃₇	—	2	2	no	—
378	C₂×C₄×C₃₇	—	2	1	no	—
379	C₂×C₄×C₃₇	—	2	2	no	—
380	C₂×C₄×C₃₇	—	2	4	no	—
381	C₂×C₄×C₃₇	—	4	2	no	—
382	C₂×C₄×C₃₇	—	4	2	no	—
383	C₂×C₄×C₃₇	—	4	2	no	—
384	C₂×C₄×C₃₇	—	4	4	no	—
385	C₂×C₄×C₃₇	—	4	2	no	—
386	C₂×C₄×C₃₇	—	4	4	no	—
387	C₂×C₄×C₃₇	—	4	8	no	—
388	C₂×C₄×C₃₇	—	4	8	no	—
389	C₂×C₄×C₃₇	—	4	4	no	—
390	C₂×C₄×C₃₇	—	4	4	no	—
391	C₂×C₄×C₃₇	—	4	2	no	—
392	C₂×C₄×C₃₇	—	8	2	no	—
393	C₂×C₄×C₃₇	—	8	2	no	—
394	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
402	C₈×C₃₇	—	2	2	no	—
403	C₈×C₃₇	—	2	4	no	—
404	C₈×C₃₇	—	2	2	no	—
405	#61737	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
406	C₂²×C₃₇	—	2	1	no	—
407	C₂²×C₃₇	—	2	2	no	—
408	C₂²×C₃₇	—	2	1	no	—
409	C₂²×C₃₇	—	2	2	no	—
410	C₂²×C₃₇	—	2	2	no	—
411	C₂²×C₃₇	—	2	2	no	—
412	C₂²×C₃₇	—	2	2	no	—
413	C₂²×C₃₇	—	4	8	no	—
414	C₂²×C₃₇	—	4	1	no	—
415	C₂²×C₃₇	—	4	2	no	—
416	C₂²×C₃₇	—	4	2	no	—
417	C₂²×C₃₇	—	4	1	no	—
418	C₂²×C₃₇	—	4	1	no	—
419	C₂²×C₃₇	—	4	2	no	—
420	C₂²×C₃₇	—	8	4	no	—
421	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
422	C₂²×C₃₇	#578	1	2	yes	—
423	C₂²×C₃₇	C₂³×D₄	1	1	yes	characteristic
424	C₄×C₃₇	—	2	1	no	—
425	C₄×C₃₇	—	2	2	no	—
426	C₄×C₃₇	—	2	2	no	—
427	C₄×C₃₇	—	2	1	no	—
428	C₄×C₃₇	—	2	1	no	—
429	C₄×C₃₇	—	2	1	no	—
430	C₄×C₃₇	—	4	2	no	—
431	C₄×C₃₇	—	4	1	no	—
432	C₄×C₃₇	—	4	1	no	—
433	C₄×C₃₇	—	4	2	no	—
434	C₄×C₃₇	—	4	4	no	—
435	C₄×C₃₇	—	4	2	no	—
436	C₄×C₃₇	—	4	1	no	—
437	C₄×C₃₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
438	C₄×C₃₇	#585	1	2	yes	—
439	#3520	C₂×C₃₇	1	1	yes	characteristic, complemented
440	C₂×#547	C₂×C₃₇	1	1	yes	characteristic, complemented
441	#3353	C₂×C₃₇	1	2	yes	complemented
442	#3343	C₂×C₃₇	1	4	yes	complemented
443	#3334	C₂×C₃₇	1	2	yes	complemented
444	#3330	C₂×C₃₇	1	2	yes	complemented
445	#3308	C₂×C₃₇	1	4	yes	complemented
446	#3298	C₂×C₃₇	1	2	yes	complemented
447	#3239	C₂×C₃₇	1	1	yes	characteristic, complemented
448	#3230	C₂×C₃₇	1	1	yes	characteristic, complemented
449	#3193	C₂×C₃₇	1	2	yes	complemented
450	#3188	C₂×C₃₇	1	2	yes	complemented
451	#3110	C₂×C₃₇	1	1	yes	characteristic, complemented
452	#3105	C₂×C₃₇	1	1	yes	characteristic, complemented
453	#3092	C₂×C₃₇	1	2	yes	complemented
454	C₂×#484	C₂×C₃₇	1	2	yes	complemented
455	#2974	C₂×C₃₇	1	1	yes	characteristic, complemented
456	C₂×C₃₇	—	2	2	no	—
457	C₂×C₃₇	—	2	4	no	—
458	C₂×C₃₇	—	4	2	no	—
459	C₂×C₃₇	—	8	1	no	—
460	C₂×C₃₇	—	8	2	no	—
461	C₂×C₃₇	#3485	1	1	yes	characteristic
462	C₂×C₃₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
