Subgroups — C₃₇×#28461 #22649714

Order 9472.

1266 conjugacy classes of subgroups.

The subgroup lattice has 538 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, complemented
2	C₂×C₃₇×#492	C₂	1	2	yes	maximal, complemented
3	C₂×C₃₇×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#461	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×SD₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2546	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2541	C₂	1	1	yes	maximal, characteristic
8	C₃₇×#2014	C₂	1	2	yes	maximal, complemented
9	C₃₇×#2013	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1968	C₂	1	2	yes	maximal, complemented
11	C₈×C₄⋊C₄×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
15	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
16	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
17	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₃₇	C₂²	1	2	yes	—
19	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
20	C₂×#127×C₃₇	C₂²	1	2	yes	—
21	C₂×#121×C₃₇	—	2	2	no	—
22	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
24	C₃₇×#492	—	2	8	no	—
25	C₃₇×#492	—	2	4	no	—
26	C₃₇×#461	—	2	4	no	—
27	C₃₇×#460	—	2	4	no	—
28	C₄×SD₁₆×C₃₇	—	2	4	no	—
29	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
32	C₂×#103×C₃₇	C₂²	1	2	yes	—
33	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
34	C₂×#102×C₃₇	C₂²	1	2	yes	—
35	C₂×C₄×C₈×C₃₇	C₂²	1	2	yes	—
36	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
37	C₃₇×#398	—	2	2	no	—
38	C₃₇×#392	—	2	2	no	—
39	C₃₇×#391	C₂²	1	2	yes	—
40	C₃₇×#390	C₂²	1	2	yes	—
41	C₃₇×#389	—	2	2	no	—
42	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
43	C₃₇×#336	C₂²	1	2	yes	—
44	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
45	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₃₇	—	2	1	no	—
47	C₂²×D₄×C₃₇	—	2	4	no	—
48	C₂²×D₄×C₃₇	—	2	1	no	—
49	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
50	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₃₇	—	2	1	no	—
52	C₂×SD₁₆×C₃₇	—	2	4	no	—
53	C₂×SD₁₆×C₃₇	—	2	4	no	—
54	C₂×SD₁₆×C₃₇	—	2	2	no	—
55	C₂×SD₁₆×C₃₇	—	2	4	no	—
56	C₂×SD₁₆×C₃₇	—	2	4	no	—
57	C₂×SD₁₆×C₃₇	—	2	4	no	—
58	C₂×SD₁₆×C₃₇	—	2	4	no	—
59	C₂×SD₁₆×C₃₇	—	2	4	no	—
60	C₂×SD₁₆×C₃₇	—	2	2	no	—
61	C₂×SD₁₆×C₃₇	—	2	4	no	—
62	C₂×SD₁₆×C₃₇	—	4	2	no	—
63	C₂×SD₁₆×C₃₇	—	4	2	no	—
64	C₂×SD₁₆×C₃₇	—	4	2	no	—
65	C₂×SD₁₆×C₃₇	—	4	2	no	—
66	C₂×SD₁₆×C₃₇	D₄	1	4	yes	complemented
67	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
69	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
70	C₄⋊Q₈×C₃₇	—	2	4	no	—
71	C₄⋊Q₈×C₃₇	—	2	2	no	—
72	C₄⋊Q₈×C₃₇	—	2	2	no	—
73	C₄⋊Q₈×C₃₇	—	4	2	no	—
74	#127×C₃₇	—	2	4	no	—
75	#127×C₃₇	—	2	2	no	—
76	#127×C₃₇	—	2	2	no	—
77	#127×C₃₇	—	4	2	no	—
78	#121×C₃₇	—	4	8	no	—
