Subgroups — C₃₇×#62889 #22684142

Order 9472.

6186 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3564	C₂	1	8	yes	maximal, complemented
2	C₃₇×#3563	C₂	1	8	yes	maximal, complemented
3	C₃₇×#3563	C₂	1	8	yes	maximal, complemented
4	C₃₇×#3557	C₂	1	4	yes	maximal, complemented
5	C₃₇×#3556	C₂	1	4	yes	maximal, complemented
6	C₃₇×#3555	C₂	1	8	yes	maximal, complemented
7	C₃₇×#3555	C₂	1	8	yes	maximal, complemented
8	C₃₇×#3509	C₂	1	2	yes	maximal, complemented
9	C₃₇×#3507	C₂	1	2	yes	maximal, complemented
10	C₃₇×#3504	C₂	1	2	yes	maximal, complemented
11	C₃₇×#3502	C₂	1	2	yes	maximal, complemented
12	C₃₇×#3495	C₂	1	4	yes	maximal, complemented
13	C₃₇×#3458	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#3455	C₂	1	1	yes	maximal, characteristic
15	C₂×C₃₇×#541	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₇×#564	C₂²	1	16	yes	complemented
17	C₃₇×#563	C₂²	1	16	yes	—
18	C₃₇×#563	C₂²	1	16	yes	—
19	C₃₇×#563	C₂²	1	16	yes	complemented
20	C₃₇×#559	C₂²	1	4	yes	complemented
21	Q₈²×C₃₇	C₂²	1	4	yes	complemented
22	Q₈²×C₃₇	C₂²	1	4	yes	complemented
23	C₃₇×#557	C₂²	1	4	yes	complemented
24	C₃₇×#557	C₂²	1	8	yes	complemented
25	C₃₇×#557	C₂²	1	8	yes	complemented
26	C₃₇×#557	C₂²	1	4	yes	complemented
27	C₃₇×#557	C₂²	1	8	yes	complemented
28	C₃₇×#557	C₂²	1	4	yes	complemented
29	C₃₇×#557	C₂²	1	8	yes	complemented
30	C₃₇×#557	C₂²	1	16	yes	complemented
31	C₃₇×#556	C₂²	1	8	yes	—
32	C₃₇×#556	C₂²	1	16	yes	—
33	C₃₇×#556	C₂²	1	4	yes	complemented
34	C₃₇×#556	C₂²	1	8	yes	complemented
35	C₃₇×#556	C₂²	1	8	yes	complemented
36	C₃₇×#554	C₂²	1	8	yes	—
37	C₃₇×#554	C₂²	1	16	yes	—
38	C₃₇×#554	C₂²	1	8	yes	complemented
39	C₃₇×#554	C₂²	1	4	yes	complemented
40	C₃₇×#552	C₂²	1	8	yes	—
41	C₃₇×#552	C₂²	1	8	yes	—
42	C₃₇×#552	C₂²	1	16	yes	—
43	C₃₇×#552	C₂²	1	16	yes	—
44	C₃₇×#552	C₂²	1	16	yes	—
45	C₃₇×#552	C₂²	1	8	yes	complemented
46	C₃₇×#552	C₂²	1	16	yes	complemented
47	C₃₇×#551	C₂²	1	16	yes	—
48	C₃₇×#544	C₂²	1	4	yes	—
49	C₃₇×#544	C₂²	1	4	yes	—
50	C₃₇×#544	C₂²	1	4	yes	—
51	C₃₇×#544	C₂²	1	4	yes	—
52	C₃₇×#544	C₂²	1	8	yes	—
53	C₃₇×#544	C₂²	1	8	yes	complemented
54	C₃₇×#544	C₂²	1	16	yes	complemented
55	C₃₇×#543	C₂²	1	4	yes	—
56	C₃₇×#542	C₂²	1	4	yes	—
57	C₃₇×#542	C₂²	1	8	yes	—
58	C₃₇×#542	C₂²	1	16	yes	—
59	C₃₇×#541	C₂²	1	4	yes	—
60	C₃₇×#541	C₂²	1	8	yes	—
61	C₃₇×#541	C₂²	1	4	yes	—
62	C₃₇×#541	C₂²	1	2	yes	—
63	C₃₇×#541	C₂²	1	8	yes	—
64	C₃₇×#541	C₂²	1	16	yes	—
65	C₃₇×#541	C₂²	1	16	yes	—
66	C₃₇×#541	C₂²	1	4	yes	complemented
67	C₃₇×#541	C₂²	1	4	yes	complemented
68	C₃₇×#541	C₂²	1	16	yes	complemented
69	C₃₇×#541	C₂²	1	16	yes	complemented
70	C₃₇×#541	C₂²	1	16	yes	complemented
71	C₃₇×#540	C₂²	1	2	yes	—
72	C₃₇×#539	C₂²	1	4	yes	—
73	C₃₇×#539	C₂²	1	8	yes	—
74	C₃₇×#539	C₂²	1	16	yes	—
75	C₃₇×#538	C₂²	1	4	yes	—
76	C₃₇×#536	C₂²	1	4	yes	—
77	C₃₇×#533	C₂²	1	1	yes	characteristic
78	C₃₇×#533	C₂²	1	2	yes	—
79	C₃₇×#533	C₂²	1	2	yes	—
80	C₃₇×#533	C₂²	1	4	yes	—
81	C₃₇×#533	C₂²	1	4	yes	—
82	C₃₇×#533	C₂²	1	8	yes	—
83	C₃₇×#533	C₂²	1	8	yes	—
84	C₃₇×#533	C₂²	1	4	yes	complemented
85	C₃₇×#533	C₂²	1	8	yes	complemented
86	C₃₇×#532	C₂²	1	1	yes	characteristic
87	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
88	C₃₇×#529	C₂²	1	8	yes	—
89	C₃₇×#529	C₂²	1	8	yes	—
90	C₃₇×#529	C₂²	1	8	yes	—
91	C₂×#126×C₃₇	C₂²	1	4	yes	—
92	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
93	C₂×#125×C₃₇	C₂²	1	4	yes	—
94	C₂×#125×C₃₇	C₂²	1	4	yes	complemented
95	C₃₇×#525	C₂²	1	2	yes	—
96	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	—
97	C₃₇×#520	C₂²	1	4	yes	—
98	C₃₇×#519	C₂²	1	4	yes	—
99	C₄×#41×C₃₇	C₂²	1	2	yes	—
100	C₂×C₄×Q₈×C₃₇	C₂²	1	2	yes	—
101	C₂×#117×C₃₇	C₂²	1	1	yes	characteristic
102	C₂×#117×C₃₇	C₂²	1	2	yes	—
103	C₂×#41×C₃₇	C₂³	1	2	yes	—
104	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
