Subgroups — C₃₇×#28614 #22649867

Order 9472.

982 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#492	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#2858	C₂	1	1	yes	maximal, characteristic
4	C₄×C₄⋊Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2055	C₂	1	4	yes	maximal, complemented
6	C₃₇×#1990	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#1957	C₂	1	1	yes	maximal, characteristic
8	C₃₇×#1880	C₂	1	4	yes	maximal, complemented
9	C₄×C₄⋊C₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₃₇	C₂²	1	4	yes	—
11	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×#124×C₃₇	—	2	1	no	—
15	C₂×#124×C₃₇	—	2	1	no	—
16	C₂×C₄×Q₈×C₃₇	C₂²	1	2	yes	—
17	C₃₇×#492	—	2	4	no	—
18	C₃₇×#487	—	2	4	no	—
19	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
20	C₂×#103×C₃₇	C₂²	1	4	yes	—
21	C₂×#102×C₃₇	C₂²	1	4	yes	—
22	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
24	C₃₇×#391	C₂²	1	2	yes	—
25	C₃₇×#390	—	2	1	no	—
26	C₃₇×#390	—	2	1	no	—
27	C₃₇×#390	C₂²	1	2	yes	—
28	C₃₇×#390	C₂²	1	2	yes	—
29	C₃₇×#389	—	2	1	no	—
30	C₃₇×#389	—	2	1	no	—
31	C₃₇×#384	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₃₇	—	2	1	no	—
33	C₄×C₄⋊C₄×C₃₇	—	2	1	no	—
34	C₄³×C₃₇	C₂²	1	1	yes	characteristic
35	C₃₇×#340	C₂²	1	4	yes	—
36	C₃₇×#336	C₂²	1	2	yes	—
37	C₂²×Q₈×C₃₇	—	2	1	no	—
38	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
39	C₂²×D₄×C₃₇	—	2	1	no	—
40	C₂²×D₄×C₃₇	—	2	1	no	—
41	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
42	C₂×SD₁₆×C₃₇	—	2	8	no	—
43	C₂×SD₁₆×C₃₇	—	2	8	no	—
44	C₂×SD₁₆×C₃₇	—	4	4	no	—
45	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
46	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
47	C₄⋊Q₈×C₃₇	—	2	2	no	—
48	C₄⋊Q₈×C₃₇	—	2	2	no	—
49	C₄⋊Q₈×C₃₇	—	2	2	no	—
50	C₄⋊Q₈×C₃₇	D₄	1	4	yes	—
51	#127×C₃₇	—	2	2	no	—
52	#127×C₃₇	—	2	2	no	—
53	#124×C₃₇	—	4	4	no	—
54	#124×C₃₇	—	4	4	no	—
55	C₄×Q₈×C₃₇	—	4	4	no	—
56	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
68	C₂×C₄²×C₃₇	—	2	2	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	C₄⋊C₈×C₃₇	—	2	4	no	—
77	#103×C₃₇	—	2	8	no	—
78	#102×C₃₇	—	4	4	no	—
79	C₄×C₈×C₃₇	—	2	2	no	—
80	C₄×C₈×C₃₇	—	2	2	no	—
81	#95×C₃₇	—	2	2	no	—
82	#95×C₃₇	—	2	2	no	—
83	C₂⁴×C₃₇	—	2	2	no	—
84	C₂×Q₈×C₃₇	—	2	2	no	—
85	C₂×Q₈×C₃₇	—	2	4	no	—
86	C₂×Q₈×C₃₇	—	2	4	no	—
87	C₂×Q₈×C₃₇	—	4	2	no	—
88	C₂×Q₈×C₃₇	—	4	2	no	—
89	C₂×Q₈×C₃₇	—	4	2	no	—
90	C₂×Q₈×C₃₇	C₂×D₄	1	4	yes	—
91	C₂×D₄×C₃₇	—	2	2	no	—
92	C₂×D₄×C₃₇	—	2	2	no	—
93	C₂×D₄×C₃₇	—	2	4	no	—
94	C₂×D₄×C₃₇	—	2	4	no	—
95	C₂×D₄×C₃₇	—	4	2	no	—
96	C₂×D₄×C₃₇	—	4	2	no	—
97	C₂×D₄×C₃₇	—	4	2	no	—
98	C₂×D₄×C₃₇	—	4	2	no	—
99	C₂×D₄×C₃₇	—	4	2	no	—
100	C₂×D₄×C₃₇	—	4	2	no	—
101	C₂²×C₄×C₃₇	—	2	2	no	—
102	C₂²×C₄×C₃₇	—	2	2	no	—
103	C₂²×C₄×C₃₇	—	2	2	no	—
104	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
111	SD₁₆×C₃₇	—	4	16	no	—
112	C₂×C₈×C₃₇	—	2	2	no	—
113	C₂×C₈×C₃₇	—	2	2	no	—
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	#41	1	4	yes	—
118	C₄⋊C₄×C₃₇	—	2	4	no	—
119	C₄⋊C₄×C₃₇	—	2	4	no	—