79	C₄×Q₈×C₃₇	—	2	2	no	—
80	C₄×Q₈×C₃₇	—	2	2	no	—
81	C₄×D₄×C₃₇	—	2	2	no	—
82	C₄×D₄×C₃₇	—	2	2	no	—
83	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₃₇	—	2	4	no	—
85	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
86	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
87	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
88	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
91	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
92	C₂×C₄²×C₃₇	—	2	1	no	—
93	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
94	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
95	#106×C₃₇	—	2	2	no	—
96	C₄⋊C₈×C₃₇	D₄	1	4	yes	complemented
97	#103×C₃₇	—	2	2	no	—
98	#103×C₃₇	—	2	4	no	—
99	#102×C₃₇	—	2	2	no	—
100	#102×C₃₇	—	2	4	no	—
101	C₄×C₈×C₃₇	—	2	4	no	—
102	C₄×C₈×C₃₇	D₄	1	4	yes	complemented
103	#95×C₃₇	—	2	4	no	—
104	#95×C₃₇	D₄	1	2	yes	—
105	C₂⁴×C₃₇	—	2	1	no	—
106	C₂⁴×C₃₇	—	2	2	no	—
107	C₂×Q₈×C₃₇	—	2	1	no	—
108	C₂×Q₈×C₃₇	—	2	1	no	—
109	C₂×Q₈×C₃₇	—	2	1	no	—
110	C₂×Q₈×C₃₇	—	2	2	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	2	no	—
115	C₂×Q₈×C₃₇	—	2	1	no	—
116	C₂×Q₈×C₃₇	—	2	2	no	—
117	C₂×Q₈×C₃₇	—	2	2	no	—
118	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
119	C₂×D₄×C₃₇	—	2	1	no	—
120	C₂×D₄×C₃₇	—	2	1	no	—
121	C₂×D₄×C₃₇	—	2	2	no	—
122	C₂×D₄×C₃₇	—	2	2	no	—
123	C₂×D₄×C₃₇	—	2	2	no	—
124	C₂×D₄×C₃₇	—	2	1	no	—
125	C₂×D₄×C₃₇	—	2	2	no	—
126	C₂×D₄×C₃₇	—	2	1	no	—
127	C₂×D₄×C₃₇	—	2	1	no	—
128	C₂×D₄×C₃₇	—	2	2	no	—
129	C₂×D₄×C₃₇	—	2	2	no	—
130	C₂×D₄×C₃₇	—	4	8	no	—
131	C₂×D₄×C₃₇	—	4	2	no	—
132	C₂×D₄×C₃₇	—	4	2	no	—
133	C₂×D₄×C₃₇	—	4	8	no	—
134	C₂×D₄×C₃₇	—	4	4	no	—
135	C₂×D₄×C₃₇	—	8	4	no	—
136	C₂×D₄×C₃₇	—	8	2	no	—
137	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₃₇	—	2	1	no	—
139	C₂²×C₄×C₃₇	—	2	1	no	—
140	C₂²×C₄×C₃₇	—	2	2	no	—
141	C₂²×C₄×C₃₇	—	2	1	no	—
142	C₂²×C₄×C₃₇	—	4	2	no	—
143	C₂²×C₄×C₃₇	—	4	4	no	—
144	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₃₇	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
148	SD₁₆×C₃₇	—	2	8	no	—
149	SD₁₆×C₃₇	—	4	8	no	—
150	SD₁₆×C₃₇	—	4	8	no	—
151	SD₁₆×C₃₇	—	4	8	no	—
152	SD₁₆×C₃₇	—	4	8	no	—
153	C₂×C₈×C₃₇	—	2	2	no	—
154	C₂×C₈×C₃₇	—	2	1	no	—
155	C₂×C₈×C₃₇	—	2	1	no	—
156	C₂×C₈×C₃₇	—	2	2	no	—
157	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
158	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
159	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
160	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
161	C₂×C₈×C₃₇	#41	1	2	yes	—
162	C₄⋊C₄×C₃₇	—	2	1	no	—
163	C₄⋊C₄×C₃₇	—	2	1	no	—
164	C₄⋊C₄×C₃₇	—	2	1	no	—
165	C₄⋊C₄×C₃₇	—	2	1	no	—
166	C₄⋊C₄×C₃₇	—	4	8	no	—
167	C₄⋊C₄×C₃₇	—	4	2	no	—
168	C₄⋊C₄×C₃₇	—	4	2	no	—
169	C₄⋊C₄×C₃₇	—	4	2	no	—
170	C₄⋊C₄×C₃₇	SD₁₆	1	8	yes	complemented
