Finite Group Databasebeta

← #20255149

Subgroups — #20255149

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#15689933C211yesmaximal, characteristic, complemented
3#15689927C211yesmaximal, characteristic, complemented
4#15689926C211yesmaximal, characteristic, complemented
5#15689510C211yesmaximal, characteristic, complemented
6#15689392C211yesmaximal, characteristic, complemented
7#15689391C211yesmaximal, characteristic, complemented
8#15689385C211yesmaximal, characteristic, complemented
9#15689384C211yesmaximal, characteristic, complemented
10#15689302C211yesmaximal, characteristic, complemented
11#15689297C211yesmaximal, characteristic, complemented
12#15689290C211yesmaximal, characteristic, complemented
13#15689242C211yesmaximal, characteristic, complemented
14#15689242C211yesmaximal, characteristic, complemented
15C47×#453C211yesmaximal, characteristic, complemented
16#13094071C2211yescharacteristic, complemented
17#13094070C2211yescharacteristic
18#13094069C2211yescharacteristic, complemented
19#13094057C2211yescharacteristic, complemented
20#13094054—21no—
21#13094054C2211yescharacteristic, complemented
22#13094053—21no—
23#13094052C2211yescharacteristic, complemented
24#13094051—21no—
25#13094050—21no—
26#13094050—21no—
27#13094050C2211yescharacteristic
28#13094050C2211yescharacteristic, complemented
29#13094049—21no—
30#13094049C2211yescharacteristic, complemented
31#13094048—21no—
32#13094048—21no—
33#13094045—21no—
34#13094044—21no—
35#13094044—21no—
36#13094044C2211yescharacteristic
37#13094044C2211yescharacteristic
38#13094043—21no—
39C2×#10625335—21no—
40C2×#10625335C2211yescharacteristic, complemented
41C2×#10625335C2211yescharacteristic, complemented
42SD16×D47—21no—
43C2×#10625334—21no—
44C2×#10625334C2211yescharacteristic, complemented
45C2×#10625334C2211yescharacteristic, complemented
46D8×D47—21no—
47#13094032C2211yescharacteristic, complemented
48#13094032C2211yescharacteristic, complemented
49#13094031C2211yescharacteristic, complemented
50#13094031C2211yescharacteristic, complemented
51#13094012C2211yescharacteristic, complemented
52#13093959C2211yescharacteristic, complemented
53#13093959C2211yescharacteristic, complemented
54#13093952C2211yescharacteristic, complemented
55#13093952C2211yescharacteristic, complemented
56#13093942C2211yescharacteristic, complemented
57#13093941C2211yescharacteristic, complemented
58#13093940C2211yescharacteristic, complemented
59#13093935C2211yescharacteristic, complemented
60H(5,𝔽2)×C47C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C47C2211yescharacteristic
62AGL(1,ℤ/8)×C47C2211yescharacteristic, complemented
63#127×C47C2211yescharacteristic, complemented
64#104×C47C2211yescharacteristic, complemented
65#104×C47C2211yescharacteristic, complemented
66#100×C47C2211yescharacteristic, complemented
67#41×C47—21no—
68#41×C47—21no—
69#41×C47C2311yescharacteristic
70#41×C47C2311yescharacteristic
71C2×D4×C47—21no—
72C2×D4×C47—21no—
73C2×D4×C47—41no—
74C2×D4×C47—41no—
75C2×D4×C47C2311yescharacteristic
76C2×D4×C47C2311yescharacteristic
77C2×C22⋊D47—41no—
78#10625354—21no—
79Q8×D47—21no—
80#10625352—21no—
81#10625352—21no—
82#10625352—21no—
83#10625352—41no—
84D4×D47—21no—
85D4×D47—21no—
86D4×D47—21no—
87D4×D47—41no—
88#10625350—21no—
