Subgroups — C₃₇×#28594 #22649847

Order 9472.

780 conjugacy classes of subgroups.

The subgroup lattice has 434 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×#470	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#2930	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2090	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2079	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	C₃₇×#1738	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	C₂²×M₁₆×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×#470	—	2	2	no	—
21	C₃₇×#470	—	2	2	no	—
22	C₃₇×#468	—	2	2	no	—
23	C₃₇×#467	—	2	2	no	—
24	C₃₇×#465	—	2	2	no	—
25	C₃₇×#436	—	2	2	no	—
26	C₃₇×#435	—	2	2	no	—
27	C₃₇×#428	C₂²	1	2	yes	—
28	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
29	C₃₇×#424	C₂²	1	1	yes	characteristic
30	C₃₇×#419	C₂²	1	2	yes	—
31	C₃₇×#417	C₂²	1	2	yes	—
32	C₂×#103×C₃₇	C₂²	1	2	yes	—
33	C₂×#101×C₃₇	C₂²	1	2	yes	—
34	C₂×#101×C₃₇	C₂²	1	2	yes	—
35	C₃₇×#408	C₂²	1	1	yes	characteristic
36	C₃₇×#407	C₂²	1	1	yes	characteristic
37	C₃₇×#405	C₂²	1	1	yes	characteristic
38	C₃₇×#343	C₂²	1	2	yes	—
39	C₃₇×#343	C₂²	1	2	yes	—
40	C₃₇×#341	C₂²	1	2	yes	—
41	C₃₇×#341	C₂²	1	1	yes	characteristic
42	C₃₇×#341	C₂²	1	1	yes	characteristic
43	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
45	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
46	#137×C₃₇	—	2	4	no	—
47	#137×C₃₇	—	4	2	no	—
48	C₂×Q₁₆×C₃₇	—	2	2	no	—
49	C₂×Q₁₆×C₃₇	—	2	2	no	—
50	C₂×Q₁₆×C₃₇	—	4	2	no	—
51	C₂×SD₁₆×C₃₇	—	2	2	no	—
52	#131×C₃₇	—	4	2	no	—
53	C₂×M₁₆×C₃₇	—	2	2	no	—
54	C₂×M₁₆×C₃₇	—	2	1	no	—
55	C₂×M₁₆×C₃₇	—	2	4	no	—
56	C₂×M₁₆×C₃₇	—	4	2	no	—
57	C₂×M₁₆×C₃₇	—	4	2	no	—
58	C₂×M₁₆×C₃₇	D₄	1	2	yes	—
59	C₂×M₁₆×C₃₇	D₄	1	2	yes	—
60	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
61	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
63	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
64	C₂²×C₈×C₃₇	—	2	2	no	—
65	C₂²×C₈×C₃₇	—	2	1	no	—
66	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
68	#123×C₃₇	—	2	1	no	—
69	C₂²⋊Q₈×C₃₇	—	2	2	no	—
70	C₂²⋊Q₈×C₃₇	—	2	2	no	—
71	C₂²⋊Q₈×C₃₇	—	2	2	no	—
72	C₂²⋊Q₈×C₃₇	—	2	2	no	—
73	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
74	#121×C₃₇	D₄	1	2	yes	—
75	#120×C₃₇	—	2	1	no	—
76	C₄×D₄×C₃₇	—	2	2	no	—
77	#117×C₃₇	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
79	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
80	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
81	#107×C₃₇	—	2	2	no	—
82	#106×C₃₇	—	2	2	no	—
83	#106×C₃₇	—	2	2	no	—
84	C₄⋊C₈×C₃₇	—	2	2	no	—
85	#103×C₃₇	—	2	2	no	—
86	#103×C₃₇	—	2	2	no	—
87	#103×C₃₇	—	2	2	no	—
88	#103×C₃₇	—	2	2	no	—
89	#103×C₃₇	—	2	2	no	—
90	#102×C₃₇	—	2	2	no	—
91	#101×C₃₇	—	2	4	no	—
92	#101×C₃₇	—	4	2	no	—
93	C₂²⋊C₈×C₃₇	—	2	2	no	—
94	C₂²⋊C₈×C₃₇	—	2	2	no	—
95	#97×C₃₇	—	2	1	no	—
96	C₄×C₈×C₃₇	—	2	1	no	—
97	C₂⁴×C₃₇	#41	1	1	yes	characteristic
98	#41×C₃₇	—	2	2	no	—
99	#41×C₃₇	—	2	2	no	—
100	C₂×Q₈×C₃₇	—	2	2	no	—
101	C₂×Q₈×C₃₇	—	2	2	no	—
102	C₂×Q₈×C₃₇	—	2	2	no	—
