Subgroups — C₃₇×#28254 #22649507

Order 9472.

964 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#464	C₂	1	2	yes	maximal
2	C₂×C₃₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#461	C₂	1	1	yes	maximal, characteristic
4	C₄×C₄⋊Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#124×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₃₇×#2056	C₂	1	2	yes	maximal, complemented
7	C₃₇×#2055	C₂	1	2	yes	maximal
8	C₃₇×#1842	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1805	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1802	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₃₇	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₃₇	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
19	C₃₇×#464	—	2	8	no	—
20	C₃₇×#462	—	2	4	no	—
21	C₃₇×#461	—	2	4	no	—
22	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
25	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
26	C₂×#103×C₃₇	C₂²	1	2	yes	—
27	C₂×#103×C₃₇	C₂²	1	2	yes	—
28	C₂×#103×C₃₇	C₂²	1	2	yes	—
29	C₂×#102×C₃₇	C₂²	1	2	yes	—
30	C₃₇×#391	C₂²	1	1	yes	characteristic
31	C₃₇×#391	C₂²	1	2	yes	—
32	C₃₇×#390	C₂²	1	1	yes	characteristic
33	C₃₇×#389	—	2	1	no	—
34	C₃₇×#389	—	2	1	no	—
35	C₃₇×#388	—	2	1	no	—
36	C₃₇×#388	—	2	1	no	—
37	C₃₇×#384	C₂²	1	1	yes	characteristic
38	C₃₇×#382	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₃₇	—	2	1	no	—
40	C₄×C₄⋊C₄×C₃₇	—	2	1	no	—
41	C₄×C₂²⋊C₄×C₃₇	—	2	1	no	—
42	C₄×C₂²⋊C₄×C₃₇	—	2	1	no	—
43	C₄³×C₃₇	C₂²	1	1	yes	characteristic
44	C₃₇×#340	C₂²	1	2	yes	—
45	C₃₇×#340	C₂²	1	2	yes	—
46	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
48	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₃₇	—	2	1	no	—
50	C₂×Q₁₆×C₃₇	—	2	4	no	—
51	C₂×Q₁₆×C₃₇	—	2	4	no	—
52	C₂×Q₁₆×C₃₇	—	4	2	no	—
53	C₂×SD₁₆×C₃₇	—	2	4	no	—
54	C₂×SD₁₆×C₃₇	—	2	4	no	—
55	C₂×SD₁₆×C₃₇	—	4	2	no	—
56	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
57	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
58	C₄⋊Q₈×C₃₇	—	2	2	no	—
59	C₄⋊Q₈×C₃₇	D₄	1	4	yes	—
60	#124×C₃₇	—	2	2	no	—
61	#124×C₃₇	D₄	1	4	yes	—
62	C₄×Q₈×C₃₇	—	2	2	no	—
63	C₄×Q₈×C₃₇	—	2	4	no	—
64	C₄×Q₈×C₃₇	—	2	2	no	—
65	C₄×Q₈×C₃₇	—	2	4	no	—
66	C₄×D₄×C₃₇	—	2	2	no	—
67	C₄×D₄×C₃₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
72	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
73	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
74	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