120	C₄⋊C₄×C₃₇	—	2	2	no	—
121	C₄⋊C₄×C₃₇	—	2	2	no	—
122	C₄⋊C₄×C₃₇	—	2	4	no	—
123	C₄⋊C₄×C₃₇	—	4	4	no	—
124	C₄⋊C₄×C₃₇	—	4	2	no	—
125	C₄⋊C₄×C₃₇	—	4	2	no	—
126	C₄⋊C₄×C₃₇	—	4	2	no	—
127	C₂²⋊C₄×C₃₇	—	4	4	no	—
128	C₂²⋊C₄×C₃₇	—	4	4	no	—
129	C₂²⋊C₄×C₃₇	—	4	4	no	—
130	C₂²⋊C₄×C₃₇	—	4	4	no	—
131	C₄²×C₃₇	—	2	2	no	—
132	C₄²×C₃₇	—	2	2	no	—
133	C₄²×C₃₇	—	2	2	no	—
134	C₄²×C₃₇	—	2	2	no	—
135	C₄²×C₃₇	—	2	2	no	—
136	C₄²×C₃₇	—	4	4	no	—
137	C₄²×C₃₇	SD₁₆	1	4	yes	complemented
138	C₄²×C₃₇	C₂×D₄	1	2	yes	—
139	C₄²×C₃₇	#41	1	2	yes	—
140	C₂³×C₃₇	—	4	2	no	—
141	C₂³×C₃₇	—	4	2	no	—
142	C₂³×C₃₇	—	4	2	no	—
143	C₂³×C₃₇	—	4	2	no	—
144	C₂³×C₃₇	—	4	2	no	—
145	C₂³×C₃₇	—	4	2	no	—
146	C₂³×C₃₇	—	4	2	no	—
147	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₃₇	—	2	8	no	—
149	Q₈×C₃₇	—	4	4	no	—
150	Q₈×C₃₇	—	8	4	no	—
151	D₄×C₃₇	—	4	4	no	—
152	D₄×C₃₇	—	4	4	no	—
153	D₄×C₃₇	—	8	4	no	—
154	D₄×C₃₇	—	8	4	no	—
155	C₂×C₄×C₃₇	—	2	1	no	—
156	C₂×C₄×C₃₇	—	2	1	no	—
157	C₂×C₄×C₃₇	—	2	1	no	—
158	C₂×C₄×C₃₇	—	2	1	no	—
159	C₂×C₄×C₃₇	—	2	4	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	—	4	2	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	2	no	—
172	C₂×C₄×C₃₇	—	4	2	no	—
173	C₂×C₄×C₃₇	—	4	2	no	—
174	C₂×C₄×C₃₇	#121	1	2	yes	—
175	C₂×C₄×C₃₇	#121	1	2	yes	—
176	C₂×C₄×C₃₇	C₂×SD₁₆	1	2	yes	—
177	C₂×C₄×C₃₇	C₂×SD₁₆	1	2	yes	—
178	C₂×C₄×C₃₇	C₂×SD₁₆	1	2	yes	—
179	C₂×C₄×C₃₇	#135	1	2	yes	—
180	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
181	C₂×C₄×C₃₇	#137	1	2	yes	—
182	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
184	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
186	C₈×C₃₇	—	2	4	no	—
187	C₈×C₃₇	—	4	2	no	—
188	#28614	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂²×C₃₇	—	8	2	no	—
190	C₂²×C₃₇	—	8	2	no	—
191	C₂²×C₃₇	—	8	2	no	—
192	C₂²×C₃₇	—	8	2	no	—
193	C₂²×C₃₇	—	8	2	no	—
194	C₂²×C₃₇	—	8	2	no	—
195	C₂²×C₃₇	—	8	2	no	—
196	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
197	C₂²×C₃₇	#532	1	1	yes	characteristic
198	C₂²×C₃₇	#535	1	1	yes	characteristic
199	C₂²×C₃₇	C₂²×SD₁₆	1	1	yes	characteristic
200	C₂²×C₃₇	C₂×#135	1	1	yes	characteristic
201	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
202	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
203	C₄×C₃₇	—	2	2	no	—
204	C₄×C₃₇	—	2	2	no	—
205	C₄×C₃₇	—	4	1	no	—
206	C₄×C₃₇	—	4	1	no	—
207	C₄×C₃₇	—	4	4	no	—
208	C₄×C₃₇	—	8	2	no	—
209	C₄×C₃₇	—	8	2	no	—
210	C₄×C₃₇	#460	1	4	yes	—
211	C₄×C₃₇	#464	1	4	yes	—
212	C₄×C₃₇	#546	1	2	yes	—
213	C₄×C₃₇	#559	1	2	yes	—
214	C₂×#492	C₂×C₃₇	1	1	yes	characteristic
215	C₂×#487	C₂×C₃₇	1	1	yes	characteristic, complemented
216	#2858	C₂×C₃₇	1	1	yes	characteristic
217	C₄×C₄⋊Q₈	C₂×C₃₇	1	1	yes	characteristic, complemented
218	#2055	C₂×C₃₇	1	4	yes	complemented
219	#1990	C₂×C₃₇	1	1	yes	characteristic, complemented
220	#1957	C₂×C₃₇	1	1	yes	characteristic
221	#1880	C₂×C₃₇	1	4	yes	complemented
222	C₄×C₄⋊C₈	C₂×C₃₇	1	1	yes	characteristic, complemented
223	C₂×C₃₇	—	16	2	no	—
224	C₂×C₃₇	#2544	1	1	yes	characteristic