103	C₂×Q₈×C₃₇	—	2	2	no	—
104	C₂×Q₈×C₃₇	—	2	2	no	—
105	C₂×Q₈×C₃₇	—	2	2	no	—
106	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
107	C₂×D₄×C₃₇	—	2	1	no	—
108	C₂×D₄×C₃₇	—	2	2	no	—
109	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₃₇	—	2	2	no	—
111	C₂²×C₄×C₃₇	—	2	2	no	—
112	C₂²×C₄×C₃₇	—	2	1	no	—
113	C₂²×C₄×C₃₇	—	2	2	no	—
114	C₂²×C₄×C₃₇	—	2	2	no	—
115	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
118	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
119	Q₁₆×C₃₇	—	4	4	no	—
120	Q₁₆×C₃₇	—	4	4	no	—
121	SD₁₆×C₃₇	—	4	4	no	—
122	M₁₆×C₃₇	—	2	2	no	—
123	M₁₆×C₃₇	—	2	2	no	—
124	M₁₆×C₃₇	—	2	2	no	—
125	M₁₆×C₃₇	—	2	2	no	—
126	M₁₆×C₃₇	—	2	2	no	—
127	M₁₆×C₃₇	—	4	2	no	—
128	M₁₆×C₃₇	—	4	2	no	—
129	M₁₆×C₃₇	—	4	4	no	—
130	M₁₆×C₃₇	—	4	2	no	—
131	M₁₆×C₃₇	#41	1	4	yes	—
132	C₂×C₈×C₃₇	—	2	2	no	—
133	C₂×C₈×C₃₇	—	2	2	no	—
134	C₂×C₈×C₃₇	—	2	2	no	—
135	C₂×C₈×C₃₇	—	2	1	no	—
136	C₂×C₈×C₃₇	—	2	1	no	—
137	C₂×C₈×C₃₇	—	2	2	no	—
138	C₂×C₈×C₃₇	—	4	4	no	—
139	C₂×C₈×C₃₇	—	4	2	no	—
140	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
143	C₄⋊C₄×C₃₇	—	2	2	no	—
144	C₄⋊C₄×C₃₇	—	2	2	no	—
145	C₄⋊C₄×C₃₇	—	2	2	no	—
146	C₄⋊C₄×C₃₇	—	4	2	no	—
147	C₄⋊C₄×C₃₇	—	4	2	no	—
148	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
149	C₂²⋊C₄×C₃₇	—	2	2	no	—
150	C₂²⋊C₄×C₃₇	—	2	1	no	—
151	C₂²⋊C₄×C₃₇	—	2	2	no	—
152	C₂²⋊C₄×C₃₇	—	4	2	no	—
153	C₂²⋊C₄×C₃₇	—	4	2	no	—
154	C₄²×C₃₇	—	2	1	no	—
155	C₂³×C₃₇	—	2	2	no	—
156	C₂³×C₃₇	—	2	1	no	—
157	C₂³×C₃₇	—	4	2	no	—
158	C₂³×C₃₇	#121	1	2	yes	—
159	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
160	Q₈×C₃₇	—	2	2	no	—
161	Q₈×C₃₇	—	4	2	no	—
162	Q₈×C₃₇	—	4	2	no	—
163	Q₈×C₃₇	—	4	2	no	—
164	Q₈×C₃₇	—	4	2	no	—
165	D₄×C₃₇	—	2	2	no	—
166	D₄×C₃₇	—	4	2	no	—
167	D₄×C₃₇	—	8	2	no	—
168	C₂×C₄×C₃₇	—	2	2	no	—
169	C₂×C₄×C₃₇	—	2	2	no	—
170	C₂×C₄×C₃₇	—	2	2	no	—
171	C₂×C₄×C₃₇	—	2	2	no	—
172	C₂×C₄×C₃₇	—	2	2	no	—
173	C₂×C₄×C₃₇	—	2	2	no	—
174	C₂×C₄×C₃₇	—	2	1	no	—
175	C₂×C₄×C₃₇	—	4	1	no	—
176	C₂×C₄×C₃₇	—	4	1	no	—
177	C₂×C₄×C₃₇	—	4	2	no	—
178	C₂×C₄×C₃₇	—	4	2	no	—
179	C₂×C₄×C₃₇	—	4	2	no	—
180	C₂×C₄×C₃₇	—	4	2	no	—
181	C₂×C₄×C₃₇	—	8	2	no	—
182	C₂×C₄×C₃₇	#121	1	2	yes	—
183	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
186	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
187	C₈×C₃₇	—	2	1	no	—
188	C₈×C₃₇	—	2	1	no	—
189	C₈×C₃₇	—	2	2	no	—
190	C₈×C₃₇	—	2	4	no	—
191	C₈×C₃₇	—	4	1	no	—
192	C₈×C₃₇	—	4	1	no	—
193	C₈×C₃₇	—	4	2	no	—
194	#28594	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂²×C₃₇	—	2	2	no	—
196	C₂²×C₃₇	—	2	2	no	—
197	C₂²×C₃₇	—	2	2	no	—
198	C₂²×C₃₇	—	2	2	no	—
199	C₂²×C₃₇	—	4	1	no	—
200	C₂²×C₃₇	—	4	2	no	—
201	C₂²×C₃₇	—	8	2	no	—
202	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
203	C₂²×C₃₇	#553	1	2	yes	—
204	C₄×C₃₇	—	2	2	no	—
205	C₄×C₃₇	—	4	1	no	—
206	C₄×C₃₇	—	4	2	no	—
207	C₄×C₃₇	—	8	2	no	—
208	C₄×C₃₇	—	8	2	no	—
209	C₄×C₃₇	#532	1	1	yes	characteristic
210	C₄×C₃₇	#534	1	1	yes	characteristic
211	C₄×C₃₇	#546	1	2	yes	—
212	#3056	C₂×C₃₇	1	2	yes	—
