Subgroups — C₂×C₃₇×#1627 #22639741

Order 9472.

1290 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#459	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#1627	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃₇×#332	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₇×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₇×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₃₇	—	2	1	no	—
10	C₂²×SD₁₆×C₃₇	—	2	1	no	—
11	C₂²×D₈×C₃₇	—	2	1	no	—
12	D₄×Q₈×C₃₇	—	2	2	no	—
13	D₄×Q₈×C₃₇	—	2	2	no	—
14	D₄×Q₈×C₃₇	—	2	2	no	—
15	D₄×Q₈×C₃₇	C₂²	1	4	yes	complemented
16	C₂×C₄⋊Q₈×C₃₇	—	2	1	no	—
17	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₃₇	—	2	1	no	—
20	C₂×C₂²⋊Q₈×C₃₇	—	2	2	no	—
21	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₃₇	—	2	1	no	—
23	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
24	C₃₇×#486	—	2	2	no	—
25	C₃₇×#486	C₂²	1	4	yes	complemented
26	C₃₇×#460	—	2	2	no	—
27	C₃₇×#460	C₂²	1	4	yes	complemented
28	C₃₇×#459	—	2	2	no	—
29	C₃₇×#459	C₂²	1	4	yes	—
30	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
32	C₂×#102×C₃₇	—	2	2	no	—
33	C₂×#102×C₃₇	—	2	1	no	—
34	C₂×#102×C₃₇	—	2	1	no	—
35	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
36	C₃₇×#332	C₂²	1	4	yes	complemented
37	C₃₇×Q₈⋊C₈	C₂²	1	4	yes	complemented
38	C₃₇×D₄⋊C₈	C₂²	1	4	yes	complemented
39	C₂²×Q₈×C₃₇	—	2	2	no	—
40	C₂²×Q₈×C₃₇	—	2	4	no	—
41	C₂²×Q₈×C₃₇	—	2	4	no	—
42	C₂²×Q₈×C₃₇	—	2	1	no	—
43	C₂²×Q₈×C₃₇	—	4	4	no	—
44	C₂²×Q₈×C₃₇	—	4	4	no	—
45	C₂²×Q₈×C₃₇	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₃₇	—	2	1	no	—
47	C₂²×D₄×C₃₇	—	2	1	no	—
48	C₂²×D₄×C₃₇	—	2	1	no	—
49	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₃₇	—	2	2	no	—
51	C₂³×C₄×C₃₇	—	2	1	no	—
52	C₂×SD₁₆×C₃₇	—	2	4	no	—
53	C₂×SD₁₆×C₃₇	—	4	4	no	—
54	C₂×D₈×C₃₇	—	2	4	no	—
55	C₂×D₈×C₃₇	—	4	4	no	—
56	C₂²×C₈×C₃₇	—	2	1	no	—
57	C₂²×C₈×C₃₇	—	2	1	no	—
58	C₂²×C₈×C₃₇	—	2	1	no	—
59	C₄⋊Q₈×C₃₇	—	2	4	no	—
60	C₄⋊Q₈×C₃₇	—	2	4	no	—
61	C₄⋊Q₈×C₃₇	—	2	1	no	—
62	C₄⋊Q₈×C₃₇	—	2	1	no	—
63	C₄⋊Q₈×C₃₇	D₄	1	2	yes	—
64	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
65	#127×C₃₇	—	2	1	no	—
66	#127×C₃₇	—	2	1	no	—
67	#127×C₃₇	—	2	1	no	—
68	#127×C₃₇	C₂³	1	2	yes	—
69	C₂²⋊Q₈×C₃₇	—	2	4	no	—
70	C₂²⋊Q₈×C₃₇	—	2	8	no	—
71	C₂²⋊Q₈×C₃₇	—	2	4	no	—
72	C₂²⋊Q₈×C₃₇	—	2	8	no	—
73	C₄×Q₈×C₃₇	—	2	1	no	—
74	C₄×Q₈×C₃₇	—	2	1	no	—
75	C₄×Q₈×C₃₇	D₄	1	2	yes	—
76	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
77	C₄×D₄×C₃₇	—	2	4	no	—
78	C₄×D₄×C₃₇	—	2	4	no	—
79	C₄×D₄×C₃₇	—	2	1	no	—
80	C₄×D₄×C₃₇	—	2	1	no	—
81	C₄×D₄×C₃₇	D₄	1	2	yes	—
82	C₄×D₄×C₃₇	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
