Finite Group Databasebeta

← #463×D61 #21455239

Subgroups — #463×D61 #21455239

Order 7808.

564 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D61C211yesmaximal, characteristic, complemented
2C2×D8×D61C211yesmaximal, characteristic
3#124×D61C211yesmaximal, characteristic, complemented
4C4×D4×D61C211yesmaximal, characteristic, complemented
5#16839980C211yesmaximal, characteristic, complemented
6#16839979C211yesmaximal, characteristic, complemented
7#16839978C211yesmaximal, characteristic, complemented
8#16839977C211yesmaximal, characteristic, complemented
9#16839976C211yesmaximal, characteristic, complemented
10#16839975C211yesmaximal, characteristic, complemented
11#16839974C211yesmaximal, characteristic, complemented
12C4⋊C8×D61C211yesmaximal, characteristic, complemented
13#103×D61C211yesmaximal, characteristic, complemented
14#102×D61C211yesmaximal, characteristic, complemented
15C61×#463C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C2×D4×D61C2211yescharacteristic
19C22×C4×D61—21no—
20C2×#11758190C2211yescharacteristic, complemented
21C2×#11758200C2211yescharacteristic, complemented
22C2×#11758201C2211yescharacteristic, complemented
23SD16×D61—24no—
24C2×D488C2211yescharacteristic
25C2×#11758199C2211yescharacteristic
26C2×#11758199C2211yescharacteristic
27D8×D61—24no—
28C2×C8×D61C2211yescharacteristic
29C2×C8×D61C2211yescharacteristic
30#14519766C2211yescharacteristic, complemented
31#14519765C2211yescharacteristic, complemented
32#14519764C2211yescharacteristic, complemented
33#14519763—21no—
34#14519763—21no—
35C4×D244C2211yescharacteristic, complemented
36D4×Dic61C2211yescharacteristic, complemented
37#14519739C2211yescharacteristic, complemented
38C4×C22⋊D61—21no—
39#14519737—21no—
40C4⋊C4×D61C2211yescharacteristic
41C22⋊C4×D61—21no—
42C22⋊C4×D61—21no—
43C22⋊C4×D61—21no—
44C42×D61C2211yescharacteristic
45C4⋊#92418C2211yescharacteristic, complemented
46#14519706C2211yescharacteristic, complemented
47#14519706C2211yescharacteristic, complemented
48#14519702C2211yescharacteristic, complemented
49#14519701C2211yescharacteristic, complemented
50#14519700C2211yescharacteristic, complemented
51#14519699C2211yescharacteristic, complemented
52#14519698C2211yescharacteristic, complemented
53#14519697C2211yescharacteristic, complemented
54C2×SD16×C61C2211yescharacteristic, complemented
55C2×D8×C61C2211yescharacteristic
56#124×C61C2211yescharacteristic, complemented
57C4×D4×C61C2211yescharacteristic, complemented
58C4⋊C8×C61C2211yescharacteristic, complemented
59#103×C61C2211yescharacteristic, complemented
60#102×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C23×D61—21no—
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C22×Dic61—21no—
70Q8×D61—22no—
71Q8×D61—22no—
72D4×D61—22no—
73D4×D61—22no—
74D4×D61—22no—
75D4×D61D414yes—
76C2×D244C2311yescharacteristic
77C2×D244C2311yescharacteristic
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—44no—
83C2×C4×D61D411yescharacteristic
84C2×C4×D61D411yescharacteristic
85C2×C4×D61C2311yescharacteristic
86C2×Dic122—21no—
87C2×Dic122C2311yescharacteristic
88SD16×C61—22no—
89D8×C61—22no—
90C2×C8×C61C2311yescharacteristic
91C2×C8×C61C2311yescharacteristic
92C4⋊C4×C61C2311yescharacteristic
93C22⋊C4×C61—21no—
94C22⋊C4×C61—21no—
95C22⋊C4×C61—21no—
96C42×C61C2311yescharacteristic
97C22⋊Dic61—21no—
98C22⋊Dic61—21no—
99C22⋊Dic61—21no—
100#11758201—22no—
101#11758200—22no—
102#11758199—22no—
103#11758199—22no—
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107#11758198—21no—
108#11758198—21no—
109#11758198—21no—
