Subgroups — C₃₇×#28591 #22649844

Order 9472.

794 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3056	C₂	1	2	yes	maximal
2	C₂×C₃₇×#467	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#2929	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2089	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2078	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2047	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2020	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1930	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1908	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1901	C₂	1	2	yes	maximal, complemented
11	C₂×C₃₇×#341	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₃₇	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×#131×C₃₇	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₃₇	C₂²	1	2	yes	—
16	C₂³×C₈×C₃₇	C₂²	1	1	yes	characteristic
17	C₃₇×#525	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	—
19	C₃₇×#470	—	2	2	no	—
20	C₃₇×#468	—	2	2	no	—
21	C₃₇×#467	—	2	1	no	—
22	C₃₇×#467	—	2	1	no	—
23	C₃₇×#467	—	2	1	no	—
24	C₃₇×#467	—	2	1	no	—
25	C₃₇×#467	—	2	2	no	—
26	C₃₇×#465	—	2	2	no	—
27	C₃₇×#435	—	2	1	no	—
28	C₃₇×#435	—	2	1	no	—
29	C₈×D₄×C₃₇	—	2	1	no	—
30	C₈×D₄×C₃₇	—	2	1	no	—
31	C₃₇×#428	C₂²	1	2	yes	—
32	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
33	C₃₇×#424	C₂²	1	1	yes	characteristic
34	C₃₇×#419	C₂²	1	2	yes	—
35	C₃₇×#417	C₂²	1	2	yes	—
36	C₂×#103×C₃₇	C₂²	1	2	yes	—
37	C₂×#101×C₃₇	C₂²	1	2	yes	—
38	C₂×#101×C₃₇	C₂²	1	2	yes	—
39	C₃₇×#408	C₂²	1	1	yes	characteristic
40	C₃₇×#407	C₂²	1	1	yes	characteristic
41	C₃₇×#405	C₂²	1	1	yes	characteristic
42	C₃₇×#343	C₂²	1	2	yes	—
43	C₃₇×#343	C₂²	1	2	yes	—
44	C₃₇×#341	C₂²	1	2	yes	—
45	C₃₇×#341	C₂²	1	1	yes	characteristic
46	C₃₇×#341	C₂²	1	1	yes	characteristic
47	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
49	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
50	#137×C₃₇	—	2	4	no	—
51	#137×C₃₇	—	4	2	no	—
52	C₂×Q₁₆×C₃₇	—	2	2	no	—
53	C₂×Q₁₆×C₃₇	—	2	1	no	—
54	C₂×Q₁₆×C₃₇	—	2	1	no	—
55	C₂×Q₁₆×C₃₇	—	4	2	no	—
56	C₂×SD₁₆×C₃₇	—	2	2	no	—
57	#131×C₃₇	—	4	2	no	—
58	C₂×M₁₆×C₃₇	—	2	2	no	—
59	C₂×M₁₆×C₃₇	—	2	1	no	—
60	C₂×M₁₆×C₃₇	—	2	4	no	—
61	C₂×M₁₆×C₃₇	—	4	2	no	—
62	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
63	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
64	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
65	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
66	C₂²×C₈×C₃₇	—	2	2	no	—
67	C₂²×C₈×C₃₇	—	2	1	no	—
68	C₂²×C₈×C₃₇	—	4	2	no	—
