Subgroups — C₃₇×#28402 #22649655

Order 9472.

958 conjugacy classes of subgroups.

The subgroup lattice has 472 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
2	C₂×C₃₇×#475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#460	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×Q₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2568	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2548	C₂	1	1	yes	maximal, characteristic
7	C₃₇×#2092	C₂	1	2	yes	maximal, complemented
8	C₃₇×#2015	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1968	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×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×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×Q₈×C₃₇	C₂²	1	1	yes	characteristic
19	C₃₇×#486	—	2	4	no	—
20	C₃₇×#475	—	2	4	no	—
21	C₃₇×#460	—	2	4	no	—
22	C₄×Q₁₆×C₃₇	—	2	4	no	—
23	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
24	C₂×#106×C₃₇	C₂²	1	2	yes	—
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	1	yes	characteristic
28	C₂×#103×C₃₇	C₂²	1	2	yes	—
29	C₂×#102×C₃₇	C₂²	1	2	yes	—
30	C₂×#102×C₃₇	C₂²	1	2	yes	—
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×#400	—	2	2	no	—
35	C₃₇×#394	—	2	2	no	—
36	C₃₇×#391	—	2	2	no	—
37	C₃₇×#391	C₂²	1	2	yes	—
38	C₃₇×#390	—	2	2	no	—
39	C₃₇×#390	C₂²	1	2	yes	—
40	C₃₇×#382	C₂²	1	2	yes	—
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×Q₈×C₃₇	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₃₇	—	2	1	no	—
47	C₂²×D₄×C₃₇	—	2	1	no	—
48	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
49	C₂×Q₁₆×C₃₇	—	2	2	no	—
50	C₂×Q₁₆×C₃₇	—	2	2	no	—
51	C₂×Q₁₆×C₃₇	—	2	2	no	—
52	C₂×SD₁₆×C₃₇	—	2	4	no	—
53	C₂×SD₁₆×C₃₇	—	2	4	no	—
54	C₂×SD₁₆×C₃₇	—	4	2	no	—
55	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
56	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₃₇	—	2	2	no	—
59	C₄⋊Q₈×C₃₇	—	2	2	no	—
60	#127×C₃₇	—	2	2	no	—
61	#127×C₃₇	—	2	2	no	—
62	#124×C₃₇	—	2	4	no	—
63	#124×C₃₇	—	4	2	no	—
64	C₄×Q₈×C₃₇	—	2	2	no	—
65	C₄×Q₈×C₃₇	—	2	2	no	—
66	C₄×Q₈×C₃₇	—	2	2	no	—
67	C₄×Q₈×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	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	4	no	—
77	C₂×C₄²×C₃₇	—	2	1	no	—
78	C₂×C₄²×C₃₇	—	2	1	no	—
79	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
80	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
81	#107×C₃₇	—	2	2	no	—
82	#106×C₃₇	—	2	4	no	—
83	C₄⋊C₈×C₃₇	D₄	1	4	yes	—
84	#103×C₃₇	—	2	2	no	—
85	#103×C₃₇	—	2	2	no	—
86	#103×C₃₇	—	2	4	no	—
87	#102×C₃₇	—	2	4	no	—
88	#102×C₃₇	—	2	4	no	—
89	#102×C₃₇	—	2	4	no	—
90	C₄×C₈×C₃₇	—	4	2	no	—
91	C₄×C₈×C₃₇	D₄	1	4	yes	—
92	#95×C₃₇	—	2	4	no	—
93	#95×C₃₇	—	2	4	no	—
94	#95×C₃₇	D₄	1	2	yes	—
95	C₂⁴×C₃₇	—	2	2	no	—
96	C₂×Q₈×C₃₇	—	2	1	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	—	2	1	no	—
103	C₂×Q₈×C₃₇	—	2	1	no	—
104	C₂×Q₈×C₃₇	—	2	1	no	—
105	C₂×Q₈×C₃₇	—	2	1	no	—
106	C₂×Q₈×C₃₇	—	4	2	no	—
107	C₂×Q₈×C₃₇	—	4	4	no	—
108	C₂×Q₈×C₃₇	#41	1	2	yes	—
109	C₂×Q₈×C₃₇	#41	1	2	yes	—
110	C₂×D₄×C₃₇	—	2	2	no	—
111	C₂×D₄×C₃₇	—	2	2	no	—
112	C₂×D₄×C₃₇	—	2	2	no	—
113	C₂×D₄×C₃₇	—	2	2	no	—
114	C₂×D₄×C₃₇	—	2	2	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	C₂²×C₄×C₃₇	—	2	1	no	—
