Finite Group Databasebeta

← #20255152

Subgroups — #20255152

Order 6016.

464 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689934C211yesmaximal, characteristic, complemented
2#15689930C211yesmaximal, characteristic, complemented
3#15689926C211yesmaximal, characteristic, complemented
4#15689511C211yesmaximal, characteristic, complemented
5#15689391C211yesmaximal, characteristic, complemented
6#15689390C211yesmaximal, characteristic, complemented
7#15689386C211yesmaximal, characteristic, complemented
8#15689384C211yesmaximal, characteristic, complemented
9#15689301C211yesmaximal, characteristic, complemented
10#15689294C211yesmaximal, characteristic, complemented
11#15689291C211yesmaximal, characteristic, complemented
12#15689289C211yesmaximal, characteristic, complemented
13#15689245C211yesmaximal, characteristic, complemented
14#15689243C211yesmaximal, characteristic, complemented
15C47×#576C211yesmaximal, characteristic, complemented
16#13094071C2211yescharacteristic, complemented
17#13094070C2211yescharacteristic, complemented
18#13094056—21no—
19#13094054—21no—
20#13094054C2211yescharacteristic, complemented
21#13094054C2211yescharacteristic, complemented
22#13094050—21no—
23#13094050—21no—
24#13094050C2211yescharacteristic, complemented
25#13094050C2211yescharacteristic, complemented
26#13094049—21no—
27#13094049C2211yescharacteristic
28#13094049C2211yescharacteristic, complemented
29#13094048—21no—
30#13094045—21no—
31#13094044—21no—
32#13094044—21no—
33#13094044C2211yescharacteristic
34C2×#10625325C2211yescharacteristic, complemented
35C2×#10625335—21no—
36C2×#10625335C2211yescharacteristic, complemented
37SD16×D47—21no—
38C2×#10625334—21no—
39C2×#10625334C2211yescharacteristic, complemented
40#13094031C2211yescharacteristic, complemented
41#13094031C2211yescharacteristic, complemented
42#13094030C2211yescharacteristic, complemented
43#13094020C2211yescharacteristic, complemented
44#13094011C2211yescharacteristic, complemented
45#13093960C2211yescharacteristic, complemented
46#13093959C2211yescharacteristic, complemented
47#13093951C2211yescharacteristic, complemented
48#13093951C2211yescharacteristic, complemented
49#13093951C2211yescharacteristic, complemented
50#13093950C2211yescharacteristic, complemented
51#13093942C2211yescharacteristic, complemented
52#13093941C2211yescharacteristic, complemented
53#13093941C2211yescharacteristic, complemented
54#13093940C2211yescharacteristic, complemented
55#13093934C2211yescharacteristic, complemented
56H(5,𝔽2)×C47C2211yescharacteristic
57H(5,𝔽2)×C47C2211yescharacteristic, complemented
58AGL(1,ℤ/8)×C47—21no—
59AGL(1,ℤ/8)×C47—21no—
60AGL(1,ℤ/8)×C47C2211yescharacteristic
61AGL(1,ℤ/8)×C47C2211yescharacteristic, complemented
62#135×C47—21no—
63#135×C47C2211yescharacteristic
64C2×D8×C47—21no—
65C2×D8×C47C2211yescharacteristic, complemented
66#131×C47C2211yescharacteristic, complemented
67#41×C47—21no—
68#41×C47—21no—
69#41×C47—21no—
70#41×C47—21no—
71#41×C47C2311yescharacteristic
72#41×C47C2311yescharacteristic
73#41×C47C2311yescharacteristic
74C2×D4×C47—21no—
75C2×D4×C47—21no—
76C2×D4×C47—21no—
77C2×D4×C47—21no—
78C2×D4×C47—41no—
79C2×D4×C47—41no—
80C2×D4×C47C2311yescharacteristic
81C2×D4×C47C2311yescharacteristic
82C2×C22⋊D47—41no—
83#10625354—21no—
84Q8×D47—21no—
85#10625352—21no—
86#10625352—41no—
87D4×D47—21no—
88D4×D47—41no—
89#10625350—21no—
90#10625350—21no—
91#10625350C2311yescharacteristic
92C2×D188—21no—
93C2×D188C2311yescharacteristic
94C2×Dic94—21no—
95C2×Dic94C2311yescharacteristic
96Q16×C47D411yescharacteristic, complemented