69	C₂²×C₈×C₃₇	D₄	1	1	yes	characteristic
70	C₂²×C₈×C₃₇	D₄	1	1	yes	characteristic
71	C₂²×C₈×C₃₇	D₄	1	1	yes	characteristic
72	C₂²×C₈×C₃₇	D₄	1	1	yes	characteristic
73	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
75	#123×C₃₇	—	2	1	no	—
76	C₂²⋊Q₈×C₃₇	—	2	2	no	—
77	C₂²⋊Q₈×C₃₇	—	2	2	no	—
78	C₂²⋊Q₈×C₃₇	—	2	2	no	—
79	C₂²⋊Q₈×C₃₇	—	2	2	no	—
80	C₂²⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
81	C₂²⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
82	#121×C₃₇	D₄	1	1	yes	characteristic
83	#121×C₃₇	D₄	1	1	yes	characteristic
84	#120×C₃₇	—	2	1	no	—
85	C₄×D₄×C₃₇	—	2	1	no	—
86	C₄×D₄×C₃₇	—	2	1	no	—
87	#117×C₃₇	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
89	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
90	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
91	#107×C₃₇	—	2	1	no	—
92	#107×C₃₇	—	2	1	no	—
93	#107×C₃₇	—	2	2	no	—
94	#106×C₃₇	—	2	2	no	—
95	C₄⋊C₈×C₃₇	—	2	1	no	—
96	C₄⋊C₈×C₃₇	—	2	1	no	—
97	#103×C₃₇	—	2	2	no	—
98	#103×C₃₇	—	2	2	no	—
99	#103×C₃₇	—	2	2	no	—
100	#103×C₃₇	—	2	2	no	—
101	#103×C₃₇	—	2	2	no	—
102	#102×C₃₇	—	2	2	no	—
103	#101×C₃₇	—	2	4	no	—
104	#101×C₃₇	—	4	2	no	—
105	C₂²⋊C₈×C₃₇	—	2	1	no	—
106	C₂²⋊C₈×C₃₇	—	2	1	no	—
107	C₂²⋊C₈×C₃₇	—	2	1	no	—
108	C₂²⋊C₈×C₃₇	—	2	1	no	—
109	#97×C₃₇	—	2	1	no	—
110	C₄×C₈×C₃₇	—	2	1	no	—
111	C₂⁴×C₃₇	#41	1	1	yes	characteristic
112	#41×C₃₇	—	2	2	no	—
113	#41×C₃₇	—	2	2	no	—
114	C₂×Q₈×C₃₇	—	2	2	no	—
115	C₂×Q₈×C₃₇	—	2	2	no	—
116	C₂×Q₈×C₃₇	—	2	2	no	—
117	C₂×Q₈×C₃₇	—	2	2	no	—
118	C₂×Q₈×C₃₇	—	2	2	no	—
119	C₂×Q₈×C₃₇	—	2	2	no	—
120	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
121	C₂×D₄×C₃₇	—	2	1	no	—
122	C₂×D₄×C₃₇	—	2	1	no	—
123	C₂×D₄×C₃₇	—	2	1	no	—
124	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₃₇	—	2	2	no	—
126	C₂²×C₄×C₃₇	—	2	2	no	—
127	C₂²×C₄×C₃₇	—	2	1	no	—
128	C₂²×C₄×C₃₇	—	2	2	no	—
129	C₂²×C₄×C₃₇	—	2	2	no	—
130	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
135	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
136	Q₁₆×C₃₇	—	4	4	no	—
137	Q₁₆×C₃₇	—	4	2	no	—
138	Q₁₆×C₃₇	—	4	2	no	—
139	SD₁₆×C₃₇	—	4	4	no	—
140	M₁₆×C₃₇	—	2	2	no	—
141	M₁₆×C₃₇	—	2	2	no	—
142	M₁₆×C₃₇	—	2	2	no	—
143	M₁₆×C₃₇	—	2	2	no	—
144	M₁₆×C₃₇	—	2	2	no	—
145	M₁₆×C₃₇	—	4	4	no	—
146	M₁₆×C₃₇	—	4	2	no	—
147	M₁₆×C₃₇	#41	1	4	yes	—
148	C₂×C₈×C₃₇	—	2	2	no	—
149	C₂×C₈×C₃₇	—	2	2	no	—
150	C₂×C₈×C₃₇	—	2	2	no	—
151	C₂×C₈×C₃₇	—	2	1	no	—
152	C₂×C₈×C₃₇	—	2	1	no	—
153	C₂×C₈×C₃₇	—	2	2	no	—
154	C₂×C₈×C₃₇	—	4	1	no	—
155	C₂×C₈×C₃₇	—	4	1	no	—
156	C₂×C₈×C₃₇	—	4	1	no	—
157	C₂×C₈×C₃₇	—	4	1	no	—
158	C₂×C₈×C₃₇	—	4	4	no	—