105	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
106	C₄⋊Q₈×C₃₇	C₂³	1	4	yes	—
107	C₄⋊Q₈×C₃₇	C₂³	1	4	yes	—
108	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
109	C₄⋊Q₈×C₃₇	C₂³	1	4	yes	—
110	C₄⋊Q₈×C₃₇	C₂³	1	8	yes	—
111	C₄⋊Q₈×C₃₇	C₂³	1	8	yes	—
112	C₄⋊Q₈×C₃₇	C₂³	1	8	yes	—
113	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₃₇	C₂³	1	8	yes	—
115	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
116	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
117	C₄⋊Q₈×C₃₇	C₂³	1	8	yes	—
118	C₄⋊Q₈×C₃₇	C₂³	1	8	yes	—
119	C₄⋊Q₈×C₃₇	C₂³	1	8	yes	—
120	C₄⋊Q₈×C₃₇	C₂³	1	16	yes	—
121	C₄⋊Q₈×C₃₇	C₂³	1	16	yes	—
122	C₄⋊Q₈×C₃₇	C₂³	1	16	yes	—
123	#127×C₃₇	C₂³	1	1	yes	characteristic
124	#126×C₃₇	C₂³	1	16	yes	—
125	#126×C₃₇	C₂³	1	16	yes	—
126	#126×C₃₇	C₂³	1	8	yes	—
127	#126×C₃₇	C₂³	1	8	yes	—
128	#126×C₃₇	C₂³	1	16	yes	—
129	#126×C₃₇	C₂³	1	16	yes	—
130	#126×C₃₇	C₂³	1	16	yes	—
131	#126×C₃₇	C₂³	1	16	yes	—
132	#126×C₃₇	C₂³	1	16	yes	—
133	#126×C₃₇	C₂³	1	16	yes	—
134	#126×C₃₇	C₂³	1	16	yes	—
135	#126×C₃₇	C₂³	1	16	yes	—
136	#125×C₃₇	C₂³	1	4	yes	—
137	#125×C₃₇	C₂³	1	16	yes	—
138	#125×C₃₇	C₂³	1	16	yes	—
139	#125×C₃₇	C₂³	1	4	yes	—
140	#125×C₃₇	C₂³	1	2	yes	—
141	#125×C₃₇	C₂³	1	16	yes	—
142	#125×C₃₇	C₂³	1	8	yes	—
143	#125×C₃₇	C₂³	1	8	yes	—
144	#125×C₃₇	C₂³	1	8	yes	—
145	#125×C₃₇	C₂³	1	8	yes	—
146	#125×C₃₇	C₂³	1	2	yes	—
147	#125×C₃₇	C₂³	1	16	yes	—
148	#125×C₃₇	C₂³	1	2	yes	—
149	#125×C₃₇	C₂³	1	8	yes	—
150	#125×C₃₇	C₂³	1	16	yes	—
151	#125×C₃₇	C₂³	1	4	yes	—
152	#125×C₃₇	C₂³	1	8	yes	—
153	#125×C₃₇	C₂³	1	16	yes	—
154	#125×C₃₇	C₂³	1	16	yes	—
155	#125×C₃₇	C₂³	1	16	yes	—
156	#125×C₃₇	C₂³	1	16	yes	—
157	#125×C₃₇	C₂³	1	16	yes	—
158	#125×C₃₇	C₂³	1	16	yes	—
159	#125×C₃₇	C₂³	1	16	yes	—
160	#125×C₃₇	C₂³	1	16	yes	—
161	#125×C₃₇	C₂³	1	16	yes	—
162	#124×C₃₇	C₂³	1	8	yes	—
163	#124×C₃₇	C₂³	1	8	yes	—
164	#124×C₃₇	C₂³	1	8	yes	—
165	#124×C₃₇	C₂³	1	2	yes	—
166	#124×C₃₇	C₂³	1	16	yes	—
167	#123×C₃₇	C₂³	1	4	yes	—
168	#123×C₃₇	C₂³	1	16	yes	—
169	#123×C₃₇	C₂³	1	8	yes	—
170	#123×C₃₇	C₂³	1	8	yes	—
171	#123×C₃₇	C₂³	1	16	yes	—
172	#123×C₃₇	C₂³	1	16	yes	—
173	#123×C₃₇	C₂³	1	16	yes	—
174	C₂²⋊Q₈×C₃₇	C₂³	1	8	yes	—
175	C₂²⋊Q₈×C₃₇	C₂³	1	8	yes	—
176	C₂²⋊Q₈×C₃₇	C₂³	1	4	yes	—
177	C₂²⋊Q₈×C₃₇	C₂³	1	4	yes	—
178	C₂²⋊Q₈×C₃₇	C₂³	1	8	yes	—
179	C₂²⋊Q₈×C₃₇	C₂³	1	4	yes	—
180	C₂²⋊Q₈×C₃₇	C₂³	1	4	yes	—
181	C₂²⋊Q₈×C₃₇	C₂³	1	8	yes	—
182	C₂²⋊Q₈×C₃₇	C₂³	1	8	yes	—
183	C₂²⋊Q₈×C₃₇	C₂³	1	16	yes	—
184	C₂²⋊Q₈×C₃₇	C₂³	1	8	yes	—
185	C₂²⋊Q₈×C₃₇	C₂³	1	8	yes	—
186	C₂²⋊Q₈×C₃₇	C₂³	1	8	yes	—
187	C₂²⋊Q₈×C₃₇	C₂³	1	16	yes	—
188	C₂²⋊Q₈×C₃₇	C₂³	1	8	yes	—
189	C₂²⋊Q₈×C₃₇	C₂³	1	8	yes	—
190	C₂²⋊Q₈×C₃₇	C₂³	1	16	yes	—
191	C₂²⋊Q₈×C₃₇	C₂³	1	16	yes	—
192	C₂²⋊Q₈×C₃₇	C₂³	1	16	yes	—
193	C₂²⋊Q₈×C₃₇	C₂³	1	16	yes	—
194	C₂²⋊Q₈×C₃₇	C₂³	1	16	yes	—
195	C₂²⋊Q₈×C₃₇	C₂³	1	16	yes	—
196	#121×C₃₇	C₂³	1	4	yes	—
197	#121×C₃₇	C₂³	1	4	yes	—
198	#121×C₃₇	C₂³	1	8	yes	—
199	#120×C₃₇	C₂³	1	4	yes	—
200	C₄×Q₈×C₃₇	C₂³	1	8	yes	—
201	C₄×Q₈×C₃₇	C₂³	1	8	yes	—
202	C₄×Q₈×C₃₇	C₂³	1	8	yes	—
203	C₄×Q₈×C₃₇	C₂³	1	8	yes	—
204	C₄×Q₈×C₃₇	C₂³	1	8	yes	—
205	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
206	C₄×Q₈×C₃₇	C₂³	1	8	yes	—
207	C₄×Q₈×C₃₇	C₂³	1	8	yes	—
208	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
209	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
210	C₄×Q₈×C₃₇	C₂³	1	16	yes	—
211	C₄×Q₈×C₃₇	C₂³	1	8	yes	—
212	C₄×Q₈×C₃₇	C₂³	1	16	yes	—
213	C₄×Q₈×C₃₇	C₂³	1	8	yes	—
214	C₄×Q₈×C₃₇	C₂³	1	16	yes	—
215	C₄×Q₈×C₃₇	C₂³	1	16	yes	—
216	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
217	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
218	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
219	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
220	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
221	C₄×D₄×C₃₇	C₂³	1	16	yes	—
222	C₄×D₄×C₃₇	C₂³	1	8	yes	—
