Subgroups — C₃₇×#28563 #22649816

Order 9472.

920 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#467	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#435	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2417	C₂	1	2	yes	maximal
4	C₃₇×#2086	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2075	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2056	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2001	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1935	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1894	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1872	C₂	1	2	yes	maximal, complemented
11	C₂×C₃₇×#340	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
19	C₃₇×#467	—	2	4	no	—
20	C₃₇×#435	—	2	4	no	—
21	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×#103×C₃₇	C₂²	1	2	yes	—
24	C₂×#103×C₃₇	C₂²	1	2	yes	—
25	C₂×#103×C₃₇	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
28	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
29	C₃₇×#398	—	2	2	no	—
30	C₃₇×#396	—	2	2	no	—
31	C₃₇×#391	C₂²	1	2	yes	—
32	C₃₇×#389	C₂²	1	2	yes	—
33	C₃₇×#386	—	2	2	no	—
34	C₃₇×#380	—	2	2	no	—
35	C₃₇×#380	C₂²	1	2	yes	—
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	1	yes	characteristic
40	C₃₇×#340	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
42	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₃₇	—	2	2	no	—
44	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
46	C₂×Q₁₆×C₃₇	—	2	2	no	—
47	C₂×Q₁₆×C₃₇	—	4	2	no	—
48	C₂×M₁₆×C₃₇	—	2	2	no	—
49	C₂×M₁₆×C₃₇	—	4	2	no	—
50	C₂²×C₈×C₃₇	—	4	2	no	—
51	C₂²×C₈×C₃₇	D₄	1	4	yes	—
52	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
56	C₂²⋊Q₈×C₃₇	—	2	4	no	—
57	C₂²⋊Q₈×C₃₇	—	2	4	no	—
58	C₂²⋊Q₈×C₃₇	—	2	4	no	—
59	C₂²⋊Q₈×C₃₇	—	4	2	no	—
60	C₄×D₄×C₃₇	—	2	2	no	—
61	C₄×D₄×C₃₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₇	—	2	4	no	—
63	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
66	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
67	C₂×C₄⋊C₄×C₃₇	—	4	2	no	—
68	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
72	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₃₇	D₄	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₃₇	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
78	#107×C₃₇	—	2	2	no	—
79	C₄⋊C₈×C₃₇	—	2	2	no	—
80	#103×C₃₇	—	2	4	no	—
81	#103×C₃₇	—	2	4	no	—
82	#103×C₃₇	—	4	2	no	—
83	C₂²⋊C₈×C₃₇	—	2	2	no	—
84	C₂²⋊C₈×C₃₇	—	2	2	no	—
85	#97×C₃₇	—	2	2	no	—
86	#95×C₃₇	—	2	2	no	—
87	#95×C₃₇	—	2	2	no	—
88	#95×C₃₇	—	2	2	no	—
89	#95×C₃₇	—	2	2	no	—
90	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
91	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
92	C₂×Q₈×C₃₇	—	2	2	no	—
93	C₂×Q₈×C₃₇	—	2	2	no	—
94	C₂×Q₈×C₃₇	—	2	2	no	—
95	C₂×Q₈×C₃₇	—	2	2	no	—
96	C₂×Q₈×C₃₇	—	2	2	no	—
97	C₂×Q₈×C₃₇	—	2	2	no	—
98	C₂×D₄×C₃₇	—	2	2	no	—
99	C₂×D₄×C₃₇	—	2	4	no	—
100	C₂²×C₄×C₃₇	—	2	2	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	—	2	2	no	—
106	C₂²×C₄×C₃₇	—	2	2	no	—
107	C₂²×C₄×C₃₇	—	2	2	no	—
108	C₂²×C₄×C₃₇	—	2	2	no	—
109	C₂²×C₄×C₃₇	—	2	2	no	—