77	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
82	C₂×C₄²×C₃₇	—	2	1	no	—
83	C₂×C₄²×C₃₇	—	2	2	no	—
84	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₃₇	—	2	2	no	—
92	C₄⋊C₈×C₃₇	—	2	2	no	—
93	C₄⋊C₈×C₃₇	—	2	4	no	—
94	C₄⋊C₈×C₃₇	—	4	2	no	—
95	#103×C₃₇	—	2	4	no	—
96	#103×C₃₇	—	2	4	no	—
97	#103×C₃₇	—	2	4	no	—
98	#102×C₃₇	—	2	4	no	—
99	#95×C₃₇	—	2	1	no	—
100	#95×C₃₇	—	2	1	no	—
101	#95×C₃₇	—	2	1	no	—
102	#95×C₃₇	—	2	1	no	—
103	#95×C₃₇	—	2	2	no	—
104	#95×C₃₇	—	2	2	no	—
105	C₂⁴×C₃₇	—	2	1	no	—
106	C₂×Q₈×C₃₇	—	2	1	no	—
107	C₂×Q₈×C₃₇	—	2	2	no	—
108	C₂×Q₈×C₃₇	—	2	2	no	—
109	C₂×Q₈×C₃₇	—	2	1	no	—
110	C₂×Q₈×C₃₇	—	2	1	no	—
111	C₂×Q₈×C₃₇	—	2	2	no	—
112	C₂×Q₈×C₃₇	—	2	2	no	—
113	C₂×Q₈×C₃₇	—	2	1	no	—
114	C₂×Q₈×C₃₇	—	2	1	no	—
115	C₂×Q₈×C₃₇	—	2	2	no	—
116	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
117	C₂×Q₈×C₃₇	C₂×D₄	1	4	yes	—
118	C₂×D₄×C₃₇	—	2	1	no	—
119	C₂×D₄×C₃₇	—	2	1	no	—
120	C₂×D₄×C₃₇	—	2	1	no	—
121	C₂×D₄×C₃₇	—	2	1	no	—
122	C₂×D₄×C₃₇	—	2	1	no	—
123	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₃₇	—	2	1	no	—
125	C₂²×C₄×C₃₇	—	2	2	no	—
126	C₂²×C₄×C₃₇	—	2	1	no	—
127	C₂²×C₄×C₃₇	—	2	1	no	—
128	C₂²×C₄×C₃₇	—	2	2	no	—
129	C₂²×C₄×C₃₇	—	4	2	no	—
130	C₂²×C₄×C₃₇	—	4	2	no	—
131	C₂²×C₄×C₃₇	—	4	2	no	—
132	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
139	Q₁₆×C₃₇	—	4	8	no	—
140	SD₁₆×C₃₇	—	4	8	no	—
141	C₂×C₈×C₃₇	—	2	2	no	—
142	C₂×C₈×C₃₇	—	2	2	no	—
143	C₂×C₈×C₃₇	—	2	2	no	—
144	C₂×C₈×C₃₇	—	2	2	no	—
145	C₂×C₈×C₃₇	—	2	2	no	—
146	C₂×C₈×C₃₇	—	2	2	no	—
147	C₄⋊C₄×C₃₇	—	2	4	no	—
148	C₄⋊C₄×C₃₇	—	2	4	no	—
149	C₄⋊C₄×C₃₇	—	2	2	no	—
150	C₄⋊C₄×C₃₇	—	2	1	no	—
151	C₄⋊C₄×C₃₇	—	2	1	no	—
152	C₄⋊C₄×C₃₇	—	2	1	no	—
153	C₄⋊C₄×C₃₇	—	2	1	no	—
154	C₄⋊C₄×C₃₇	—	2	2	no	—
155	C₄⋊C₄×C₃₇	—	4	2	no	—
156	C₄⋊C₄×C₃₇	—	4	4	no	—
157	C₄⋊C₄×C₃₇	—	4	2	no	—
158	C₄⋊C₄×C₃₇	—	4	2	no	—
159	C₂²⋊C₄×C₃₇	—	2	4	no	—
160	C₂²⋊C₄×C₃₇	—	2	4	no	—
161	C₂²⋊C₄×C₃₇	—	4	2	no	—
162	C₂²⋊C₄×C₃₇	—	4	2	no	—
163	C₂²⋊C₄×C₃₇	—	4	2	no	—
164	C₄²×C₃₇	—	2	2	no	—
165	C₄²×C₃₇	—	2	2	no	—
166	C₄²×C₃₇	—	2	2	no	—
167	C₄²×C₃₇	—	2	1	no	—
168	C₄²×C₃₇	—	2	1	no	—
169	C₄²×C₃₇	—	4	1	no	—
170	C₄²×C₃₇	—	4	4	no	—
171	C₄²×C₃₇	—	4	2	no	—
172	C₄²×C₃₇	C₂×D₄	1	2	yes	—
173	C₄²×C₃₇	C₂×D₄	1	2	yes	—
174	C₄²×C₃₇	#41	1	2	yes	—
175	C₄²×C₃₇	#41	1	2	yes	—
176	C₂³×C₃₇	—	2	2	no	—
177	C₂³×C₃₇	—	4	1	no	—
178	C₂³×C₃₇	—	4	1	no	—
179	C₂³×C₃₇	—	4	1	no	—
180	C₂³×C₃₇	—	4	1	no	—
181	C₂³×C₃₇	—	4	1	no	—
182	C₂³×C₃₇	—	4	1	no	—