223	C₄×D₄×C₃₇	C₂³	1	8	yes	—
224	C₄×D₄×C₃₇	C₂³	1	4	yes	—
225	C₄×D₄×C₃₇	C₂³	1	8	yes	—
226	C₄×D₄×C₃₇	C₂³	1	16	yes	—
227	C₄×D₄×C₃₇	C₂³	1	8	yes	—
228	C₄×D₄×C₃₇	C₂³	1	4	yes	—
229	#117×C₃₇	C₂³	1	2	yes	—
230	#117×C₃₇	C₂³	1	4	yes	—
231	#117×C₃₇	C₂³	1	16	yes	—
232	#117×C₃₇	C₂³	1	8	yes	—
233	#117×C₃₇	C₂³	1	4	yes	—
234	#117×C₃₇	C₂³	1	4	yes	—
235	#117×C₃₇	C₂³	1	16	yes	—
236	#117×C₃₇	C₂³	1	16	yes	—
237	#117×C₃₇	C₂³	1	2	yes	—
238	#117×C₃₇	C₂³	1	2	yes	—
239	#117×C₃₇	C₂³	1	4	yes	—
240	#117×C₃₇	C₂³	1	16	yes	—
241	#117×C₃₇	C₂³	1	16	yes	—
242	#117×C₃₇	C₂³	1	2	yes	—
243	#117×C₃₇	C₂³	1	4	yes	—
244	#117×C₃₇	C₂³	1	2	yes	—
245	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
246	C₂×C₄⋊C₄×C₃₇	C₂³	1	8	yes	—
247	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
248	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
249	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
250	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
251	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
252	C₂×C₄⋊C₄×C₃₇	C₂³	1	16	yes	—
253	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
254	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
255	C₂×C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
256	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
257	C₂×C₄²×C₃₇	C₂³	1	4	yes	—
258	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
259	C₂×C₄²×C₃₇	C₂³	1	4	yes	—
260	C₂×C₄²×C₃₇	C₂³	1	4	yes	—
261	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
262	C₂⁴×C₃₇	C₂⁴	1	1	yes	characteristic
263	#41×C₃₇	—	2	8	no	—
264	C₂×Q₈×C₃₇	—	2	8	no	—
265	C₂×Q₈×C₃₇	C₂⁴	1	4	yes	—
266	C₂×Q₈×C₃₇	C₂⁴	1	4	yes	—
267	C₂×Q₈×C₃₇	C₂⁴	1	2	yes	—
268	C₂×Q₈×C₃₇	C₂⁴	1	8	yes	—
269	C₂×Q₈×C₃₇	C₂⁴	1	4	yes	—
270	C₂×Q₈×C₃₇	C₂⁴	1	16	yes	—
271	C₂×Q₈×C₃₇	C₂⁴	1	4	yes	—
272	C₂×Q₈×C₃₇	C₂⁴	1	4	yes	—
273	C₂×D₄×C₃₇	C₂⁴	1	4	yes	—
274	C₂×D₄×C₃₇	C₂⁴	1	2	yes	—
275	C₂×D₄×C₃₇	C₂⁴	1	8	yes	—
276	C₂×D₄×C₃₇	C₂⁴	1	4	yes	—
277	C₂²×C₄×C₃₇	—	2	4	no	—
278	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
280	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
281	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
285	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₃₇	C₂⁴	1	8	yes	—
287	C₂²×C₄×C₃₇	C₂⁴	1	8	yes	—
288	C₂²×C₄×C₃₇	C₂⁴	1	16	yes	—
289	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
290	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
291	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
292	C₄⋊C₄×C₃₇	C₂⁴	1	16	yes	—
293	C₄⋊C₄×C₃₇	C₂⁴	1	8	yes	—
294	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
295	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
296	C₄⋊C₄×C₃₇	C₂⁴	1	8	yes	—
297	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
298	C₄⋊C₄×C₃₇	C₂⁴	1	16	yes	—
299	C₄⋊C₄×C₃₇	C₂⁴	1	16	yes	—
300	C₄⋊C₄×C₃₇	C₂⁴	1	16	yes	—
301	C₄⋊C₄×C₃₇	C₂⁴	1	16	yes	—
302	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
303	C₄⋊C₄×C₃₇	C₂⁴	1	16	yes	—
304	C₄⋊C₄×C₃₇	C₂⁴	1	8	yes	—
305	C₄⋊C₄×C₃₇	C₂⁴	1	8	yes	—
306	C₄⋊C₄×C₃₇	C₂⁴	1	8	yes	—
307	C₄⋊C₄×C₃₇	C₂⁴	1	8	yes	—
308	C₄⋊C₄×C₃₇	C₂⁴	1	16	yes	—
309	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
310	C₄⋊C₄×C₃₇	C₂⁴	1	8	yes	—
311	C₄⋊C₄×C₃₇	C₂⁴	1	16	yes	—
312	C₄⋊C₄×C₃₇	C₂⁴	1	16	yes	—
313	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
314	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
315	C₄⋊C₄×C₃₇	C₂⁴	1	16	yes	—
316	C₄⋊C₄×C₃₇	C₂⁴	1	8	yes	—
317	C₄⋊C₄×C₃₇	C₂⁴	1	8	yes	—
318	C₄⋊C₄×C₃₇	C₂⁴	1	8	yes	—
319	C₄⋊C₄×C₃₇	C₂⁴	1	8	yes	—
320	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
321	C₄⋊C₄×C₃₇	C₂⁴	1	16	yes	—
322	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
323	C₂²⋊C₄×C₃₇	C₂⁴	1	8	yes	—
324	C₂²⋊C₄×C₃₇	C₂⁴	1	4	yes	—
325	C₂²⋊C₄×C₃₇	C₂⁴	1	4	yes	—
326	C₂²⋊C₄×C₃₇	C₂⁴	1	4	yes	—
327	C₂²⋊C₄×C₃₇	C₂⁴	1	4	yes	—