110	C₂²×C₄×C₃₇	—	4	4	no	—
111	C₂²×C₄×C₃₇	—	4	4	no	—
112	C₂²×C₄×C₃₇	—	8	2	no	—
113	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₃₇	#41	1	2	yes	—
119	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
120	Q₁₆×C₃₇	—	4	4	no	—
121	M₁₆×C₃₇	—	4	4	no	—
122	C₂×C₈×C₃₇	—	2	2	no	—
123	C₂×C₈×C₃₇	—	2	2	no	—
124	C₂×C₈×C₃₇	—	2	1	no	—
125	C₂×C₈×C₃₇	—	2	1	no	—
126	C₂×C₈×C₃₇	—	2	2	no	—
127	C₂×C₈×C₃₇	—	2	2	no	—
128	C₂×C₈×C₃₇	—	4	4	no	—
129	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
131	C₄⋊C₄×C₃₇	—	2	2	no	—
132	C₄⋊C₄×C₃₇	—	2	2	no	—
133	C₄⋊C₄×C₃₇	—	2	2	no	—
134	C₄⋊C₄×C₃₇	—	2	2	no	—
135	C₄⋊C₄×C₃₇	—	2	2	no	—
136	C₄⋊C₄×C₃₇	—	2	2	no	—
137	C₄⋊C₄×C₃₇	—	4	4	no	—
138	C₄⋊C₄×C₃₇	—	4	4	no	—
139	C₄⋊C₄×C₃₇	—	4	4	no	—
140	C₄⋊C₄×C₃₇	—	8	2	no	—
141	C₄⋊C₄×C₃₇	#41	1	4	yes	—
142	C₂²⋊C₄×C₃₇	—	2	2	no	—
143	C₂²⋊C₄×C₃₇	—	2	2	no	—
144	C₂²⋊C₄×C₃₇	—	4	4	no	—
145	C₂²⋊C₄×C₃₇	—	4	4	no	—
146	C₂²⋊C₄×C₃₇	—	8	2	no	—
147	C₄²×C₃₇	—	2	1	no	—
148	C₄²×C₃₇	—	2	1	no	—
149	C₂³×C₃₇	—	2	2	no	—
150	C₂³×C₃₇	—	2	1	no	—
151	C₂³×C₃₇	—	2	1	no	—
152	C₂³×C₃₇	—	2	1	no	—
153	C₂³×C₃₇	—	2	2	no	—
154	C₂³×C₃₇	—	2	2	no	—
155	C₂³×C₃₇	—	2	1	no	—
156	C₂³×C₃₇	—	2	1	no	—
157	C₂³×C₃₇	#121	1	2	yes	—
158	C₂³×C₃₇	#137	1	4	yes	—
159	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₃₇	—	4	2	no	—
161	Q₈×C₃₇	—	4	2	no	—
162	Q₈×C₃₇	—	4	2	no	—
163	Q₈×C₃₇	—	4	2	no	—
164	D₄×C₃₇	—	4	4	no	—
165	C₂×C₄×C₃₇	—	2	2	no	—
166	C₂×C₄×C₃₇	—	2	2	no	—
167	C₂×C₄×C₃₇	—	2	2	no	—
168	C₂×C₄×C₃₇	—	2	4	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	4	no	—
173	C₂×C₄×C₃₇	—	2	2	no	—
174	C₂×C₄×C₃₇	—	2	2	no	—
175	C₂×C₄×C₃₇	—	2	1	no	—
176	C₂×C₄×C₃₇	—	2	1	no	—
177	C₂×C₄×C₃₇	—	4	2	no	—
178	C₂×C₄×C₃₇	—	4	2	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	2	no	—
183	C₂×C₄×C₃₇	—	4	2	no	—
184	C₂×C₄×C₃₇	—	4	2	no	—
185	C₂×C₄×C₃₇	—	4	2	no	—
186	C₂×C₄×C₃₇	—	4	2	no	—
187	C₂×C₄×C₃₇	—	4	2	no	—
188	C₂×C₄×C₃₇	—	4	2	no	—
189	C₂×C₄×C₃₇	—	4	2	no	—
190	C₂×C₄×C₃₇	—	4	2	no	—
191	C₂×C₄×C₃₇	—	8	8	no	—
192	C₂×C₄×C₃₇	#121	1	2	yes	—
193	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
195	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
197	C₈×C₃₇	—	2	2	no	—
198	C₈×C₃₇	—	2	2	no	—
199	C₈×C₃₇	—	4	1	no	—
200	C₈×C₃₇	—	4	1	no	—
201	#28563	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂²×C₃₇	—	2	2	no	—
203	C₂²×C₃₇	—	2	4	no	—
204	C₂²×C₃₇	—	2	4	no	—
205	C₂²×C₃₇	—	2	2	no	—
206	C₂²×C₃₇	—	4	1	no	—
207	C₂²×C₃₇	—	4	1	no	—
208	C₂²×C₃₇	—	4	2	no	—
209	C₂²×C₃₇	—	4	2	no	—
210	C₂²×C₃₇	—	4	1	no	—
211	C₂²×C₃₇	#470	1	4	yes	—
212	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
213	C₂²×C₃₇	#546	1	2	yes	—
214	C₂²×C₃₇	C₂×#137	1	2	yes	—
215	C₂²×C₃₇	#576	1	1	yes	characteristic
216	C₂²×C₃₇	#578	1	1	yes	characteristic
217	C₄×C₃₇	—	2	2	no	—
218	C₄×C₃₇	—	4	1	no	—
219	C₄×C₃₇	—	4	1	no	—
220	C₄×C₃₇	—	4	4	no	—
221	C₄×C₃₇	—	4	1	no	—
222	C₄×C₃₇	—	8	2	no	—
223	C₄×C₃₇	—	8	2	no	—
224	C₄×C₃₇	—	8	2	no	—
225	C₄×C₃₇	#532	1	1	yes	characteristic
226	C₄×C₃₇	#534	1	1	yes	characteristic
227	C₄×C₃₇	#553	1	2	yes	—
228	C₂×#467	C₂×C₃₇	1	1	yes	characteristic, complemented
