Subgroups — #2110×D₆₇ #31008486

Order 17152.

738 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₆₇	C₂	1	2	yes	maximal
2	#405×D₆₇	C₂	1	1	yes	maximal, characteristic
3	#22561814	C₂	1	1	yes	maximal, characteristic, complemented
4	#22561813	C₂	1	2	yes	maximal, complemented
5	#22561812	C₂	1	4	yes	maximal, complemented
6	#347×D₆₇	C₂	1	4	yes	maximal, complemented
7	C₆₇×#2110	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₆₇	C₄	1	1	yes	characteristic
9	C₂²×C₈×D₆₇	C₂²	1	1	yes	characteristic
10	#117×D₆₇	C₄	1	1	yes	characteristic
11	C₂×#14523983	C₂²	1	2	yes	—
12	C₂×#14523982	C₄	1	4	yes	complemented
13	M₃₂×D₆₇	C₄	1	4	yes	complemented
14	M₃₂×D₆₇	C₄	1	4	yes	complemented
15	M₃₂×D₆₇	C₂²	1	4	yes	—
16	M₃₂×D₆₇	C₂²	1	4	yes	—
17	C₂×C₁₆×D₆₇	C₄	1	4	yes	complemented
18	#16863354	C₄	1	1	yes	characteristic
19	#16863353	C₂²	1	2	yes	—
20	#16863352	C₄	1	1	yes	characteristic
21	#16863351	C₂²	1	1	yes	characteristic
22	#16863350	C₄	1	2	yes	—
23	#97×D₆₇	C₂²	1	2	yes	—
24	C₄×C₈×D₆₇	C₄	1	2	yes	—
25	#16863174	C₂²	1	4	yes	complemented
26	#16863173	C₂²	1	8	yes	complemented
27	C₂×M₃₂×C₆₇	C₂²	1	2	yes	—
28	#405×C₆₇	C₂²	1	1	yes	characteristic
29	#347×C₆₇	C₂²	1	4	yes	complemented
30	C₂²×C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
31	C₂×#11761612	C₂×C₄	1	1	yes	characteristic
32	C₂×#11761611	C₂×C₄	1	2	yes	—
33	M₁₆×D₆₇	—	2	2	no	—
34	M₁₆×D₆₇	—	2	2	no	—
35	C₂²×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₂×C₈×D₆₇	C₂×C₄	1	2	yes	—
37	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
38	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₈×D₆₇	C₂×C₄	1	2	yes	—
40	C₂×C₈×D₆₇	C₂×C₄	1	2	yes	—
41	C₂×C₈×D₆₇	C₂×C₄	1	2	yes	—
42	C₂×C₈×D₆₇	C₂×C₄	1	2	yes	—
43	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
44	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
45	#14524002	C₂×C₄	1	1	yes	characteristic
46	#14524001	—	2	1	no	—
47	#14524000	C₂×C₄	1	2	yes	—
48	#14523999	—	2	1	no	—
49	C₄⋊C₄×D₆₇	—	2	1	no	—
50	C₂²⋊C₄×D₆₇	—	2	1	no	—
51	C₄²×D₆₇	C₂×C₄	1	2	yes	—
52	#14523983	C₂×C₄	1	4	yes	complemented
53	#14523983	C₂³	1	4	yes	—
54	#14523982	C₂×C₄	1	8	yes	—
55	#14523982	C₂×C₄	1	8	yes	complemented
56	C₂×C₆₇⋊C₁₆	C₂×C₄	1	4	yes	complemented
57	C₁₆×D₆₇	C₂×C₄	1	8	yes	—
58	C₁₆×D₆₇	C₂×C₄	1	8	yes	complemented
59	#14523954	C₂×C₄	1	2	yes	—
60	#14523953	C₂×C₄	1	2	yes	—
61	#14523953	C₂³	1	2	yes	—
62	C₄×C₆₇⋊C₈	C₂×C₄	1	2	yes	—
63	C₈×Dic₆₇	C₂×C₄	1	2	yes	—
64	C₈×Dic₆₇	C₂×C₄	1	2	yes	—