213	C₂×#470	C₂×C₃₇	1	1	yes	characteristic, complemented
214	#2930	C₂×C₃₇	1	1	yes	characteristic
215	#2090	C₂×C₃₇	1	1	yes	characteristic, complemented
216	#2079	C₂×C₃₇	1	1	yes	characteristic, complemented
217	#2047	C₂×C₃₇	1	1	yes	characteristic, complemented
218	#2020	C₂×C₃₇	1	1	yes	characteristic, complemented
219	#1930	C₂×C₃₇	1	2	yes	complemented
220	#1908	C₂×C₃₇	1	2	yes	complemented
221	#1901	C₂×C₃₇	1	2	yes	complemented
222	#1738	C₂×C₃₇	1	1	yes	characteristic, complemented
223	C₂×C₃₇	—	2	2	no	—
224	C₂×C₃₇	—	4	2	no	—
225	C₂×C₃₇	—	8	1	no	—
226	C₂×C₃₇	#2543	1	1	yes	characteristic
227	C₂×C₃₇	#3069	1	2	yes	—
228	C₂×#137	C₂²×C₃₇	1	2	yes	—
229	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
230	C₂×#131	C₂²×C₃₇	1	1	yes	characteristic
231	C₂²×M₁₆	C₂²×C₃₇	1	2	yes	—
232	C₂²×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
233	#525	C₂²×C₃₇	1	1	yes	characteristic
234	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	2	yes	—
235	#470	—	2	2	no	—
236	#470	—	2	2	no	—
237	#470	—	2	2	no	—
238	#468	—	2	2	no	—
239	#467	—	2	2	no	—
240	#465	—	2	2	no	—
241	#436	—	2	2	no	—
242	#435	—	2	2	no	—
243	#428	C₂²×C₃₇	1	2	yes	—
244	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
245	#424	C₂²×C₃₇	1	1	yes	characteristic
246	#419	C₂²×C₃₇	1	2	yes	—
247	#417	C₂²×C₃₇	1	2	yes	—
248	C₂×#103	C₂²×C₃₇	1	2	yes	—
249	C₂×#101	C₂²×C₃₇	1	2	yes	—
250	C₂×#101	C₂²×C₃₇	1	2	yes	—
251	#408	C₂²×C₃₇	1	1	yes	characteristic
252	#407	C₂²×C₃₇	1	1	yes	characteristic
253	#405	C₂²×C₃₇	1	1	yes	characteristic
254	#343	C₂²×C₃₇	1	2	yes	—
255	#343	C₂²×C₃₇	1	2	yes	—
256	#341	C₂²×C₃₇	1	1	yes	characteristic
257	#341	C₂²×C₃₇	1	1	yes	characteristic
258	#341	C₂²×C₃₇	1	2	yes	—
259	C₃₇	#28594	1	1	yes	characteristic, direct product factor, Sylow
260	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
261	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
262	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
263	#137	—	2	4	no	—
264	#137	—	4	2	no	—
265	C₂×Q₁₆	—	2	2	no	—
266	C₂×Q₁₆	—	2	2	no	—
267	C₂×Q₁₆	—	4	2	no	—
268	C₂×SD₁₆	—	2	2	no	—
269	#131	—	4	2	no	—
270	C₂×M₁₆	—	2	2	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	—	2	4	no	—
273	C₂×M₁₆	—	4	2	no	—
274	C₂×M₁₆	—	4	2	no	—
275	C₂×M₁₆	D₄×C₃₇	1	2	yes	—
276	C₂×M₁₆	D₄×C₃₇	1	2	yes	—
277	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
278	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
279	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
280	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
285	#123	—	2	1	no	—
286	C₂²⋊Q₈	—	2	2	no	—
287	C₂²⋊Q₈	—	2	2	no	—
288	C₂²⋊Q₈	—	2	2	no	—
289	C₂²⋊Q₈	—	2	2	no	—
290	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
291	#121	D₄×C₃₇	1	2	yes	—
292	#120	—	2	1	no	—
293	C₄×D₄	—	2	2	no	—
294	#117	C₂³×C₃₇	1	1	yes	characteristic
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	#107	—	2	2	no	—
299	#106	—	2	2	no	—
300	#106	—	2	2	no	—
301	C₄⋊C₈	—	2	2	no	—
302	#103	—	2	2	no	—
303	#103	—	2	2	no	—
304	#103	—	2	2	no	—