110C4⋊Dic61C2311yescharacteristic
111#11758196—21no—
112C4×Dic61D411yescharacteristic
113C4×Dic61D411yescharacteristic
114C4×Dic61C2311yescharacteristic
115C2×#92418C2311yescharacteristic
116C2×#92418C2311yescharacteristic
117D488—22no—
118#11758190—22no—
119C8×D61—22no—
120C8×D61—22no—
121C23×C61—21no—
122C23×C61—21no—
123C22×D61—21no—
124C22×D61—24no—
125C22×D61—21no—
126C22×D61—42no—
127C22×D61—42no—
128C22×D61—42no—
129C22×D61—42no—
130C22×D61—42no—
131C22×D61C2×D411yescharacteristic
132Q8×C61—21no—
133Q8×C61—21no—
134D4×C61—21no—
135D4×C61—21no—
136D4×C61—21no—
137D4×C61C2×D412yes—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—42no—
141C2×C4×C61C2×D411yescharacteristic
142C2×C4×C61C2×D411yescharacteristic
143C2×C4×C61C2411yescharacteristic
144C22⋊D61—24no—
145C22⋊D61—42no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—42no—
149C2×Dic61C2×D411yescharacteristic
150C2×Dic61C2×D411yescharacteristic
151C2×Dic61C2×D411yescharacteristic
152D244—21no—
153D244—21no—
154D244—21no—
155D244C2×D412yes—
156C4×D61—22no—
157C4×D61—22no—
158C4×D61—42no—
159C4×D61—42no—
160C4×D61—42no—
161C4×D61—42no—
162C4×D61C2×D412yes—
163C4×D61#4112yes—
164Dic122—21no—
165Dic122—21no—
166Dic122—42no—
167C8×C61—21no—
168C8×C61—21no—
169#92418—21no—
170#92418—21no—
171C22×C61—22no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61C22×D411yescharacteristic
178C2×D61—22no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—48no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—84no—
186C2×D61#12112yes—
187C2×D61#13512yes—
188C2×D61AGL(1,ℤ/8)12yes—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—41no—
192C4×C61—41no—
193C4×C61C22×D411yescharacteristic
194C4×C61C2×#4111yescharacteristic
195Dic61—21no—
196Dic61—21no—
197Dic61—41no—
198Dic61—41no—
199Dic61#12112yes—
200C2×#463—611nomaximal, Sylow
201C2×C61—42no—
202C2×C61—81no—
203C2×C61C2×#12111yescharacteristic
204C2×C61C2×#13511yescharacteristic
205C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
206D61—42no—
207D61—81no—
208D61#46314yesdirect product factor
209C22×SD16—611no—
210C22×D8—611no—
211C2×#124—611no—
212C2×C4×D4—611no—
213#463—611no—
214#463—611no—
215#463—611no—
216#463—611no—
217#463—611no—
218#463—611no—
219#463—611no—
220#463D6111yescharacteristic, direct product factor
221C2×C4⋊C8—611no—
222C2×#103—611no—
223C2×#102—611no—
224C61C2×#46311yescharacteristic, complemented, Sylow
225C22×Q8—611no—
226C22×D4—611no—
227C22×D4—611no—
228C23×C4—1221no—
229C2×SD16—611no—
230C2×SD16—611no—
231C2×SD16—611no—
232C2×SD16—1224no—
233C2×SD16C2×D6111yescharacteristic, complemented
234C2×D8—611no—
235C2×D8—611no—
236C2×D8—611no—
237C2×D8—1224no—
238C2×D8C2×D6111yescharacteristic
239C22×C8—611no—
240C22×C8—611no—
241#124—611no—
242#124—611no—
243#124—611no—
244#124—1221no—
245#124—1221no—
246#124C2×D6111yescharacteristic, complemented
247C4×D4—611no—
248C4×D4—611no—
249C4×D4—611no—
250C4×D4—1221no—
251C4×D4—1221no—
252C4×D4C2×D6111yescharacteristic, complemented
253C2×C4⋊C4—611no—
254C2×C22⋊C4—1221no—
255C2×C22⋊C4—1221no—
256C2×C22⋊C4—1221no—
257C2×C42—611no—
258C4⋊C8—611no—
259C4⋊C8—611no—
260C4⋊C8—611no—
261C4⋊C8C2×D6111yescharacteristic, complemented
262#103—611no—
263#103—611no—
264#103—611no—
265#103C2×D6111yescharacteristic, complemented
266#102—611no—
267#102—611no—
268#102—611no—
269#102C2×D6111yescharacteristic, complemented
270C24—1221no—
271C24—1221no—
272C2×Q8—611no—
273C2×Q8—1221no—
274C2×Q8—1222no—
275C2×Q8—1222no—
276C2×Q8C22×D6111yescharacteristic
277C2×D4—614no—
278C2×D4—611no—
279C2×D4—611no—
280C2×D4—1222no—
281C2×D4—1222no—