65	C₂×M₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
67	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
68	M₃₂×C₆₇	C₂×C₄	1	4	yes	complemented
69	M₃₂×C₆₇	C₂³	1	4	yes	—
70	C₂×C₁₆×C₆₇	C₂×C₄	1	4	yes	complemented
71	#97×C₆₇	C₂³	1	2	yes	—
72	C₄×C₈×C₆₇	C₂×C₄	1	2	yes	—
73	C₂³×D₆₇	M₁₆	1	1	yes	characteristic
74	C₂²×Dic₆₇	M₁₆	1	1	yes	characteristic
75	C₂×C₄×D₆₇	—	2	2	no	—
76	C₂×C₄×D₆₇	C₄²	1	2	yes	—
77	C₂×C₄×D₆₇	C₄²	1	2	yes	—
78	C₂×C₄×D₆₇	M₁₆	1	1	yes	characteristic
79	C₂×C₄×D₆₇	M₁₆	1	1	yes	characteristic
80	C₂×C₄×D₆₇	M₁₆	1	2	yes	—
81	C₂×C₄×D₆₇	M₁₆	1	2	yes	—
82	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
84	#11761612	—	2	2	no	—
85	#11761611	—	2	4	no	—
86	C₂×C₆₇⋊C₈	C₄²	1	2	yes	—
87	C₂×C₆₇⋊C₈	C₄²	1	2	yes	—
88	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
89	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
91	C₈×D₆₇	—	2	2	no	—
92	C₈×D₆₇	—	2	2	no	—
93	C₈×D₆₇	C₄²	1	1	yes	characteristic
94	C₈×D₆₇	C₄²	1	1	yes	characteristic
95	C₈×D₆₇	C₄²	1	2	yes	—
96	C₈×D₆₇	C₄²	1	1	yes	characteristic
97	C₈×D₆₇	C₄²	1	1	yes	characteristic
98	C₈×D₆₇	C₄²	1	2	yes	—
99	C₈×D₆₇	C₂²×C₄	1	2	yes	—
100	C₈×D₆₇	C₂²×C₄	1	2	yes	—
101	C₈×D₆₇	C₂²×C₄	1	2	yes	—
102	C₈×D₆₇	C₂²×C₄	1	2	yes	—
103	C₄⋊Dic₆₇	—	2	1	no	—
104	Dic₆₇⋊C₄	—	2	2	no	—
105	C₂²⋊Dic₆₇	—	2	1	no	—
106	(C₂×D₆₇)⋊C₄	—	2	2	no	—
107	C₄×Dic₆₇	—	2	2	no	—
108	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
109	C₆₇⋊C₁₆	C₂²×C₄	1	8	yes	—
110	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
111	M₁₆×C₆₇	—	2	2	no	—
112	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
117	C₄⋊C₄×C₆₇	—	2	1	no	—
118	C₂²⋊C₄×C₆₇	—	2	1	no	—
119	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
120	C₁₆×C₆₇	C₂²×C₄	1	8	yes	—
121	C₂³×C₆₇	C₂×M₁₆	1	1	yes	characteristic
122	C₂²×D₆₇	—	4	2	no	—
123	C₂²×D₆₇	#97	1	2	yes	—
124	C₂²×D₆₇	#97	1	2	yes	—
125	C₂²×D₆₇	C₂×M₁₆	1	1	yes	characteristic
126	C₂²×D₆₇	C₂×M₁₆	1	1	yes	characteristic
127	C₂×C₄×C₆₇	—	2	2	no	—
128	C₂×C₄×C₆₇	C₂×C₄²	1	2	yes	—
129	C₂×C₄×C₆₇	C₂×M₁₆	1	2	yes	—
130	C₂×C₄×C₆₇	C₂×M₁₆	1	1	yes	characteristic
131	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
132	C₂×Dic₆₇	—	2	2	no	—
133	C₂×Dic₆₇	#97	1	2	yes	—
134	C₂×Dic₆₇	#97	1	2	yes	—
135	C₂×Dic₆₇	C₂×M₁₆	1	1	yes	characteristic
136	C₂×Dic₆₇	C₂×M₁₆	1	1	yes	characteristic
137	C₄×D₆₇	—	4	4	no	—
138	C₄×D₆₇	#97	1	2	yes	—
139	C₄×D₆₇	#97	1	2	yes	—
140	C₄×D₆₇	#97	1	2	yes	—
141	C₄×D₆₇	#97	1	2	yes	—
142	C₄×D₆₇	C₂×C₄²	1	2	yes	—