305	#103	—	2	2	no	—
306	#103	—	2	2	no	—
307	#102	—	2	2	no	—
308	#101	—	2	4	no	—
309	#101	—	4	2	no	—
310	C₂²⋊C₈	—	2	2	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	#97	—	2	1	no	—
313	C₄×C₈	—	2	1	no	—
314	C₂⁴	#41×C₃₇	1	1	yes	characteristic
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
334	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
335	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
336	Q₁₆	—	4	4	no	—
337	Q₁₆	—	4	4	no	—
338	SD₁₆	—	4	4	no	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	2	2	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	—	4	2	no	—
345	M₁₆	—	4	2	no	—
346	M₁₆	—	4	4	no	—
347	M₁₆	—	4	2	no	—
348	M₁₆	#41×C₃₇	1	4	yes	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	4	4	no	—
356	C₂×C₈	—	4	2	no	—
357	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
358	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
359	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	4	2	no	—
370	C₂²⋊C₄	—	4	2	no	—
371	C₄²	—	2	1	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	4	2	no	—
375	C₂³	#121×C₃₇	1	2	yes	—
376	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
377	Q₈	—	2	2	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	4	2	no	—
381	Q₈	—	4	2	no	—
382	D₄	—	2	2	no	—
383	D₄	—	4	2	no	—
384	D₄	—	8	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	8	2	no	—
399	C₂×C₄	#121×C₃₇	1	2	yes	—
400	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
402	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
403	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
404	C₈	—	2	1	no	—
405	C₈	—	2	1	no	—
406	C₈	—	2	2	no	—
407	C₈	—	2	4	no	—
408	C₈	—	4	1	no	—
409	C₈	—	4	1	no	—
410	C₈	—	4	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	8	2	no	—
418	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
419	C₂²	C₃₇×#553	1	2	yes	—
420	C₄	—	2	2	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	2	no	—
423	C₄	—	8	2	no	—
424	C₄	—	8	2	no	—
425	C₄	C₃₇×#532	1	1	yes	characteristic
426	C₄	C₃₇×#534	1	1	yes	characteristic
427	C₄	C₃₇×#546	1	2	yes	—
428	C₂	—	2	2	no	—
429	C₂	—	4	2	no	—
430	C₂	—	8	1	no	—
431	C₂	C₃₇×#2543	1	1	yes	characteristic
432	C₂	C₃₇×#3069	1	2	yes	—

	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×#470	C₂	semidirect
4. C₃₇×#2090	C₂	semidirect
5. C₃₇×#2079	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. C₃₇×#1738	C₂	semidirect
194. #28594	C₃₇	direct (N × H)
213. C₂×#470	C₂×C₃₇	semidirect
215. #2090	C₂×C₃₇	semidirect
216. #2079	C₂×C₃₇	semidirect
217. #2047	C₂×C₃₇	semidirect
218. #2020	C₂×C₃₇	semidirect
219. #1930	C₂×C₃₇	semidirect
220. #1908	C₂×C₃₇	semidirect
221. #1901	C₂×C₃₇	semidirect
222. #1738	C₂×C₃₇	semidirect
259. C₃₇	#28594	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×#470	2
C₃₇×#2930	2
C₃₇×#2090	2
C₃₇×#2079	2
C₃₇×#2047	2
C₃₇×#2020	2
C₃₇×#1930	2
C₃₇×#1908	2
C₃₇×#1901	2
C₃₇×#1738	2
#28594	37

Subgroups — C37×#28594 #22649847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28594 #22649847