Subgroups — C₃₇×#29982 #22651235

Order 9472.

734 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#2862	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#2293	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2101	C₂	1	2	yes	maximal, complemented
4	C₃₇×#2092	C₂	1	2	yes	maximal
5	C₃₇×#2058	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2057	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2023	C₂	1	1	yes	maximal, characteristic
8	C₃₇×#2023	C₂	1	1	yes	maximal, characteristic
9	C₃₇×#1949	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1831	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1804	C₂	1	2	yes	maximal
12	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×#117×C₃₇	—	2	1	no	—
16	C₂×#107×C₃₇	C₂²	1	2	yes	—
17	C₂×#106×C₃₇	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
19	C₂×#102×C₃₇	C₂²	1	2	yes	—
20	C₂×#102×C₃₇	C₂²	1	2	yes	—
21	C₃₇×#391	—	2	1	no	—
22	C₃₇×#391	—	2	1	no	—
23	C₃₇×#391	—	2	1	no	—
24	C₃₇×#391	—	2	1	no	—
25	C₃₇×#390	C₂²	1	1	yes	characteristic
26	C₃₇×#390	C₂²	1	1	yes	characteristic
27	C₃₇×#389	C₂²	1	1	yes	characteristic
28	C₃₇×#389	C₂²	1	1	yes	characteristic
29	C₃₇×#388	—	2	1	no	—
30	C₃₇×#388	—	2	1	no	—
31	C₃₇×#382	C₂²	1	2	yes	—
32	C₃₇×#382	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
34	C₄×C₂²⋊C₄×C₃₇	—	2	1	no	—
35	C₄³×C₃₇	C₂²	1	1	yes	characteristic
36	C₃₇×#340	C₂²	1	2	yes	—
37	C₃₇×#340	C₂²	1	2	yes	—
38	C₃₇×#340	C₂²	1	2	yes	—
39	C₃₇×#340	C₂²	1	2	yes	—
40	C₃₇×#336	C₂²	1	2	yes	—
41	C₃₇×#336	C₂²	1	1	yes	characteristic
42	C₃₇×#336	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₃₇	—	2	1	no	—
44	C₂²×Q₈×C₃₇	—	2	1	no	—
45	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₃₇	—	2	1	no	—
47	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
48	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
49	C₄⋊Q₈×C₃₇	—	4	2	no	—
50	C₄⋊Q₈×C₃₇	—	4	2	no	—
51	C₄×D₄×C₃₇	—	2	2	no	—
52	C₄×D₄×C₃₇	Q₈	1	4	yes	complemented
53	#117×C₃₇	—	4	4	no	—
54	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
68	C₂×C₄²×C₃₇	—	2	1	no	—
69	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
76	#107×C₃₇	—	4	2	no	—
77	#106×C₃₇	—	4	2	no	—
78	C₄⋊C₈×C₃₇	—	2	4	no	—
79	#102×C₃₇	—	4	2	no	—
80	#102×C₃₇	—	4	2	no	—
81	#95×C₃₇	—	2	1	no	—
82	#95×C₃₇	—	2	1	no	—
83	#95×C₃₇	—	2	1	no	—
84	#95×C₃₇	—	2	2	no	—
85	#95×C₃₇	—	2	2	no	—
86	#95×C₃₇	—	2	2	no	—
87	#95×C₃₇	—	2	2	no	—
88	C₂⁴×C₃₇	—	2	1	no	—
89	C₂×Q₈×C₃₇	—	4	2	no	—
90	C₂×Q₈×C₃₇	—	4	2	no	—
91	C₂×Q₈×C₃₇	—	4	2	no	—
92	C₂×Q₈×C₃₇	—	4	2	no	—
93	C₂×Q₈×C₃₇	—	4	2	no	—
94	C₂×Q₈×C₃₇	—	4	2	no	—
95	C₂×D₄×C₃₇	—	2	1	no	—
96	C₂×D₄×C₃₇	—	2	2	no	—
97	C₂×D₄×C₃₇	—	2	2	no	—
98	C₂×D₄×C₃₇	C₂×Q₈	1	2	yes	—
99	C₂²×C₄×C₃₇	—	2	1	no	—
100	C₂²×C₄×C₃₇	—	2	4	no	—
101	C₂²×C₄×C₃₇	—	2	2	no	—
102	C₂²×C₄×C₃₇	—	2	2	no	—
103	C₂²×C₄×C₃₇	—	2	1	no	—
104	C₂²×C₄×C₃₇	—	2	1	no	—
105	C₂²×C₄×C₃₇	—	4	2	no	—
106	C₂²×C₄×C₃₇	—	4	2	no	—
107	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
114	C₂×C₈×C₃₇	—	2	2	no	—
115	C₂×C₈×C₃₇	—	2	2	no	—