143	C₄×D₆₇	C₂×C₄²	1	1	yes	characteristic
144	C₄×D₆₇	C₂×C₄²	1	1	yes	characteristic
145	C₄×D₆₇	C₂×M₁₆	1	1	yes	characteristic
146	C₄×D₆₇	C₂×M₁₆	1	1	yes	characteristic
147	C₄×D₆₇	C₂×M₁₆	1	2	yes	—
148	C₈×C₆₇	—	2	2	no	—
149	C₈×C₆₇	C₂×C₄²	1	1	yes	characteristic
150	C₈×C₆₇	C₂×C₄²	1	1	yes	characteristic
151	C₈×C₆₇	C₂³×C₄	1	2	yes	—
152	C₆₇⋊C₈	—	2	2	no	—
153	C₆₇⋊C₈	C₂×C₄²	1	2	yes	—
154	C₆₇⋊C₈	C₂×C₄²	1	1	yes	characteristic
155	C₆₇⋊C₈	C₂×C₄²	1	1	yes	characteristic
156	C₂²×C₆₇	—	4	1	no	—
157	C₂²×C₆₇	C₂×#97	1	2	yes	—
158	C₂²×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
159	C₂×D₆₇	—	2	2	no	—
160	C₂×D₆₇	—	2	4	no	—
161	C₂×D₆₇	—	4	2	no	—
162	C₂×D₆₇	—	4	1	no	—
163	C₂×D₆₇	C₂×#97	1	1	yes	characteristic
164	C₂×D₆₇	C₂×#97	1	2	yes	—
165	C₂×D₆₇	C₂×#97	1	1	yes	characteristic
166	C₄×C₆₇	—	4	2	no	—
167	C₄×C₆₇	C₂×#97	1	2	yes	—
168	C₄×C₆₇	C₂²×C₄²	1	1	yes	characteristic
169	C₄×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
170	Dic₆₇	—	4	2	no	—
171	Dic₆₇	C₂×#97	1	1	yes	characteristic
172	Dic₆₇	C₂×#97	1	1	yes	characteristic
173	Dic₆₇	C₂×#97	1	2	yes	—
174	C₂×#2110	—	67	1	no	maximal, Sylow
175	C₂×C₆₇	—	2	1	no	—
176	C₂×C₆₇	—	2	2	no	—
177	C₂×C₆₇	C₂²×#97	1	1	yes	characteristic
178	D₆₇	—	2	1	no	—
179	D₆₇	—	2	2	no	—
180	D₆₇	#2110	1	2	yes	direct product factor
181	C₂²×M₃₂	—	67	2	no	—
182	C₂×#405	—	67	1	no	—
183	#2110	—	67	2	no	—
184	#2110	—	67	1	no	—
185	#2110	—	67	4	no	—
186	#2110	D₆₇	1	1	yes	characteristic, direct product factor
187	C₂×#347	—	67	4	no	—
188	C₆₇	C₂×#2110	1	1	yes	characteristic, complemented, Sylow
189	C₂²×M₁₆	—	67	1	no	—
190	C₂³×C₈	—	67	1	no	—
191	C₂×#117	—	67	1	no	—
192	C₂×M₃₂	—	67	2	no	—
193	C₂×M₃₂	—	67	4	no	—
194	C₂×M₃₂	—	67	4	no	—
195	C₂×M₃₂	—	67	4	no	—
196	C₂×M₃₂	—	67	4	no	—
197	C₂×M₃₂	—	67	4	no	—
198	C₂×M₃₂	C₂×D₆₇	1	2	yes	—
199	C₂²×C₁₆	—	67	4	no	—
200	#405	—	67	1	no	—
201	#405	—	67	1	no	—
202	#405	—	67	1	no	—
203	#405	—	67	2	no	—
204	#405	—	67	2	no	—
205	#405	C₂×D₆₇	1	1	yes	characteristic
206	C₂×#97	—	67	2	no	—
207	C₂×C₄×C₈	—	67	2	no	—
208	#347	—	67	8	no	—
209	#347	—	67	4	no	—
210	#347	C₂×D₆₇	1	4	yes	complemented
211	C₂³×C₄	—	67	1	no	—
212	C₂×M₁₆	—	67	1	no	—
213	C₂×M₁₆	—	67	2	no	—
214	C₂×M₁₆	—	134	2	no	—
215	C₂×M₁₆	—	134	2	no	—
216	C₂×M₁₆	C₄×D₆₇	1	1	yes	characteristic
217	C₂²×C₈	—	67	1	no	—
218	C₂²×C₈	—	67	1	no	—
219	C₂²×C₈	—	67	1	no	—
220	C₂²×C₈	—	67	2	no	—
221	C₂²×C₈	—	67	2	no	—
222	C₂²×C₈	—	67	2	no	—
223	C₂²×C₈	—	67	2	no	—
224	C₂²×C₈	—	67	1	no	—
