Subgroups — C₃₇×#28632 #22649885

Order 9472.

830 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3151	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#3141	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2051	C₂	1	4	yes	maximal, complemented
6	C₃₇×#1997	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#1965	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1907	C₂	1	4	yes	maximal, complemented
9	C₄×#108×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	4	yes	—
11	C₂×#131×C₃₇	C₂²	1	2	yes	—
12	C₃₇×#532	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
15	C₃₇×#496	—	2	2	no	—
16	C₃₇×#493	—	2	1	no	—
17	C₃₇×#492	—	2	1	no	—
18	C₃₇×#489	—	2	2	no	—
19	C₃₇×#487	—	2	1	no	—
20	C₃₇×#486	—	2	1	no	—
21	C₃₇×#486	—	2	1	no	—
22	C₃₇×#486	—	2	1	no	—
23	C₃₇×#486	—	2	1	no	—
24	C₃₇×#486	—	2	1	no	—
25	C₃₇×#436	—	2	1	no	—
26	C₃₇×#436	—	2	1	no	—
27	C₈×D₄×C₃₇	—	2	1	no	—
28	C₈×D₄×C₃₇	—	2	1	no	—
29	C₂×#108×C₃₇	C₂²	1	2	yes	—
30	C₃₇×#423	C₂²	1	1	yes	characteristic
31	C₃₇×#417	C₂²	1	4	yes	—
32	C₂×#102×C₃₇	C₂²	1	2	yes	—
33	C₂×#102×C₃₇	C₂²	1	2	yes	—
34	C₂×#100×C₃₇	C₂²	1	4	yes	—
35	C₃₇×#408	C₂²	1	2	yes	—
36	C₄×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
37	C₄×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
39	C₃₇×#343	C₂²	1	4	yes	—
40	C₃₇×#341	C₂²	1	2	yes	—
41	C₂×#41×C₃₇	C₂³	1	2	yes	—
42	C₂²×Q₈×C₃₇	—	2	1	no	—
43	C₂²×D₄×C₃₇	—	2	1	no	—
44	C₂²×D₄×C₃₇	—	2	1	no	—
45	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
46	AGL(1,ℤ/8)×C₃₇	—	2	8	no	—
47	AGL(1,ℤ/8)×C₃₇	—	4	4	no	—
48	C₂×SD₁₆×C₃₇	—	2	4	no	—
49	C₂×D₈×C₃₇	—	2	4	no	—
50	#131×C₃₇	—	4	4	no	—
51	C₂×M₁₆×C₃₇	—	2	2	no	—
52	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
53	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
54	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
55	C₂²×C₈×C₃₇	—	2	2	no	—
56	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₃₇	—	2	1	no	—
59	C₄⋊Q₈×C₃₇	—	2	1	no	—
60	C₄⋊Q₈×C₃₇	—	2	1	no	—
61	C₄⋊Q₈×C₃₇	—	2	1	no	—
62	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
63	#127×C₃₇	—	2	1	no	—
64	#127×C₃₇	—	2	1	no	—
65	#127×C₃₇	—	2	1	no	—
66	#127×C₃₇	—	2	1	no	—
67	#127×C₃₇	D₄	1	1	yes	characteristic
68	#124×C₃₇	D₄	1	2	yes	—
69	#121×C₃₇	—	2	1	no	—
70	#121×C₃₇	—	2	1	no	—
71	C₄×D₄×C₃₇	—	2	1	no	—
72	C₄×D₄×C₃₇	—	2	1	no	—
73	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
74	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
75	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
76	#108×C₃₇	—	2	4	no	—
77	C₄⋊C₈×C₃₇	—	2	1	no	—
78	C₄⋊C₈×C₃₇	—	2	1	no	—
79	#103×C₃₇	—	2	4	no	—
80	#102×C₃₇	—	2	4	no	—
81	#102×C₃₇	—	2	2	no	—
82	#102×C₃₇	—	2	2	no	—
83	#102×C₃₇	—	2	2	no	—
84	#102×C₃₇	—	2	2	no	—
85	#100×C₃₇	—	4	4	no	—
86	C₂²⋊C₈×C₃₇	—	2	2	no	—
87	C₂²⋊C₈×C₃₇	—	2	2	no	—
88	#97×C₃₇	—	2	1	no	—
89	#97×C₃₇	—	2	1	no	—
90	C₄×C₈×C₃₇	—	2	1	no	—
91	C₄×C₈×C₃₇	—	2	1	no	—
92	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
93	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
94	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
95	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
96	C₂⁴×C₃₇	—	2	2	no	—
97	#41×C₃₇	—	2	4	no	—
98	#41×C₃₇	—	2	4	no	—
99	C₂×Q₈×C₃₇	—	4	1	no	—
100	C₂×Q₈×C₃₇	—	4	1	no	—
101	C₂×Q₈×C₃₇	—	8	2	no	—