282C2×D4—1222no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4C22×D6111yescharacteristic
286C2×D4C22×D6111yescharacteristic
287C22×C4—21no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—2444no—
297SD16—22no—
298SD16—1222no—
299SD16—1222no—
300SD16—1222no—
301D8—22no—
302D8—1222no—
303D8—1222no—
304D8—1222no—
305C2×C8—611no—
306C2×C8—611no—
307C2×C8—1222no—
308C2×C8—1222no—
309C2×C8C22×D6111yescharacteristic
310C2×C8C22×D6111yescharacteristic
311C4⋊C4—611no—
312C4⋊C4—1221no—
313C4⋊C4C22×D6111yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—1221no—
318C22⋊C4—1221no—
319C22⋊C4—1221no—
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C22⋊C4—1221no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C42—611no—
327C42—611no—
328C42—611no—
329C42C22×D6111yescharacteristic
330C23—21no—
331C23—21no—
332C23—611no—
333C23—1224no—
334C23—1221no—
335C23—1221no—
336C23—2442no—
337C23—2442no—
338C23—2442no—
339C23—2442no—
340C23—2442no—
341Q8—21no—
342Q8—21no—
343Q8—1221no—
344Q8—1221no—
345Q8—2442no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—612no—
350D4—1224no—
351D4—1221no—
352D4—1221no—
353D4—1221no—
354D4—2442no—
355D4D4×D6112yes—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—611no—
360C2×C4—612no—
361C2×C4—612no—
362C2×C4—611no—
363C2×C4—611no—
364C2×C4—1222no—
365C2×C4—1222no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—2442no—
369C2×C4—2442no—
370C2×C4—2442no—
371C2×C4—2442no—
372C2×C4—2442no—
373C2×C4D4×D6111yescharacteristic
374C2×C4D4×D6111yescharacteristic
375C2×C4C23×D6111yescharacteristic
376C8—21no—
377C8—21no—
378C8—1221no—
379C8—1221no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—612no—
387C22—612no—
388C22—612no—
389C22—1222no—
390C22—4884no—
391C22—2448no—
392C22—2441no—
393C22—2441no—
394C22—2441no—
395C22—2441no—
396C22—2441no—
397C22C2×D4×D6111yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—612no—
403C4—1221no—
404C4—1221no—
405C4—2441no—
406C4—2441no—
407C4C2×D4×D6111yescharacteristic
408C4#41×D6111yescharacteristic
409C2—42no—
410C2—81no—
411C2—614no—
412C2—4881no—
413C2—2442no—
414C2#121×D6111yescharacteristic
415C2#135×D6111yescharacteristic
416C2AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#463C2
socleC22×C61C22×D4
hypercenter#463D61
hypocenterC61C2×#463
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D61C2semidirect
3. #124×D61C2semidirect
4. C4×D4×D61C2semidirect
5. #16839980C2semidirect
6. #16839979C2semidirect
7. #16839978C2semidirect
8. #16839977C2semidirect
9. #16839976C2semidirect
10. #16839975C2semidirect
11. #16839974C2semidirect
12. C4⋊C8×D61C2semidirect
13. #103×D61C2semidirect
14. #102×D61C2semidirect
15. C61×#463C2semidirect
20. C2×#11758190C22semidirect
21. C2×#11758200C22semidirect
22. C2×#11758201C22semidirect
30. #14519766C22semidirect
31. #14519765C22semidirect
32. #14519764C22semidirect
35. C4×D244C22semidirect
36. D4×Dic61C22semidirect
37. #14519739C22semidirect
45. C4⋊#92418C22semidirect
46. #14519706C22semidirect
47. #14519706C22semidirect
48. #14519702C22semidirect
49. #14519701C22semidirect
50. #14519700C22semidirect
51. #14519699C22semidirect
52. #14519698C22semidirect
53. #14519697C22semidirect
54. C2×SD16×C61C22semidirect
56. #124×C61C22semidirect
57. C4×D4×C61C22semidirect
58. C4⋊C8×C61C22semidirect
59. #103×C61C22semidirect
60. #102×C61C22semidirect
208. D61#463direct (N × H)
220. #463D61direct (N × H)
224. C61C2×#463semidirect
233. C2×SD16C2×D61semidirect
246. #124C2×D61semidirect
252. C4×D4C2×D61semidirect
261. C4⋊C8C2×D61semidirect
265. #103C2×D61semidirect
269. #102C2×D61semidirect