225	C₂²×C₈	—	67	1	no	—
226	C₂²×C₈	—	67	2	no	—
227	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
228	#117	—	67	1	no	—
229	#117	—	67	2	no	—
230	#117	—	134	1	no	—
231	#117	—	134	1	no	—
232	#117	C₄×D₆₇	1	1	yes	characteristic
233	C₂×C₄⋊C₄	—	134	1	no	—
234	C₂×C₂²⋊C₄	—	134	1	no	—
235	C₂×C₄²	—	67	2	no	—
236	M₃₂	—	67	4	no	—
237	M₃₂	—	67	4	no	—
238	M₃₂	—	67	8	no	—
239	M₃₂	—	67	8	no	—
240	M₃₂	C₄×D₆₇	1	4	yes	complemented
241	M₃₂	C₂²×D₆₇	1	4	yes	—
242	C₂×C₁₆	—	67	4	no	—
243	C₂×C₁₆	—	67	8	no	—
244	C₂×C₁₆	—	67	8	no	—
245	C₂×C₁₆	C₄×D₆₇	1	4	yes	complemented
246	#97	—	67	2	no	—
247	#97	—	67	2	no	—
248	#97	—	67	2	no	—
249	#97	C₂²×D₆₇	1	2	yes	—
250	C₄×C₈	—	67	2	no	—
251	C₄×C₈	—	67	2	no	—
252	C₄×C₈	—	67	2	no	—
253	C₄×C₈	C₄×D₆₇	1	2	yes	—
254	C₂⁴	—	67	1	no	—
255	C₂²×C₄	—	67	1	no	—
256	C₂²×C₄	—	67	2	no	—
257	C₂²×C₄	—	67	2	no	—
258	C₂²×C₄	—	67	1	no	—
259	C₂²×C₄	—	67	1	no	—
260	C₂²×C₄	—	67	2	no	—
261	C₂²×C₄	—	67	2	no	—
262	C₂²×C₄	—	67	1	no	—
263	C₂²×C₄	—	67	1	no	—
264	C₂²×C₄	—	134	2	no	—
265	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
266	M₁₆	—	2	2	no	—
267	M₁₆	—	134	4	no	—
268	M₁₆	—	134	2	no	—
269	C₂×C₈	—	67	2	no	—
270	C₂×C₈	—	67	2	no	—
271	C₂×C₈	—	67	1	no	—
272	C₂×C₈	—	67	1	no	—
273	C₂×C₈	—	67	1	no	—
274	C₂×C₈	—	67	1	no	—
275	C₂×C₈	—	67	2	no	—
276	C₂×C₈	—	67	1	no	—
277	C₂×C₈	—	67	1	no	—
278	C₂×C₈	—	67	2	no	—
279	C₂×C₈	—	67	2	no	—
280	C₂×C₈	—	67	2	no	—
281	C₂×C₈	—	67	2	no	—
282	C₂×C₈	—	67	2	no	—
283	C₂×C₈	—	67	2	no	—
284	C₂×C₈	—	134	2	no	—
285	C₂×C₈	—	134	2	no	—
286	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
287	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
288	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
289	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
290	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
291	C₄⋊C₄	—	2	1	no	—
292	C₄⋊C₄	—	134	2	no	—
293	C₄⋊C₄	—	134	1	no	—
294	C₂²⋊C₄	—	2	1	no	—
295	C₂²⋊C₄	—	134	2	no	—
296	C₂²⋊C₄	—	134	1	no	—
297	C₄²	—	67	2	no	—
298	C₄²	—	134	2	no	—
299	C₄²	C₂×C₄×D₆₇	1	2	yes	—
300	C₁₆	—	67	8	no	—
301	C₁₆	C₂×C₄×D₆₇	1	8	yes	—
302	C₂³	—	268	2	no	—
303	C₂³	—	67	2	no	—
304	C₂³	—	67	1	no	—
305	C₂³	—	67	2	no	—
306	C₂³	—	67	1	no	—
307	C₂³	M₁₆×D₆₇	1	1	yes	characteristic
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	268	4	no	—
310	C₂×C₄	—	67	2	no	—
311	C₂×C₄	—	67	2	no	—
312	C₂×C₄	—	67	1	no	—
313	C₂×C₄	—	67	1	no	—
314	C₂×C₄	—	67	1	no	—
315	C₂×C₄	—	67	2	no	—
316	C₂×C₄	—	67	1	no	—
317	C₂×C₄	—	67	2	no	—