225	C₂×C₃₇	C₂×#460	1	1	yes	characteristic
226	C₂×C₃₇	C₂×#464	1	1	yes	characteristic
227	C₂×C₃₇	#3167	1	1	yes	characteristic
228	C₂×C₃₇	#3182	1	1	yes	characteristic
229	C₂×C₃₇	#3206	1	1	yes	characteristic
230	C₂×C₃₇	#3207	1	1	yes	characteristic
231	C₂²×SD₁₆	C₂²×C₃₇	1	4	yes	—
232	C₂×C₄⋊Q₈	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	C₂×#124	—	2	1	no	—
236	C₂×#124	—	2	1	no	—
237	C₂×C₄×Q₈	C₂²×C₃₇	1	2	yes	—
238	#492	—	2	4	no	—
239	#487	—	2	4	no	—
240	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
241	C₂×#103	C₂²×C₃₇	1	4	yes	—
242	C₂×#102	C₂²×C₃₇	1	4	yes	—
243	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
244	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
245	#391	C₂²×C₃₇	1	2	yes	—
246	#390	—	2	1	no	—
247	#390	—	2	1	no	—
248	#390	C₂²×C₃₇	1	2	yes	—
249	#390	C₂²×C₃₇	1	2	yes	—
250	#389	—	2	1	no	—
251	#389	—	2	1	no	—
252	#384	C₂²×C₃₇	1	1	yes	characteristic
253	C₄×C₄⋊C₄	—	2	1	no	—
254	C₄×C₄⋊C₄	—	2	1	no	—
255	C₄³	C₂²×C₃₇	1	1	yes	characteristic
256	#340	C₂²×C₃₇	1	4	yes	—
257	#336	C₂²×C₃₇	1	2	yes	—
258	C₃₇	#28614	1	1	yes	characteristic, direct product factor, Sylow
259	C₂²×Q₈	—	2	1	no	—
260	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
261	C₂²×D₄	—	2	1	no	—
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
264	C₂×SD₁₆	—	2	8	no	—
265	C₂×SD₁₆	—	2	8	no	—
266	C₂×SD₁₆	—	4	4	no	—
267	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
268	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
269	C₄⋊Q₈	—	2	2	no	—
270	C₄⋊Q₈	—	2	2	no	—
271	C₄⋊Q₈	—	2	2	no	—
272	C₄⋊Q₈	D₄×C₃₇	1	4	yes	—
273	#127	—	2	2	no	—
274	#127	—	2	2	no	—
275	#124	—	4	4	no	—
276	#124	—	4	4	no	—
277	C₄×Q₈	—	4	4	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₂²⋊C₄	—	2	2	no	—
290	C₂×C₄²	—	2	2	no	—
291	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
292	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
293	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
294	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
295	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
296	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
297	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
298	C₄⋊C₈	—	2	4	no	—
299	#103	—	2	8	no	—
300	#102	—	4	4	no	—
301	C₄×C₈	—	2	2	no	—
302	C₄×C₈	—	2	2	no	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	C₂⁴	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	4	no	—
308	C₂×Q₈	—	2	4	no	—
309	C₂×Q₈	—	4	2	no	—
310	C₂×Q₈	—	4	2	no	—
311	C₂×Q₈	—	4	2	no	—
312	C₂×Q₈	C₂×D₄×C₃₇	1	4	yes	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	4	no	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	4	2	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	—	4	2	no	—
322	C₂×D₄	—	4	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
332	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
333	SD₁₆	—	4	16	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	#41×C₃₇	1	4	yes	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	4	4	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	4	4	no	—