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	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
129	Q₁₆×C₃₇	—	2	8	no	—
130	SD₁₆×C₃₇	—	4	8	no	—
131	C₂×C₈×C₃₇	—	2	2	no	—
132	C₂×C₈×C₃₇	—	2	1	no	—
133	C₂×C₈×C₃₇	—	2	1	no	—
134	C₂×C₈×C₃₇	—	2	1	no	—
135	C₂×C₈×C₃₇	—	2	2	no	—
136	C₂×C₈×C₃₇	—	2	1	no	—
137	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
140	C₄⋊C₄×C₃₇	—	2	4	no	—
141	C₄⋊C₄×C₃₇	—	2	1	no	—
142	C₄⋊C₄×C₃₇	—	2	2	no	—
143	C₄⋊C₄×C₃₇	—	2	2	no	—
144	C₄⋊C₄×C₃₇	—	2	1	no	—
145	C₄⋊C₄×C₃₇	—	2	1	no	—
146	C₄⋊C₄×C₃₇	—	2	1	no	—
147	C₄⋊C₄×C₃₇	—	4	2	no	—
148	C₄⋊C₄×C₃₇	—	4	2	no	—
149	C₄⋊C₄×C₃₇	—	4	2	no	—
150	C₂²⋊C₄×C₃₇	—	4	8	no	—
151	C₂²⋊C₄×C₃₇	—	8	4	no	—
152	C₄²×C₃₇	—	2	2	no	—
153	C₄²×C₃₇	—	2	2	no	—
154	C₄²×C₃₇	—	4	2	no	—
155	C₄²×C₃₇	—	4	2	no	—
156	C₄²×C₃₇	C₂×D₄	1	2	yes	—
157	C₄²×C₃₇	C₂×D₄	1	2	yes	—
158	C₂³×C₃₇	—	4	2	no	—
159	C₂³×C₃₇	—	4	2	no	—
160	C₂³×C₃₇	—	4	2	no	—
161	C₂³×C₃₇	—	4	4	no	—
162	C₂³×C₃₇	—	4	4	no	—
163	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₃₇	—	2	2	no	—
165	Q₈×C₃₇	—	2	2	no	—
166	Q₈×C₃₇	—	2	2	no	—
167	Q₈×C₃₇	—	2	2	no	—
168	Q₈×C₃₇	—	4	1	no	—
169	Q₈×C₃₇	—	4	1	no	—
170	Q₈×C₃₇	—	4	1	no	—
171	Q₈×C₃₇	—	4	1	no	—
172	Q₈×C₃₇	—	8	4	no	—
173	D₄×C₃₇	—	4	2	no	—
174	D₄×C₃₇	—	4	2	no	—
175	D₄×C₃₇	—	4	2	no	—
176	D₄×C₃₇	—	4	2	no	—
177	D₄×C₃₇	—	8	4	no	—
178	D₄×C₃₇	—	8	4	no	—
179	C₂×C₄×C₃₇	—	2	2	no	—
180	C₂×C₄×C₃₇	—	2	4	no	—
181	C₂×C₄×C₃₇	—	2	2	no	—
182	C₂×C₄×C₃₇	—	2	2	no	—
183	C₂×C₄×C₃₇	—	2	4	no	—
184	C₂×C₄×C₃₇	—	2	4	no	—
185	C₂×C₄×C₃₇	—	4	1	no	—
186	C₂×C₄×C₃₇	—	4	1	no	—
187	C₂×C₄×C₃₇	—	4	1	no	—
188	C₂×C₄×C₃₇	—	4	1	no	—
189	C₂×C₄×C₃₇	—	4	1	no	—
190	C₂×C₄×C₃₇	—	4	1	no	—
191	C₂×C₄×C₃₇	—	4	2	no	—
192	C₂×C₄×C₃₇	—	4	4	no	—
193	C₂×C₄×C₃₇	—	4	2	no	—
194	C₂×C₄×C₃₇	—	4	2	no	—
195	C₂×C₄×C₃₇	#127	1	2	yes	—
196	C₂×C₄×C₃₇	#127	1	2	yes	—
197	C₂×C₄×C₃₇	#135	1	4	yes	—
198	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
203	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
204	C₈×C₃₇	—	2	2	no	—
205	C₈×C₃₇	—	2	2	no	—
206	C₈×C₃₇	—	2	4	no	—
207	#28402	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂²×C₃₇	—	8	4	no	—
209	C₂²×C₃₇	—	8	2	no	—
210	C₂²×C₃₇	—	8	2	no	—
211	C₂²×C₃₇	—	8	4	no	—
212	C₂²×C₃₇	—	8	2	no	—
213	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
214	C₂²×C₃₇	#546	1	1	yes	characteristic
215	C₂²×C₃₇	#548	1	1	yes	characteristic
216	C₂²×C₃₇	C₂×#135	1	2	yes	—
217	C₂²×C₃₇	#577	1	2	yes	—
218	C₄×C₃₇	—	2	2	no	—
219	C₄×C₃₇	—	4	4	no	—
220	C₄×C₃₇	—	4	2	no	—
221	C₄×C₃₇	—	4	2	no	—
222	C₄×C₃₇	—	8	2	no	—
223	C₄×C₃₇	—	8	1	no	—
224	C₄×C₃₇	—	8	1	no	—
225	C₄×C₃₇	#495	1	4	yes	—
226	C₄×C₃₇	#525	1	1	yes	characteristic
227	C₄×C₃₇	#537	1	1	yes	characteristic
228	C₄×C₃₇	#546	1	1	yes	characteristic
229	C₄×C₃₇	#548	1	1	yes	characteristic
230	C₂×#486	C₂×C₃₇	1	1	yes	characteristic
231	C₂×#475	C₂×C₃₇	1	1	yes	characteristic, complemented
232	C₂×#460	C₂×C₃₇	1	1	yes	characteristic
233	C₂×C₄×Q₁₆	C₂×C₃₇	1	1	yes	characteristic, complemented
234	#2568	C₂×C₃₇	1	1	yes	characteristic, complemented
235	#2548	C₂×C₃₇	1	1	yes	characteristic
236	#2092	C₂×C₃₇	1	2	yes	complemented
237	#2015	C₂×C₃₇	1	2	yes	complemented
238	#1968	C₂×C₃₇	1	2	yes	complemented