328	C₂²⋊C₄×C₃₇	C₂⁴	1	16	yes	—
329	C₂²⋊C₄×C₃₇	C₂⁴	1	4	yes	—
330	C₂²⋊C₄×C₃₇	C₂⁴	1	8	yes	—
331	C₂²⋊C₄×C₃₇	C₂⁴	1	8	yes	—
332	C₂²⋊C₄×C₃₇	C₂⁴	1	8	yes	—
333	C₂²⋊C₄×C₃₇	C₂⁴	1	16	yes	—
334	C₂²⋊C₄×C₃₇	C₂⁴	1	16	yes	—
335	C₂²⋊C₄×C₃₇	C₂⁴	1	8	yes	—
336	C₂²⋊C₄×C₃₇	C₂⁴	1	16	yes	—
337	C₄²×C₃₇	C₂⁴	1	2	yes	—
338	C₄²×C₃₇	C₂⁴	1	4	yes	—
339	C₄²×C₃₇	C₂⁴	1	2	yes	—
340	C₄²×C₃₇	C₂⁴	1	4	yes	—
341	C₄²×C₃₇	C₂⁴	1	2	yes	—
342	C₄²×C₃₇	C₂⁴	1	8	yes	—
343	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
344	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
345	C₄²×C₃₇	C₂⁴	1	8	yes	—
346	C₄²×C₃₇	C₂⁴	1	4	yes	—
347	C₄²×C₃₇	C₂⁴	1	8	yes	—
348	C₄²×C₃₇	C₂⁴	1	8	yes	—
349	C₄²×C₃₇	C₂⁴	1	16	yes	—
350	C₄²×C₃₇	C₂⁴	1	16	yes	—
351	C₄²×C₃₇	C₂⁴	1	16	yes	—
352	C₂³×C₃₇	—	2	2	no	—
353	C₂³×C₃₇	—	4	2	no	—
354	C₂³×C₃₇	C₂⁵	1	2	yes	—
355	C₂³×C₃₇	C₂⁵	1	4	yes	—
356	C₂³×C₃₇	C₂⁵	1	1	yes	characteristic
357	Q₈×C₃₇	—	2	8	no	—
358	Q₈×C₃₇	—	2	8	no	—
359	Q₈×C₃₇	—	2	4	no	—
360	Q₈×C₃₇	—	4	8	no	—
361	Q₈×C₃₇	—	4	4	no	—
362	Q₈×C₃₇	—	4	16	no	—
363	Q₈×C₃₇	—	4	4	no	—
364	Q₈×C₃₇	—	4	4	no	—
365	D₄×C₃₇	—	2	8	no	—
366	D₄×C₃₇	—	2	4	no	—
367	D₄×C₃₇	—	4	4	no	—
368	D₄×C₃₇	—	4	8	no	—
369	C₂×C₄×C₃₇	—	2	2	no	—
370	C₂×C₄×C₃₇	—	2	8	no	—
371	C₂×C₄×C₃₇	—	2	4	no	—
372	C₂×C₄×C₃₇	—	2	4	no	—
373	C₂×C₄×C₃₇	—	2	8	no	—
374	C₂×C₄×C₃₇	—	4	4	no	—
375	C₂×C₄×C₃₇	—	4	2	no	—
376	C₂×C₄×C₃₇	—	4	16	no	—
377	C₂×C₄×C₃₇	—	4	8	no	—
378	C₂×C₄×C₃₇	—	4	8	no	—
379	C₂×C₄×C₃₇	—	4	2	no	—
380	C₂×C₄×C₃₇	2₋¹⁺⁴	1	4	yes	—
381	C₂×C₄×C₃₇	C₂⁵	1	8	yes	—
382	C₂×C₄×C₃₇	C₂⁵	1	2	yes	—
383	C₂×C₄×C₃₇	C₂⁵	1	8	yes	—
384	C₂×C₄×C₃₇	C₂⁵	1	4	yes	—
385	C₂×C₄×C₃₇	C₂⁵	1	8	yes	—
386	C₂×C₄×C₃₇	C₂⁵	1	2	yes	—
387	C₂×C₄×C₃₇	C₂⁵	1	2	yes	—
388	C₂×C₄×C₃₇	C₂⁵	1	4	yes	—
389	C₂×C₄×C₃₇	C₂⁵	1	8	yes	—
390	C₂×C₄×C₃₇	C₂⁵	1	8	yes	—
391	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
392	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
393	#62889	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
394	C₂²×C₃₇	—	2	2	no	—
395	C₂²×C₃₇	—	2	2	no	—
396	C₂²×C₃₇	—	2	4	no	—
397	C₂²×C₃₇	—	2	8	no	—
398	C₂²×C₃₇	—	2	4	no	—
399	C₂²×C₃₇	—	8	2	no	—
400	C₂²×C₃₇	C₂×2₋¹⁺⁴	1	2	yes	—
401	C₂²×C₃₇	C₂⁶	1	1	yes	characteristic
402	C₄×C₃₇	—	2	2	no	—
403	C₄×C₃₇	—	2	4	no	—
404	C₄×C₃₇	—	2	8	no	—
405	C₄×C₃₇	—	2	8	no	—
406	C₄×C₃₇	—	2	4	no	—
407	C₄×C₃₇	—	2	8	no	—
408	C₄×C₃₇	—	2	2	no	—
409	C₄×C₃₇	—	2	8	no	—
410	C₄×C₃₇	—	2	8	no	—
411	C₄×C₃₇	—	2	2	no	—
412	C₄×C₃₇	C₂×2₋¹⁺⁴	1	2	yes	—
413	C₄×C₃₇	C₂×2₋¹⁺⁴	1	2	yes	—
414	#3564	C₂×C₃₇	1	8	yes	complemented
415	#3563	C₂×C₃₇	1	8	yes	complemented
416	#3563	C₂×C₃₇	1	8	yes	complemented
417	#3557	C₂×C₃₇	1	4	yes	complemented
418	#3556	C₂×C₃₇	1	4	yes	complemented
419	#3555	C₂×C₃₇	1	8	yes	complemented
420	#3555	C₂×C₃₇	1	8	yes	complemented
421	#3509	C₂×C₃₇	1	2	yes	complemented
422	#3507	C₂×C₃₇	1	2	yes	complemented
423	#3504	C₂×C₃₇	1	2	yes	complemented
424	#3502	C₂×C₃₇	1	2	yes	complemented
425	#3495	C₂×C₃₇	1	4	yes	complemented
426	#3458	C₂×C₃₇	1	1	yes	characteristic, complemented
427	#3455	C₂×C₃₇	1	1	yes	characteristic
428	C₂×#541	C₂×C₃₇	1	1	yes	characteristic, complemented
429	C₂×C₃₇	—	2	2	no	—
430	C₂×C₃₇	—	4	4	no	—
431	C₂×C₃₇	—	4	2	no	—
432	C₂×C₃₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
433	C₂×C₃₇	2₋¹⁺⁶	1	2	yes	—
434	#564	C₂²×C₃₇	1	16	yes	complemented
435	#563	C₂²×C₃₇	1	16	yes	—
436	#563	C₂²×C₃₇	1	16	yes	—
437	#563	C₂²×C₃₇	1	16	yes	complemented
438	#559	C₂²×C₃₇	1	4	yes	complemented
439	Q₈²	C₂²×C₃₇	1	4	yes	complemented
440	Q₈²	C₂²×C₃₇	1	4	yes	complemented
441	#557	C₂²×C₃₇	1	4	yes	complemented
442	#557	C₂²×C₃₇	1	8	yes	complemented
443	#557	C₂²×C₃₇	1	8	yes	complemented
444	#557	C₂²×C₃₇	1	4	yes	complemented
445	#557	C₂²×C₃₇	1	8	yes	complemented
446	#557	C₂²×C₃₇	1	4	yes	complemented
447	#557	C₂²×C₃₇	1	8	yes	complemented
448	#557	C₂²×C₃₇	1	16	yes	complemented