171	C₂²⋊C₄×C₃₇	—	4	2	no	—
172	C₂²⋊C₄×C₃₇	—	4	8	no	—
173	C₄²×C₃₇	—	2	2	no	—
174	C₄²×C₃₇	—	2	2	no	—
175	C₄²×C₃₇	—	4	2	no	—
176	C₄²×C₃₇	C₂×D₄	1	2	yes	—
177	C₄²×C₃₇	C₂×D₄	1	2	yes	—
178	C₂³×C₃₇	—	2	2	no	—
179	C₂³×C₃₇	—	4	1	no	—
180	C₂³×C₃₇	—	4	1	no	—
181	C₂³×C₃₇	—	4	2	no	—
182	C₂³×C₃₇	—	4	2	no	—
183	C₂³×C₃₇	—	4	2	no	—
184	C₂³×C₃₇	—	4	2	no	—
185	C₂³×C₃₇	—	4	2	no	—
186	C₂³×C₃₇	—	4	4	no	—
187	C₂³×C₃₇	—	4	4	no	—
188	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
189	Q₈×C₃₇	—	2	2	no	—
190	Q₈×C₃₇	—	2	2	no	—
191	Q₈×C₃₇	—	4	1	no	—
192	Q₈×C₃₇	—	4	1	no	—
193	Q₈×C₃₇	—	4	2	no	—
194	Q₈×C₃₇	—	4	2	no	—
195	Q₈×C₃₇	—	4	2	no	—
196	Q₈×C₃₇	—	4	2	no	—
197	D₄×C₃₇	—	2	2	no	—
198	D₄×C₃₇	—	2	2	no	—
199	D₄×C₃₇	—	4	2	no	—
200	D₄×C₃₇	—	4	1	no	—
201	D₄×C₃₇	—	4	2	no	—
202	D₄×C₃₇	—	4	2	no	—
203	D₄×C₃₇	—	4	1	no	—
204	D₄×C₃₇	—	4	2	no	—
205	D₄×C₃₇	—	8	16	no	—
206	D₄×C₃₇	—	8	4	no	—
207	D₄×C₃₇	—	8	4	no	—
208	C₂×C₄×C₃₇	—	2	4	no	—
209	C₂×C₄×C₃₇	—	2	2	no	—
210	C₂×C₄×C₃₇	—	2	4	no	—
211	C₂×C₄×C₃₇	—	2	2	no	—
212	C₂×C₄×C₃₇	—	4	1	no	—
213	C₂×C₄×C₃₇	—	4	1	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	2	no	—
218	C₂×C₄×C₃₇	—	4	2	no	—
219	C₂×C₄×C₃₇	—	4	2	no	—
220	C₂×C₄×C₃₇	—	4	2	no	—
221	C₂×C₄×C₃₇	—	8	4	no	—
222	C₂×C₄×C₃₇	#127	1	2	yes	—
223	C₂×C₄×C₃₇	#127	1	2	yes	—
224	C₂×C₄×C₃₇	C₂×SD₁₆	1	8	yes	—
225	C₂×C₄×C₃₇	C₂×SD₁₆	1	4	yes	—
226	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
231	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
232	C₈×C₃₇	—	2	2	no	—
233	C₈×C₃₇	—	2	4	no	—
234	C₈×C₃₇	#121	1	4	yes	complemented
235	#28461	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂²×C₃₇	—	4	4	no	—
237	C₂²×C₃₇	—	4	2	no	—
238	C₂²×C₃₇	—	8	2	no	—
239	C₂²×C₃₇	—	8	1	no	—
240	C₂²×C₃₇	—	8	1	no	—
241	C₂²×C₃₇	—	8	4	no	—
242	C₂²×C₃₇	—	8	2	no	—
243	C₂²×C₃₇	—	8	2	no	—
244	C₂²×C₃₇	—	8	4	no	—
245	C₂²×C₃₇	—	8	2	no	—
246	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
247	C₂²×C₃₇	D₄²	1	1	yes	characteristic
248	C₂²×C₃₇	#550	1	1	yes	characteristic
249	C₂²×C₃₇	C₂²×SD₁₆	1	2	yes	—
250	C₂²×C₃₇	#577	1	2	yes	—
251	C₄×C₃₇	—	2	2	no	—
252	C₄×C₃₇	—	2	8	no	—
253	C₄×C₃₇	—	4	2	no	—
254	C₄×C₃₇	—	8	1	no	—
255	C₄×C₃₇	—	8	1	no	—
256	C₄×C₃₇	—	8	2	no	—
257	C₄×C₃₇	#492	1	4	yes	complemented
258	C₄×C₃₇	C₂×#121	1	1	yes	characteristic
259	C₄×C₃₇	#535	1	1	yes	characteristic
260	C₄×C₃₇	D₄²	1	1	yes	characteristic
261	C₄×C₃₇	#550	1	1	yes	characteristic
262	C₂×#492	C₂×C₃₇	1	1	yes	characteristic, complemented
263	C₂×#492	C₂×C₃₇	1	2	yes	complemented
264	C₂×#460	C₂×C₃₇	1	1	yes	characteristic, complemented
265	C₂×#461	C₂×C₃₇	1	1	yes	characteristic, complemented
266	C₂×C₄×SD₁₆	C₂×C₃₇	1	1	yes	characteristic, complemented
267	#2546	C₂×C₃₇	1	1	yes	characteristic, complemented
268	#2541	C₂×C₃₇	1	1	yes	characteristic