102	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
103	C₂×D₄×C₃₇	—	2	2	no	—
104	C₂×D₄×C₃₇	—	2	1	no	—
105	C₂×D₄×C₃₇	—	2	1	no	—
106	C₂×D₄×C₃₇	—	2	2	no	—
107	C₂×D₄×C₃₇	—	2	2	no	—
108	C₂×D₄×C₃₇	—	2	4	no	—
109	C₂×D₄×C₃₇	—	2	4	no	—
110	C₂×D₄×C₃₇	—	4	1	no	—
111	C₂×D₄×C₃₇	—	4	1	no	—
112	C₂×D₄×C₃₇	—	4	1	no	—
113	C₂×D₄×C₃₇	—	4	1	no	—
114	C₂×D₄×C₃₇	—	8	2	no	—
115	C₂×D₄×C₃₇	—	8	2	no	—
116	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₃₇	—	2	2	no	—
118	C₂²×C₄×C₃₇	—	2	2	no	—
119	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
120	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
121	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
122	SD₁₆×C₃₇	—	4	8	no	—
123	D₈×C₃₇	—	4	8	no	—
124	M₁₆×C₃₇	—	2	2	no	—
125	M₁₆×C₃₇	—	2	2	no	—
126	M₁₆×C₃₇	—	2	2	no	—
127	M₁₆×C₃₇	—	2	4	no	—
128	M₁₆×C₃₇	—	4	4	no	—
129	M₁₆×C₃₇	#41	1	4	yes	—
130	C₂×C₈×C₃₇	—	2	2	no	—
131	C₂×C₈×C₃₇	—	2	2	no	—
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	—	4	4	no	—
136	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
140	C₄⋊C₄×C₃₇	—	2	1	no	—
141	C₄⋊C₄×C₃₇	—	2	1	no	—
142	C₄⋊C₄×C₃₇	—	2	2	no	—
143	C₄⋊C₄×C₃₇	—	2	2	no	—
144	C₄⋊C₄×C₃₇	—	4	1	no	—
145	C₄⋊C₄×C₃₇	—	4	1	no	—
146	C₂²⋊C₄×C₃₇	—	2	2	no	—
147	C₂²⋊C₄×C₃₇	—	2	2	no	—
148	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
152	C₂³×C₃₇	—	2	2	no	—
153	C₂³×C₃₇	—	4	2	no	—
154	C₂³×C₃₇	—	4	4	no	—
155	C₂³×C₃₇	—	8	2	no	—
156	C₂³×C₃₇	—	8	2	no	—
157	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
158	Q₈×C₃₇	—	2	4	no	—
159	Q₈×C₃₇	—	8	2	no	—
160	Q₈×C₃₇	—	8	2	no	—
161	D₄×C₃₇	—	2	4	no	—
162	D₄×C₃₇	—	4	4	no	—
163	D₄×C₃₇	—	4	2	no	—
164	D₄×C₃₇	—	4	2	no	—
165	D₄×C₃₇	—	4	4	no	—
166	D₄×C₃₇	—	4	2	no	—
167	D₄×C₃₇	—	4	2	no	—
168	D₄×C₃₇	—	8	2	no	—
169	D₄×C₃₇	—	8	2	no	—
170	D₄×C₃₇	—	8	2	no	—
171	D₄×C₃₇	—	8	2	no	—
172	C₂×C₄×C₃₇	—	2	2	no	—
173	C₂×C₄×C₃₇	—	2	2	no	—
174	C₂×C₄×C₃₇	—	2	2	no	—
175	C₂×C₄×C₃₇	—	4	2	no	—
176	C₂×C₄×C₃₇	—	4	2	no	—
177	C₂×C₄×C₃₇	—	4	2	no	—
178	C₂×C₄×C₃₇	—	8	2	no	—
179	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
180	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
181	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
182	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
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	1	no	—
190	C₈×C₃₇	—	2	1	no	—
191	C₈×C₃₇	—	2	4	no	—
192	C₈×C₃₇	—	4	2	no	—
193	C₈×C₃₇	—	4	2	no	—
194	#28632	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂²×C₃₇	—	2	1	no	—
196	C₂²×C₃₇	—	2	1	no	—
197	C₂²×C₃₇	—	4	2	no	—
198	C₂²×C₃₇	—	4	2	no	—
199	C₂²×C₃₇	—	4	2	no	—
200	C₂²×C₃₇	—	8	2	no	—
201	C₂²×C₃₇	—	8	2	no	—
202	C₂²×C₃₇	—	8	2	no	—
203	C₂²×C₃₇	—	16	4	no	—
204	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
205	C₂²×C₃₇	#559	1	2	yes	—
206	C₄×C₃₇	—	2	1	no	—
207	C₄×C₃₇	—	2	1	no	—
208	C₄×C₃₇	—	4	2	no	—
209	C₄×C₃₇	—	8	2	no	—
210	C₄×C₃₇	#471	1	2	yes	—
211	C₄×C₃₇	#472	1	2	yes	—
212	C₄×C₃₇	#532	1	1	yes	characteristic
213	C₄×C₃₇	#535	1	1	yes	characteristic
214	C₄×C₃₇	#546	1	2	yes	—
215	#3151	C₂×C₃₇	1	1	yes	characteristic
216	#3141	C₂×C₃₇	1	1	yes	characteristic, complemented
217	C₂×#486	C₂×C₃₇	1	1	yes	characteristic, complemented
218	#2931	C₂×C₃₇	1	1	yes	characteristic, complemented
219	#2051	C₂×C₃₇	1	4	yes	complemented