449	#556	C₂²×C₃₇	1	8	yes	—
450	#556	C₂²×C₃₇	1	16	yes	—
451	#556	C₂²×C₃₇	1	4	yes	complemented
452	#556	C₂²×C₃₇	1	8	yes	complemented
453	#556	C₂²×C₃₇	1	8	yes	complemented
454	#554	C₂²×C₃₇	1	8	yes	—
455	#554	C₂²×C₃₇	1	16	yes	—
456	#554	C₂²×C₃₇	1	8	yes	complemented
457	#554	C₂²×C₃₇	1	4	yes	complemented
458	#552	C₂²×C₃₇	1	8	yes	—
459	#552	C₂²×C₃₇	1	8	yes	—
460	#552	C₂²×C₃₇	1	16	yes	—
461	#552	C₂²×C₃₇	1	16	yes	—
462	#552	C₂²×C₃₇	1	16	yes	—
463	#552	C₂²×C₃₇	1	8	yes	complemented
464	#552	C₂²×C₃₇	1	16	yes	complemented
465	#551	C₂²×C₃₇	1	16	yes	—
466	#544	C₂²×C₃₇	1	4	yes	—
467	#544	C₂²×C₃₇	1	4	yes	—
468	#544	C₂²×C₃₇	1	4	yes	—
469	#544	C₂²×C₃₇	1	4	yes	—
470	#544	C₂²×C₃₇	1	8	yes	—
471	#544	C₂²×C₃₇	1	8	yes	complemented
472	#544	C₂²×C₃₇	1	16	yes	complemented
473	#543	C₂²×C₃₇	1	4	yes	—
474	#542	C₂²×C₃₇	1	4	yes	—
475	#542	C₂²×C₃₇	1	8	yes	—
476	#542	C₂²×C₃₇	1	16	yes	—
477	#541	C₂²×C₃₇	1	4	yes	—
478	#541	C₂²×C₃₇	1	8	yes	—
479	#541	C₂²×C₃₇	1	4	yes	—
480	#541	C₂²×C₃₇	1	2	yes	—
481	#541	C₂²×C₃₇	1	8	yes	—
482	#541	C₂²×C₃₇	1	16	yes	—
483	#541	C₂²×C₃₇	1	16	yes	—
484	#541	C₂²×C₃₇	1	4	yes	complemented
485	#541	C₂²×C₃₇	1	4	yes	complemented
486	#541	C₂²×C₃₇	1	16	yes	complemented
487	#541	C₂²×C₃₇	1	16	yes	complemented
488	#541	C₂²×C₃₇	1	16	yes	complemented
489	#540	C₂²×C₃₇	1	2	yes	—
490	#539	C₂²×C₃₇	1	4	yes	—
491	#539	C₂²×C₃₇	1	8	yes	—
492	#539	C₂²×C₃₇	1	16	yes	—
493	#538	C₂²×C₃₇	1	4	yes	—
494	#536	C₂²×C₃₇	1	4	yes	—
495	#533	C₂²×C₃₇	1	1	yes	characteristic
496	#533	C₂²×C₃₇	1	2	yes	—
497	#533	C₂²×C₃₇	1	2	yes	—
498	#533	C₂²×C₃₇	1	4	yes	—
499	#533	C₂²×C₃₇	1	4	yes	—
500	#533	C₂²×C₃₇	1	8	yes	—
501	#533	C₂²×C₃₇	1	8	yes	—
502	#533	C₂²×C₃₇	1	4	yes	complemented
503	#533	C₂²×C₃₇	1	8	yes	complemented
504	#532	C₂²×C₃₇	1	1	yes	characteristic
505	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
506	#529	C₂²×C₃₇	1	8	yes	—
507	#529	C₂²×C₃₇	1	8	yes	—
508	#529	C₂²×C₃₇	1	8	yes	—
509	C₂×#126	C₂²×C₃₇	1	4	yes	—
510	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
511	C₂×#125	C₂²×C₃₇	1	4	yes	—
512	C₂×#125	C₂²×C₃₇	1	4	yes	complemented
513	#525	C₂²×C₃₇	1	2	yes	—
514	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	2	yes	—
515	#520	C₂²×C₃₇	1	4	yes	—
516	#519	C₂²×C₃₇	1	4	yes	—
517	C₄×#41	C₂²×C₃₇	1	2	yes	—
518	C₂×C₄×Q₈	C₂²×C₃₇	1	2	yes	—
519	C₂×#117	C₂²×C₃₇	1	1	yes	characteristic
520	C₂×#117	C₂²×C₃₇	1	2	yes	—
521	C₃₇	#62889	1	1	yes	characteristic, direct product factor, Sylow
522	C₂×#41	C₂³×C₃₇	1	2	yes	—
523	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
524	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
525	C₄⋊Q₈	C₂³×C₃₇	1	4	yes	—
526	C₄⋊Q₈	C₂³×C₃₇	1	4	yes	—
527	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
528	C₄⋊Q₈	C₂³×C₃₇	1	4	yes	—
529	C₄⋊Q₈	C₂³×C₃₇	1	8	yes	—
530	C₄⋊Q₈	C₂³×C₃₇	1	8	yes	—
531	C₄⋊Q₈	C₂³×C₃₇	1	8	yes	—
532	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
533	C₄⋊Q₈	C₂³×C₃₇	1	8	yes	—
534	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
535	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
536	C₄⋊Q₈	C₂³×C₃₇	1	8	yes	—
537	C₄⋊Q₈	C₂³×C₃₇	1	8	yes	—
538	C₄⋊Q₈	C₂³×C₃₇	1	8	yes	—
539	C₄⋊Q₈	C₂³×C₃₇	1	16	yes	—
540	C₄⋊Q₈	C₂³×C₃₇	1	16	yes	—
541	C₄⋊Q₈	C₂³×C₃₇	1	16	yes	—
542	#127	C₂³×C₃₇	1	1	yes	characteristic
543	#126	C₂³×C₃₇	1	16	yes	—
544	#126	C₂³×C₃₇	1	16	yes	—
545	#126	C₂³×C₃₇	1	8	yes	—
546	#126	C₂³×C₃₇	1	8	yes	—
547	#126	C₂³×C₃₇	1	16	yes	—
548	#126	C₂³×C₃₇	1	16	yes	—
549	#126	C₂³×C₃₇	1	16	yes	—
550	#126	C₂³×C₃₇	1	16	yes	—
551	#126	C₂³×C₃₇	1	16	yes	—
552	#126	C₂³×C₃₇	1	16	yes	—
553	#126	C₂³×C₃₇	1	16	yes	—
554	#126	C₂³×C₃₇	1	16	yes	—
555	#125	C₂³×C₃₇	1	4	yes	—
556	#125	C₂³×C₃₇	1	16	yes	—
557	#125	C₂³×C₃₇	1	16	yes	—
558	#125	C₂³×C₃₇	1	4	yes	—
559	#125	C₂³×C₃₇	1	2	yes	—
560	#125	C₂³×C₃₇	1	16	yes	—
561	#125	C₂³×C₃₇	1	8	yes	—
562	#125	C₂³×C₃₇	1	8	yes	—