463	C₂×C₃₇	C₂×#578	1	1	yes	characteristic
464	C₂²×#41	—	2	1	no	—
465	#556	C₂²×C₃₇	1	1	yes	characteristic, complemented
466	#554	—	2	1	no	—
467	#552	C₂²×C₃₇	1	2	yes	complemented
468	#551	—	2	2	no	—
469	D₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic, complemented
470	#548	C₂²×C₃₇	1	2	yes	complemented
471	#547	—	2	1	no	—
472	#547	—	2	2	no	—
473	#547	—	2	1	no	—
474	#547	C₂²×C₃₇	1	2	yes	—
475	#547	C₂²×C₃₇	1	2	yes	—
476	#547	C₂²×C₃₇	1	4	yes	—
477	#547	C₂²×C₃₇	1	1	yes	characteristic, complemented
478	#547	C₂²×C₃₇	1	1	yes	characteristic, complemented
479	#546	—	2	1	no	—
480	#542	—	2	1	no	—
481	#539	—	2	2	no	—
482	#533	C₂²×C₃₇	1	1	yes	characteristic
483	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
484	#529	C₂²×C₃₇	1	1	yes	characteristic
485	#525	C₂²×C₃₇	1	2	yes	—
486	C₂×#123	—	2	2	no	—
487	C₂×C₂²⋊Q₈	—	2	1	no	—
488	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	2	yes	—
489	C₂×#121	C₂²×C₃₇	1	2	yes	—
490	#520	—	2	1	no	—
491	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
492	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
493	C₂²×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
494	#501	C₂²×C₃₇	1	2	yes	complemented
495	#500	C₂²×C₃₇	1	2	yes	complemented
496	#489	C₂²×C₃₇	1	2	yes	complemented
497	#487	C₂²×C₃₇	1	2	yes	complemented
498	#484	C₂²×C₃₇	1	1	yes	characteristic
499	#484	C₂²×C₃₇	1	2	yes	—
500	#484	C₂²×C₃₇	1	2	yes	—
501	#484	C₂²×C₃₇	1	2	yes	—
502	#484	C₂²×C₃₇	1	2	yes	—
503	#484	C₂²×C₃₇	1	4	yes	complemented
504	#484	C₂²×C₃₇	1	4	yes	complemented
505	#483	C₂²×C₃₇	1	4	yes	complemented
506	#482	C₂²×C₃₇	1	4	yes	complemented
507	#481	C₂²×C₃₇	1	1	yes	characteristic
508	#481	C₂²×C₃₇	1	2	yes	—
509	#480	C₂²×C₃₇	1	4	yes	complemented
510	#480	C₂²×C₃₇	1	4	yes	complemented
511	#478	C₂²×C₃₇	1	2	yes	complemented
512	#477	C₂²×C₃₇	1	4	yes	complemented
513	#475	C₂²×C₃₇	1	2	yes	complemented
514	#474	C₂²×C₃₇	1	2	yes	complemented
515	#474	C₂²×C₃₇	1	2	yes	complemented
516	#468	C₂²×C₃₇	1	4	yes	complemented
517	#468	C₂²×C₃₇	1	4	yes	complemented
518	#466	C₂²×C₃₇	1	4	yes	complemented
519	#465	C₂²×C₃₇	1	4	yes	complemented
520	#463	C₂²×C₃₇	1	2	yes	complemented
521	#461	C₂²×C₃₇	1	2	yes	complemented
522	#450	C₂²×C₃₇	1	1	yes	characteristic
523	#450	C₂²×C₃₇	1	2	yes	—
524	#449	C₂²×C₃₇	1	4	yes	complemented
525	#448	C₂²×C₃₇	1	4	yes	complemented
526	#447	C₂²×C₃₇	1	1	yes	characteristic
527	#440	C₂²×C₃₇	1	4	yes	complemented
528	C₄×SD₁₆	C₂²×C₃₇	1	2	yes	complemented
529	C₄×D₈	C₂²×C₃₇	1	2	yes	complemented
530	#436	C₂²×C₃₇	1	2	yes	complemented