97SD16×C47—21no—
98SD16×C47—21no—
99SD16×C47D411yescharacteristic, complemented
100SD16×C47D411yescharacteristic, complemented
101D8×C47—21no—
102D8×C47—21no—
103D8×C47—21no—
104D8×C47—21no—
105D8×C47D411yescharacteristic, complemented
106M16×C47—21no—
107M16×C47C2311yescharacteristic
108C2×C8×C47—21no—
109C2×C8×C47C2311yescharacteristic
110C22⋊Dic47—41no—
111#10625337—21no—
112#10625337—21no—
113#10625337D411yescharacteristic, complemented
114#10625336—21no—
115#10625336—21no—
116#10625336D411yescharacteristic, complemented
117#10625335—21no—
118#10625335—21no—
119#10625335—21no—
120#10625335—21no—
121#10625335—21no—
122#10625335—21no—
123#10625335D411yescharacteristic, complemented
124#10625334—21no—
125#10625334—21no—
126#10625334—21no—
127#10625334—21no—
128#10625334—21no—
129#10625334—21no—
130#10625334D411yescharacteristic, complemented
131C4×Dic47C2311yescharacteristic
132#10625329—21no—
133#10625329—21no—
134#10625329C2311yescharacteristic
135#10625329C2311yescharacteristic
136#10625329C2311yescharacteristic
137C2×C47⋊C8—21no—
138C2×C47⋊C8—21no—
139C2×C47⋊C8C2311yescharacteristic
140#10625325—21no—
141#10625325—21no—
142#10625324—21no—
143C8×D47—21no—
144C23×C47—21no—
145C23×C47—21no—
146C23×C47—41no—
147C23×C47—41no—
148C22×D47—21no—
149C22×D47—41no—
150Q8×C47C2×D411yescharacteristic
151Q8×C47C2×D411yescharacteristic
152Q8×C47C2×D411yescharacteristic
153D4×C47—21no—
154D4×C47—21no—
155D4×C47—21no—
156D4×C47—21no—
157D4×C47—21no—
158D4×C47—21no—
159D4×C47—21no—
160D4×C47—41no—
161D4×C47—41no—
162D4×C47—41no—
163D4×C47—41no—
164D4×C47C2×D411yescharacteristic
165D4×C47C2×D411yescharacteristic
166D4×C47C2×D411yescharacteristic
167C2×C4×C47—21no—
168C2×C4×C47—21no—
169C2×C4×C47—21no—
170C2×C4×C47—41no—
171C2×C4×C47—41no—
172C2×C4×C47C2411yescharacteristic
173C22⋊D47—21no—
174C22⋊D47—41no—
175C22⋊D47—41no—
176C22⋊D47—82no—
177C2×Dic47—21no—
178C2×Dic47—21no—
179C2×Dic47—41no—
180D188—21no—
181D188—21no—
182D188—41no—
183D188C2×D411yescharacteristic
184C4×D47—21no—
185C4×D47—41no—
186C4×D47—41no—
187Dic94—21no—
188Dic94—21no—
189Dic94—41no—
190Dic94C2×D411yescharacteristic
191C8×C47—21no—
192C8×C47C2×D411yescharacteristic
193C8×C47C2×D411yescharacteristic
194C47⋊C8—21no—
195C47⋊C8—21no—
196C47⋊C8—21no—
197C47⋊C8C2×D411yescharacteristic
198C47⋊C8C2×D411yescharacteristic
199C22×C47—21no—
200C22×C47—21no—
201C22×C47—21no—
202C22×C47—41no—
203C22×C47—41no—
204C22×C47—81no—
205C22×C47—81no—
206C22×C47—161no—
207C22×C47—161no—
208C22×C47H(5,𝔽2)11yescharacteristic
209C2×D47—21no—
210C2×D47—41no—
211C2×D47—81no—
212C2×D47—161no—
213C4×C47—21no—
214C4×C47—21no—
215C4×C47—21no—
216C4×C47C22×D411yescharacteristic
217C4×C47C22×D411yescharacteristic
218Dic47—21no—
219Dic47—41no—
220Dic47—41no—
221#3288—471nomaximal, Sylow
222C2×C47—21no—
223C2×C47—41no—
224C2×C47—41no—
225C2×C47—41no—
226C2×C47—81no—
227C2×C47—81no—
228C2×C47D4211yescharacteristic
229D47—41no—
230D47—81no—
231#577—471no—
232#577—471no—
233#576—471no—
234#576D4711yescharacteristic, complemented
235#496—471no—
236#472—471no—
237#472—471no—
238#471—471no—
239#471—471no—
240#455—471no—
241#454—471no—
242#453—471no—
243#453—471no—
244#444—471no—
245#444—471no—
246C47#328811yescharacteristic, complemented, Sylow
2472−1+4—471no—
248H(5,𝔽2)—471no—
249H(5,𝔽2)C2×D4711yescharacteristic
250H(5,𝔽2)C2×D4711yescharacteristic, complemented
251#137—471no—
252#137—471no—
253#137—941no—
254#137—941no—
255AGL(1,ℤ/8)—21no—
256AGL(1,ℤ/8)—21no—
257AGL(1,ℤ/8)—471no—
258AGL(1,ℤ/8)—471no—
259AGL(1,ℤ/8)—471no—
260AGL(1,ℤ/8)—471no—
261AGL(1,ℤ/8)—941no—
262AGL(1,ℤ/8)—941no—