229	C₂×#435	C₂×C₃₇	1	1	yes	characteristic
230	#2417	C₂×C₃₇	1	2	yes	—
231	#2086	C₂×C₃₇	1	1	yes	characteristic, complemented
232	#2075	C₂×C₃₇	1	1	yes	characteristic, complemented
233	#2056	C₂×C₃₇	1	1	yes	characteristic, complemented
234	#2001	C₂×C₃₇	1	1	yes	characteristic, complemented
235	#1935	C₂×C₃₇	1	2	yes	complemented
236	#1894	C₂×C₃₇	1	2	yes	complemented
237	#1872	C₂×C₃₇	1	2	yes	complemented
238	C₂×#340	C₂×C₃₇	1	1	yes	characteristic, complemented
239	C₂×C₃₇	—	2	4	no	—
240	C₂×C₃₇	—	8	1	no	—
241	C₂×C₃₇	#2543	1	1	yes	characteristic
242	C₂×C₃₇	C₂×#470	1	1	yes	characteristic
243	C₂×C₃₇	#3061	1	1	yes	characteristic
244	C₂×C₃₇	#3312	1	2	yes	—
245	C₂×C₃₇	#3314	1	2	yes	—
246	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
247	C₂²×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
248	C₂³×C₈	C₂²×C₃₇	1	1	yes	characteristic
249	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	2	yes	—
250	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	2	yes	—
251	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
252	C₂²×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
253	#467	—	2	4	no	—
254	#435	—	2	4	no	—
255	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
257	C₂×#103	C₂²×C₃₇	1	2	yes	—
258	C₂×#103	C₂²×C₃₇	1	2	yes	—
259	C₂×#103	C₂²×C₃₇	1	2	yes	—
260	C₂×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
261	C₂×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
262	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
263	#398	—	2	2	no	—
264	#396	—	2	2	no	—
265	#391	C₂²×C₃₇	1	2	yes	—
266	#389	C₂²×C₃₇	1	2	yes	—
267	#386	—	2	2	no	—
268	#380	—	2	2	no	—
269	#380	C₂²×C₃₇	1	2	yes	—
270	#340	C₂²×C₃₇	1	1	yes	characteristic
271	#340	C₂²×C₃₇	1	2	yes	—
272	#340	C₂²×C₃₇	1	2	yes	—
273	#340	C₂²×C₃₇	1	1	yes	characteristic
274	#340	C₂²×C₃₇	1	2	yes	—
275	C₃₇	#28563	1	1	yes	characteristic, direct product factor, Sylow
276	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
277	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
278	C₂³×C₄	—	2	2	no	—
279	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
280	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
281	C₂×Q₁₆	—	2	2	no	—
282	C₂×Q₁₆	—	4	2	no	—
283	C₂×M₁₆	—	2	2	no	—
284	C₂×M₁₆	—	4	2	no	—
285	C₂²×C₈	—	4	2	no	—
286	C₂²×C₈	D₄×C₃₇	1	4	yes	—
287	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
291	C₂²⋊Q₈	—	2	4	no	—
292	C₂²⋊Q₈	—	2	4	no	—
293	C₂²⋊Q₈	—	2	4	no	—
294	C₂²⋊Q₈	—	4	2	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	4	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	4	2	no	—
303	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	D₄×C₃₇	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	D₄×C₃₇	1	1	yes	characteristic
312	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
313	#107	—	2	2	no	—
314	C₄⋊C₈	—	2	2	no	—
315	#103	—	2	4	no	—
316	#103	—	2	4	no	—
317	#103	—	4	2	no	—
318	C₂²⋊C₈	—	2	2	no	—
319	C₂²⋊C₈	—	2	2	no	—
320	#97	—	2	2	no	—
321	#95	—	2	2	no	—
322	#95	—	2	2	no	—
323	#95	—	2	2	no	—
324	#95	—	2	2	no	—
