Subgroups — C₃₇×#28399 #22649652

Order 9472.

1006 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#486	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#477	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#459	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×SD₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2563	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2548	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2092	C₂	1	2	yes	maximal, complemented
8	C₃₇×#2012	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1970	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1958	C₂	1	2	yes	maximal, complemented
11	C₈×C₄⋊C₄×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
13	C₂²×D₈×C₃₇	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
16	C₂×#124×C₃₇	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
19	C₃₇×#486	—	2	4	no	—
20	C₃₇×#477	—	2	4	no	—
21	C₃₇×#459	—	2	4	no	—
22	C₄×SD₁₆×C₃₇	—	2	4	no	—
23	C₂×#107×C₃₇	C₂²	1	2	yes	—
24	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
26	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
27	C₂×#103×C₃₇	C₂²	1	2	yes	—
28	C₂×#102×C₃₇	C₂²	1	2	yes	—
29	C₂×#102×C₃₇	C₂²	1	2	yes	—
30	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×#102×C₃₇	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₃₇	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
34	C₃₇×#394	—	2	2	no	—
35	C₃₇×#393	—	2	2	no	—
36	C₃₇×#390	—	2	2	no	—
37	C₃₇×#390	C₂²	1	2	yes	—
38	C₃₇×#390	C₂²	1	2	yes	—
39	C₃₇×#382	C₂²	1	2	yes	—
40	C₃₇×#380	—	2	2	no	—
41	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
42	C₃₇×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₃₇	—	2	1	no	—
44	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₃₇	—	2	1	no	—
46	C₂²×D₄×C₃₇	—	2	1	no	—
47	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
48	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₃₇	—	2	1	no	—
50	C₂×SD₁₆×C₃₇	—	2	2	no	—
51	C₂×SD₁₆×C₃₇	—	2	2	no	—
52	C₂×SD₁₆×C₃₇	—	2	2	no	—
53	C₂×D₈×C₃₇	—	2	4	no	—
54	C₂×D₈×C₃₇	—	2	4	no	—
55	C₂×D₈×C₃₇	—	4	2	no	—
56	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
57	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
59	C₄⋊Q₈×C₃₇	—	2	2	no	—
60	C₄⋊Q₈×C₃₇	—	2	2	no	—
61	#127×C₃₇	—	2	2	no	—
62	#127×C₃₇	—	2	2	no	—
63	#124×C₃₇	—	2	4	no	—
64	#124×C₃₇	—	4	2	no	—
65	C₄×Q₈×C₃₇	—	2	2	no	—
66	C₄×Q₈×C₃₇	—	2	2	no	—
67	C₄×D₄×C₃₇	—	2	2	no	—
68	C₄×D₄×C₃₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
76	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
78	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
79	C₂×C₄²×C₃₇	—	2	1	no	—
80	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
81	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
