Subgroups — C₃₇×#9233 #22630486

Order 9472.

724 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×#3100	C₂	1	1	yes	maximal, characteristic
2	C₄²×D₄×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#1962	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#1502	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#1486	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#1303	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#1276	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#532	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₄×C₃₇	—	2	1	no	—
10	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₃₇	—	2	1	no	—
12	C₃₇×#480	—	2	1	no	—
13	C₃₇×#474	C₄	1	2	yes	complemented
14	C₃₇×#459	C₄	1	2	yes	complemented
15	C₃₇×#447	—	2	1	no	—
16	C₄×D₈×C₃₇	—	2	2	no	—
17	C₃₇×#431	C₂²	1	1	yes	characteristic
18	C₃₇×#431	C₂²	1	1	yes	characteristic
19	C₃₇×#423	C₂²	1	1	yes	characteristic
20	C₂×#104×C₃₇	—	2	1	no	—
21	C₂×#104×C₃₇	—	2	1	no	—
22	C₄×C₄⋊C₄×C₃₇	—	2	1	no	—
23	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊C₄×C₃₇	—	2	1	no	—
25	C₄×C₂²⋊C₄×C₃₇	—	2	2	no	—
26	C₄³×C₃₇	C₂²	1	1	yes	characteristic
27	C₃₇×#327	—	2	2	no	—
28	C₃₇×D₄⋊C₈	—	2	2	no	—
29	C₂×#41×C₃₇	—	2	1	no	—
30	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₃₇	—	2	2	no	—
32	C₂³×C₄×C₃₇	—	2	1	no	—
33	C₂×D₈×C₃₇	—	2	2	no	—
34	C₂×M₁₆×C₃₇	—	2	1	no	—
35	C₄⋊Q₈×C₃₇	C₂×C₄	1	1	yes	characteristic, complemented
36	#127×C₃₇	C₂×C₄	1	1	yes	characteristic, complemented
37	#124×C₃₇	—	2	1	no	—
38	#121×C₃₇	—	2	1	no	—
39	#121×C₃₇	—	2	1	no	—
40	C₄×D₄×C₃₇	—	2	8	no	—
41	C₄×D₄×C₃₇	—	2	1	no	—
42	C₄×D₄×C₃₇	—	2	1	no	—
43	C₄×D₄×C₃₇	—	2	1	no	—
44	C₄×D₄×C₃₇	—	2	1	no	—
45	C₄×D₄×C₃₇	C₂×C₄	1	2	yes	—
46	C₄×D₄×C₃₇	D₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
48	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
51	C₂×C₄²×C₃₇	—	2	1	no	—
52	C₂×C₄²×C₃₇	—	2	2	no	—
53	C₂×C₄²×C₃₇	—	2	1	no	—
54	C₂×C₄²×C₃₇	—	2	1	no	—
55	C₂×C₄²×C₃₇	—	4	2	no	—
56	C₂×C₄²×C₃₇	—	4	2	no	—
57	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
60	#107×C₃₇	—	2	2	no	—
61	C₄⋊C₈×C₃₇	—	2	1	no	—
62	C₄⋊C₈×C₃₇	—	2	1	no	—
63	C₄⋊C₈×C₃₇	—	2	1	no	—
64	C₄⋊C₈×C₃₇	C₂×C₄	1	2	yes	complemented
65	#104×C₃₇	—	4	2	no	—
66	#104×C₃₇	—	4	2	no	—
67	#102×C₃₇	—	2	2	no	—
68	#102×C₃₇	—	2	2	no	—
69	C₂²⋊C₈×C₃₇	—	2	1	no	—
70	C₂²⋊C₈×C₃₇	—	2	1	no	—
71	C₄×C₈×C₃₇	—	2	1	no	—
72	C₄×C₈×C₃₇	—	2	1	no	—
73	#95×C₃₇	—	2	2	no	—
74	#95×C₃₇	D₄	1	2	yes	—
75	C₂⁴×C₃₇	—	2	1	no	—
76	#41×C₃₇	—	4	1	no	—
77	#41×C₃₇	—	4	1	no	—
78	#41×C₃₇	—	4	1	no	—
79	#41×C₃₇	—	4	1	no	—