159	C₂×C₈×C₃₇	—	4	2	no	—
160	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
164	C₄⋊C₄×C₃₇	—	2	1	no	—
165	C₄⋊C₄×C₃₇	—	2	1	no	—
166	C₄⋊C₄×C₃₇	—	2	2	no	—
167	C₄⋊C₄×C₃₇	—	2	2	no	—
168	C₄⋊C₄×C₃₇	—	4	2	no	—
169	C₄⋊C₄×C₃₇	—	4	2	no	—
170	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
171	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
172	C₂²⋊C₄×C₃₇	—	2	1	no	—
173	C₂²⋊C₄×C₃₇	—	2	1	no	—
174	C₂²⋊C₄×C₃₇	—	2	1	no	—
175	C₂²⋊C₄×C₃₇	—	2	1	no	—
176	C₂²⋊C₄×C₃₇	—	2	1	no	—
177	C₂²⋊C₄×C₃₇	—	4	2	no	—
178	C₂²⋊C₄×C₃₇	—	4	2	no	—
179	C₄²×C₃₇	—	2	1	no	—
180	C₂³×C₃₇	—	2	2	no	—
181	C₂³×C₃₇	—	2	2	no	—
182	C₂³×C₃₇	—	2	1	no	—
183	C₂³×C₃₇	—	4	1	no	—
184	C₂³×C₃₇	#121	1	1	yes	characteristic
185	C₂³×C₃₇	#121	1	1	yes	characteristic
186	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
187	Q₈×C₃₇	—	2	2	no	—
188	Q₈×C₃₇	—	4	2	no	—
189	Q₈×C₃₇	—	4	2	no	—
190	Q₈×C₃₇	—	4	2	no	—
191	Q₈×C₃₇	—	4	2	no	—
192	D₄×C₃₇	—	2	2	no	—
193	D₄×C₃₇	—	4	2	no	—
194	D₄×C₃₇	—	4	2	no	—
195	D₄×C₃₇	—	4	2	no	—
196	C₂×C₄×C₃₇	—	2	2	no	—
197	C₂×C₄×C₃₇	—	2	1	no	—
198	C₂×C₄×C₃₇	—	2	1	no	—
199	C₂×C₄×C₃₇	—	2	1	no	—
200	C₂×C₄×C₃₇	—	2	1	no	—
201	C₂×C₄×C₃₇	—	2	2	no	—
202	C₂×C₄×C₃₇	—	2	2	no	—
203	C₂×C₄×C₃₇	—	2	1	no	—
204	C₂×C₄×C₃₇	—	2	1	no	—
205	C₂×C₄×C₃₇	—	2	1	no	—
206	C₂×C₄×C₃₇	—	4	1	no	—
207	C₂×C₄×C₃₇	—	4	1	no	—
208	C₂×C₄×C₃₇	—	4	2	no	—
209	C₂×C₄×C₃₇	—	4	2	no	—
210	C₂×C₄×C₃₇	—	4	2	no	—
211	C₂×C₄×C₃₇	—	4	2	no	—
212	C₂×C₄×C₃₇	—	8	2	no	—
213	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
214	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
215	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
218	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
219	C₈×C₃₇	—	2	1	no	—
220	C₈×C₃₇	—	2	1	no	—
221	C₈×C₃₇	—	2	1	no	—
222	C₈×C₃₇	—	2	1	no	—
223	C₈×C₃₇	—	2	4	no	—
224	C₈×C₃₇	—	4	1	no	—
225	C₈×C₃₇	—	4	1	no	—
226	C₈×C₃₇	—	4	2	no	—
227	#28591	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂²×C₃₇	—	2	1	no	—
229	C₂²×C₃₇	—	2	1	no	—
230	C₂²×C₃₇	—	2	1	no	—
231	C₂²×C₃₇	—	2	1	no	—
232	C₂²×C₃₇	—	2	1	no	—
233	C₂²×C₃₇	—	2	1	no	—
234	C₂²×C₃₇	—	2	1	no	—
235	C₂²×C₃₇	—	4	4	no	—
236	C₂²×C₃₇	—	4	1	no	—
237	C₂²×C₃₇	—	4	1	no	—
238	C₂²×C₃₇	—	4	1	no	—
239	C₂²×C₃₇	#473	1	2	yes	—
240	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
241	C₂²×C₃₇	#553	1	2	yes	—
242	C₄×C₃₇	—	2	1	no	—
243	C₄×C₃₇	—	2	1	no	—
244	C₄×C₃₇	—	4	1	no	—
245	C₄×C₃₇	—	4	1	no	—
246	C₄×C₃₇	—	4	1	no	—
247	C₄×C₃₇	—	8	2	no	—
248	C₄×C₃₇	—	8	2	no	—
249	C₄×C₃₇	#532	1	1	yes	characteristic
250	C₄×C₃₇	#534	1	1	yes	characteristic
251	C₄×C₃₇	#546	1	2	yes	—