84	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
85	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
86	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
87	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
91	C₂×C₄²×C₃₇	—	2	1	no	—
92	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₃₇	—	2	1	no	—
94	C₄⋊C₈×C₃₇	—	2	1	no	—
95	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
96	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
97	#102×C₃₇	—	2	4	no	—
98	#102×C₃₇	—	2	4	no	—
99	#102×C₃₇	—	2	8	no	—
100	C₄×C₈×C₃₇	—	2	1	no	—
101	C₄×C₈×C₃₇	C₂³	1	2	yes	—
102	C₂⁴×C₃₇	—	2	1	no	—
103	C₂⁴×C₃₇	—	4	1	no	—
104	C₂×Q₈×C₃₇	—	2	8	no	—
105	C₂×Q₈×C₃₇	—	2	1	no	—
106	C₂×Q₈×C₃₇	—	2	2	no	—
107	C₂×Q₈×C₃₇	—	2	2	no	—
108	C₂×Q₈×C₃₇	—	2	2	no	—
109	C₂×Q₈×C₃₇	—	4	8	no	—
110	C₂×Q₈×C₃₇	—	4	8	no	—
111	C₂×Q₈×C₃₇	—	4	16	no	—
112	C₂×Q₈×C₃₇	—	4	8	no	—
113	C₂×Q₈×C₃₇	—	4	2	no	—
114	C₂×Q₈×C₃₇	—	4	2	no	—
115	C₂×Q₈×C₃₇	D₈	1	4	yes	complemented
116	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
117	C₂×D₄×C₃₇	—	2	1	no	—
118	C₂×D₄×C₃₇	—	2	2	no	—
119	C₂×D₄×C₃₇	—	2	2	no	—
120	C₂×D₄×C₃₇	—	2	2	no	—
121	C₂×D₄×C₃₇	—	2	2	no	—
122	C₂×D₄×C₃₇	—	4	4	no	—
123	C₂×D₄×C₃₇	—	4	1	no	—
124	C₂×D₄×C₃₇	—	4	1	no	—
125	C₂×D₄×C₃₇	—	4	1	no	—
126	C₂×D₄×C₃₇	—	4	2	no	—
127	C₂×D₄×C₃₇	—	4	2	no	—
128	C₂×D₄×C₃₇	—	4	2	no	—
129	C₂×D₄×C₃₇	—	4	2	no	—
130	C₂×D₄×C₃₇	SD₁₆	1	4	yes	complemented
131	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₃₇	—	2	1	no	—
133	C₂²×C₄×C₃₇	—	2	8	no	—
134	C₂²×C₄×C₃₇	—	2	1	no	—
135	C₂²×C₄×C₃₇	—	2	2	no	—
136	C₂²×C₄×C₃₇	—	2	1	no	—
137	C₂²×C₄×C₃₇	—	2	2	no	—
138	C₂²×C₄×C₃₇	—	2	2	no	—
139	C₂²×C₄×C₃₇	—	4	8	no	—
140	C₂²×C₄×C₃₇	—	4	2	no	—
141	C₂²×C₄×C₃₇	—	4	2	no	—
142	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
145	SD₁₆×C₃₇	—	4	8	no	—
146	D₈×C₃₇	—	4	8	no	—
147	C₂×C₈×C₃₇	—	2	2	no	—
148	C₂×C₈×C₃₇	—	2	2	no	—
149	C₂×C₈×C₃₇	—	2	2	no	—
150	C₂×C₈×C₃₇	—	4	2	no	—
151	C₂×C₈×C₃₇	—	4	2	no	—
152	C₂×C₈×C₃₇	—	4	2	no	—
153	C₄⋊C₄×C₃₇	—	2	8	no	—
154	C₄⋊C₄×C₃₇	—	2	2	no	—
155	C₄⋊C₄×C₃₇	—	2	2	no	—
156	C₄⋊C₄×C₃₇	—	2	1	no	—
157	C₄⋊C₄×C₃₇	—	2	1	no	—
158	C₄⋊C₄×C₃₇	—	2	2	no	—
159	C₄⋊C₄×C₃₇	—	2	2	no	—
160	C₄⋊C₄×C₃₇	—	2	2	no	—
161	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
162	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
163	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
164	C₂²⋊C₄×C₃₇	—	2	8	no	—
165	C₂²⋊C₄×C₃₇	—	2	2	no	—
166	C₂²⋊C₄×C₃₇	—	2	2	no	—
167	C₄²×C₃₇	—	2	2	no	—
168	C₄²×C₃₇	—	2	2	no	—
169	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
173	C₂³×C₃₇	—	2	2	no	—
174	C₂³×C₃₇	—	2	4	no	—
175	C₂³×C₃₇	—	4	2	no	—
176	C₂³×C₃₇	—	4	2	no	—
177	C₂³×C₃₇	—	4	2	no	—