531	#435	C₂²×C₃₇	1	4	yes	complemented
532	C₈×D₄	C₂²×C₃₇	1	2	yes	complemented
533	#432	C₂²×C₃₇	1	1	yes	characteristic
534	#431	C₂²×C₃₇	1	1	yes	characteristic
535	#428	C₂²×C₃₇	1	4	yes	complemented
536	C₂×#107	C₂²×C₃₇	1	4	yes	complemented
537	#417	C₂²×C₃₇	1	4	yes	complemented
538	C₂×#103	C₂²×C₃₇	1	4	yes	complemented
539	#407	C₂²×C₃₇	1	2	yes	—
540	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	—
541	C₃₇	#61737	1	1	yes	characteristic, direct product factor, Sylow
542	C₂×#41	—	2	1	no	—
543	C₂×#41	—	2	4	no	—
544	C₂×#41	—	2	2	no	—
545	C₂×#41	—	2	2	no	—
546	C₂×#41	—	4	8	no	—
547	C₂×#41	C₂³×C₃₇	1	2	yes	—
548	C₂²×Q₈	—	2	1	no	—
549	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
550	C₂²×D₄	—	2	2	no	—
551	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
552	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
553	C₂³×C₄	—	2	2	no	—
554	C₂³×C₄	—	2	1	no	—
555	C₂³×C₄	C₂³×C₃₇	1	2	yes	—
556	C₂×SD₁₆	C₂³×C₃₇	1	2	yes	—
557	C₂×SD₁₆	C₂³×C₃₇	1	4	yes	—
558	C₂×D₈	C₂³×C₃₇	1	2	yes	—
559	C₂×M₁₆	C₂³×C₃₇	1	4	yes	—
560	C₂²×C₈	C₂³×C₃₇	1	4	yes	—
561	C₄⋊Q₈	—	2	1	no	—
562	C₄⋊Q₈	—	2	1	no	—
563	C₄⋊Q₈	—	2	1	no	—
564	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
565	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
566	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
567	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
568	#126	—	2	2	no	—
569	#126	—	2	2	no	—
570	#126	—	2	1	no	—
571	#125	—	2	2	no	—
572	#125	—	2	1	no	—
573	#125	C₂³×C₃₇	1	1	yes	characteristic
574	#124	—	2	1	no	—
575	#124	—	2	2	no	—
576	#124	C₂³×C₃₇	1	1	yes	characteristic
577	#123	—	2	2	no	—
578	#123	—	2	2	no	—
579	#123	—	2	1	no	—
580	#123	—	2	4	no	—
581	#123	—	2	4	no	—
582	#123	—	2	4	no	—
583	#123	—	2	4	no	—
584	#123	—	2	2	no	—
585	#123	—	2	2	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	2	no	—
588	C₂²⋊Q₈	—	2	1	no	—
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	—	2	4	no	—
591	C₂²⋊Q₈	—	2	2	no	—
592	C₂²⋊Q₈	—	2	2	no	—
593	C₂²⋊Q₈	—	2	1	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
596	C₂²⋊Q₈	C₂³×C₃₇	1	2	yes	—
597	C₂²⋊Q₈	C₂³×C₃₇	1	2	yes	—
598	C₂²⋊Q₈	C₂³×C₃₇	1	2	yes	—
599	C₂²⋊Q₈	C₂³×C₃₇	1	2	yes	—
600	#121	—	2	2	no	—
601	#121	—	2	1	no	—
602	#121	—	2	2	no	—
603	#121	—	2	2	no	—
604	#121	C₂³×C₃₇	1	4	yes	—
605	#121	C₂³×C₃₇	1	4	yes	—
606	#121	C₂³×C₃₇	1	1	yes	characteristic
607	#121	C₂³×C₃₇	1	2	yes	—
608	#120	—	2	2	no	—
609	C₄×Q₈	—	2	1	no	—
610	C₄×Q₈	—	2	1	no	—
611	C₄×Q₈	C₂³×C₃₇	1	1	yes	characteristic