82	#107×C₃₇	—	2	4	no	—
83	#106×C₃₇	—	2	2	no	—
84	C₄⋊C₈×C₃₇	D₄	1	4	yes	—
85	#103×C₃₇	—	2	2	no	—
86	#103×C₃₇	—	2	4	no	—
87	#102×C₃₇	—	2	2	no	—
88	#102×C₃₇	—	2	4	no	—
89	#102×C₃₇	—	2	4	no	—
90	#102×C₃₇	—	2	4	no	—
91	C₄×C₈×C₃₇	—	4	2	no	—
92	C₄×C₈×C₃₇	D₄	1	4	yes	—
93	#95×C₃₇	—	2	4	no	—
94	#95×C₃₇	D₄	1	2	yes	—
95	C₂⁴×C₃₇	—	2	1	no	—
96	C₂⁴×C₃₇	—	2	2	no	—
97	C₂×Q₈×C₃₇	—	2	1	no	—
98	C₂×Q₈×C₃₇	—	2	1	no	—
99	C₂×Q₈×C₃₇	—	2	1	no	—
100	C₂×Q₈×C₃₇	—	2	1	no	—
101	C₂×Q₈×C₃₇	—	2	1	no	—
102	C₂×Q₈×C₃₇	—	4	2	no	—
103	C₂×Q₈×C₃₇	—	8	2	no	—
104	C₂×Q₈×C₃₇	#41	1	2	yes	—
105	C₂×D₄×C₃₇	—	2	1	no	—
106	C₂×D₄×C₃₇	—	2	1	no	—
107	C₂×D₄×C₃₇	—	2	2	no	—
108	C₂×D₄×C₃₇	—	2	2	no	—
109	C₂×D₄×C₃₇	—	2	1	no	—
110	C₂×D₄×C₃₇	—	2	2	no	—
111	C₂×D₄×C₃₇	—	2	2	no	—
112	C₂×D₄×C₃₇	—	2	1	no	—
113	C₂×D₄×C₃₇	—	2	2	no	—
114	C₂×D₄×C₃₇	—	2	1	no	—
115	C₂×D₄×C₃₇	—	2	2	no	—
116	C₂×D₄×C₃₇	—	4	2	no	—
117	C₂×D₄×C₃₇	—	4	2	no	—
118	C₂×D₄×C₃₇	—	4	4	no	—
119	C₂×D₄×C₃₇	—	8	2	no	—
120	C₂×D₄×C₃₇	#41	1	2	yes	—
121	C₂²×C₄×C₃₇	—	2	1	no	—
122	C₂²×C₄×C₃₇	—	2	1	no	—
123	C₂²×C₄×C₃₇	—	2	2	no	—
124	C₂²×C₄×C₃₇	—	2	1	no	—
125	C₂²×C₄×C₃₇	—	4	2	no	—
126	C₂²×C₄×C₃₇	—	4	4	no	—
127	C₂²×C₄×C₃₇	C₂×D₄	1	4	yes	—
128	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
131	SD₁₆×C₃₇	—	2	8	no	—
132	D₈×C₃₇	—	4	8	no	—
133	C₂×C₈×C₃₇	—	2	2	no	—
134	C₂×C₈×C₃₇	—	2	1	no	—
135	C₂×C₈×C₃₇	—	2	1	no	—
136	C₂×C₈×C₃₇	—	2	1	no	—
137	C₂×C₈×C₃₇	—	2	2	no	—
138	C₂×C₈×C₃₇	—	2	1	no	—
139	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
142	C₄⋊C₄×C₃₇	—	2	4	no	—
143	C₄⋊C₄×C₃₇	—	2	1	no	—
144	C₄⋊C₄×C₃₇	—	2	2	no	—
145	C₄⋊C₄×C₃₇	—	2	1	no	—
146	C₄⋊C₄×C₃₇	—	2	1	no	—
147	C₄⋊C₄×C₃₇	—	2	2	no	—
148	C₄⋊C₄×C₃₇	—	2	1	no	—
149	C₄⋊C₄×C₃₇	—	4	2	no	—
150	C₄⋊C₄×C₃₇	—	4	2	no	—
151	C₂²⋊C₄×C₃₇	—	4	8	no	—
152	C₂²⋊C₄×C₃₇	—	4	2	no	—
153	C₂²⋊C₄×C₃₇	—	8	4	no	—
154	C₂²⋊C₄×C₃₇	—	8	4	no	—
155	C₄²×C₃₇	—	2	2	no	—
156	C₄²×C₃₇	—	2	2	no	—
157	C₄²×C₃₇	—	4	2	no	—
158	C₄²×C₃₇	C₂×D₄	1	2	yes	—
159	C₄²×C₃₇	C₂×D₄	1	2	yes	—
160	C₂³×C₃₇	—	2	2	no	—
161	C₂³×C₃₇	—	4	1	no	—
162	C₂³×C₃₇	—	4	1	no	—
163	C₂³×C₃₇	—	4	2	no	—
164	C₂³×C₃₇	—	4	2	no	—
165	C₂³×C₃₇	—	4	2	no	—
166	C₂³×C₃₇	—	4	2	no	—
167	C₂³×C₃₇	—	4	2	no	—
168	C₂³×C₃₇	—	4	4	no	—
169	C₂³×C₃₇	—	4	4	no	—
170	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₃₇	—	2	2	no	—
172	Q₈×C₃₇	—	2	2	no	—
173	Q₈×C₃₇	—	4	1	no	—
174	Q₈×C₃₇	—	4	1	no	—
175	Q₈×C₃₇	—	8	4	no	—
176	D₄×C₃₇	—	2	2	no	—
177	D₄×C₃₇	—	2	2	no	—
178	D₄×C₃₇	—	4	2	no	—
179	D₄×C₃₇	—	4	1	no	—
180	D₄×C₃₇	—	4	2	no	—
181	D₄×C₃₇	—	4	2	no	—
182	D₄×C₃₇	—	4	1	no	—
183	D₄×C₃₇	—	4	2	no	—
184	D₄×C₃₇	—	8	4	no	—
185	D₄×C₃₇	—	8	4	no	—
186	C₂×C₄×C₃₇	—	2	2	no	—
187	C₂×C₄×C₃₇	—	2	4	no	—
188	C₂×C₄×C₃₇	—	2	2	no	—
189	C₂×C₄×C₃₇	—	2	4	no	—
190	C₂×C₄×C₃₇	—	2	4	no	—
191	C₂×C₄×C₃₇	—	4	1	no	—