183	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₃₇	—	2	4	no	—
185	Q₈×C₃₇	—	2	2	no	—
186	Q₈×C₃₇	—	2	2	no	—
187	Q₈×C₃₇	—	2	4	no	—
188	Q₈×C₃₇	—	4	2	no	—
189	Q₈×C₃₇	—	4	1	no	—
190	Q₈×C₃₇	—	4	1	no	—
191	Q₈×C₃₇	—	4	2	no	—
192	D₄×C₃₇	—	2	2	no	—
193	D₄×C₃₇	—	2	2	no	—
194	D₄×C₃₇	—	4	1	no	—
195	D₄×C₃₇	—	4	1	no	—
196	C₂×C₄×C₃₇	—	2	1	no	—
197	C₂×C₄×C₃₇	—	2	1	no	—
198	C₂×C₄×C₃₇	—	2	1	no	—
199	C₂×C₄×C₃₇	—	2	1	no	—
200	C₂×C₄×C₃₇	—	2	1	no	—
201	C₂×C₄×C₃₇	—	2	1	no	—
202	C₂×C₄×C₃₇	—	2	1	no	—
203	C₂×C₄×C₃₇	—	2	1	no	—
204	C₂×C₄×C₃₇	—	2	2	no	—
205	C₂×C₄×C₃₇	—	2	4	no	—
206	C₂×C₄×C₃₇	—	2	1	no	—
207	C₂×C₄×C₃₇	—	2	1	no	—
208	C₂×C₄×C₃₇	—	2	1	no	—
209	C₂×C₄×C₃₇	—	4	1	no	—
210	C₂×C₄×C₃₇	—	4	2	no	—
211	C₂×C₄×C₃₇	—	4	1	no	—
212	C₂×C₄×C₃₇	—	4	2	no	—
213	C₂×C₄×C₃₇	—	4	2	no	—
214	C₂×C₄×C₃₇	—	4	1	no	—
215	C₂×C₄×C₃₇	—	4	1	no	—
216	C₂×C₄×C₃₇	—	4	2	no	—
217	C₂×C₄×C₃₇	—	4	1	no	—
218	C₂×C₄×C₃₇	—	4	1	no	—
219	C₂×C₄×C₃₇	—	4	1	no	—
220	C₂×C₄×C₃₇	—	4	1	no	—
221	C₂×C₄×C₃₇	—	4	2	no	—
222	C₂×C₄×C₃₇	—	8	4	no	—
223	C₂×C₄×C₃₇	#121	1	2	yes	—
224	C₂×C₄×C₃₇	#121	1	2	yes	—
225	C₂×C₄×C₃₇	#121	1	2	yes	—
226	C₂×C₄×C₃₇	#121	1	2	yes	—
227	C₂×C₄×C₃₇	#135	1	2	yes	—
228	C₂×C₄×C₃₇	#137	1	2	yes	—
229	C₂×C₄×C₃₇	#137	1	2	yes	—
230	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
236	C₈×C₃₇	—	4	2	no	—
237	C₈×C₃₇	—	4	2	no	—
238	#28254	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂²×C₃₇	—	4	2	no	—
240	C₂²×C₃₇	—	4	2	no	—
241	C₂²×C₃₇	—	4	2	no	—
242	C₂²×C₃₇	—	8	1	no	—
243	C₂²×C₃₇	—	8	1	no	—
244	C₂²×C₃₇	—	8	1	no	—
245	C₂²×C₃₇	—	8	1	no	—
246	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
247	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
248	C₂²×C₃₇	#537	1	1	yes	characteristic
249	C₂²×C₃₇	C₂×#135	1	1	yes	characteristic
250	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
251	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
252	C₂²×C₃₇	#575	1	1	yes	characteristic
253	C₄×C₃₇	—	2	2	no	—
254	C₄×C₃₇	—	2	2	no	—
255	C₄×C₃₇	—	2	2	no	—
256	C₄×C₃₇	—	2	2	no	—
257	C₄×C₃₇	—	4	1	no	—
258	C₄×C₃₇	—	4	2	no	—
259	C₄×C₃₇	—	4	4	no	—
260	C₄×C₃₇	—	8	1	no	—
261	C₄×C₃₇	—	8	2	no	—
262	C₄×C₃₇	—	8	1	no	—
263	C₄×C₃₇	#464	1	4	yes	complemented
264	C₄×C₃₇	D₄²	1	1	yes	characteristic
265	C₄×C₃₇	#547	1	1	yes	characteristic
266	C₄×C₃₇	#547	1	1	yes	characteristic
267	C₄×C₃₇	#555	1	1	yes	characteristic
268	C₂×#464	C₂×C₃₇	1	2	yes	—
269	C₂×#462	C₂×C₃₇	1	1	yes	characteristic, complemented
270	C₂×#461	C₂×C₃₇	1	1	yes	characteristic