263AGL(1,ℤ/8)—941no—
264AGL(1,ℤ/8)—941no—
265AGL(1,ℤ/8)C2×D4711yescharacteristic
266AGL(1,ℤ/8)C2×D4711yescharacteristic, complemented
267#135—21no—
268#135—471no—
269#135—941no—
270#135—941no—
271#135—941no—
272#135C2×D4711yescharacteristic
273C2×SD16—471no—
274C2×SD16—471no—
275C2×SD16—941no—
276C2×SD16—941no—
277C2×D8—21no—
278C2×D8—471no—
279C2×D8—941no—
280C2×D8C2×D4711yescharacteristic, complemented
281#131—471no—
282#131—471no—
283#131—471no—
284#131C2×D4711yescharacteristic, complemented
285#127—471no—
286#124—471no—
287#108—471no—
288#108—471no—
289#104—471no—
290#104—471no—
291#104—471no—
292#104—471no—
293#101—471no—
294#100—471no—
295#100—471no—
296#100—471no—
297#97—471no—
298#41—21no—
299#41—21no—
300#41—21no—
301#41—21no—
302#41—471no—
303#41—941no—
304#41—941no—
305#41—941no—
306#41—941no—
307#41—1881no—
308#41C22×D4711yescharacteristic
309#41C22×D4711yescharacteristic
310#41C22×D4711yescharacteristic
311C2×Q8—471no—
312C2×Q8—941no—
313C2×Q8—941no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—471no—
321C2×D4—941no—
322C2×D4—941no—
323C2×D4—1881no—
324C2×D4—1881no—
325C2×D4C22×D4711yescharacteristic
326C2×D4C22×D4711yescharacteristic
327Q16—471no—
328Q16—941no—
329Q16—941no—
330Q16C22⋊D4711yescharacteristic, complemented
331SD16—21no—
332SD16—21no—
333SD16—471no—
334SD16—471no—
335SD16—941no—
336SD16—941no—
337SD16—941no—
338SD16—941no—
339SD16—941no—
340SD16—941no—
341SD16—941no—
342SD16—941no—
343SD16—941no—
344SD16—941no—
345SD16C22⋊D4711yescharacteristic, complemented
346SD16C22⋊D4711yescharacteristic, complemented
347D8—21no—
348D8—21no—
349D8—21no—
350D8—21no—
351D8—471no—
352D8—941no—
353D8—941no—
354D8—941no—
355D8—941no—
356D8—941no—
357D8—941no—
358D8C22⋊D4711yescharacteristic, complemented
359M16—21no—
360M16—471no—
361M16—471no—
362M16—471no—
363M16—941no—
364M16—941no—
365M16—941no—
366M16C22×D4711yescharacteristic
367C2×C8—21no—
368C2×C8—471no—
369C2×C8—941no—
370C2×C8—941no—
371C2×C8—941no—
372C2×C8C22×D4711yescharacteristic
373C22⋊C4—1881no—
374C42—471no—
375C23—21no—
376C23—21no—
377C23—41no—
378C23—41no—
379C23—941no—
380C23—1881no—
381Q8—471no—
382Q8—941no—
383Q8—941no—
384Q8—1881no—
385Q8D4×D4711yescharacteristic
386Q8C2×C22⋊D4711yescharacteristic
387Q8C2×C22⋊D4711yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—21no—
394D4—21no—
395D4—41no—
396D4—41no—
397D4—41no—
398D4—41no—
399D4—471no—
400D4—941no—
401D4—941no—
402D4—941no—
403D4—3762no—
404D4—1881no—
405D4—1881no—
406D4—1881no—
407D4D4×D4711yescharacteristic
408D4C2×C22⋊D4711yescharacteristic
409D4C2×C22⋊D4711yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—941no—
416C2×C4—941no—
417C2×C4—941no—
418C2×C4—1881no—
419C2×C4—1881no—
420C2×C4—1881no—
421C2×C4C23×D4711yescharacteristic
422C8—21no—
423C8—471no—
424C8—471no—
425C8—941no—
426C8—941no—
427C8—941no—
428C8C2×C22⋊D4711yescharacteristic
429C8C2×C22⋊D4711yescharacteristic
430C22—21no—
431C22—21no—
432C22—21no—
433C22—41no—
434C22—41no—
435C22—81no—
436C22—81no—
437C22—161no—
438C22—161no—
439C22—941no—
440C22—3761no—
441C22—1881no—
442C22—7521no—
443C22#1309406911yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—941no—
448C4—1881no—
449C4—1881no—
450C4C2×D4×D4711yescharacteristic
451C4C22×C22⋊D4711yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—41no—
456C2—81no—
457C2—81no—
458C2—3761no—
459C2—1881no—
460C2D4×C22⋊D4711yescharacteristic
subgroupG/H
centerC2D4×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#576C2
socleC2×C47D42
hypercenter#576D47
hypocenterC47#3288
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #576