80	C₂×Q₈×C₃₇	—	2	1	no	—
81	C₂×D₄×C₃₇	—	2	4	no	—
82	C₂×D₄×C₃₇	—	2	1	no	—
83	C₂×D₄×C₃₇	—	2	1	no	—
84	C₂×D₄×C₃₇	—	2	1	no	—
85	C₂×D₄×C₃₇	—	2	1	no	—
86	C₂×D₄×C₃₇	—	4	1	no	—
87	C₂×D₄×C₃₇	C₂²⋊C₄	1	2	yes	—
88	C₂²×C₄×C₃₇	—	2	1	no	—
89	C₂²×C₄×C₃₇	—	2	8	no	—
90	C₂²×C₄×C₃₇	—	2	1	no	—
91	C₂²×C₄×C₃₇	—	2	1	no	—
92	C₂²×C₄×C₃₇	—	2	2	no	—
93	C₂²×C₄×C₃₇	—	2	2	no	—
94	C₂²×C₄×C₃₇	—	2	2	no	—
95	C₂²×C₄×C₃₇	—	4	4	no	—
96	C₂²×C₄×C₃₇	—	4	4	no	—
97	C₂²×C₄×C₃₇	—	4	1	no	—
98	C₂²×C₄×C₃₇	—	4	1	no	—
99	C₂²×C₄×C₃₇	—	4	1	no	—
100	C₂²×C₄×C₃₇	—	4	1	no	—
101	C₂²×C₄×C₃₇	—	4	1	no	—
102	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
105	D₈×C₃₇	—	4	4	no	—
106	M₁₆×C₃₇	—	4	1	no	—
107	M₁₆×C₃₇	—	4	1	no	—
108	C₂×C₈×C₃₇	—	2	2	no	—
109	C₂×C₈×C₃₇	—	4	1	no	—
110	C₂×C₈×C₃₇	—	4	1	no	—
111	C₄⋊C₄×C₃₇	—	2	4	no	—
112	C₄⋊C₄×C₃₇	—	2	1	no	—
113	C₄⋊C₄×C₃₇	—	2	1	no	—
114	C₄⋊C₄×C₃₇	—	2	1	no	—
115	C₄⋊C₄×C₃₇	C₂²⋊C₄	1	2	yes	—
116	C₂²⋊C₄×C₃₇	—	2	8	no	—
117	C₂²⋊C₄×C₃₇	—	2	2	no	—
118	C₂²⋊C₄×C₃₇	—	2	2	no	—
119	C₂²⋊C₄×C₃₇	—	4	1	no	—
120	C₂²⋊C₄×C₃₇	—	4	1	no	—
121	C₄²×C₃₇	—	2	4	no	—
122	C₄²×C₃₇	—	2	1	no	—
123	C₄²×C₃₇	—	2	1	no	—
124	C₄²×C₃₇	—	2	1	no	—
125	C₄²×C₃₇	—	4	2	no	—
126	C₄²×C₃₇	—	4	4	no	—
127	C₄²×C₃₇	—	4	1	no	—
128	C₄²×C₃₇	—	4	1	no	—
129	C₄²×C₃₇	D₈	1	2	yes	complemented
130	C₄²×C₃₇	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₃₇	#41	1	1	yes	characteristic
133	C₄²×C₃₇	#41	1	1	yes	characteristic
134	C₂³×C₃₇	—	2	4	no	—
135	C₂³×C₃₇	—	2	2	no	—
136	C₂³×C₃₇	—	4	2	no	—
137	C₂³×C₃₇	—	4	1	no	—
138	C₂³×C₃₇	—	4	1	no	—
139	C₂³×C₃₇	—	4	1	no	—
140	C₂³×C₃₇	#120	1	1	yes	characteristic
141	Q₈×C₃₇	—	4	1	no	—
142	Q₈×C₃₇	—	4	1	no	—
143	D₄×C₃₇	—	2	4	no	—
144	D₄×C₃₇	—	2	2	no	—
145	D₄×C₃₇	—	4	2	no	—
146	D₄×C₃₇	—	4	1	no	—
147	D₄×C₃₇	—	4	1	no	—
148	D₄×C₃₇	—	8	1	no	—
149	D₄×C₃₇	—	8	1	no	—
150	D₄×C₃₇	—	8	1	no	—
151	D₄×C₃₇	#104	1	4	yes	complemented
152	C₂×C₄×C₃₇	—	2	2	no	—
153	C₂×C₄×C₃₇	—	2	2	no	—
154	C₂×C₄×C₃₇	—	2	2	no	—
155	C₂×C₄×C₃₇	—	2	2	no	—
156	C₂×C₄×C₃₇	—	2	2	no	—
157	C₂×C₄×C₃₇	—	2	4	no	—
158	C₂×C₄×C₃₇	—	2	2	no	—
159	C₂×C₄×C₃₇	—	4	1	no	—
160	C₂×C₄×C₃₇	—	4	16	no	—
161	C₂×C₄×C₃₇	—	4	1	no	—
162	C₂×C₄×C₃₇	—	4	2	no	—
163	C₂×C₄×C₃₇	—	4	2	no	—
164	C₂×C₄×C₃₇	—	4	1	no	—
165	C₂×C₄×C₃₇	—	4	1	no	—
166	C₂×C₄×C₃₇	—	4	1	no	—
167	C₂×C₄×C₃₇	—	4	2	no	—
168	C₂×C₄×C₃₇	—	4	2	no	—
169	C₂×C₄×C₃₇	—	4	2	no	—
170	C₂×C₄×C₃₇	—	4	2	no	—
171	C₂×C₄×C₃₇	—	4	1	no	—
172	C₂×C₄×C₃₇	—	8	1	no	—
173	C₂×C₄×C₃₇	—	8	1	no	—
174	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₃₇	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₃₇	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