271	C₄×C₄⋊Q₈	C₂×C₃₇	1	1	yes	characteristic, complemented
272	C₄×#124	C₂×C₃₇	1	1	yes	characteristic
273	#2056	C₂×C₃₇	1	2	yes	complemented
274	#2055	C₂×C₃₇	1	2	yes	—
275	#1842	C₂×C₃₇	1	1	yes	characteristic, complemented
276	#1805	C₂×C₃₇	1	2	yes	complemented
277	#1803	C₂×C₃₇	1	1	yes	characteristic, complemented
278	#1802	C₂×C₃₇	1	1	yes	characteristic
279	C₂×C₃₇	—	8	2	no	—
280	C₂×C₃₇	#2537	1	1	yes	characteristic
281	C₂×C₃₇	C₂×#464	1	1	yes	characteristic
282	C₂×C₃₇	#3035	1	1	yes	characteristic
283	C₂×C₃₇	#3037	1	1	yes	characteristic
284	C₂×C₃₇	#3039	1	1	yes	characteristic
285	C₂×C₃₇	#3248	1	1	yes	characteristic
286	C₂×C₃₇	#3252	1	1	yes	characteristic
287	C₂²×Q₁₆	C₂²×C₃₇	1	2	yes	—
288	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
289	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
290	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
291	C₂×C₄×Q₈	C₂²×C₃₇	1	2	yes	—
292	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
293	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
294	#464	—	2	8	no	—
295	#462	—	2	4	no	—
296	#461	—	2	4	no	—
297	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
298	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
299	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
300	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
301	C₂×#103	C₂²×C₃₇	1	2	yes	—
302	C₂×#103	C₂²×C₃₇	1	2	yes	—
303	C₂×#103	C₂²×C₃₇	1	2	yes	—
304	C₂×#102	C₂²×C₃₇	1	2	yes	—
305	#391	C₂²×C₃₇	1	2	yes	—
306	#391	C₂²×C₃₇	1	1	yes	characteristic
307	#390	C₂²×C₃₇	1	1	yes	characteristic
308	#389	—	2	1	no	—
309	#389	—	2	1	no	—
310	#388	—	2	1	no	—
311	#388	—	2	1	no	—
312	#384	C₂²×C₃₇	1	1	yes	characteristic
313	#382	C₂²×C₃₇	1	1	yes	characteristic
314	C₄×C₄⋊C₄	—	2	1	no	—
315	C₄×C₄⋊C₄	—	2	1	no	—
316	C₄×C₂²⋊C₄	—	2	1	no	—
317	C₄×C₂²⋊C₄	—	2	1	no	—
318	C₄³	C₂²×C₃₇	1	1	yes	characteristic
319	#340	C₂²×C₃₇	1	2	yes	—
320	#340	C₂²×C₃₇	1	2	yes	—
321	C₃₇	#28254	1	1	yes	characteristic, direct product factor, Sylow
322	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
323	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
324	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
325	C₂³×C₄	—	2	1	no	—
326	C₂×Q₁₆	—	2	4	no	—
327	C₂×Q₁₆	—	2	4	no	—
328	C₂×Q₁₆	—	4	2	no	—
329	C₂×SD₁₆	—	2	4	no	—
330	C₂×SD₁₆	—	2	4	no	—
331	C₂×SD₁₆	—	4	2	no	—
332	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