192	C₂×C₄×C₃₇	—	4	1	no	—
193	C₂×C₄×C₃₇	—	4	1	no	—
194	C₂×C₄×C₃₇	—	4	1	no	—
195	C₂×C₄×C₃₇	—	4	2	no	—
196	C₂×C₄×C₃₇	—	4	2	no	—
197	C₂×C₄×C₃₇	—	4	2	no	—
198	C₂×C₄×C₃₇	—	4	4	no	—
199	C₂×C₄×C₃₇	—	8	4	no	—
200	C₂×C₄×C₃₇	#127	1	2	yes	—
201	C₂×C₄×C₃₇	#127	1	2	yes	—
202	C₂×C₄×C₃₇	#135	1	4	yes	—
203	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
209	C₈×C₃₇	—	2	2	no	—
210	C₈×C₃₇	—	2	2	no	—
211	C₈×C₃₇	—	2	4	no	—
212	#28399	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂²×C₃₇	—	4	4	no	—
214	C₂²×C₃₇	—	4	2	no	—
215	C₂²×C₃₇	—	8	1	no	—
216	C₂²×C₃₇	—	8	1	no	—
217	C₂²×C₃₇	—	8	2	no	—
218	C₂²×C₃₇	—	8	4	no	—
219	C₂²×C₃₇	—	8	2	no	—
220	C₂²×C₃₇	—	8	2	no	—
221	C₂²×C₃₇	—	8	4	no	—
222	C₂²×C₃₇	—	8	2	no	—
223	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
224	C₂²×C₃₇	#546	1	1	yes	characteristic
225	C₂²×C₃₇	#548	1	1	yes	characteristic
226	C₂²×C₃₇	C₂×#135	1	2	yes	—
227	C₂²×C₃₇	#576	1	2	yes	—
228	C₄×C₃₇	—	2	2	no	—
229	C₄×C₃₇	—	4	4	no	—
230	C₄×C₃₇	—	4	2	no	—
231	C₄×C₃₇	—	8	1	no	—
232	C₄×C₃₇	—	8	1	no	—
233	C₄×C₃₇	—	8	2	no	—
234	C₄×C₃₇	#495	1	4	yes	—
235	C₄×C₃₇	#525	1	1	yes	characteristic
236	C₄×C₃₇	#537	1	1	yes	characteristic
237	C₄×C₃₇	#546	1	1	yes	characteristic
238	C₄×C₃₇	#548	1	1	yes	characteristic
239	C₂×#486	C₂×C₃₇	1	1	yes	characteristic, complemented
240	C₂×#477	C₂×C₃₇	1	1	yes	characteristic, complemented
241	C₂×#459	C₂×C₃₇	1	1	yes	characteristic
242	C₂×C₄×SD₁₆	C₂×C₃₇	1	1	yes	characteristic, complemented
243	#2563	C₂×C₃₇	1	1	yes	characteristic, complemented
244	#2548	C₂×C₃₇	1	1	yes	characteristic, complemented
245	#2092	C₂×C₃₇	1	2	yes	complemented
246	#2012	C₂×C₃₇	1	2	yes	complemented
247	#1970	C₂×C₃₇	1	2	yes	complemented
248	#1958	C₂×C₃₇	1	2	yes	complemented
249	C₈×C₄⋊C₄	C₂×C₃₇	1	1	yes	characteristic, complemented
250	C₂×C₃₇	—	8	2	no	—
251	C₂×C₃₇	—	16	2	no	—
252	C₂×C₃₇	#2540	1	1	yes	characteristic
253	C₂×C₃₇	C₂×#495	1	1	yes	characteristic
254	C₂×C₃₇	#3155	1	1	yes	characteristic
255	C₂×C₃₇	#3305	1	2	yes	—
256	C₂×C₃₇	#3361	1	2	yes	—
257	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
258	C₂²×D₈	C₂²×C₃₇	1	2	yes	—
259	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
260	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
261	C₂×#124	C₂²×C₃₇	1	2	yes	—
262	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
263	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
264	#486	—	2	4	no	—
265	#477	—	2	4	no	—
266	#459	—	2	4	no	—
267	C₄×SD₁₆	—	2	4	no	—
268	C₂×#107	C₂²×C₃₇	1	2	yes	—
269	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
270	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
271	C₂×#103	C₂²×C₃₇	1	2	yes	—
272	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
273	C₂×#102	C₂²×C₃₇	1	2	yes	—
274	C₂×#102	C₂²×C₃₇	1	2	yes	—