612	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	D₄×C₃₇	1	1	yes	characteristic
621	C₄×D₄	D₄×C₃₇	1	2	yes	—
622	C₄×D₄	D₄×C₃₇	1	1	yes	characteristic
623	C₄×D₄	C₂³×C₃₇	1	2	yes	—
624	C₄×D₄	C₂³×C₃₇	1	2	yes	—
625	C₄×D₄	C₂³×C₃₇	1	1	yes	characteristic
626	C₄×D₄	C₂³×C₃₇	1	1	yes	characteristic
627	C₄×D₄	C₂³×C₃₇	1	1	yes	characteristic
628	C₄×D₄	C₂³×C₃₇	1	2	yes	—
629	#117	—	2	1	no	—
630	#117	—	2	2	no	—
631	#117	—	2	1	no	—
632	#117	C₂³×C₃₇	1	2	yes	—
633	C₂×C₄⋊C₄	—	2	2	no	—
634	C₂×C₄⋊C₄	—	2	2	no	—
635	C₂×C₄⋊C₄	—	2	2	no	—
636	C₂×C₄⋊C₄	—	2	2	no	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	—	2	1	no	—
639	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
643	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
644	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
645	C₂×C₂²⋊C₄	—	2	2	no	—
646	C₂×C₂²⋊C₄	—	2	1	no	—
647	C₂×C₂²⋊C₄	—	2	2	no	—
648	C₂×C₂²⋊C₄	D₄×C₃₇	1	2	yes	—
649	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
650	#107	C₂³×C₃₇	1	2	yes	—
651	#107	C₂³×C₃₇	1	4	yes	—
652	#107	C₂³×C₃₇	1	4	yes	—
653	#107	C₂³×C₃₇	1	4	yes	—
654	#107	C₂³×C₃₇	1	4	yes	—
655	#106	C₂³×C₃₇	1	2	yes	—
656	#106	C₂³×C₃₇	1	4	yes	—
657	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
658	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
659	#103	C₂³×C₃₇	1	2	yes	—
660	#103	C₂³×C₃₇	1	4	yes	—
661	#103	C₂³×C₃₇	1	4	yes	—
662	#103	C₂³×C₃₇	1	4	yes	—
663	#103	C₂³×C₃₇	1	4	yes	—
664	#102	C₂³×C₃₇	1	2	yes	—
665	#102	C₂³×C₃₇	1	4	yes	—
666	#102	C₂³×C₃₇	1	2	yes	—
667	#102	C₂³×C₃₇	1	2	yes	—
668	#102	C₂³×C₃₇	1	4	yes	—
669	C₂²⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
670	C₂²⋊C₈	C₂³×C₃₇	1	2	yes	—
671	C₂²⋊C₈	C₂³×C₃₇	1	4	yes	—
672	C₂²⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
673	C₂²⋊C₈	C₂³×C₃₇	1	4	yes	—
674	#97	C₂³×C₃₇	1	2	yes	—
675	C₄×C₈	C₂³×C₃₇	1	2	yes	—
676	C₂⁴	—	2	1	no	—
677	C₂⁴	C₂×D₄×C₃₇	1	2	yes	—
678	#41	—	4	4	no	—
679	#41	—	4	16	no	—
680	#41	—	4	8	no	—
681	#41	—	4	4	no	—
682	#41	—	4	8	no	—
683	C₂×Q₈	—	2	1	no	—
684	C₂×Q₈	—	2	2	no	—
685	C₂×Q₈	—	2	2	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	4	4	no	—
688	C₂×Q₈	—	4	4	no	—
689	C₂×Q₈	C₂⁴×C₃₇	1	1	yes	characteristic
690	C₂×Q₈	C₂⁴×C₃₇	1	2	yes	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	—	4	8	no	—
700	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
701	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
702	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
703	C₂×D₄	C₂⁴×C₃₇	1	1	yes	characteristic