563	#125	C₂³×C₃₇	1	8	yes	—
564	#125	C₂³×C₃₇	1	8	yes	—
565	#125	C₂³×C₃₇	1	2	yes	—
566	#125	C₂³×C₃₇	1	16	yes	—
567	#125	C₂³×C₃₇	1	2	yes	—
568	#125	C₂³×C₃₇	1	8	yes	—
569	#125	C₂³×C₃₇	1	16	yes	—
570	#125	C₂³×C₃₇	1	4	yes	—
571	#125	C₂³×C₃₇	1	8	yes	—
572	#125	C₂³×C₃₇	1	16	yes	—
573	#125	C₂³×C₃₇	1	16	yes	—
574	#125	C₂³×C₃₇	1	16	yes	—
575	#125	C₂³×C₃₇	1	16	yes	—
576	#125	C₂³×C₃₇	1	16	yes	—
577	#125	C₂³×C₃₇	1	16	yes	—
578	#125	C₂³×C₃₇	1	16	yes	—
579	#125	C₂³×C₃₇	1	16	yes	—
580	#125	C₂³×C₃₇	1	16	yes	—
581	#124	C₂³×C₃₇	1	8	yes	—
582	#124	C₂³×C₃₇	1	8	yes	—
583	#124	C₂³×C₃₇	1	8	yes	—
584	#124	C₂³×C₃₇	1	2	yes	—
585	#124	C₂³×C₃₇	1	16	yes	—
586	#123	C₂³×C₃₇	1	4	yes	—
587	#123	C₂³×C₃₇	1	16	yes	—
588	#123	C₂³×C₃₇	1	8	yes	—
589	#123	C₂³×C₃₇	1	8	yes	—
590	#123	C₂³×C₃₇	1	16	yes	—
591	#123	C₂³×C₃₇	1	16	yes	—
592	#123	C₂³×C₃₇	1	16	yes	—
593	C₂²⋊Q₈	C₂³×C₃₇	1	8	yes	—
594	C₂²⋊Q₈	C₂³×C₃₇	1	8	yes	—
595	C₂²⋊Q₈	C₂³×C₃₇	1	4	yes	—
596	C₂²⋊Q₈	C₂³×C₃₇	1	4	yes	—
597	C₂²⋊Q₈	C₂³×C₃₇	1	8	yes	—
598	C₂²⋊Q₈	C₂³×C₃₇	1	4	yes	—
599	C₂²⋊Q₈	C₂³×C₃₇	1	4	yes	—
600	C₂²⋊Q₈	C₂³×C₃₇	1	8	yes	—
601	C₂²⋊Q₈	C₂³×C₃₇	1	8	yes	—
602	C₂²⋊Q₈	C₂³×C₃₇	1	16	yes	—
603	C₂²⋊Q₈	C₂³×C₃₇	1	8	yes	—
604	C₂²⋊Q₈	C₂³×C₃₇	1	8	yes	—
605	C₂²⋊Q₈	C₂³×C₃₇	1	8	yes	—
606	C₂²⋊Q₈	C₂³×C₃₇	1	16	yes	—
607	C₂²⋊Q₈	C₂³×C₃₇	1	8	yes	—
608	C₂²⋊Q₈	C₂³×C₃₇	1	8	yes	—
609	C₂²⋊Q₈	C₂³×C₃₇	1	16	yes	—
610	C₂²⋊Q₈	C₂³×C₃₇	1	16	yes	—
611	C₂²⋊Q₈	C₂³×C₃₇	1	16	yes	—
612	C₂²⋊Q₈	C₂³×C₃₇	1	16	yes	—
613	C₂²⋊Q₈	C₂³×C₃₇	1	16	yes	—
614	C₂²⋊Q₈	C₂³×C₃₇	1	16	yes	—
615	#121	C₂³×C₃₇	1	4	yes	—
616	#121	C₂³×C₃₇	1	4	yes	—
617	#121	C₂³×C₃₇	1	8	yes	—
618	#120	C₂³×C₃₇	1	4	yes	—
619	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
620	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
621	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
622	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
623	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
624	C₄×Q₈	C₂³×C₃₇	1	8	yes	—
625	C₄×Q₈	C₂³×C₃₇	1	8	yes	—
626	C₄×Q₈	C₂³×C₃₇	1	8	yes	—
627	C₄×Q₈	C₂³×C₃₇	1	8	yes	—
628	C₄×Q₈	C₂³×C₃₇	1	8	yes	—
629	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
630	C₄×Q₈	C₂³×C₃₇	1	8	yes	—
631	C₄×Q₈	C₂³×C₃₇	1	8	yes	—
632	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
633	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
634	C₄×Q₈	C₂³×C₃₇	1	16	yes	—
635	C₄×Q₈	C₂³×C₃₇	1	8	yes	—
636	C₄×Q₈	C₂³×C₃₇	1	16	yes	—
637	C₄×Q₈	C₂³×C₃₇	1	8	yes	—
638	C₄×Q₈	C₂³×C₃₇	1	16	yes	—
639	C₄×Q₈	C₂³×C₃₇	1	16	yes	—
640	C₄×D₄	C₂³×C₃₇	1	8	yes	—
641	C₄×D₄	C₂³×C₃₇	1	4	yes	—
642	C₄×D₄	C₂³×C₃₇	1	16	yes	—
643	C₄×D₄	C₂³×C₃₇	1	8	yes	—
644	C₄×D₄	C₂³×C₃₇	1	8	yes	—
645	C₄×D₄	C₂³×C₃₇	1	4	yes	—
646	C₄×D₄	C₂³×C₃₇	1	8	yes	—
647	C₄×D₄	C₂³×C₃₇	1	16	yes	—
648	#117	C₂³×C₃₇	1	4	yes	—
649	#117	C₂³×C₃₇	1	4	yes	—
650	#117	C₂³×C₃₇	1	2	yes	—
651	#117	C₂³×C₃₇	1	2	yes	—
652	#117	C₂³×C₃₇	1	4	yes	—
653	#117	C₂³×C₃₇	1	2	yes	—
654	#117	C₂³×C₃₇	1	4	yes	—
655	#117	C₂³×C₃₇	1	2	yes	—
656	#117	C₂³×C₃₇	1	2	yes	—
657	#117	C₂³×C₃₇	1	4	yes	—
658	#117	C₂³×C₃₇	1	16	yes	—
659	#117	C₂³×C₃₇	1	8	yes	—
660	#117	C₂³×C₃₇	1	16	yes	—
661	#117	C₂³×C₃₇	1	16	yes	—
662	#117	C₂³×C₃₇	1	16	yes	—
663	#117	C₂³×C₃₇	1	16	yes	—
664	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
666	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
668	C₂×C₄⋊C₄	C₂³×C₃₇	1	8	yes	—
669	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
670	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
671	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
672	C₂×C₄⋊C₄	C₂³×C₃₇	1	16	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₃₇	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
676	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
678	C₂×C₄²	C₂³×C₃₇	1	4	yes	—
679	C₂×C₄²	C₂³×C₃₇	1	4	yes	—
680	C₂×C₄²	C₂³×C₃₇	1	4	yes	—