275	C₂×#102	C₂²×C₃₇	1	2	yes	—
276	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
277	C₂×C₄×C₈	C₂²×C₃₇	1	2	yes	—
278	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
279	#394	—	2	2	no	—
280	#393	—	2	2	no	—
281	#390	—	2	2	no	—
282	#390	C₂²×C₃₇	1	2	yes	—
283	#390	C₂²×C₃₇	1	2	yes	—
284	#382	C₂²×C₃₇	1	2	yes	—
285	#380	—	2	2	no	—
286	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
287	#336	C₂²×C₃₇	1	2	yes	—
288	C₃₇	#28399	1	1	yes	characteristic, direct product factor, Sylow
289	C₂²×Q₈	—	2	1	no	—
290	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
294	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
295	C₂³×C₄	—	2	1	no	—
296	C₂×SD₁₆	—	2	2	no	—
297	C₂×SD₁₆	—	2	2	no	—
298	C₂×SD₁₆	—	2	2	no	—
299	C₂×D₈	—	2	4	no	—
300	C₂×D₈	—	2	4	no	—
301	C₂×D₈	—	4	2	no	—
302	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
303	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
305	C₄⋊Q₈	—	2	2	no	—
306	C₄⋊Q₈	—	2	2	no	—
307	#127	—	2	2	no	—
308	#127	—	2	2	no	—
309	#124	—	2	4	no	—
310	#124	—	4	2	no	—
311	C₄×Q₈	—	2	2	no	—
312	C₄×Q₈	—	2	2	no	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
318	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	—	2	4	no	—
323	C₂×C₂²⋊C₄	—	2	4	no	—
324	C₂×C₂²⋊C₄	—	2	4	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
327	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
328	#107	—	2	4	no	—
329	#106	—	2	2	no	—
330	C₄⋊C₈	D₄×C₃₇	1	4	yes	—
331	#103	—	2	2	no	—
332	#103	—	2	4	no	—
333	#102	—	2	2	no	—
334	#102	—	2	4	no	—
335	#102	—	2	4	no	—
336	#102	—	2	4	no	—
337	C₄×C₈	—	4	2	no	—
338	C₄×C₈	D₄×C₃₇	1	4	yes	—
339	#95	—	2	4	no	—
340	#95	D₄×C₃₇	1	2	yes	—
341	C₂⁴	—	2	1	no	—
342	C₂⁴	—	2	2	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	4	2	no	—
349	C₂×Q₈	—	8	2	no	—
350	C₂×Q₈	#41×C₃₇	1	2	yes	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	—	4	4	no	—
365	C₂×D₄	—	8	2	no	—
366	C₂×D₄	#41×C₃₇	1	2	yes	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	—	4	4	no	—
373	C₂²×C₄	C₂×D₄×C₃₇	1	4	yes	—
374	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
376	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
377	SD₁₆	—	2	8	no	—
378	D₈	—	4	8	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
386	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
387	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₄⋊C₄	—	4	2	no	—
397	C₂²⋊C₄	—	4	8	no	—
398	C₂²⋊C₄	—	4	2	no	—
399	C₂²⋊C₄	—	8	4	no	—
400	C₂²⋊C₄	—	8	4	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	4	2	no	—
404	C₄²	C₂×D₄×C₃₇	1	2	yes	—
405	C₄²	C₂×D₄×C₃₇	1	2	yes	—
406	C₂³	—	2	2	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	4	no	—
415	C₂³	—	4	4	no	—
416	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