178	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
179	C₂×C₄×C₃₇	#123	1	1	yes	characteristic
180	C₂×C₄×C₃₇	C₂×D₈	1	1	yes	characteristic
181	C₂×C₄×C₃₇	#135	1	1	yes	characteristic
182	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₈×C₃₇	—	4	2	no	—
185	C₈×C₃₇	—	8	1	no	—
186	C₈×C₃₇	—	8	1	no	—
187	#9233	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂²×C₃₇	—	2	1	no	—
189	C₂²×C₃₇	—	2	1	no	—
190	C₂²×C₃₇	—	2	4	no	—
191	C₂²×C₃₇	—	4	4	no	—
192	C₂²×C₃₇	—	4	4	no	—
193	C₂²×C₃₇	—	4	2	no	—
194	C₂²×C₃₇	—	4	2	no	—
195	C₂²×C₃₇	—	8	1	no	—
196	C₂²×C₃₇	—	8	1	no	—
197	C₂²×C₃₇	—	8	1	no	—
198	C₂²×C₃₇	#386	1	1	yes	characteristic
199	C₂²×C₃₇	#447	1	1	yes	characteristic
200	C₂²×C₃₇	#449	1	1	yes	characteristic
201	C₄×C₃₇	—	2	4	no	—
202	C₄×C₃₇	—	2	1	no	—
203	C₄×C₃₇	—	2	1	no	—
204	C₄×C₃₇	—	2	1	no	—
205	C₄×C₃₇	—	4	2	no	—
206	C₄×C₃₇	—	4	4	no	—
207	C₄×C₃₇	—	4	2	no	—
208	C₄×C₃₇	—	8	1	no	—
209	C₄×C₃₇	C₂×#104	1	2	yes	—
210	C₄×C₃₇	C₄×D₈	1	1	yes	characteristic
211	C₄×C₃₇	#442	1	1	yes	characteristic
212	C₄×C₃₇	#459	1	1	yes	characteristic
213	C₄×C₃₇	#463	1	1	yes	characteristic
214	#3100	C₂×C₃₇	1	1	yes	characteristic
215	C₄²×D₄	C₂×C₃₇	1	1	yes	characteristic, complemented
216	#1962	C₂×C₃₇	1	1	yes	characteristic, complemented
217	#1502	C₂×C₃₇	1	1	yes	characteristic, complemented
218	#1486	C₂×C₃₇	1	1	yes	characteristic, complemented
219	#1303	C₂×C₃₇	1	1	yes	characteristic, complemented
220	#1276	C₂×C₃₇	1	1	yes	characteristic, complemented
221	C₂×C₃₇	—	2	1	no	—
222	C₂×C₃₇	—	2	1	no	—
223	C₂×C₃₇	—	4	4	no	—
224	C₂×C₃₇	—	16	1	no	—
225	C₂×C₃₇	#1879	1	1	yes	characteristic
226	C₂×C₃₇	#1896	1	1	yes	characteristic
227	C₂×C₃₇	#1906	1	1	yes	characteristic
228	#532	C₂²×C₃₇	1	1	yes	characteristic
229	C₂×C₄×D₄	—	2	1	no	—
230	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
231	C₂²×C₄²	—	2	1	no	—
232	#480	—	2	1	no	—
233	#474	C₄×C₃₇	1	2	yes	complemented
234	#459	C₄×C₃₇	1	2	yes	complemented
235	#447	—	2	1	no	—
236	C₄×D₈	—	2	2	no	—
237	#431	C₂²×C₃₇	1	1	yes	characteristic
238	#431	C₂²×C₃₇	1	1	yes	characteristic
239	#423	C₂²×C₃₇	1	1	yes	characteristic
240	C₂×#104	—	2	1	no	—
241	C₂×#104	—	2	1	no	—
242	C₄×C₄⋊C₄	—	2	1	no	—
243	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
244	C₄×C₂²⋊C₄	—	2	1	no	—
245	C₄×C₂²⋊C₄	—	2	2	no	—
246	C₄³	C₂²×C₃₇	1	1	yes	characteristic
247	#327	—	2	2	no	—
248	D₄⋊C₈	—	2	2	no	—
249	C₃₇	#9233	1	1	yes	characteristic, direct product factor, Sylow
250	C₂×#41	—	2	1	no	—
251	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
252	C₂³×C₄	—	2	2	no	—