325	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
326	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	4	4	no	—
346	C₂²×C₄	—	4	4	no	—
347	C₂²×C₄	—	8	2	no	—
348	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
353	C₂²×C₄	#41×C₃₇	1	2	yes	—
354	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
355	Q₁₆	—	4	4	no	—
356	M₁₆	—	4	4	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	4	4	no	—
364	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
365	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	4	4	no	—
373	C₄⋊C₄	—	4	4	no	—
374	C₄⋊C₄	—	4	4	no	—
375	C₄⋊C₄	—	8	2	no	—
376	C₄⋊C₄	#41×C₃₇	1	4	yes	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	—	4	4	no	—
381	C₂²⋊C₄	—	8	2	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	2	1	no	—
392	C₂³	#121×C₃₇	1	2	yes	—
393	C₂³	#137×C₃₇	1	4	yes	—
394	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
395	Q₈	—	4	2	no	—
396	Q₈	—	4	2	no	—
397	Q₈	—	4	2	no	—
398	Q₈	—	4	2	no	—
399	D₄	—	4	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	8	8	no	—
427	C₂×C₄	#121×C₃₇	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
429	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
430	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
431	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₈	—	4	1	no	—
435	C₈	—	4	1	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	4	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	1	no	—
445	C₂²	C₃₇×#470	1	4	yes	—
446	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
447	C₂²	C₃₇×#546	1	2	yes	—
448	C₂²	C₂×#137×C₃₇	1	2	yes	—
449	C₂²	C₃₇×#576	1	1	yes	characteristic
450	C₂²	C₃₇×#578	1	1	yes	characteristic
451	C₄	—	2	2	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	4	4	no	—
455	C₄	—	4	1	no	—
456	C₄	—	8	2	no	—
457	C₄	—	8	2	no	—
458	C₄	—	8	2	no	—
459	C₄	C₃₇×#532	1	1	yes	characteristic
460	C₄	C₃₇×#534	1	1	yes	characteristic
461	C₄	C₃₇×#553	1	2	yes	—
462	C₂	—	2	4	no	—
463	C₂	—	8	1	no	—
464	C₂	C₃₇×#2543	1	1	yes	characteristic
465	C₂	C₂×C₃₇×#470	1	1	yes	characteristic
466	C₂	C₃₇×#3061	1	1	yes	characteristic
467	C₂	C₃₇×#3312	1	2	yes	—
468	C₂	C₃₇×#3314	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#467	C₂	semidirect
4. C₃₇×#2086	C₂	semidirect
5. C₃₇×#2075	C₂	semidirect
6. C₃₇×#2056	C₂	semidirect
7. C₃₇×#2001	C₂	semidirect
8. C₃₇×#1935	C₂	semidirect
9. C₃₇×#1894	C₂	semidirect
10. C₃₇×#1872	C₂	semidirect
11. C₂×C₃₇×#340	C₂	semidirect
201. #28563	C₃₇	direct (N × H)
228. C₂×#467	C₂×C₃₇	semidirect
231. #2086	C₂×C₃₇	semidirect
232. #2075	C₂×C₃₇	semidirect
233. #2056	C₂×C₃₇	semidirect
234. #2001	C₂×C₃₇	semidirect
235. #1935	C₂×C₃₇	semidirect
236. #1894	C₂×C₃₇	semidirect
237. #1872	C₂×C₃₇	semidirect
238. C₂×#340	C₂×C₃₇	semidirect
275. C₃₇	#28563	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#467	2
C₂×C₃₇×#435	2
C₃₇×#2417	2
C₃₇×#2086	2
C₃₇×#2075	2
C₃₇×#2056	2
C₃₇×#2001	2
C₃₇×#1935	2
C₃₇×#1894	2
C₃₇×#1872	2
C₂×C₃₇×#340	2
#28563	37

Subgroups — C37×#28563 #22649816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28563 #22649816