333	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
334	C₄⋊Q₈	—	2	2	no	—
335	C₄⋊Q₈	D₄×C₃₇	1	4	yes	—
336	#124	—	2	2	no	—
337	#124	D₄×C₃₇	1	4	yes	—
338	C₄×Q₈	—	2	2	no	—
339	C₄×Q₈	—	2	4	no	—
340	C₄×Q₈	—	2	2	no	—
341	C₄×Q₈	—	2	4	no	—
342	C₄×D₄	—	2	2	no	—
343	C₄×D₄	—	2	2	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
353	C₂×C₂²⋊C₄	—	2	1	no	—
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₄²	—	2	1	no	—
359	C₂×C₄²	—	2	2	no	—
360	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
361	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
362	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
363	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
364	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
367	C₄⋊C₈	—	2	2	no	—
368	C₄⋊C₈	—	2	2	no	—
369	C₄⋊C₈	—	2	4	no	—
370	C₄⋊C₈	—	4	2	no	—
371	#103	—	2	4	no	—
372	#103	—	2	4	no	—
373	#103	—	2	4	no	—
374	#102	—	2	4	no	—
375	#95	—	2	1	no	—
376	#95	—	2	1	no	—
377	#95	—	2	1	no	—
378	#95	—	2	1	no	—
379	#95	—	2	2	no	—
380	#95	—	2	2	no	—
381	C₂⁴	—	2	1	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
393	C₂×Q₈	C₂×D₄×C₃₇	1	4	yes	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	4	2	no	—
406	C₂²×C₄	—	4	2	no	—
407	C₂²×C₄	—	4	2	no	—
408	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
414	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
415	Q₁₆	—	4	8	no	—
416	SD₁₆	—	4	8	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	4	2	no	—
432	C₄⋊C₄	—	4	4	no	—
433	C₄⋊C₄	—	4	2	no	—
434	C₄⋊C₄	—	4	2	no	—
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	2	4	no	—
437	C₂²⋊C₄	—	4	2	no	—
438	C₂²⋊C₄	—	4	2	no	—
439	C₂²⋊C₄	—	4	2	no	—
440	C₄²	—	2	2	no	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	4	1	no	—
446	C₄²	—	4	4	no	—
447	C₄²	—	4	2	no	—
448	C₄²	C₂×D₄×C₃₇	1	2	yes	—
449	C₄²	C₂×D₄×C₃₇	1	2	yes	—
450	C₄²	#41×C₃₇	1	2	yes	—
451	C₄²	#41×C₃₇	1	2	yes	—
452	C₂³	—	2	2	no	—
453	C₂³	—	4	1	no	—
454	C₂³	—	4	1	no	—
455	C₂³	—	4	1	no	—
456	C₂³	—	4	1	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
460	Q₈	—	2	4	no	—
461	Q₈	—	2	2	no	—
462	Q₈	—	2	2	no	—
463	Q₈	—	2	4	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	4	1	no	—
466	Q₈	—	4	1	no	—
467	Q₈	—	4	2	no	—
468	D₄	—	2	2	no	—
469	D₄	—	2	2	no	—
470	D₄	—	4	1	no	—
471	D₄	—	4	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	8	4	no	—
499	C₂×C₄	#121×C₃₇	1	2	yes	—
500	C₂×C₄	#121×C₃₇	1	2	yes	—
501	C₂×C₄	#121×C₃₇	1	2	yes	—