253	C₂³×C₄	—	2	1	no	—
254	C₂×D₈	—	2	2	no	—
255	C₂×M₁₆	—	2	1	no	—
256	C₄⋊Q₈	C₂×C₄×C₃₇	1	1	yes	characteristic, complemented
257	#127	C₂×C₄×C₃₇	1	1	yes	characteristic, complemented
258	#124	—	2	1	no	—
259	#121	—	2	1	no	—
260	#121	—	2	1	no	—
261	C₄×D₄	—	2	8	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	C₂×C₄×C₃₇	1	2	yes	—
267	C₄×D₄	D₄×C₃₇	1	2	yes	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	—	4	2	no	—
277	C₂×C₄²	—	4	2	no	—
278	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
279	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
280	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
281	#107	—	2	2	no	—
282	C₄⋊C₈	—	2	1	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	C₂×C₄×C₃₇	1	2	yes	complemented
286	#104	—	4	2	no	—
287	#104	—	4	2	no	—
288	#102	—	2	2	no	—
289	#102	—	2	2	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	C₂²⋊C₈	—	2	1	no	—
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	—	2	1	no	—
294	#95	—	2	2	no	—
295	#95	D₄×C₃₇	1	2	yes	—
296	C₂⁴	—	2	1	no	—
297	#41	—	4	1	no	—
298	#41	—	4	1	no	—
299	#41	—	4	1	no	—
300	#41	—	4	1	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	C₂²⋊C₄×C₃₇	1	2	yes	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	4	4	no	—
317	C₂²×C₄	—	4	4	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
326	D₈	—	4	4	no	—
327	M₁₆	—	4	1	no	—
328	M₁₆	—	4	1	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	C₂²⋊C₄×C₃₇	1	2	yes	—
337	C₂²⋊C₄	—	2	8	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	4	1	no	—
341	C₂²⋊C₄	—	4	1	no	—
342	C₄²	—	2	4	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	4	2	no	—
347	C₄²	—	4	4	no	—
348	C₄²	—	4	1	no	—
349	C₄²	—	4	1	no	—
350	C₄²	D₈×C₃₇	1	2	yes	complemented
351	C₄²	C₂²×C₄×C₃₇	1	1	yes	characteristic
352	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
353	C₄²	#41×C₃₇	1	1	yes	characteristic
354	C₄²	#41×C₃₇	1	1	yes	characteristic
355	C₂³	—	2	4	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	1	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	1	no	—
361	C₂³	#120×C₃₇	1	1	yes	characteristic
362	Q₈	—	4	1	no	—
363	Q₈	—	4	1	no	—
364	D₄	—	2	4	no	—
365	D₄	—	2	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	1	no	—
368	D₄	—	4	1	no	—
369	D₄	—	8	1	no	—
370	D₄	—	8	1	no	—
371	D₄	—	8	1	no	—
372	D₄	#104×C₃₇	1	4	yes	complemented
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	16	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	8	1	no	—
394	C₂×C₄	—	8	1	no	—
395	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