116	C₂×C₈×C₃₇	—	2	2	no	—
117	C₂×C₈×C₃₇	—	2	2	no	—
118	C₂×C₈×C₃₇	—	2	2	no	—
119	C₂×C₈×C₃₇	—	2	2	no	—
120	C₄⋊C₄×C₃₇	—	2	1	no	—
121	C₄⋊C₄×C₃₇	—	2	2	no	—
122	C₄⋊C₄×C₃₇	—	2	2	no	—
123	C₄⋊C₄×C₃₇	—	2	2	no	—
124	C₄⋊C₄×C₃₇	—	2	2	no	—
125	C₄⋊C₄×C₃₇	—	2	2	no	—
126	C₄⋊C₄×C₃₇	—	2	2	no	—
127	C₄⋊C₄×C₃₇	—	4	2	no	—
128	C₄⋊C₄×C₃₇	—	4	2	no	—
129	C₄⋊C₄×C₃₇	—	4	2	no	—
130	C₄⋊C₄×C₃₇	—	4	2	no	—
131	C₄⋊C₄×C₃₇	C₂×Q₈	1	2	yes	—
132	C₂²⋊C₄×C₃₇	—	2	4	no	—
133	C₂²⋊C₄×C₃₇	—	4	2	no	—
134	C₂²⋊C₄×C₃₇	—	4	2	no	—
135	C₂²⋊C₄×C₃₇	—	4	2	no	—
136	C₂²⋊C₄×C₃₇	—	4	2	no	—
137	C₄²×C₃₇	—	2	2	no	—
138	C₄²×C₃₇	—	2	2	no	—
139	C₄²×C₃₇	—	2	2	no	—
140	C₄²×C₃₇	—	2	2	no	—
141	C₄²×C₃₇	—	4	1	no	—
142	C₄²×C₃₇	—	4	1	no	—
143	C₄²×C₃₇	—	4	2	no	—
144	C₄²×C₃₇	C₂×Q₈	1	2	yes	—
145	C₄²×C₃₇	#41	1	2	yes	—
146	C₂³×C₃₇	—	2	2	no	—
147	C₂³×C₃₇	—	4	1	no	—
148	C₂³×C₃₇	—	4	1	no	—
149	C₂³×C₃₇	—	4	1	no	—
150	C₂³×C₃₇	—	4	1	no	—
151	C₂³×C₃₇	—	4	1	no	—
152	C₂³×C₃₇	—	4	1	no	—
153	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
154	Q₈×C₃₇	—	8	4	no	—
155	Q₈×C₃₇	—	8	4	no	—
156	D₄×C₃₇	—	2	4	no	—
157	D₄×C₃₇	—	4	2	no	—
158	C₂×C₄×C₃₇	—	2	1	no	—
159	C₂×C₄×C₃₇	—	2	1	no	—
160	C₂×C₄×C₃₇	—	2	1	no	—
161	C₂×C₄×C₃₇	—	2	1	no	—
162	C₂×C₄×C₃₇	—	2	1	no	—
163	C₂×C₄×C₃₇	—	2	1	no	—
164	C₂×C₄×C₃₇	—	2	1	no	—
165	C₂×C₄×C₃₇	—	2	1	no	—
166	C₂×C₄×C₃₇	—	2	2	no	—
167	C₂×C₄×C₃₇	—	2	1	no	—
168	C₂×C₄×C₃₇	—	2	1	no	—
169	C₂×C₄×C₃₇	—	2	1	no	—
170	C₂×C₄×C₃₇	—	2	1	no	—
171	C₂×C₄×C₃₇	—	2	1	no	—
172	C₂×C₄×C₃₇	—	2	1	no	—
173	C₂×C₄×C₃₇	—	4	8	no	—
174	C₂×C₄×C₃₇	—	4	1	no	—
175	C₂×C₄×C₃₇	—	4	1	no	—
176	C₂×C₄×C₃₇	—	4	2	no	—
177	C₂×C₄×C₃₇	—	4	2	no	—
178	C₂×C₄×C₃₇	—	4	1	no	—
179	C₂×C₄×C₃₇	—	4	1	no	—
180	C₂×C₄×C₃₇	—	4	1	no	—
181	C₂×C₄×C₃₇	—	4	2	no	—
182	C₂×C₄×C₃₇	—	4	1	no	—
183	C₂×C₄×C₃₇	—	4	1	no	—
184	C₂×C₄×C₃₇	—	4	2	no	—
185	C₂×C₄×C₃₇	—	4	1	no	—
186	C₂×C₄×C₃₇	—	4	2	no	—
187	C₂×C₄×C₃₇	—	4	2	no	—
188	C₂×C₄×C₃₇	C₂²⋊Q₈	1	2	yes	—
189	C₂×C₄×C₃₇	C₂²⋊Q₈	1	2	yes	—
190	C₂×C₄×C₃₇	#135	1	2	yes	—
191	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
192	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
195	C₂×C₄×C₃₇	2₋¹⁺⁴	1	2	yes	—
196	C₈×C₃₇	—	4	2	no	—
197	C₈×C₃₇	—	4	2	no	—
198	#29982	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₃₇	—	4	2	no	—
200	C₂²×C₃₇	—	4	2	no	—
201	C₂²×C₃₇	—	4	2	no	—
202	C₂²×C₃₇	—	8	1	no	—
203	C₂²×C₃₇	—	8	1	no	—
204	C₂²×C₃₇	—	8	1	no	—
205	C₂²×C₃₇	—	8	1	no	—
206	C₂²×C₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
207	C₂²×C₃₇	#535	1	1	yes	characteristic
208	C₂²×C₃₇	#536	1	1	yes	characteristic
209	C₂²×C₃₇	C₂×#135	1	1	yes	characteristic
210	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
211	C₂²×C₃₇	#575	1	1	yes	characteristic
212	C₂²×C₃₇	#575	1	1	yes	characteristic
213	C₄×C₃₇	—	2	2	no	—
214	C₄×C₃₇	—	2	2	no	—
215	C₄×C₃₇	—	2	2	no	—
216	C₄×C₃₇	—	2	2	no	—
217	C₄×C₃₇	—	4	2	no	—
218	C₄×C₃₇	—	4	1	no	—
219	C₄×C₃₇	—	4	1	no	—
220	C₄×C₃₇	—	8	2	no	—
221	C₄×C₃₇	—	8	1	no	—
222	C₄×C₃₇	—	8	2	no	—
223	C₄×C₃₇	—	8	1	no	—
224	C₄×C₃₇	#542	1	2	yes	—