252	#3056	C₂×C₃₇	1	2	yes	—
253	C₂×#467	C₂×C₃₇	1	1	yes	characteristic, complemented
254	#2929	C₂×C₃₇	1	1	yes	characteristic
255	#2089	C₂×C₃₇	1	1	yes	characteristic, complemented
256	#2078	C₂×C₃₇	1	1	yes	characteristic, complemented
257	#2047	C₂×C₃₇	1	1	yes	characteristic, complemented
258	#2020	C₂×C₃₇	1	1	yes	characteristic, complemented
259	#1930	C₂×C₃₇	1	2	yes	complemented
260	#1908	C₂×C₃₇	1	2	yes	complemented
261	#1901	C₂×C₃₇	1	2	yes	complemented
262	C₂×#341	C₂×C₃₇	1	1	yes	characteristic, complemented
263	C₂×C₃₇	—	2	2	no	—
264	C₂×C₃₇	—	2	2	no	—
265	C₂×C₃₇	—	4	1	no	—
266	C₂×C₃₇	—	8	1	no	—
267	C₂×C₃₇	#2543	1	1	yes	characteristic
268	C₂×C₃₇	C₂×#473	1	1	yes	characteristic
269	C₂×C₃₇	#3067	1	1	yes	characteristic
270	C₂×#137	C₂²×C₃₇	1	2	yes	—
271	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
272	C₂×#131	C₂²×C₃₇	1	1	yes	characteristic
273	C₂²×M₁₆	C₂²×C₃₇	1	2	yes	—
274	C₂³×C₈	C₂²×C₃₇	1	1	yes	characteristic
275	#525	C₂²×C₃₇	1	1	yes	characteristic
276	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	2	yes	—
277	#470	—	2	2	no	—
278	#468	—	2	2	no	—
279	#467	—	2	1	no	—
280	#467	—	2	1	no	—
281	#467	—	2	1	no	—
282	#467	—	2	1	no	—
283	#467	—	2	2	no	—
284	#465	—	2	2	no	—
285	#435	—	2	1	no	—
286	#435	—	2	1	no	—
287	C₈×D₄	—	2	1	no	—
288	C₈×D₄	—	2	1	no	—
289	#428	C₂²×C₃₇	1	2	yes	—
290	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
291	#424	C₂²×C₃₇	1	1	yes	characteristic
292	#419	C₂²×C₃₇	1	2	yes	—
293	#417	C₂²×C₃₇	1	2	yes	—
294	C₂×#103	C₂²×C₃₇	1	2	yes	—
295	C₂×#101	C₂²×C₃₇	1	2	yes	—
296	C₂×#101	C₂²×C₃₇	1	2	yes	—
297	#408	C₂²×C₃₇	1	1	yes	characteristic
298	#407	C₂²×C₃₇	1	1	yes	characteristic
299	#405	C₂²×C₃₇	1	1	yes	characteristic
300	#343	C₂²×C₃₇	1	2	yes	—
301	#343	C₂²×C₃₇	1	2	yes	—
302	#341	C₂²×C₃₇	1	1	yes	characteristic
303	#341	C₂²×C₃₇	1	1	yes	characteristic
304	#341	C₂²×C₃₇	1	2	yes	—
305	C₃₇	#28591	1	1	yes	characteristic, direct product factor, Sylow
306	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
307	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
308	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
309	#137	—	2	4	no	—
310	#137	—	4	2	no	—
311	C₂×Q₁₆	—	2	2	no	—
312	C₂×Q₁₆	—	2	1	no	—
313	C₂×Q₁₆	—	2	1	no	—
314	C₂×Q₁₆	—	4	2	no	—
315	C₂×SD₁₆	—	2	2	no	—
316	#131	—	4	2	no	—
317	C₂×M₁₆	—	2	2	no	—
318	C₂×M₁₆	—	2	1	no	—
319	C₂×M₁₆	—	2	4	no	—
320	C₂×M₁₆	—	4	2	no	—
321	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
322	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
323	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