681	C₂⁴	C₂⁴×C₃₇	1	1	yes	characteristic
682	#41	—	2	8	no	—
683	C₂×Q₈	—	2	8	no	—
684	C₂×Q₈	C₂⁴×C₃₇	1	4	yes	—
685	C₂×Q₈	C₂⁴×C₃₇	1	4	yes	—
686	C₂×Q₈	C₂⁴×C₃₇	1	2	yes	—
687	C₂×Q₈	C₂⁴×C₃₇	1	8	yes	—
688	C₂×Q₈	C₂⁴×C₃₇	1	4	yes	—
689	C₂×Q₈	C₂⁴×C₃₇	1	16	yes	—
690	C₂×Q₈	C₂⁴×C₃₇	1	4	yes	—
691	C₂×Q₈	C₂⁴×C₃₇	1	4	yes	—
692	C₂×D₄	C₂⁴×C₃₇	1	4	yes	—
693	C₂×D₄	C₂⁴×C₃₇	1	2	yes	—
694	C₂×D₄	C₂⁴×C₃₇	1	8	yes	—
695	C₂×D₄	C₂⁴×C₃₇	1	4	yes	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
699	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
700	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
705	C₂²×C₄	C₂⁴×C₃₇	1	8	yes	—
706	C₂²×C₄	C₂⁴×C₃₇	1	8	yes	—
707	C₂²×C₄	C₂⁴×C₃₇	1	16	yes	—
708	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
709	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
710	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
711	C₄⋊C₄	C₂⁴×C₃₇	1	16	yes	—
712	C₄⋊C₄	C₂⁴×C₃₇	1	8	yes	—
713	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
714	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
715	C₄⋊C₄	C₂⁴×C₃₇	1	8	yes	—
716	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
717	C₄⋊C₄	C₂⁴×C₃₇	1	16	yes	—
718	C₄⋊C₄	C₂⁴×C₃₇	1	16	yes	—
719	C₄⋊C₄	C₂⁴×C₃₇	1	16	yes	—
720	C₄⋊C₄	C₂⁴×C₃₇	1	16	yes	—
721	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
722	C₄⋊C₄	C₂⁴×C₃₇	1	16	yes	—
723	C₄⋊C₄	C₂⁴×C₃₇	1	8	yes	—
724	C₄⋊C₄	C₂⁴×C₃₇	1	8	yes	—
725	C₄⋊C₄	C₂⁴×C₃₇	1	8	yes	—
726	C₄⋊C₄	C₂⁴×C₃₇	1	8	yes	—
727	C₄⋊C₄	C₂⁴×C₃₇	1	16	yes	—
728	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
729	C₄⋊C₄	C₂⁴×C₃₇	1	8	yes	—
730	C₄⋊C₄	C₂⁴×C₃₇	1	16	yes	—
731	C₄⋊C₄	C₂⁴×C₃₇	1	16	yes	—
732	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
733	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
734	C₄⋊C₄	C₂⁴×C₃₇	1	16	yes	—
735	C₄⋊C₄	C₂⁴×C₃₇	1	8	yes	—
736	C₄⋊C₄	C₂⁴×C₃₇	1	8	yes	—
737	C₄⋊C₄	C₂⁴×C₃₇	1	8	yes	—
738	C₄⋊C₄	C₂⁴×C₃₇	1	8	yes	—
739	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
740	C₄⋊C₄	C₂⁴×C₃₇	1	16	yes	—
741	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
742	C₂²⋊C₄	C₂⁴×C₃₇	1	8	yes	—
743	C₂²⋊C₄	C₂⁴×C₃₇	1	4	yes	—
744	C₂²⋊C₄	C₂⁴×C₃₇	1	4	yes	—
745	C₂²⋊C₄	C₂⁴×C₃₇	1	4	yes	—
746	C₂²⋊C₄	C₂⁴×C₃₇	1	4	yes	—
747	C₂²⋊C₄	C₂⁴×C₃₇	1	16	yes	—
748	C₂²⋊C₄	C₂⁴×C₃₇	1	4	yes	—
749	C₂²⋊C₄	C₂⁴×C₃₇	1	8	yes	—
750	C₂²⋊C₄	C₂⁴×C₃₇	1	8	yes	—
751	C₂²⋊C₄	C₂⁴×C₃₇	1	8	yes	—
752	C₂²⋊C₄	C₂⁴×C₃₇	1	16	yes	—
753	C₂²⋊C₄	C₂⁴×C₃₇	1	16	yes	—
754	C₂²⋊C₄	C₂⁴×C₃₇	1	8	yes	—
755	C₂²⋊C₄	C₂⁴×C₃₇	1	16	yes	—
756	C₄²	C₂⁴×C₃₇	1	2	yes	—
757	C₄²	C₂⁴×C₃₇	1	4	yes	—
758	C₄²	C₂⁴×C₃₇	1	2	yes	—
759	C₄²	C₂⁴×C₃₇	1	4	yes	—
760	C₄²	C₂⁴×C₃₇	1	2	yes	—
761	C₄²	C₂⁴×C₃₇	1	8	yes	—
762	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
763	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
764	C₄²	C₂⁴×C₃₇	1	8	yes	—
765	C₄²	C₂⁴×C₃₇	1	4	yes	—
766	C₄²	C₂⁴×C₃₇	1	8	yes	—
767	C₄²	C₂⁴×C₃₇	1	8	yes	—
768	C₄²	C₂⁴×C₃₇	1	16	yes	—
769	C₄²	C₂⁴×C₃₇	1	16	yes	—
770	C₄²	C₂⁴×C₃₇	1	16	yes	—
771	C₂³	—	2	2	no	—
772	C₂³	—	4	2	no	—
773	C₂³	C₂⁵×C₃₇	1	2	yes	—
774	C₂³	C₂⁵×C₃₇	1	4	yes	—
775	C₂³	C₂⁵×C₃₇	1	1	yes	characteristic
776	Q₈	—	2	8	no	—
777	Q₈	—	2	8	no	—
778	Q₈	—	2	4	no	—
779	Q₈	—	4	8	no	—
780	Q₈	—	4	4	no	—
781	Q₈	—	4	16	no	—
782	Q₈	—	4	4	no	—
783	Q₈	—	4	4	no	—
784	D₄	—	2	8	no	—
785	D₄	—	2	4	no	—
786	D₄	—	4	4	no	—
787	D₄	—	4	8	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	8	no	—
790	C₂×C₄	—	2	4	no	—
791	C₂×C₄	—	2	4	no	—
792	C₂×C₄	—	2	8	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	16	no	—
796	C₂×C₄	—	4	8	no	—
797	C₂×C₄	—	4	8	no	—
798	C₂×C₄	—	4	2	no	—
799	C₂×C₄	2₋¹⁺⁴×C₃₇	1	4	yes	—
800	C₂×C₄	C₂⁵×C₃₇	1	8	yes	—
801	C₂×C₄	C₂⁵×C₃₇	1	2	yes	—
802	C₂×C₄	C₂⁵×C₃₇	1	8	yes	—
803	C₂×C₄	C₂⁵×C₃₇	1	4	yes	—
804	C₂×C₄	C₂⁵×C₃₇	1	8	yes	—
805	C₂×C₄	C₂⁵×C₃₇	1	2	yes	—
806	C₂×C₄	C₂⁵×C₃₇	1	2	yes	—
807	C₂×C₄	C₂⁵×C₃₇	1	4	yes	—