225	C₄×C₃₇	#544	1	2	yes	—
226	#2862	C₂×C₃₇	1	1	yes	characteristic, complemented
227	#2293	C₂×C₃₇	1	1	yes	characteristic
228	#2101	C₂×C₃₇	1	2	yes	complemented
229	#2092	C₂×C₃₇	1	2	yes	—
230	#2058	C₂×C₃₇	1	1	yes	characteristic, complemented
231	#2057	C₂×C₃₇	1	1	yes	characteristic, complemented
232	#2023	C₂×C₃₇	1	1	yes	characteristic
233	#2023	C₂×C₃₇	1	1	yes	characteristic
234	#1949	C₂×C₃₇	1	2	yes	complemented
235	#1831	C₂×C₃₇	1	1	yes	characteristic, complemented
236	#1804	C₂×C₃₇	1	2	yes	—
237	C₂×C₃₇	—	8	2	no	—
238	C₂×C₃₇	#2628	1	1	yes	characteristic
239	C₂×C₃₇	#3076	1	1	yes	characteristic
240	C₂×C₃₇	#3077	1	1	yes	characteristic
241	C₂×C₃₇	#3211	1	1	yes	characteristic
242	C₂×C₃₇	#3213	1	1	yes	characteristic
243	C₂×C₃₇	#3228	1	1	yes	characteristic
244	C₂×C₃₇	#3240	1	1	yes	characteristic
245	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
246	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
247	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
248	C₂×#117	—	2	1	no	—
249	C₂×#107	C₂²×C₃₇	1	2	yes	—
250	C₂×#106	C₂²×C₃₇	1	2	yes	—
251	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
252	C₂×#102	C₂²×C₃₇	1	2	yes	—
253	C₂×#102	C₂²×C₃₇	1	2	yes	—
254	#391	—	2	1	no	—
255	#391	—	2	1	no	—
256	#391	—	2	1	no	—
257	#391	—	2	1	no	—
258	#390	C₂²×C₃₇	1	1	yes	characteristic
259	#390	C₂²×C₃₇	1	1	yes	characteristic
260	#389	C₂²×C₃₇	1	1	yes	characteristic
261	#389	C₂²×C₃₇	1	1	yes	characteristic
262	#388	—	2	1	no	—
263	#388	—	2	1	no	—
264	#382	C₂²×C₃₇	1	2	yes	—
265	#382	C₂²×C₃₇	1	2	yes	—
266	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
267	C₄×C₂²⋊C₄	—	2	1	no	—
268	C₄³	C₂²×C₃₇	1	1	yes	characteristic
269	#340	C₂²×C₃₇	1	2	yes	—
270	#340	C₂²×C₃₇	1	2	yes	—
271	#340	C₂²×C₃₇	1	2	yes	—
272	#340	C₂²×C₃₇	1	2	yes	—
273	#336	C₂²×C₃₇	1	1	yes	characteristic
274	#336	C₂²×C₃₇	1	1	yes	characteristic
275	#336	C₂²×C₃₇	1	2	yes	—
276	C₃₇	#29982	1	1	yes	characteristic, direct product factor, Sylow
277	C₂²×Q₈	—	2	1	no	—
278	C₂²×Q₈	—	2	1	no	—
279	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
280	C₂³×C₄	—	2	1	no	—
281	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
282	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
283	C₄⋊Q₈	—	4	2	no	—
284	C₄⋊Q₈	—	4	2	no	—
285	C₄×D₄	—	2	2	no	—
286	C₄×D₄	Q₈×C₃₇	1	4	yes	complemented
287	#117	—	4	4	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
304	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
305	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
306	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
308	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
310	#107	—	4	2	no	—
311	#106	—	4	2	no	—
312	C₄⋊C₈	—	2	4	no	—
313	#102	—	4	2	no	—
314	#102	—	4	2	no	—
315	#95	—	2	1	no	—
316	#95	—	2	1	no	—
317	#95	—	2	1	no	—
318	#95	—	2	2	no	—
319	#95	—	2	2	no	—
320	#95	—	2	2	no	—
321	#95	—	2	2	no	—
322	C₂⁴	—	2	1	no	—
323	C₂×Q₈	—	4	2	no	—
324	C₂×Q₈	—	4	2	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	C₂×Q₈×C₃₇	1	2	yes	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