269	#2014	C₂×C₃₇	1	2	yes	complemented
270	#2013	C₂×C₃₇	1	2	yes	complemented
271	#1968	C₂×C₃₇	1	2	yes	complemented
272	C₈×C₄⋊C₄	C₂×C₃₇	1	1	yes	characteristic, complemented
273	C₂×C₃₇	—	8	2	no	—
274	C₂×C₃₇	—	16	2	no	—
275	C₂×C₃₇	#2541	1	1	yes	characteristic
276	C₂×C₃₇	C₂×#492	1	1	yes	characteristic
277	C₂×C₃₇	#3154	1	1	yes	characteristic
278	C₂×C₃₇	D₄×SD₁₆	1	2	yes	—
279	C₂×C₃₇	#3392	1	2	yes	—
280	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
281	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
282	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
283	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
284	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
285	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
286	C₂×C₄⋊Q₈	C₂²×C₃₇	1	2	yes	—
287	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
288	C₂×#127	C₂²×C₃₇	1	2	yes	—
289	C₂×#121	—	2	2	no	—
290	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
291	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
292	#492	—	2	8	no	—
293	#492	—	2	4	no	—
294	#461	—	2	4	no	—
295	#460	—	2	4	no	—
296	C₄×SD₁₆	—	2	4	no	—
297	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
298	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
299	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
300	C₂×#103	C₂²×C₃₇	1	2	yes	—
301	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
302	C₂×#102	C₂²×C₃₇	1	2	yes	—
303	C₂×C₄×C₈	C₂²×C₃₇	1	2	yes	—
304	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
305	#398	—	2	2	no	—
306	#392	—	2	2	no	—
307	#391	C₂²×C₃₇	1	2	yes	—
308	#390	C₂²×C₃₇	1	2	yes	—
309	#389	—	2	2	no	—
310	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
311	#336	C₂²×C₃₇	1	2	yes	—
312	C₃₇	#28461	1	1	yes	characteristic, direct product factor, Sylow
313	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
314	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	—	2	4	no	—
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
319	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
320	C₂³×C₄	—	2	1	no	—
321	C₂×SD₁₆	—	2	4	no	—
322	C₂×SD₁₆	—	2	4	no	—
323	C₂×SD₁₆	—	2	2	no	—
324	C₂×SD₁₆	—	2	4	no	—
325	C₂×SD₁₆	—	2	4	no	—
326	C₂×SD₁₆	—	2	4	no	—
327	C₂×SD₁₆	—	2	4	no	—
328	C₂×SD₁₆	—	2	4	no	—
329	C₂×SD₁₆	—	2	2	no	—
330	C₂×SD₁₆	—	2	4	no	—
331	C₂×SD₁₆	—	4	2	no	—
332	C₂×SD₁₆	—	4	2	no	—
333	C₂×SD₁₆	—	4	2	no	—
334	C₂×SD₁₆	—	4	2	no	—
335	C₂×SD₁₆	D₄×C₃₇	1	4	yes	complemented
336	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
337	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
338	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
339	C₄⋊Q₈	—	2	4	no	—
340	C₄⋊Q₈	—	2	2	no	—
341	C₄⋊Q₈	—	2	2	no	—
342	C₄⋊Q₈	—	4	2	no	—
343	#127	—	2	4	no	—
344	#127	—	2	2	no	—
345	#127	—	2	2	no	—