220	#1997	C₂×C₃₇	1	1	yes	characteristic, complemented
221	#1965	C₂×C₃₇	1	1	yes	characteristic, complemented
222	#1907	C₂×C₃₇	1	4	yes	complemented
223	C₄×#108	C₂×C₃₇	1	1	yes	characteristic, complemented
224	C₂×C₃₇	—	2	2	no	—
225	C₂×C₃₇	—	8	2	no	—
226	C₂×C₃₇	—	16	2	no	—
227	C₂×C₃₇	#2544	1	1	yes	characteristic
228	C₂×C₃₇	C₂×#471	1	1	yes	characteristic
229	C₂×C₃₇	C₂×#472	1	1	yes	characteristic
230	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	4	yes	—
231	C₂×#131	C₂²×C₃₇	1	2	yes	—
232	#532	C₂²×C₃₇	1	1	yes	characteristic
233	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
234	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
235	#496	—	2	2	no	—
236	#493	—	2	1	no	—
237	#492	—	2	1	no	—
238	#489	—	2	2	no	—
239	#487	—	2	1	no	—
240	#486	—	2	1	no	—
241	#486	—	2	1	no	—
242	#486	—	2	1	no	—
243	#486	—	2	1	no	—
244	#486	—	2	1	no	—
245	#436	—	2	1	no	—
246	#436	—	2	1	no	—
247	C₈×D₄	—	2	1	no	—
248	C₈×D₄	—	2	1	no	—
249	C₂×#108	C₂²×C₃₇	1	2	yes	—
250	#423	C₂²×C₃₇	1	1	yes	characteristic
251	#417	C₂²×C₃₇	1	4	yes	—
252	C₂×#102	C₂²×C₃₇	1	2	yes	—
253	C₂×#102	C₂²×C₃₇	1	2	yes	—
254	C₂×#100	C₂²×C₃₇	1	4	yes	—
255	#408	C₂²×C₃₇	1	2	yes	—
256	C₄×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
257	C₄×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
258	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
259	#343	C₂²×C₃₇	1	4	yes	—
260	#341	C₂²×C₃₇	1	2	yes	—
261	C₃₇	#28632	1	1	yes	characteristic, direct product factor, Sylow
262	C₂×#41	C₂³×C₃₇	1	2	yes	—
263	C₂²×Q₈	—	2	1	no	—
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	—	2	1	no	—
266	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
267	AGL(1,ℤ/8)	—	2	8	no	—
268	AGL(1,ℤ/8)	—	4	4	no	—
269	C₂×SD₁₆	—	2	4	no	—
270	C₂×D₈	—	2	4	no	—
271	#131	—	4	4	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
274	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
275	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
276	C₂²×C₈	—	2	2	no	—
277	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
278	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
279	C₄⋊Q₈	—	2	1	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
284	#127	—	2	1	no	—
285	#127	—	2	1	no	—
286	#127	—	2	1	no	—
287	#127	—	2	1	no	—
288	#127	D₄×C₃₇	1	1	yes	characteristic
289	#124	D₄×C₃₇	1	2	yes	—
290	#121	—	2	1	no	—
291	#121	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
296	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
297	#108	—	2	4	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	—	2	1	no	—
300	#103	—	2	4	no	—
301	#102	—	2	4	no	—
302	#102	—	2	2	no	—
303	#102	—	2	2	no	—
304	#102	—	2	2	no	—
305	#102	—	2	2	no	—
306	#100	—	4	4	no	—
307	C₂²⋊C₈	—	2	2	no	—
308	C₂²⋊C₈	—	2	2	no	—
309	#97	—	2	1	no	—
310	#97	—	2	1	no	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
314	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
315	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
316	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
317	C₂⁴	—	2	2	no	—
318	#41	—	2	4	no	—
319	#41	—	2	4	no	—
320	C₂×Q₈	—	4	1	no	—
321	C₂×Q₈	—	4	1	no	—
322	C₂×Q₈	—	8	2	no	—
323	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	—	4	1	no	—
335	C₂×D₄	—	8	2	no	—
336	C₂×D₄	—	8	2	no	—