178	C₂³×C₃₇	—	8	2	no	—
179	C₂³×C₃₇	—	8	2	no	—
180	C₂³×C₃₇	—	8	2	no	—
181	C₂³×C₃₇	#120	1	1	yes	characteristic
182	Q₈×C₃₇	—	2	2	no	—
183	Q₈×C₃₇	—	2	4	no	—
184	Q₈×C₃₇	—	4	16	no	—
185	Q₈×C₃₇	—	4	2	no	—
186	Q₈×C₃₇	—	4	2	no	—
187	Q₈×C₃₇	—	4	4	no	—
188	Q₈×C₃₇	C₂×D₈	1	4	yes	complemented
189	D₄×C₃₇	—	2	2	no	—
190	D₄×C₃₇	—	2	4	no	—
191	D₄×C₃₇	—	4	4	no	—
192	D₄×C₃₇	—	4	2	no	—
193	D₄×C₃₇	—	4	2	no	—
194	D₄×C₃₇	—	4	2	no	—
195	D₄×C₃₇	—	4	2	no	—
196	D₄×C₃₇	—	8	2	no	—
197	D₄×C₃₇	—	8	2	no	—
198	D₄×C₃₇	—	8	2	no	—
199	D₄×C₃₇	C₂×SD₁₆	1	4	yes	complemented
200	C₂×C₄×C₃₇	—	2	2	no	—
201	C₂×C₄×C₃₇	—	2	4	no	—
202	C₂×C₄×C₃₇	—	2	2	no	—
203	C₂×C₄×C₃₇	—	2	2	no	—
204	C₂×C₄×C₃₇	—	2	4	no	—
205	C₂×C₄×C₃₇	—	2	2	no	—
206	C₂×C₄×C₃₇	—	4	16	no	—
207	C₂×C₄×C₃₇	—	4	4	no	—
208	C₂×C₄×C₃₇	—	4	2	no	—
209	C₂×C₄×C₃₇	—	4	2	no	—
210	C₂×C₄×C₃₇	—	4	2	no	—
211	C₂×C₄×C₃₇	—	4	2	no	—
212	C₂×C₄×C₃₇	—	4	4	no	—
213	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
214	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
215	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
216	C₂×C₄×C₃₇	C₂×D₈	1	2	yes	—
217	C₂×C₄×C₃₇	C₂×SD₁₆	1	2	yes	—
218	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
219	C₂×C₄×C₃₇	#137	1	2	yes	—
220	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
223	C₈×C₃₇	—	4	2	no	—
224	C₈×C₃₇	—	4	2	no	—
225	C₈×C₃₇	—	4	2	no	—
226	C₂×#1627	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂²×C₃₇	—	2	4	no	—
228	C₂²×C₃₇	—	4	8	no	—
229	C₂²×C₃₇	—	4	2	no	—
230	C₂²×C₃₇	—	4	2	no	—
231	C₂²×C₃₇	—	8	2	no	—
232	C₂²×C₃₇	—	8	2	no	—
233	C₂²×C₃₇	—	8	2	no	—
234	C₂²×C₃₇	—	16	4	no	—
235	C₂²×C₃₇	#447	1	2	yes	—
236	C₂²×C₃₇	#448	1	2	yes	—
237	C₂²×C₃₇	#454	1	2	yes	—
238	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
239	C₄×C₃₇	—	2	4	no	—
240	C₄×C₃₇	—	2	1	no	—
241	C₄×C₃₇	—	2	1	no	—
242	C₄×C₃₇	—	4	4	no	—
243	C₄×C₃₇	—	4	2	no	—
244	C₄×C₃₇	—	4	2	no	—
245	C₄×C₃₇	#447	1	2	yes	—
246	C₄×C₃₇	#448	1	2	yes	—
247	C₄×C₃₇	C₂²×D₈	1	1	yes	characteristic
248	C₄×C₃₇	C₂²×SD₁₆	1	1	yes	characteristic
249	C₄×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
250	C₄×C₃₇	C₂×#137	1	1	yes	characteristic
251	C₂×D₄×Q₈	C₂×C₃₇	1	1	yes	characteristic, complemented
252	C₂×#486	C₂×C₃₇	1	1	yes	characteristic, complemented
253	C₂×#460	C₂×C₃₇	1	1	yes	characteristic, complemented
254	C₂×#459	C₂×C₃₇	1	1	yes	characteristic
255	#1627	C₂×C₃₇	1	8	yes	direct product factor
256	C₂×#332	C₂×C₃₇	1	1	yes	characteristic, complemented
257	C₂×Q₈⋊C₈	C₂×C₃₇	1	1	yes	characteristic, complemented
258	C₂×D₄⋊C₈	C₂×C₃₇	1	1	yes	characteristic, complemented
259	C₂×C₃₇	—	4	4	no	—
260	C₂×C₃₇	—	16	2	no	—