808	C₂×C₄	C₂⁵×C₃₇	1	8	yes	—
809	C₂×C₄	C₂⁵×C₃₇	1	8	yes	—
810	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
811	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	4	no	—
815	C₂²	—	2	8	no	—
816	C₂²	—	2	4	no	—
817	C₂²	—	8	2	no	—
818	C₂²	C₂×2₋¹⁺⁴×C₃₇	1	2	yes	—
819	C₂²	C₂⁶×C₃₇	1	1	yes	characteristic
820	C₄	—	2	2	no	—
821	C₄	—	2	4	no	—
822	C₄	—	2	8	no	—
823	C₄	—	2	8	no	—
824	C₄	—	2	4	no	—
825	C₄	—	2	8	no	—
826	C₄	—	2	2	no	—
827	C₄	—	2	8	no	—
828	C₄	—	2	8	no	—
829	C₄	—	2	2	no	—
830	C₄	C₂×2₋¹⁺⁴×C₃₇	1	2	yes	—
831	C₄	C₂×2₋¹⁺⁴×C₃₇	1	2	yes	—
832	C₂	—	2	2	no	—
833	C₂	—	4	2	no	—
834	C₂	—	4	4	no	—
835	C₂	C₂²×2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
836	C₂	C₃₇×2₋¹⁺⁶	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₇
prime radical	C₃₇×#3455	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3564	C₂	semidirect
2. C₃₇×#3563	C₂	semidirect
3. C₃₇×#3563	C₂	semidirect
4. C₃₇×#3557	C₂	semidirect
5. C₃₇×#3556	C₂	semidirect
6. C₃₇×#3555	C₂	semidirect
7. C₃₇×#3555	C₂	semidirect
8. C₃₇×#3509	C₂	semidirect
9. C₃₇×#3507	C₂	semidirect
10. C₃₇×#3504	C₂	semidirect
11. C₃₇×#3502	C₂	semidirect
12. C₃₇×#3495	C₂	semidirect
13. C₃₇×#3458	C₂	semidirect
15. C₂×C₃₇×#541	C₂	semidirect
16. C₃₇×#564	C₂²	semidirect
19. C₃₇×#563	C₂²	semidirect
20. C₃₇×#559	C₂²	semidirect
21. Q₈²×C₃₇	C₂²	semidirect
22. Q₈²×C₃₇	C₂²	semidirect
23. C₃₇×#557	C₂²	semidirect
24. C₃₇×#557	C₂²	semidirect
25. C₃₇×#557	C₂²	semidirect
26. C₃₇×#557	C₂²	semidirect
27. C₃₇×#557	C₂²	semidirect
28. C₃₇×#557	C₂²	semidirect
29. C₃₇×#557	C₂²	semidirect
30. C₃₇×#557	C₂²	semidirect
33. C₃₇×#556	C₂²	semidirect
34. C₃₇×#556	C₂²	semidirect
35. C₃₇×#556	C₂²	semidirect
38. C₃₇×#554	C₂²	semidirect
39. C₃₇×#554	C₂²	semidirect
45. C₃₇×#552	C₂²	semidirect
46. C₃₇×#552	C₂²	semidirect
53. C₃₇×#544	C₂²	semidirect
54. C₃₇×#544	C₂²	semidirect
66. C₃₇×#541	C₂²	semidirect
67. C₃₇×#541	C₂²	semidirect
68. C₃₇×#541	C₂²	semidirect
69. C₃₇×#541	C₂²	semidirect
70. C₃₇×#541	C₂²	semidirect
84. C₃₇×#533	C₂²	semidirect
85. C₃₇×#533	C₂²	semidirect
94. C₂×#125×C₃₇	C₂²	semidirect
393. #62889	C₃₇	direct (N × H)
414. #3564	C₂×C₃₇	semidirect
415. #3563	C₂×C₃₇	semidirect
416. #3563	C₂×C₃₇	semidirect
417. #3557	C₂×C₃₇	semidirect
418. #3556	C₂×C₃₇	semidirect
419. #3555	C₂×C₃₇	semidirect
420. #3555	C₂×C₃₇	semidirect
421. #3509	C₂×C₃₇	semidirect
422. #3507	C₂×C₃₇	semidirect
423. #3504	C₂×C₃₇	semidirect
424. #3502	C₂×C₃₇	semidirect
425. #3495	C₂×C₃₇	semidirect
426. #3458	C₂×C₃₇	semidirect
428. C₂×#541	C₂×C₃₇	semidirect
434. #564	C₂²×C₃₇	semidirect
437. #563	C₂²×C₃₇	semidirect
438. #559	C₂²×C₃₇	semidirect
439. Q₈²	C₂²×C₃₇	semidirect
440. Q₈²	C₂²×C₃₇	semidirect
441. #557	C₂²×C₃₇	semidirect
442. #557	C₂²×C₃₇	semidirect
443. #557	C₂²×C₃₇	semidirect
444. #557	C₂²×C₃₇	semidirect
445. #557	C₂²×C₃₇	semidirect
446. #557	C₂²×C₃₇	semidirect
447. #557	C₂²×C₃₇	semidirect
448. #557	C₂²×C₃₇	semidirect
451. #556	C₂²×C₃₇	semidirect
452. #556	C₂²×C₃₇	semidirect
453. #556	C₂²×C₃₇	semidirect
456. #554	C₂²×C₃₇	semidirect
457. #554	C₂²×C₃₇	semidirect
463. #552	C₂²×C₃₇	semidirect
464. #552	C₂²×C₃₇	semidirect
471. #544	C₂²×C₃₇	semidirect
472. #544	C₂²×C₃₇	semidirect
484. #541	C₂²×C₃₇	semidirect
485. #541	C₂²×C₃₇	semidirect
486. #541	C₂²×C₃₇	semidirect
487. #541	C₂²×C₃₇	semidirect
488. #541	C₂²×C₃₇	semidirect
502. #533	C₂²×C₃₇	semidirect
503. #533	C₂²×C₃₇	semidirect
512. C₂×#125	C₂²×C₃₇	semidirect
521. C₃₇	#62889	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×#3564	2
C₃₇×#3563	2
C₃₇×#3557	2
C₃₇×#3556	2
C₃₇×#3555	2
C₃₇×#3509	2
C₃₇×#3507	2
C₃₇×#3504	2
C₃₇×#3502	2
C₃₇×#3495	2
C₃₇×#3458	2
C₃₇×#3455	2
C₂×C₃₇×#541	2
#62889	37

Subgroups — C37×#62889 #22684142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#62889 #22684142