239	#1958	C₂×C₃₇	1	2	yes	complemented
240	C₈×C₄⋊C₄	C₂×C₃₇	1	1	yes	characteristic, complemented
241	C₂×C₃₇	—	16	2	no	—
242	C₂×C₃₇	#2540	1	1	yes	characteristic
243	C₂×C₃₇	C₂×#495	1	1	yes	characteristic
244	C₂×C₃₇	#3154	1	1	yes	characteristic
245	C₂×C₃₇	#3304	1	2	yes	—
246	C₂×C₃₇	#3365	1	2	yes	—
247	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
248	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
249	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
250	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
251	C₂×#124	C₂²×C₃₇	1	2	yes	—
252	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
253	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
254	#486	—	2	4	no	—
255	#475	—	2	4	no	—
256	#460	—	2	4	no	—
257	C₄×Q₁₆	—	2	4	no	—
258	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
259	C₂×#106	C₂²×C₃₇	1	2	yes	—
260	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
261	C₂×#103	C₂²×C₃₇	1	2	yes	—
262	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
263	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
264	C₂×#102	C₂²×C₃₇	1	2	yes	—
265	C₂×#102	C₂²×C₃₇	1	2	yes	—
266	C₂×#102	C₂²×C₃₇	1	2	yes	—
267	C₂×C₄×C₈	C₂²×C₃₇	1	2	yes	—
268	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
269	#400	—	2	2	no	—
270	#394	—	2	2	no	—
271	#391	—	2	2	no	—
272	#391	C₂²×C₃₇	1	2	yes	—
273	#390	—	2	2	no	—
274	#390	C₂²×C₃₇	1	2	yes	—
275	#382	C₂²×C₃₇	1	2	yes	—
276	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
277	#336	C₂²×C₃₇	1	2	yes	—
278	C₃₇	#28402	1	1	yes	characteristic, direct product factor, Sylow
279	C₂²×Q₈	—	2	1	no	—
280	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
281	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
282	C₂²×D₄	—	2	1	no	—
283	C₂²×D₄	—	2	1	no	—
284	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
285	C₂×Q₁₆	—	2	2	no	—
286	C₂×Q₁₆	—	2	2	no	—
287	C₂×Q₁₆	—	2	2	no	—
288	C₂×SD₁₆	—	2	4	no	—
289	C₂×SD₁₆	—	2	4	no	—
290	C₂×SD₁₆	—	4	2	no	—
291	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
292	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
294	C₄⋊Q₈	—	2	2	no	—
295	C₄⋊Q₈	—	2	2	no	—
296	#127	—	2	2	no	—
297	#127	—	2	2	no	—
298	#124	—	2	4	no	—
299	#124	—	4	2	no	—
300	C₄×Q₈	—	2	2	no	—
301	C₄×Q₈	—	2	2	no	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×Q₈	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
308	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
311	C₂×C₂²⋊C₄	—	2	4	no	—
312	C₂×C₂²⋊C₄	—	2	4	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	—	2	1	no	—
315	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
316	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
317	#107	—	2	2	no	—
318	#106	—	2	4	no	—
319	C₄⋊C₈	D₄×C₃₇	1	4	yes	—
320	#103	—	2	2	no	—
321	#103	—	2	2	no	—
322	#103	—	2	4	no	—
323	#102	—	2	4	no	—
324	#102	—	2	4	no	—
325	#102	—	2	4	no	—
326	C₄×C₈	—	4	2	no	—
327	C₄×C₈	D₄×C₃₇	1	4	yes	—
328	#95	—	2	4	no	—
329	#95	—	2	4	no	—
330	#95	D₄×C₃₇	1	2	yes	—
331	C₂⁴	—	2	2	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	4	2	no	—
343	C₂×Q₈	—	4	4	no	—
344	C₂×Q₈	#41×C₃₇	1	2	yes	—
345	C₂×Q₈	#41×C₃₇	1	2	yes	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	—	4	4	no	—