261	C₂×C₃₇	#1627	1	4	yes	direct product factor
262	C₂×C₃₇	C₂×#447	1	1	yes	characteristic
263	C₂×C₃₇	C₂×#448	1	1	yes	characteristic
264	C₂×C₃₇	C₂×#454	1	1	yes	characteristic
265	C₂³×Q₈	—	2	1	no	—
266	C₂²×SD₁₆	—	2	1	no	—
267	C₂²×D₈	—	2	1	no	—
268	D₄×Q₈	—	2	2	no	—
269	D₄×Q₈	—	2	2	no	—
270	D₄×Q₈	—	2	2	no	—
271	D₄×Q₈	C₂²×C₃₇	1	4	yes	complemented
272	C₂×C₄⋊Q₈	—	2	1	no	—
273	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
274	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
275	C₂×C₂²⋊Q₈	—	2	1	no	—
276	C₂×C₂²⋊Q₈	—	2	2	no	—
277	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
278	C₂×C₄×D₄	—	2	1	no	—
279	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
280	#486	—	2	2	no	—
281	#486	C₂²×C₃₇	1	4	yes	complemented
282	#460	—	2	2	no	—
283	#460	C₂²×C₃₇	1	4	yes	complemented
284	#459	—	2	2	no	—
285	#459	C₂²×C₃₇	1	4	yes	—
286	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
287	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
288	C₂×#102	—	2	2	no	—
289	C₂×#102	—	2	1	no	—
290	C₂×#102	—	2	1	no	—
291	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
292	#332	C₂²×C₃₇	1	4	yes	complemented
293	Q₈⋊C₈	C₂²×C₃₇	1	4	yes	complemented
294	D₄⋊C₈	C₂²×C₃₇	1	4	yes	complemented
295	C₃₇	C₂×#1627	1	1	yes	characteristic, direct product factor, Sylow
296	C₂²×Q₈	—	2	2	no	—
297	C₂²×Q₈	—	2	4	no	—
298	C₂²×Q₈	—	2	4	no	—
299	C₂²×Q₈	—	2	1	no	—
300	C₂²×Q₈	—	4	4	no	—
301	C₂²×Q₈	—	4	4	no	—
302	C₂²×Q₈	D₄×C₃₇	1	1	yes	characteristic
303	C₂²×D₄	—	2	1	no	—
304	C₂²×D₄	—	2	1	no	—
305	C₂²×D₄	—	2	1	no	—
306	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
307	C₂³×C₄	—	2	2	no	—
308	C₂³×C₄	—	2	1	no	—
309	C₂×SD₁₆	—	2	4	no	—
310	C₂×SD₁₆	—	4	4	no	—
311	C₂×D₈	—	2	4	no	—
312	C₂×D₈	—	4	4	no	—
313	C₂²×C₈	—	2	1	no	—
314	C₂²×C₈	—	2	1	no	—
315	C₂²×C₈	—	2	1	no	—
316	C₄⋊Q₈	—	2	4	no	—
317	C₄⋊Q₈	—	2	4	no	—
318	C₄⋊Q₈	—	2	1	no	—
319	C₄⋊Q₈	—	2	1	no	—
320	C₄⋊Q₈	D₄×C₃₇	1	2	yes	—
321	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
322	#127	—	2	1	no	—
323	#127	—	2	1	no	—
324	#127	—	2	1	no	—
325	#127	C₂³×C₃₇	1	2	yes	—
326	C₂²⋊Q₈	—	2	4	no	—
327	C₂²⋊Q₈	—	2	8	no	—
328	C₂²⋊Q₈	—	2	4	no	—
329	C₂²⋊Q₈	—	2	8	no	—
330	C₄×Q₈	—	2	1	no	—
331	C₄×Q₈	—	2	1	no	—
332	C₄×Q₈	D₄×C₃₇	1	2	yes	—
333	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
334	C₄×D₄	—	2	4	no	—
335	C₄×D₄	—	2	4	no	—
336	C₄×D₄	—	2	1	no	—
337	C₄×D₄	—	2	1	no	—
338	C₄×D₄	D₄×C₃₇	1	2	yes	—
339	C₄×D₄	C₂³×C₃₇	1	2	yes	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
344	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
345	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₄²	—	2	1	no	—