346	#127	—	4	2	no	—
347	#121	—	4	8	no	—
348	C₄×Q₈	—	2	2	no	—
349	C₄×Q₈	—	2	2	no	—
350	C₄×D₄	—	2	2	no	—
351	C₄×D₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	4	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
357	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	4	no	—
361	C₂×C₄²	—	2	1	no	—
362	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
363	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
364	#106	—	2	2	no	—
365	C₄⋊C₈	D₄×C₃₇	1	4	yes	complemented
366	#103	—	2	2	no	—
367	#103	—	2	4	no	—
368	#102	—	2	2	no	—
369	#102	—	2	4	no	—
370	C₄×C₈	—	2	4	no	—
371	C₄×C₈	D₄×C₃₇	1	4	yes	complemented
372	#95	—	2	4	no	—
373	#95	D₄×C₃₇	1	2	yes	—
374	C₂⁴	—	2	1	no	—
375	C₂⁴	—	2	2	no	—
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	4	8	no	—
400	C₂×D₄	—	4	2	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	4	8	no	—
403	C₂×D₄	—	4	4	no	—
404	C₂×D₄	—	8	4	no	—
405	C₂×D₄	—	8	2	no	—
406	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	4	2	no	—
412	C₂²×C₄	—	4	4	no	—
413	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₃₇	1	4	yes	—
415	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
416	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
417	SD₁₆	—	2	8	no	—
418	SD₁₆	—	4	8	no	—
419	SD₁₆	—	4	8	no	—
420	SD₁₆	—	4	8	no	—
421	SD₁₆	—	4	8	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
427	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
428	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
429	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
430	C₂×C₈	#41×C₃₇	1	2	yes	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	4	8	no	—
436	C₄⋊C₄	—	4	2	no	—
437	C₄⋊C₄	—	4	2	no	—
438	C₄⋊C₄	—	4	2	no	—
439	C₄⋊C₄	SD₁₆×C₃₇	1	8	yes	complemented
440	C₂²⋊C₄	—	4	2	no	—
441	C₂²⋊C₄	—	4	8	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	4	2	no	—
445	C₄²	C₂×D₄×C₃₇	1	2	yes	—
446	C₄²	C₂×D₄×C₃₇	1	2	yes	—
447	C₂³	—	2	2	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	1	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	4	no	—
456	C₂³	—	4	4	no	—
457	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
458	Q₈	—	2	2	no	—
459	Q₈	—	2	2	no	—
460	Q₈	—	4	1	no	—
461	Q₈	—	4	1	no	—
462	Q₈	—	4	2	no	—
463	Q₈	—	4	2	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	4	2	no	—
466	D₄	—	2	2	no	—
467	D₄	—	2	2	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	1	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	1	no	—
473	D₄	—	4	2	no	—
474	D₄	—	8	16	no	—
475	D₄	—	8	4	no	—
476	D₄	—	8	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	8	4	no	—
491	C₂×C₄	#127×C₃₇	1	2	yes	—
492	C₂×C₄	#127×C₃₇	1	2	yes	—
493	C₂×C₄	C₂×SD₁₆×C₃₇	1	8	yes	—
494	C₂×C₄	C₂×SD₁₆×C₃₇	1	4	yes	—
495	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