355	C₂×D₄	—	8	2	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	C₂×D₄×C₃₇	1	4	yes	—
362	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
365	Q₁₆	—	2	8	no	—
366	SD₁₆	—	4	8	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
374	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
375	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₂²⋊C₄	—	4	8	no	—
387	C₂²⋊C₄	—	8	4	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	4	2	no	—
391	C₄²	—	4	2	no	—
392	C₄²	C₂×D₄×C₃₇	1	2	yes	—
393	C₄²	C₂×D₄×C₃₇	1	2	yes	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	4	no	—
398	C₂³	—	4	4	no	—
399	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
400	Q₈	—	2	2	no	—
401	Q₈	—	2	2	no	—
402	Q₈	—	2	2	no	—
403	Q₈	—	2	2	no	—
404	Q₈	—	4	1	no	—
405	Q₈	—	4	1	no	—
406	Q₈	—	4	1	no	—
407	Q₈	—	4	1	no	—
408	Q₈	—	8	4	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	8	4	no	—
414	D₄	—	8	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	#127×C₃₇	1	2	yes	—
432	C₂×C₄	#127×C₃₇	1	2	yes	—
433	C₂×C₄	#135×C₃₇	1	4	yes	—
434	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
436	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
437	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
438	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
439	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
440	C₈	—	2	2	no	—
441	C₈	—	2	2	no	—
442	C₈	—	2	4	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	8	4	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	4	no	—
448	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
449	C₂²	C₃₇×#546	1	1	yes	characteristic
450	C₂²	C₃₇×#548	1	1	yes	characteristic
451	C₂²	C₂×#135×C₃₇	1	2	yes	—
452	C₂²	C₃₇×#577	1	2	yes	—
453	C₄	—	2	2	no	—
454	C₄	—	4	4	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	8	2	no	—
458	C₄	—	8	1	no	—
459	C₄	—	8	1	no	—
460	C₄	C₃₇×#495	1	4	yes	—
461	C₄	C₃₇×#525	1	1	yes	characteristic
462	C₄	C₃₇×#537	1	1	yes	characteristic
463	C₄	C₃₇×#546	1	1	yes	characteristic
464	C₄	C₃₇×#548	1	1	yes	characteristic
465	C₂	—	16	2	no	—
466	C₂	C₃₇×#2540	1	1	yes	characteristic
467	C₂	C₂×C₃₇×#495	1	1	yes	characteristic
468	C₂	C₃₇×#3154	1	1	yes	characteristic
469	C₂	C₃₇×#3304	1	2	yes	—
470	C₂	C₃₇×#3365	1	2	yes	—

	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 ◁ C₄×C₄⋊C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₇×#475	C₂	semidirect
4. C₂×C₄×Q₁₆×C₃₇	C₂	semidirect
5. C₃₇×#2568	C₂	semidirect
7. C₃₇×#2092	C₂	semidirect
8. C₃₇×#2015	C₂	semidirect
9. C₃₇×#1968	C₂	semidirect
10. C₃₇×#1958	C₂	semidirect
11. C₈×C₄⋊C₄×C₃₇	C₂	semidirect
207. #28402	C₃₇	direct (N × H)
231. C₂×#475	C₂×C₃₇	semidirect
233. C₂×C₄×Q₁₆	C₂×C₃₇	semidirect
234. #2568	C₂×C₃₇	semidirect
236. #2092	C₂×C₃₇	semidirect
237. #2015	C₂×C₃₇	semidirect
238. #1968	C₂×C₃₇	semidirect
239. #1958	C₂×C₃₇	semidirect
240. C₈×C₄⋊C₄	C₂×C₃₇	semidirect
278. C₃₇	#28402	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×#475	2
C₂×C₃₇×#460	2
C₂×C₄×Q₁₆×C₃₇	2
C₃₇×#2568	2
C₃₇×#2548	2
C₃₇×#2092	2
C₃₇×#2015	2
C₃₇×#1968	2
C₃₇×#1958	2
C₈×C₄⋊C₄×C₃₇	2
#28402	37

Subgroups — C37×#28402 #22649655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28402 #22649655