Complements

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

NH ≅ G/Ntype
1. #15689934C2semidirect
2. #15689930C2semidirect
3. #15689926C2semidirect
4. #15689511C2semidirect
5. #15689391C2semidirect
6. #15689390C2semidirect
7. #15689386C2semidirect
8. #15689384C2semidirect
9. #15689301C2semidirect
10. #15689294C2semidirect
11. #15689291C2semidirect
12. #15689289C2semidirect
13. #15689245C2semidirect
14. #15689243C2semidirect
15. C47×#576C2semidirect
16. #13094071C22semidirect
17. #13094070C22semidirect
20. #13094054C22semidirect
21. #13094054C22semidirect
24. #13094050C22semidirect
25. #13094050C22semidirect
28. #13094049C22semidirect
34. C2×#10625325C22semidirect
36. C2×#10625335C22semidirect
39. C2×#10625334C22semidirect
40. #13094031C22semidirect
41. #13094031C22semidirect
42. #13094030C22semidirect
43. #13094020C22semidirect
44. #13094011C22semidirect
45. #13093960C22semidirect
46. #13093959C22semidirect
47. #13093951C22semidirect
48. #13093951C22semidirect
49. #13093951C22semidirect
50. #13093950C22semidirect
51. #13093942C22semidirect
52. #13093941C22semidirect
53. #13093941C22semidirect
54. #13093940C22semidirect
55. #13093934C22semidirect
57. H(5,𝔽2)×C47C22semidirect
61. AGL(1,ℤ/8)×C47C22semidirect
65. C2×D8×C47C22semidirect
66. #131×C47C22semidirect
96. Q16×C47D4semidirect
99. SD16×C47D4semidirect
100. SD16×C47D4semidirect
105. D8×C47D4semidirect
113. #10625337D4semidirect
116. #10625336D4semidirect
123. #10625335D4semidirect
130. #10625334D4semidirect
234. #576D47semidirect
246. C47#3288semidirect
250. H(5,𝔽2)C2×D47semidirect
266. AGL(1,ℤ/8)C2×D47semidirect
280. C2×D8C2×D47semidirect
284. #131C2×D47semidirect
330. Q16C22⋊D47semidirect
345. SD16C22⋊D47semidirect
346. SD16C22⋊D47semidirect
358. D8C22⋊D47semidirect