347	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	4	2	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	C₂×Q₈×C₃₇	1	2	yes	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	4	2	no	—
368	C₂²⋊C₄	—	4	2	no	—
369	C₂²⋊C₄	—	4	2	no	—
370	C₂²⋊C₄	—	4	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	4	1	no	—
376	C₄²	—	4	1	no	—
377	C₄²	—	4	2	no	—
378	C₄²	C₂×Q₈×C₃₇	1	2	yes	—
379	C₄²	#41×C₃₇	1	2	yes	—
380	C₂³	—	2	2	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	4	1	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	1	no	—
387	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
388	Q₈	—	8	4	no	—
389	Q₈	—	8	4	no	—
390	D₄	—	2	4	no	—
391	D₄	—	4	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	4	8	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	C₂²⋊Q₈×C₃₇	1	2	yes	—
423	C₂×C₄	C₂²⋊Q₈×C₃₇	1	2	yes	—
424	C₂×C₄	#135×C₃₇	1	2	yes	—
425	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
426	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
427	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
428	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
429	C₂×C₄	2₋¹⁺⁴×C₃₇	1	2	yes	—
430	C₈	—	4	2	no	—
431	C₈	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	1	no	—
439	C₂²	C₂×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
440	C₂²	C₃₇×#535	1	1	yes	characteristic
441	C₂²	C₃₇×#536	1	1	yes	characteristic
442	C₂²	C₂×#135×C₃₇	1	1	yes	characteristic
443	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
444	C₂²	C₃₇×#575	1	1	yes	characteristic
445	C₂²	C₃₇×#575	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	2	no	—
453	C₄	—	8	2	no	—
454	C₄	—	8	2	no	—
455	C₄	—	8	1	no	—
456	C₄	—	8	1	no	—
457	C₄	C₃₇×#542	1	2	yes	—
458	C₄	C₃₇×#544	1	2	yes	—
459	C₂	—	8	2	no	—
460	C₂	C₃₇×#2628	1	1	yes	characteristic
461	C₂	C₃₇×#3076	1	1	yes	characteristic
462	C₂	C₃₇×#3077	1	1	yes	characteristic
463	C₂	C₃₇×#3211	1	1	yes	characteristic
464	C₂	C₃₇×#3213	1	1	yes	characteristic
465	C₂	C₃₇×#3228	1	1	yes	characteristic
466	C₂	C₃₇×#3240	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂²×D₄×C₃₇	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₄³×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#2862	C₂	semidirect
3. C₃₇×#2101	C₂	semidirect
5. C₃₇×#2058	C₂	semidirect
6. C₃₇×#2057	C₂	semidirect
9. C₃₇×#1949	C₂	semidirect
10. C₃₇×#1831	C₂	semidirect
52. C₄×D₄×C₃₇	Q₈	semidirect
198. #29982	C₃₇	direct (N × H)
226. #2862	C₂×C₃₇	semidirect
228. #2101	C₂×C₃₇	semidirect
230. #2058	C₂×C₃₇	semidirect
231. #2057	C₂×C₃₇	semidirect
234. #1949	C₂×C₃₇	semidirect
235. #1831	C₂×C₃₇	semidirect
276. C₃₇	#29982	direct (N × H)
286. C₄×D₄	Q₈×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#2862	2
C₃₇×#2293	2
C₃₇×#2101	2
C₃₇×#2092	2
C₃₇×#2058	2
C₃₇×#2057	2
C₃₇×#2023	2
C₃₇×#1949	2
C₃₇×#1831	2
C₃₇×#1804	2
#29982	37

Subgroups — C37×#29982 #22651235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#29982 #22651235