337	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
341	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
342	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
343	SD₁₆	—	4	8	no	—
344	D₈	—	4	8	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	—	2	4	no	—
349	M₁₆	—	4	4	no	—
350	M₁₆	#41×C₃₇	1	4	yes	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	4	4	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	1	yes	characteristic
360	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	4	1	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
370	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
371	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
372	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
373	C₂³	—	2	2	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	4	no	—
376	C₂³	—	8	2	no	—
377	C₂³	—	8	2	no	—
378	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
379	Q₈	—	2	4	no	—
380	Q₈	—	8	2	no	—
381	Q₈	—	8	2	no	—
382	D₄	—	2	4	no	—
383	D₄	—	4	4	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	8	2	no	—
390	D₄	—	8	2	no	—
391	D₄	—	8	2	no	—
392	D₄	—	8	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	8	2	no	—
400	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
401	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
402	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
403	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
404	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
405	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
406	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
407	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
408	C₈	—	2	1	no	—
409	C₈	—	2	1	no	—
410	C₈	—	2	1	no	—
411	C₈	—	2	1	no	—
412	C₈	—	2	4	no	—
413	C₈	—	4	2	no	—
414	C₈	—	4	2	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	16	4	no	—
424	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
425	C₂²	C₃₇×#559	1	2	yes	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	4	2	no	—
429	C₄	—	8	2	no	—
430	C₄	C₃₇×#471	1	2	yes	—
431	C₄	C₃₇×#472	1	2	yes	—
432	C₄	C₃₇×#532	1	1	yes	characteristic
433	C₄	C₃₇×#535	1	1	yes	characteristic
434	C₄	C₃₇×#546	1	2	yes	—
435	C₂	—	2	2	no	—
436	C₂	—	8	2	no	—
437	C₂	—	16	2	no	—
438	C₂	C₃₇×#2544	1	1	yes	characteristic
439	C₂	C₂×C₃₇×#471	1	1	yes	characteristic
440	C₂	C₂×C₃₇×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#3151	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₇×#3141	C₂	semidirect
3. C₂×C₃₇×#486	C₂	semidirect
4. C₃₇×#2931	C₂	semidirect
5. C₃₇×#2051	C₂	semidirect
6. C₃₇×#1997	C₂	semidirect
7. C₃₇×#1965	C₂	semidirect
8. C₃₇×#1907	C₂	semidirect
9. C₄×#108×C₃₇	C₂	semidirect
194. #28632	C₃₇	direct (N × H)
216. #3141	C₂×C₃₇	semidirect
217. C₂×#486	C₂×C₃₇	semidirect
218. #2931	C₂×C₃₇	semidirect
219. #2051	C₂×C₃₇	semidirect
220. #1997	C₂×C₃₇	semidirect
221. #1965	C₂×C₃₇	semidirect
222. #1907	C₂×C₃₇	semidirect
223. C₄×#108	C₂×C₃₇	semidirect
261. C₃₇	#28632	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×#3151	2
C₃₇×#3141	2
C₂×C₃₇×#486	2
C₃₇×#2931	2
C₃₇×#2051	2
C₃₇×#1997	2
C₃₇×#1965	2
C₃₇×#1907	2
C₄×#108×C₃₇	2
#28632	37

Subgroups — C37×#28632 #22649885

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28632 #22649885