349	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
350	C₄⋊C₈	—	2	1	no	—
351	C₄⋊C₈	—	2	1	no	—
352	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
353	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
354	#102	—	2	4	no	—
355	#102	—	2	4	no	—
356	#102	—	2	8	no	—
357	C₄×C₈	—	2	1	no	—
358	C₄×C₈	C₂³×C₃₇	1	2	yes	—
359	C₂⁴	—	2	1	no	—
360	C₂⁴	—	4	1	no	—
361	C₂×Q₈	—	2	8	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	4	8	no	—
367	C₂×Q₈	—	4	8	no	—
368	C₂×Q₈	—	4	16	no	—
369	C₂×Q₈	—	4	8	no	—
370	C₂×Q₈	—	4	2	no	—
371	C₂×Q₈	—	4	2	no	—
372	C₂×Q₈	D₈×C₃₇	1	4	yes	complemented
373	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	4	4	no	—
380	C₂×D₄	—	4	1	no	—
381	C₂×D₄	—	4	1	no	—
382	C₂×D₄	—	4	1	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	4	2	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	SD₁₆×C₃₇	1	4	yes	complemented
388	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	8	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	4	8	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
402	SD₁₆	—	4	8	no	—
403	D₈	—	4	8	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	4	2	no	—
408	C₂×C₈	—	4	2	no	—
409	C₂×C₈	—	4	2	no	—
410	C₄⋊C₄	—	2	8	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
419	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
420	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
427	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
428	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
429	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
430	C₂³	—	2	2	no	—
431	C₂³	—	2	4	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	8	2	no	—
436	C₂³	—	8	2	no	—
437	C₂³	—	8	2	no	—
438	C₂³	#120×C₃₇	1	1	yes	characteristic
439	Q₈	—	2	2	no	—
440	Q₈	—	2	4	no	—
441	Q₈	—	4	16	no	—
442	Q₈	—	4	2	no	—
443	Q₈	—	4	2	no	—
444	Q₈	—	4	4	no	—
445	Q₈	C₂×D₈×C₃₇	1	4	yes	complemented
446	D₄	—	2	2	no	—
447	D₄	—	2	4	no	—
448	D₄	—	4	4	no	—
449	D₄	—	4	2	no	—
450	D₄	—	4	2	no	—
451	D₄	—	4	2	no	—
452	D₄	—	4	2	no	—
453	D₄	—	8	2	no	—
454	D₄	—	8	2	no	—
455	D₄	—	8	2	no	—
456	D₄	C₂×SD₁₆×C₃₇	1	4	yes	complemented
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	4	16	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
471	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
472	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
473	C₂×C₄	C₂×D₈×C₃₇	1	2	yes	—
474	C₂×C₄	C₂×SD₁₆×C₃₇	1	2	yes	—
475	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
476	C₂×C₄	#137×C₃₇	1	2	yes	—
477	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
478	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
479	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