396	C₂×C₄	C₄×D₄×C₃₇	1	1	yes	characteristic
397	C₂×C₄	C₄×D₄×C₃₇	1	1	yes	characteristic
398	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
399	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
400	C₂×C₄	#123×C₃₇	1	1	yes	characteristic
401	C₂×C₄	C₂×D₈×C₃₇	1	1	yes	characteristic
402	C₂×C₄	#135×C₃₇	1	1	yes	characteristic
403	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
404	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
405	C₈	—	4	2	no	—
406	C₈	—	8	1	no	—
407	C₈	—	8	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	4	4	no	—
412	C₂²	—	4	4	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	1	no	—
417	C₂²	—	8	1	no	—
418	C₂²	C₃₇×#386	1	1	yes	characteristic
419	C₂²	C₃₇×#447	1	1	yes	characteristic
420	C₂²	C₃₇×#449	1	1	yes	characteristic
421	C₄	—	2	4	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	1	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	8	1	no	—
429	C₄	C₂×#104×C₃₇	1	2	yes	—
430	C₄	C₄×D₈×C₃₇	1	1	yes	characteristic
431	C₄	C₃₇×#442	1	1	yes	characteristic
432	C₄	C₃₇×#459	1	1	yes	characteristic
433	C₄	C₃₇×#463	1	1	yes	characteristic
434	C₂	—	2	1	no	—
435	C₂	—	2	1	no	—
436	C₂	—	4	4	no	—
437	C₂	—	16	1	no	—
438	C₂	C₃₇×#1879	1	1	yes	characteristic
439	C₂	C₃₇×#1896	1	1	yes	characteristic
440	C₂	C₃₇×#1906	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₇	#121
commutator	C₄²	C₂²×C₄×C₃₇
Frattini, cosocle	C₂×C₄²	C₂³×C₃₇
socle	C₂²×C₃₇	#386
prime radical	C₃₇×#3100	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄²×D₄×C₃₇	C₂	semidirect
3. C₃₇×#1962	C₂	semidirect
4. C₃₇×#1502	C₂	semidirect
5. C₃₇×#1486	C₂	semidirect
6. C₃₇×#1303	C₂	semidirect
7. C₃₇×#1276	C₂	semidirect
13. C₃₇×#474	C₄	semidirect
14. C₃₇×#459	C₄	semidirect
35. C₄⋊Q₈×C₃₇	C₂×C₄	semidirect
36. #127×C₃₇	C₂×C₄	semidirect
64. C₄⋊C₈×C₃₇	C₂×C₄	semidirect
129. C₄²×C₃₇	D₈	semidirect
151. D₄×C₃₇	#104	semidirect
187. #9233	C₃₇	direct (N × H)
215. C₄²×D₄	C₂×C₃₇	semidirect
216. #1962	C₂×C₃₇	semidirect
217. #1502	C₂×C₃₇	semidirect
218. #1486	C₂×C₃₇	semidirect
219. #1303	C₂×C₃₇	semidirect
220. #1276	C₂×C₃₇	semidirect
233. #474	C₄×C₃₇	semidirect
234. #459	C₄×C₃₇	semidirect
249. C₃₇	#9233	direct (N × H)
256. C₄⋊Q₈	C₂×C₄×C₃₇	semidirect
257. #127	C₂×C₄×C₃₇	semidirect
285. C₄⋊C₈	C₂×C₄×C₃₇	semidirect
350. C₄²	D₈×C₃₇	semidirect
372. D₄	#104×C₃₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₇×#3100	2
C₄²×D₄×C₃₇	2
C₃₇×#1962	2
C₃₇×#1502	2
C₃₇×#1486	2
C₃₇×#1303	2
C₃₇×#1276	2
#9233	37

Subgroups — C37×#9233 #22630486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#9233 #22630486