350	C₂²⋊C₄	—	4	4	no	—
351	C₂²⋊C₄	—	4	4	no	—
352	C₂²⋊C₄	—	4	4	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	4	4	no	—
359	C₄²	SD₁₆×C₃₇	1	4	yes	complemented
360	C₄²	C₂×D₄×C₃₇	1	2	yes	—
361	C₄²	#41×C₃₇	1	2	yes	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	2	no	—
369	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
370	Q₈	—	2	8	no	—
371	Q₈	—	4	4	no	—
372	Q₈	—	8	4	no	—
373	D₄	—	4	4	no	—
374	D₄	—	4	4	no	—
375	D₄	—	8	4	no	—
376	D₄	—	8	4	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	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	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	#121×C₃₇	1	2	yes	—
397	C₂×C₄	#121×C₃₇	1	2	yes	—
398	C₂×C₄	C₂×SD₁₆×C₃₇	1	2	yes	—
399	C₂×C₄	C₂×SD₁₆×C₃₇	1	2	yes	—
400	C₂×C₄	C₂×SD₁₆×C₃₇	1	2	yes	—
401	C₂×C₄	#135×C₃₇	1	2	yes	—
402	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
403	C₂×C₄	#137×C₃₇	1	2	yes	—
404	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
405	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
406	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
407	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
408	C₈	—	2	4	no	—
409	C₈	—	4	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
418	C₂²	C₃₇×#532	1	1	yes	characteristic
419	C₂²	C₃₇×#535	1	1	yes	characteristic
420	C₂²	C₂²×SD₁₆×C₃₇	1	1	yes	characteristic
421	C₂²	C₂×#135×C₃₇	1	1	yes	characteristic
422	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
423	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	4	1	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	4	no	—
429	C₄	—	8	2	no	—
430	C₄	—	8	2	no	—
431	C₄	C₃₇×#460	1	4	yes	—
432	C₄	C₃₇×#464	1	4	yes	—
433	C₄	C₃₇×#546	1	2	yes	—
434	C₄	C₃₇×#559	1	2	yes	—
435	C₂	—	16	2	no	—
436	C₂	C₃₇×#2544	1	1	yes	characteristic
437	C₂	C₂×C₃₇×#460	1	1	yes	characteristic
438	C₂	C₂×C₃₇×#464	1	1	yes	characteristic
439	C₂	C₃₇×#3167	1	1	yes	characteristic
440	C₂	C₃₇×#3182	1	1	yes	characteristic
441	C₂	C₃₇×#3206	1	1	yes	characteristic
442	C₂	C₃₇×#3207	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×#127×C₃₇	C₂²
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
2. C₂×C₃₇×#487	C₂	semidirect
4. C₄×C₄⋊Q₈×C₃₇	C₂	semidirect
5. C₃₇×#2055	C₂	semidirect
6. C₃₇×#1990	C₂	semidirect
8. C₃₇×#1880	C₂	semidirect
9. C₄×C₄⋊C₈×C₃₇	C₂	semidirect
137. C₄²×C₃₇	SD₁₆	semidirect
188. #28614	C₃₇	direct (N × H)
215. C₂×#487	C₂×C₃₇	semidirect
217. C₄×C₄⋊Q₈	C₂×C₃₇	semidirect
218. #2055	C₂×C₃₇	semidirect
219. #1990	C₂×C₃₇	semidirect
221. #1880	C₂×C₃₇	semidirect
222. C₄×C₄⋊C₈	C₂×C₃₇	semidirect
258. C₃₇	#28614	direct (N × H)
359. C₄²	SD₁₆×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#492	2
C₂×C₃₇×#487	2
C₃₇×#2858	2
C₄×C₄⋊Q₈×C₃₇	2
C₃₇×#2055	2
C₃₇×#1990	2
C₃₇×#1957	2
C₃₇×#1880	2
C₄×C₄⋊C₈×C₃₇	2
#28614	37

Subgroups — C37×#28614 #22649867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28614 #22649867