480	C₈	—	4	2	no	—
481	C₈	—	4	2	no	—
482	C₈	—	4	2	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	4	8	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	8	2	no	—
488	C₂²	—	8	2	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	16	4	no	—
491	C₂²	C₃₇×#447	1	2	yes	—
492	C₂²	C₃₇×#448	1	2	yes	—
493	C₂²	C₃₇×#454	1	2	yes	—
494	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
495	C₄	—	2	4	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	4	4	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	2	no	—
501	C₄	C₃₇×#447	1	2	yes	—
502	C₄	C₃₇×#448	1	2	yes	—
503	C₄	C₂²×D₈×C₃₇	1	1	yes	characteristic
504	C₄	C₂²×SD₁₆×C₃₇	1	1	yes	characteristic
505	C₄	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
506	C₄	C₂×#137×C₃₇	1	1	yes	characteristic
507	C₂	—	4	4	no	—
508	C₂	—	16	2	no	—
509	C₂	C₃₇×#1627	1	4	yes	direct product factor
510	C₂	C₂×C₃₇×#447	1	1	yes	characteristic
511	C₂	C₂×C₃₇×#448	1	1	yes	characteristic
512	C₂	C₂×C₃₇×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₇	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
prime radical	C₂×C₃₇×#459	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×Q₈×C₃₇	C₂	semidirect
2. C₂×C₃₇×#486	C₂	semidirect
3. C₂×C₃₇×#460	C₂	semidirect
5. C₃₇×#1627	C₂	direct (N × H)
6. C₂×C₃₇×#332	C₂	semidirect
7. C₂×C₃₇×Q₈⋊C₈	C₂	semidirect
8. C₂×C₃₇×D₄⋊C₈	C₂	semidirect
15. D₄×Q₈×C₃₇	C₂²	semidirect
25. C₃₇×#486	C₂²	semidirect
27. C₃₇×#460	C₂²	semidirect
36. C₃₇×#332	C₂²	semidirect
37. C₃₇×Q₈⋊C₈	C₂²	semidirect
38. C₃₇×D₄⋊C₈	C₂²	semidirect
115. C₂×Q₈×C₃₇	D₈	semidirect
130. C₂×D₄×C₃₇	SD₁₆	semidirect
188. Q₈×C₃₇	C₂×D₈	semidirect
199. D₄×C₃₇	C₂×SD₁₆	semidirect
226. C₂×#1627	C₃₇	direct (N × H)
251. C₂×D₄×Q₈	C₂×C₃₇	semidirect
252. C₂×#486	C₂×C₃₇	semidirect
253. C₂×#460	C₂×C₃₇	semidirect
255. #1627	C₂×C₃₇	direct (N × H)
256. C₂×#332	C₂×C₃₇	semidirect
257. C₂×Q₈⋊C₈	C₂×C₃₇	semidirect
258. C₂×D₄⋊C₈	C₂×C₃₇	semidirect
261. C₂×C₃₇	#1627	direct (N × H)
271. D₄×Q₈	C₂²×C₃₇	semidirect
281. #486	C₂²×C₃₇	semidirect
283. #460	C₂²×C₃₇	semidirect
292. #332	C₂²×C₃₇	semidirect
293. Q₈⋊C₈	C₂²×C₃₇	semidirect
294. D₄⋊C₈	C₂²×C₃₇	semidirect
295. C₃₇	C₂×#1627	direct (N × H)
372. C₂×Q₈	D₈×C₃₇	semidirect
387. C₂×D₄	SD₁₆×C₃₇	semidirect
445. Q₈	C₂×D₈×C₃₇	semidirect
456. D₄	C₂×SD₁₆×C₃₇	semidirect
509. C₂	C₃₇×#1627	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×D₄×Q₈×C₃₇	2
C₂×C₃₇×#486	2
C₂×C₃₇×#460	2
C₂×C₃₇×#459	2
C₃₇×#1627	2
C₂×C₃₇×#332	2
C₂×C₃₇×Q₈⋊C₈	2
C₂×C₃₇×D₄⋊C₈	2
C₂×#1627	37

Subgroups — C2×C37×#1627 #22639741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₇×#1627 #22639741