324	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
325	C₂²×C₈	—	2	2	no	—
326	C₂²×C₈	—	2	1	no	—
327	C₂²×C₈	—	4	2	no	—
328	C₂²×C₈	D₄×C₃₇	1	1	yes	characteristic
329	C₂²×C₈	D₄×C₃₇	1	1	yes	characteristic
330	C₂²×C₈	D₄×C₃₇	1	1	yes	characteristic
331	C₂²×C₈	D₄×C₃₇	1	1	yes	characteristic
332	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
333	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
334	#123	—	2	1	no	—
335	C₂²⋊Q₈	—	2	2	no	—
336	C₂²⋊Q₈	—	2	2	no	—
337	C₂²⋊Q₈	—	2	2	no	—
338	C₂²⋊Q₈	—	2	2	no	—
339	C₂²⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
340	C₂²⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
341	#121	D₄×C₃₇	1	1	yes	characteristic
342	#121	D₄×C₃₇	1	1	yes	characteristic
343	#120	—	2	1	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	—	2	1	no	—
346	#117	C₂³×C₃₇	1	1	yes	characteristic
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	#107	—	2	1	no	—
351	#107	—	2	1	no	—
352	#107	—	2	2	no	—
353	#106	—	2	2	no	—
354	C₄⋊C₈	—	2	1	no	—
355	C₄⋊C₈	—	2	1	no	—
356	#103	—	2	2	no	—
357	#103	—	2	2	no	—
358	#103	—	2	2	no	—
359	#103	—	2	2	no	—
360	#103	—	2	2	no	—
361	#102	—	2	2	no	—
362	#101	—	2	4	no	—
363	#101	—	4	2	no	—
364	C₂²⋊C₈	—	2	1	no	—
365	C₂²⋊C₈	—	2	1	no	—
366	C₂²⋊C₈	—	2	1	no	—
367	C₂²⋊C₈	—	2	1	no	—
368	#97	—	2	1	no	—
369	C₄×C₈	—	2	1	no	—
370	C₂⁴	#41×C₃₇	1	1	yes	characteristic
371	#41	—	2	2	no	—
372	#41	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
393	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
394	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
395	Q₁₆	—	4	4	no	—
396	Q₁₆	—	4	2	no	—
397	Q₁₆	—	4	2	no	—
398	SD₁₆	—	4	4	no	—
399	M₁₆	—	2	2	no	—
400	M₁₆	—	2	2	no	—
401	M₁₆	—	2	2	no	—
402	M₁₆	—	2	2	no	—
403	M₁₆	—	2	2	no	—
404	M₁₆	—	4	4	no	—
405	M₁₆	—	4	2	no	—
406	M₁₆	#41×C₃₇	1	4	yes	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	4	1	no	—
414	C₂×C₈	—	4	1	no	—
415	C₂×C₈	—	4	1	no	—
416	C₂×C₈	—	4	1	no	—
417	C₂×C₈	—	4	4	no	—
418	C₂×C₈	—	4	2	no	—
419	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
420	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
421	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
422	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	4	2	no	—
428	C₄⋊C₄	—	4	2	no	—
429	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
430	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
431	C₂²⋊C₄	—	2	1	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	1	no	—
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	4	2	no	—
437	C₂²⋊C₄	—	4	2	no	—