704	C₂×D₄	C₂⁴×C₃₇	1	2	yes	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	4	4	no	—
716	C₂²×C₄	—	4	4	no	—
717	C₂²×C₄	—	4	8	no	—
718	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
719	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
721	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
722	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
726	SD₁₆	—	4	4	no	—
727	SD₁₆	—	4	2	no	—
728	D₈	—	4	2	no	—
729	M₁₆	—	4	4	no	—
730	C₂×C₈	—	4	4	no	—
731	C₂×C₈	C₂⁴×C₃₇	1	2	yes	—
732	C₂×C₈	C₂⁴×C₃₇	1	2	yes	—
733	C₂×C₈	C₂⁴×C₃₇	1	4	yes	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
754	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
755	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
756	C₄⋊C₄	C₂⁴×C₃₇	1	1	yes	characteristic
757	C₄⋊C₄	C₂⁴×C₃₇	1	1	yes	characteristic
758	C₄⋊C₄	C₂⁴×C₃₇	1	2	yes	—
759	C₄⋊C₄	C₂⁴×C₃₇	1	2	yes	—
760	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
761	C₂²⋊C₄	—	2	1	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	1	no	—
772	C₂²⋊C₄	—	2	1	no	—
773	C₂²⋊C₄	—	2	1	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
777	C₂²⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
778	C₂²⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
779	C₂²⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
780	C₄²	—	2	2	no	—
781	C₄²	—	2	2	no	—
782	C₄²	—	2	1	no	—
783	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
784	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
785	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
786	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
787	C₂³	—	2	4	no	—
788	C₂³	—	2	4	no	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	4	2	no	—
792	C₂³	—	4	2	no	—
793	C₂³	—	4	2	no	—
794	C₂³	—	4	2	no	—
795	C₂³	C₂²×D₄×C₃₇	1	2	yes	—
796	C₂³	C₂²×D₄×C₃₇	1	2	yes	—
797	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
798	Q₈	—	2	2	no	—
799	Q₈	—	2	4	no	—
800	Q₈	—	4	4	no	—
801	Q₈	—	4	4	no	—
802	Q₈	—	4	2	no	—
803	Q₈	—	8	2	no	—
804	D₄	—	2	4	no	—
805	D₄	—	2	2	no	—
806	D₄	—	2	2	no	—
807	D₄	—	2	2	no	—
808	D₄	—	2	2	no	—
809	D₄	—	4	2	no	—
810	D₄	—	4	8	no	—
811	D₄	—	4	8	no	—
812	D₄	—	4	4	no	—
813	D₄	—	4	2	no	—
814	D₄	—	8	2	no	—
815	D₄	AGL(1,ℤ/8)×C₃₇	1	4	yes	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	4	no	—
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	4	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	2	no	—
831	C₂×C₄	—	4	4	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	8	no	—