417	Q₈	—	2	2	no	—
418	Q₈	—	2	2	no	—
419	Q₈	—	4	1	no	—
420	Q₈	—	4	1	no	—
421	Q₈	—	8	4	no	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	1	no	—
426	D₄	—	4	2	no	—
427	D₄	—	4	2	no	—
428	D₄	—	4	1	no	—
429	D₄	—	4	2	no	—
430	D₄	—	8	4	no	—
431	D₄	—	8	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	8	4	no	—
446	C₂×C₄	#127×C₃₇	1	2	yes	—
447	C₂×C₄	#127×C₃₇	1	2	yes	—
448	C₂×C₄	#135×C₃₇	1	4	yes	—
449	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
450	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
451	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
453	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
454	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
455	C₈	—	2	2	no	—
456	C₈	—	2	2	no	—
457	C₈	—	2	4	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	8	1	no	—
461	C₂²	—	8	1	no	—
462	C₂²	—	8	2	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	4	no	—
466	C₂²	—	8	2	no	—
467	C₂²	—	8	4	no	—
468	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
469	C₂²	C₃₇×#546	1	1	yes	characteristic
470	C₂²	C₃₇×#548	1	1	yes	characteristic
471	C₂²	C₂×#135×C₃₇	1	2	yes	—
472	C₂²	C₃₇×#576	1	2	yes	—
473	C₄	—	2	2	no	—
474	C₄	—	4	4	no	—
475	C₄	—	4	2	no	—
476	C₄	—	8	1	no	—
477	C₄	—	8	2	no	—
478	C₄	—	8	1	no	—
479	C₄	C₃₇×#495	1	4	yes	—
480	C₄	C₃₇×#525	1	1	yes	characteristic
481	C₄	C₃₇×#537	1	1	yes	characteristic
482	C₄	C₃₇×#546	1	1	yes	characteristic
483	C₄	C₃₇×#548	1	1	yes	characteristic
484	C₂	—	8	2	no	—
485	C₂	—	16	2	no	—
486	C₂	C₃₇×#2540	1	1	yes	characteristic
487	C₂	C₂×C₃₇×#495	1	1	yes	characteristic
488	C₂	C₃₇×#3155	1	1	yes	characteristic
489	C₂	C₃₇×#3305	1	2	yes	—
490	C₂	C₃₇×#3361	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×C₃₇×#459	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×#486	C₂	semidirect
2. C₂×C₃₇×#477	C₂	semidirect
4. C₂×C₄×SD₁₆×C₃₇	C₂	semidirect
5. C₃₇×#2563	C₂	semidirect
6. C₃₇×#2548	C₂	semidirect
7. C₃₇×#2092	C₂	semidirect
8. C₃₇×#2012	C₂	semidirect
9. C₃₇×#1970	C₂	semidirect
10. C₃₇×#1958	C₂	semidirect
11. C₈×C₄⋊C₄×C₃₇	C₂	semidirect
212. #28399	C₃₇	direct (N × H)
239. C₂×#486	C₂×C₃₇	semidirect
240. C₂×#477	C₂×C₃₇	semidirect
242. C₂×C₄×SD₁₆	C₂×C₃₇	semidirect
243. #2563	C₂×C₃₇	semidirect
244. #2548	C₂×C₃₇	semidirect
245. #2092	C₂×C₃₇	semidirect
246. #2012	C₂×C₃₇	semidirect
247. #1970	C₂×C₃₇	semidirect
248. #1958	C₂×C₃₇	semidirect
249. C₈×C₄⋊C₄	C₂×C₃₇	semidirect
288. C₃₇	#28399	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×#486	2
C₂×C₃₇×#477	2
C₂×C₃₇×#459	2
C₂×C₄×SD₁₆×C₃₇	2
C₃₇×#2563	2
C₃₇×#2548	2
C₃₇×#2092	2
C₃₇×#2012	2
C₃₇×#1970	2
C₃₇×#1958	2
C₈×C₄⋊C₄×C₃₇	2
#28399	37

Subgroups — C37×#28399 #22649652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28399 #22649652