438	C₄²	—	2	1	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	#121×C₃₇	1	1	yes	characteristic
444	C₂³	#121×C₃₇	1	1	yes	characteristic
445	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
446	Q₈	—	2	2	no	—
447	Q₈	—	4	2	no	—
448	Q₈	—	4	2	no	—
449	Q₈	—	4	2	no	—
450	Q₈	—	4	2	no	—
451	D₄	—	2	2	no	—
452	D₄	—	4	2	no	—
453	D₄	—	4	2	no	—
454	D₄	—	4	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	8	2	no	—
472	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
473	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
474	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
475	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
476	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
477	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
478	C₈	—	2	1	no	—
479	C₈	—	2	1	no	—
480	C₈	—	2	1	no	—
481	C₈	—	2	1	no	—
482	C₈	—	2	4	no	—
483	C₈	—	4	1	no	—
484	C₈	—	4	1	no	—
485	C₈	—	4	2	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	1	no	—
497	C₂²	C₃₇×#473	1	2	yes	—
498	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
499	C₂²	C₃₇×#553	1	2	yes	—
500	C₄	—	2	1	no	—
501	C₄	—	2	1	no	—
502	C₄	—	4	1	no	—
503	C₄	—	4	1	no	—
504	C₄	—	4	1	no	—
505	C₄	—	8	2	no	—
506	C₄	—	8	2	no	—
507	C₄	C₃₇×#532	1	1	yes	characteristic
508	C₄	C₃₇×#534	1	1	yes	characteristic
509	C₄	C₃₇×#546	1	2	yes	—
510	C₂	—	2	2	no	—
511	C₂	—	2	2	no	—
512	C₂	—	4	1	no	—
513	C₂	—	8	1	no	—
514	C₂	C₃₇×#2543	1	1	yes	characteristic
515	C₂	C₂×C₃₇×#473	1	1	yes	characteristic
516	C₂	C₃₇×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#525	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂³×C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₇×#467	C₂	semidirect
4. C₃₇×#2089	C₂	semidirect
5. C₃₇×#2078	C₂	semidirect
6. C₃₇×#2047	C₂	semidirect
7. C₃₇×#2020	C₂	semidirect
8. C₃₇×#1930	C₂	semidirect
9. C₃₇×#1908	C₂	semidirect
10. C₃₇×#1901	C₂	semidirect
11. C₂×C₃₇×#341	C₂	semidirect
227. #28591	C₃₇	direct (N × H)
253. C₂×#467	C₂×C₃₇	semidirect
255. #2089	C₂×C₃₇	semidirect
256. #2078	C₂×C₃₇	semidirect
257. #2047	C₂×C₃₇	semidirect
258. #2020	C₂×C₃₇	semidirect
259. #1930	C₂×C₃₇	semidirect
260. #1908	C₂×C₃₇	semidirect
261. #1901	C₂×C₃₇	semidirect
262. C₂×#341	C₂×C₃₇	semidirect
305. C₃₇	#28591	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×#3056	2
C₂×C₃₇×#467	2
C₃₇×#2929	2
C₃₇×#2089	2
C₃₇×#2078	2
C₃₇×#2047	2
C₃₇×#2020	2
C₃₇×#1930	2
C₃₇×#1908	2
C₃₇×#1901	2
C₂×C₃₇×#341	2
#28591	37

Subgroups — C37×#28591 #22649844

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28591 #22649844