835	C₂×C₄	—	4	8	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	4	4	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	8	2	no	—
840	C₂×C₄	—	8	2	no	—
841	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
843	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
848	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
849	C₈	—	2	2	no	—
850	C₈	—	2	4	no	—
851	C₈	—	2	2	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	2	no	—
856	C₂²	—	2	2	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	4	8	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	8	4	no	—
867	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	4	yes	—
868	C₂²	C₃₇×#578	1	2	yes	—
869	C₂²	C₂³×D₄×C₃₇	1	1	yes	characteristic
870	C₄	—	2	1	no	—
871	C₄	—	2	2	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	1	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	4	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	1	no	—
883	C₄	C₂×AGL(1,ℤ/8)×C₃₇	1	2	yes	—
884	C₄	C₃₇×#585	1	2	yes	—
885	C₂	—	2	2	no	—
886	C₂	—	2	4	no	—
887	C₂	—	4	2	no	—
888	C₂	—	8	2	no	—
889	C₂	—	8	1	no	—
890	C₂	C₃₇×#3485	1	1	yes	characteristic
891	C₂	C₂²×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
892	C₂	C₂×C₃₇×#578	1	1	yes	characteristic

	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 ◁ C₂×C₄×D₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3520	C₂	semidirect
2. C₂×C₃₇×#547	C₂	semidirect
3. C₃₇×#3353	C₂	semidirect
4. C₃₇×#3343	C₂	semidirect
5. C₃₇×#3334	C₂	semidirect
6. C₃₇×#3330	C₂	semidirect
7. C₃₇×#3308	C₂	semidirect
8. C₃₇×#3298	C₂	semidirect
9. C₃₇×#3239	C₂	semidirect
10. C₃₇×#3230	C₂	semidirect
11. C₃₇×#3193	C₂	semidirect
12. C₃₇×#3188	C₂	semidirect
13. C₃₇×#3110	C₂	semidirect
14. C₃₇×#3105	C₂	semidirect
15. C₃₇×#3092	C₂	semidirect
16. C₂×C₃₇×#484	C₂	semidirect
17. C₃₇×#2974	C₂	semidirect
19. C₃₇×#556	C₂²	semidirect
21. C₃₇×#552	C₂²	semidirect
23. D₄×Q₈×C₃₇	C₂²	semidirect
24. C₃₇×#548	C₂²	semidirect
31. C₃₇×#547	C₂²	semidirect
32. C₃₇×#547	C₂²	semidirect
48. C₃₇×#501	C₂²	semidirect
49. C₃₇×#500	C₂²	semidirect
50. C₃₇×#489	C₂²	semidirect
51. C₃₇×#487	C₂²	semidirect
57. C₃₇×#484	C₂²	semidirect
58. C₃₇×#484	C₂²	semidirect
59. C₃₇×#483	C₂²	semidirect
60. C₃₇×#482	C₂²	semidirect
63. C₃₇×#480	C₂²	semidirect
64. C₃₇×#480	C₂²	semidirect
65. C₃₇×#478	C₂²	semidirect
66. C₃₇×#477	C₂²	semidirect
67. C₃₇×#475	C₂²	semidirect
68. C₃₇×#474	C₂²	semidirect
69. C₃₇×#474	C₂²	semidirect
70. C₃₇×#468	C₂²	semidirect
71. C₃₇×#468	C₂²	semidirect
72. C₃₇×#466	C₂²	semidirect
73. C₃₇×#465	C₂²	semidirect
74. C₃₇×#463	C₂²	semidirect