496	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
498	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
499	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
500	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
501	C₈	—	2	2	no	—
502	C₈	—	2	4	no	—
503	C₈	#121×C₃₇	1	4	yes	complemented
504	C₂²	—	4	4	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	8	2	no	—
507	C₂²	—	8	1	no	—
508	C₂²	—	8	1	no	—
509	C₂²	—	8	4	no	—
510	C₂²	—	8	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	8	4	no	—
513	C₂²	—	8	2	no	—
514	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
515	C₂²	D₄²×C₃₇	1	1	yes	characteristic
516	C₂²	C₃₇×#550	1	1	yes	characteristic
517	C₂²	C₂²×SD₁₆×C₃₇	1	2	yes	—
518	C₂²	C₃₇×#577	1	2	yes	—
519	C₄	—	2	2	no	—
520	C₄	—	2	8	no	—
521	C₄	—	4	2	no	—
522	C₄	—	8	1	no	—
523	C₄	—	8	1	no	—
524	C₄	—	8	2	no	—
525	C₄	C₃₇×#492	1	4	yes	complemented
526	C₄	C₂×#121×C₃₇	1	1	yes	characteristic
527	C₄	C₃₇×#535	1	1	yes	characteristic
528	C₄	D₄²×C₃₇	1	1	yes	characteristic
529	C₄	C₃₇×#550	1	1	yes	characteristic
530	C₂	—	8	2	no	—
531	C₂	—	16	2	no	—
532	C₂	C₃₇×#2541	1	1	yes	characteristic
533	C₂	C₂×C₃₇×#492	1	1	yes	characteristic
534	C₂	C₃₇×#3154	1	1	yes	characteristic
535	C₂	D₄×SD₁₆×C₃₇	1	2	yes	—
536	C₂	C₃₇×#3392	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#2541	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₄×C₄⋊C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#492	C₂	semidirect
2. C₂×C₃₇×#492	C₂	semidirect
3. C₂×C₃₇×#460	C₂	semidirect
4. C₂×C₃₇×#461	C₂	semidirect
5. C₂×C₄×SD₁₆×C₃₇	C₂	semidirect
6. C₃₇×#2546	C₂	semidirect
8. C₃₇×#2014	C₂	semidirect
9. C₃₇×#2013	C₂	semidirect
10. C₃₇×#1968	C₂	semidirect
11. C₈×C₄⋊C₄×C₃₇	C₂	semidirect
66. C₂×SD₁₆×C₃₇	D₄	semidirect
96. C₄⋊C₈×C₃₇	D₄	semidirect
102. C₄×C₈×C₃₇	D₄	semidirect
170. C₄⋊C₄×C₃₇	SD₁₆	semidirect
234. C₈×C₃₇	#121	semidirect
235. #28461	C₃₇	direct (N × H)
257. C₄×C₃₇	#492	semidirect
262. C₂×#492	C₂×C₃₇	semidirect
263. C₂×#492	C₂×C₃₇	semidirect
264. C₂×#460	C₂×C₃₇	semidirect
265. C₂×#461	C₂×C₃₇	semidirect
266. C₂×C₄×SD₁₆	C₂×C₃₇	semidirect
267. #2546	C₂×C₃₇	semidirect
269. #2014	C₂×C₃₇	semidirect
270. #2013	C₂×C₃₇	semidirect
271. #1968	C₂×C₃₇	semidirect
272. C₈×C₄⋊C₄	C₂×C₃₇	semidirect
312. C₃₇	#28461	direct (N × H)
335. C₂×SD₁₆	D₄×C₃₇	semidirect
365. C₄⋊C₈	D₄×C₃₇	semidirect
371. C₄×C₈	D₄×C₃₇	semidirect
439. C₄⋊C₄	SD₁₆×C₃₇	semidirect
503. C₈	#121×C₃₇	semidirect
525. C₄	C₃₇×#492	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×#460	2
C₂×C₃₇×#461	2
C₂×C₄×SD₁₆×C₃₇	2
C₃₇×#2546	2
C₃₇×#2541	2
C₃₇×#2014	2
C₃₇×#2013	2
C₃₇×#1968	2
C₈×C₄⋊C₄×C₃₇	2
#28461	37

Subgroups — C37×#28461 #22649714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28461 #22649714