318	C₂×C₄	—	67	2	no	—
319	C₂×C₄	—	67	2	no	—
320	C₂×C₄	—	67	2	no	—
321	C₂×C₄	—	67	1	no	—
322	C₂×C₄	—	67	1	no	—
323	C₂×C₄	—	67	2	no	—
324	C₂×C₄	—	134	2	no	—
325	C₂×C₄	C₄²×D₆₇	1	2	yes	—
326	C₂×C₄	M₁₆×D₆₇	1	1	yes	characteristic
327	C₂×C₄	M₁₆×D₆₇	1	2	yes	—
328	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
329	C₈	—	2	2	no	—
330	C₈	—	67	1	no	—
331	C₈	—	67	1	no	—
332	C₈	—	67	2	no	—
333	C₈	—	134	2	no	—
334	C₈	C₄²×D₆₇	1	1	yes	characteristic
335	C₈	C₄²×D₆₇	1	1	yes	characteristic
336	C₈	C₂²×C₄×D₆₇	1	2	yes	—
337	C₂²	—	4	1	no	—
338	C₂²	—	268	1	no	—
339	C₂²	—	268	2	no	—
340	C₂²	—	67	1	no	—
341	C₂²	—	67	1	no	—
342	C₂²	—	67	2	no	—
343	C₂²	—	134	2	no	—
344	C₂²	—	134	4	no	—
345	C₂²	#97×D₆₇	1	2	yes	—
346	C₂²	C₂×M₁₆×D₆₇	1	1	yes	characteristic
347	C₄	—	4	2	no	—
348	C₄	—	268	2	no	—
349	C₄	—	67	1	no	—
350	C₄	—	67	1	no	—
351	C₄	—	67	2	no	—
352	C₄	#97×D₆₇	1	2	yes	—
353	C₄	C₂×C₄²×D₆₇	1	1	yes	characteristic
354	C₄	C₂×M₁₆×D₆₇	1	1	yes	characteristic
355	C₂	—	2	1	no	—
356	C₂	—	2	2	no	—
357	C₂	—	67	2	no	—
358	C₂	—	134	1	no	—
359	C₂	—	134	2	no	—
360	C₂	C₂×#97×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄²×D₆₇
commutator	C₄×C₆₇	C₂²×C₄²
Frattini	C₂×C₈	C₂³×D₆₇
Fitting	C₆₇×#2110	C₂
socle	C₂×C₆₇	C₂²×#97
prime radical	C₂³×D₆₇	M₁₆
cosocle	C₂×C₈×C₆₇	C₂⁴
hypercenter	#2110	D₆₇
hypocenter	C₆₇	C₂×#2110
LCS	G ▷ C₄×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₈ ◁ #2110

Complements

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

N	H ≅ G/N	type
3. #22561814	C₂	semidirect
4. #22561813	C₂	semidirect
5. #22561812	C₂	semidirect
6. #347×D₆₇	C₂	semidirect
7. C₆₇×#2110	C₂	semidirect
12. C₂×#14523982	C₄	semidirect
13. M₃₂×D₆₇	C₄	semidirect
14. M₃₂×D₆₇	C₄	semidirect
17. C₂×C₁₆×D₆₇	C₄	semidirect
25. #16863174	C₂²	semidirect
26. #16863173	C₂²	semidirect
29. #347×C₆₇	C₂²	semidirect
52. #14523983	C₂×C₄	semidirect
55. #14523982	C₂×C₄	semidirect
56. C₂×C₆₇⋊C₁₆	C₂×C₄	semidirect
58. C₁₆×D₆₇	C₂×C₄	semidirect
68. M₃₂×C₆₇	C₂×C₄	semidirect
70. C₂×C₁₆×C₆₇	C₂×C₄	semidirect
180. D₆₇	#2110	direct (N × H)
186. #2110	D₆₇	direct (N × H)
188. C₆₇	C₂×#2110	semidirect
210. #347	C₂×D₆₇	semidirect
240. M₃₂	C₄×D₆₇	semidirect
245. C₂×C₁₆	C₄×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₃₂×D₆₇	2
#405×D₆₇	2
#22561814	2
#22561813	2
#22561812	2
#347×D₆₇	2
C₆₇×#2110	2
C₂×#2110	67

Subgroups — #2110×D67 #31008486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2110×D₆₇ #31008486