75. C₃₇×#461	C₂²	semidirect
78. C₃₇×#449	C₂²	semidirect
79. C₃₇×#448	C₂²	semidirect
81. C₃₇×#440	C₂²	semidirect
82. C₄×SD₁₆×C₃₇	C₂²	semidirect
83. C₄×D₈×C₃₇	C₂²	semidirect
84. C₃₇×#436	C₂²	semidirect
85. C₃₇×#435	C₂²	semidirect
86. C₈×D₄×C₃₇	C₂²	semidirect
89. C₃₇×#428	C₂²	semidirect
90. C₂×#107×C₃₇	C₂²	semidirect
91. C₃₇×#417	C₂²	semidirect
92. C₂×#103×C₃₇	C₂²	semidirect
405. #61737	C₃₇	direct (N × H)
439. #3520	C₂×C₃₇	semidirect
440. C₂×#547	C₂×C₃₇	semidirect
441. #3353	C₂×C₃₇	semidirect
442. #3343	C₂×C₃₇	semidirect
443. #3334	C₂×C₃₇	semidirect
444. #3330	C₂×C₃₇	semidirect
445. #3308	C₂×C₃₇	semidirect
446. #3298	C₂×C₃₇	semidirect
447. #3239	C₂×C₃₇	semidirect
448. #3230	C₂×C₃₇	semidirect
449. #3193	C₂×C₃₇	semidirect
450. #3188	C₂×C₃₇	semidirect
451. #3110	C₂×C₃₇	semidirect
452. #3105	C₂×C₃₇	semidirect
453. #3092	C₂×C₃₇	semidirect
454. C₂×#484	C₂×C₃₇	semidirect
455. #2974	C₂×C₃₇	semidirect
465. #556	C₂²×C₃₇	semidirect
467. #552	C₂²×C₃₇	semidirect
469. D₄×Q₈	C₂²×C₃₇	semidirect
470. #548	C₂²×C₃₇	semidirect
477. #547	C₂²×C₃₇	semidirect
478. #547	C₂²×C₃₇	semidirect
494. #501	C₂²×C₃₇	semidirect
495. #500	C₂²×C₃₇	semidirect
496. #489	C₂²×C₃₇	semidirect
497. #487	C₂²×C₃₇	semidirect
503. #484	C₂²×C₃₇	semidirect
504. #484	C₂²×C₃₇	semidirect
505. #483	C₂²×C₃₇	semidirect
506. #482	C₂²×C₃₇	semidirect
509. #480	C₂²×C₃₇	semidirect
510. #480	C₂²×C₃₇	semidirect
511. #478	C₂²×C₃₇	semidirect
512. #477	C₂²×C₃₇	semidirect
513. #475	C₂²×C₃₇	semidirect
514. #474	C₂²×C₃₇	semidirect
515. #474	C₂²×C₃₇	semidirect
516. #468	C₂²×C₃₇	semidirect
517. #468	C₂²×C₃₇	semidirect
518. #466	C₂²×C₃₇	semidirect
519. #465	C₂²×C₃₇	semidirect
520. #463	C₂²×C₃₇	semidirect
521. #461	C₂²×C₃₇	semidirect
524. #449	C₂²×C₃₇	semidirect
525. #448	C₂²×C₃₇	semidirect
527. #440	C₂²×C₃₇	semidirect
528. C₄×SD₁₆	C₂²×C₃₇	semidirect
529. C₄×D₈	C₂²×C₃₇	semidirect
530. #436	C₂²×C₃₇	semidirect
531. #435	C₂²×C₃₇	semidirect
532. C₈×D₄	C₂²×C₃₇	semidirect
535. #428	C₂²×C₃₇	semidirect
536. C₂×#107	C₂²×C₃₇	semidirect
537. #417	C₂²×C₃₇	semidirect
538. C₂×#103	C₂²×C₃₇	semidirect
541. C₃₇	#61737	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×#3520	2
C₂×C₃₇×#547	2
C₃₇×#3353	2
C₃₇×#3343	2
C₃₇×#3334	2
C₃₇×#3330	2
C₃₇×#3308	2
C₃₇×#3298	2
C₃₇×#3239	2
C₃₇×#3230	2
C₃₇×#3193	2
C₃₇×#3188	2
C₃₇×#3110	2
C₃₇×#3105	2
C₃₇×#3092	2
C₂×C₃₇×#484	2
C₃₇×#2974	2
#61737	37

Subgroups — C37×#61737 #22682990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#61737 #22682990