502	C₂×C₄	#121×C₃₇	1	2	yes	—
503	C₂×C₄	#135×C₃₇	1	2	yes	—
504	C₂×C₄	#137×C₃₇	1	2	yes	—
505	C₂×C₄	#137×C₃₇	1	2	yes	—
506	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
508	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
509	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
510	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
511	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
512	C₈	—	4	2	no	—
513	C₈	—	4	2	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	8	1	no	—
518	C₂²	—	8	1	no	—
519	C₂²	—	8	1	no	—
520	C₂²	—	8	1	no	—
521	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
522	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
523	C₂²	C₃₇×#537	1	1	yes	characteristic
524	C₂²	C₂×#135×C₃₇	1	1	yes	characteristic
525	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
526	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
527	C₂²	C₃₇×#575	1	1	yes	characteristic
528	C₄	—	2	2	no	—
529	C₄	—	2	2	no	—
530	C₄	—	2	2	no	—
531	C₄	—	2	2	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	4	no	—
535	C₄	—	8	1	no	—
536	C₄	—	8	2	no	—
537	C₄	—	8	1	no	—
538	C₄	C₃₇×#464	1	4	yes	complemented
539	C₄	D₄²×C₃₇	1	1	yes	characteristic
540	C₄	C₃₇×#547	1	1	yes	characteristic
541	C₄	C₃₇×#547	1	1	yes	characteristic
542	C₄	C₃₇×#555	1	1	yes	characteristic
543	C₂	—	8	2	no	—
544	C₂	C₃₇×#2537	1	1	yes	characteristic
545	C₂	C₂×C₃₇×#464	1	1	yes	characteristic
546	C₂	C₃₇×#3035	1	1	yes	characteristic
547	C₂	C₃₇×#3037	1	1	yes	characteristic
548	C₂	C₃₇×#3039	1	1	yes	characteristic
549	C₂	C₃₇×#3248	1	1	yes	characteristic
550	C₂	C₃₇×#3252	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
2. C₂×C₃₇×#462	C₂	semidirect
4. C₄×C₄⋊Q₈×C₃₇	C₂	semidirect
6. C₃₇×#2056	C₂	semidirect
8. C₃₇×#1842	C₂	semidirect
9. C₃₇×#1805	C₂	semidirect
10. C₃₇×#1803	C₂	semidirect
238. #28254	C₃₇	direct (N × H)
263. C₄×C₃₇	#464	semidirect
269. C₂×#462	C₂×C₃₇	semidirect
271. C₄×C₄⋊Q₈	C₂×C₃₇	semidirect
273. #2056	C₂×C₃₇	semidirect
275. #1842	C₂×C₃₇	semidirect
276. #1805	C₂×C₃₇	semidirect
277. #1803	C₂×C₃₇	semidirect
321. C₃₇	#28254	direct (N × H)
538. C₄	C₃₇×#464	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#464	2
C₂×C₃₇×#462	2
C₂×C₃₇×#461	2
C₄×C₄⋊Q₈×C₃₇	2
C₄×#124×C₃₇	2
C₃₇×#2056	2
C₃₇×#2055	2
C₃₇×#1842	2
C₃₇×#1805	2
C₃₇×#1803	2
C₃₇×#1802	2
#28254	37

Subgroups — C37×#28254 #22649507

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28254 #22649507