89#10625350—21no—
90#10625350C2311yescharacteristic
91#10625350C2311yescharacteristic
92C2×D188—21no—
93C2×D188C2311yescharacteristic
94C2×Dic94—21no—
95C2×Dic94C2311yescharacteristic
96SD16×C47—21no—
97SD16×C47—21no—
98D8×C47—21no—
99D8×C47—21no—
100M16×C47C2311yescharacteristic
101M16×C47C2311yescharacteristic
102C42×C47C2311yescharacteristic
103#10625337—21no—
104#10625337D411yescharacteristic, complemented
105#10625337D411yescharacteristic, complemented
106#10625336—21no—
107#10625336D411yescharacteristic, complemented
108#10625336D411yescharacteristic, complemented
109#10625335—21no—
110#10625335—21no—
111#10625335—21no—
112#10625335—21no—
113#10625335—21no—
114#10625335—21no—
115#10625335—21no—
116#10625335D411yescharacteristic, complemented
117#10625335D411yescharacteristic, complemented
118#10625334—21no—
119#10625334—21no—
120#10625334—21no—
121#10625334—21no—
122#10625334—21no—
123#10625334—21no—
124#10625334—21no—
125#10625334D411yescharacteristic, complemented
126#10625334D411yescharacteristic, complemented
127(C2×D47)⋊C4—41no—
128#10625329—21no—
129#10625329—21no—
130#10625329C2311yescharacteristic
131#10625329C2311yescharacteristic
132C2×C47⋊C8—21no—
133C2×C47⋊C8—21no—
134C2×C47⋊C8C2311yescharacteristic
135C2×C47⋊C8C2311yescharacteristic
136Dic188—21no—
137D376—21no—
138#10625325—21no—
139#10625325—21no—
140#10625324—21no—
141#10625324—21no—
142C8×D47—21no—
143C8×D47—21no—
144C23×C47—21no—
145C23×C47—21no—
146C23×C47—41no—
147C22×D47—21no—
148C22×D47—41no—
149C22×D47—41no—
150Q8×C47C2×D411yescharacteristic
151Q8×C47C2×D411yescharacteristic
152D4×C47—21no—
153D4×C47—21no—
154D4×C47—21no—
155D4×C47—21no—
156D4×C47—21no—
157D4×C47—21no—
158D4×C47—41no—
159D4×C47—41no—
160D4×C47—82no—
161D4×C47C2×D411yescharacteristic
162D4×C47C2×D411yescharacteristic
163C2×C4×C47—21no—
164C2×C4×C47—21no—
165C2×C4×C47—21no—
166C2×C4×C47—41no—
167C2×C4×C47C2411yescharacteristic
168C22⋊D47—21no—
169C22⋊D47—21no—
170C22⋊D47—41no—
171C22⋊D47—41no—
172C22⋊D47—41no—
173C22⋊D47—41no—
174C2×Dic47—21no—
175C2×Dic47—41no—
176C2×Dic47—41no—
177D188—21no—
178D188—21no—
179D188—41no—
180D188C2×D411yescharacteristic
181D188C2×D411yescharacteristic
182C4×D47—21no—
183C4×D47—21no—
184C4×D47—41no—
185C4×D47—41no—
186Dic94—21no—
187Dic94—21no—
188Dic94—41no—
189Dic94C2×D411yescharacteristic
190Dic94C2×D411yescharacteristic
191C8×C47—21no—
192C8×C47—21no—
193C47⋊C8—21no—
194C47⋊C8—21no—
195C47⋊C8C2×D411yescharacteristic
196C47⋊C8C2×D411yescharacteristic
197C47⋊C8C2×D411yescharacteristic
198C47⋊C8C2×D411yescharacteristic
199C22×C47—21no—
200C22×C47—21no—
201C22×C47—41no—
202C22×C47—41no—
203C22×C47—81no—
204C22×C47—81no—
205C22×C47—161no—
206C22×C47H(5,𝔽2)11yescharacteristic
207C2×D47—21no—
208C2×D47—21no—
209C2×D47—41no—
210C2×D47—81no—
211C2×D47—161no—
212C2×D47—161no—
213C4×C47—21no—
214C4×C47—21no—
215C4×C47—41no—
216C4×C47C22×D411yescharacteristic
217C4×C47C22×D411yescharacteristic
218Dic47—21no—
219Dic47—21no—
220Dic47—41no—
221#3288—471nomaximal, Sylow
222C2×C47—21no—
223C2×C47—41no—
224C2×C47—41no—
225C2×C47—81no—
226C2×C47—81no—
227C2×C47D4211yescharacteristic
228D47—41no—
229D47—41no—
230D47—81no—
231#577—471no—
232#577—471no—
233#576—471no—
234#576—471no—
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#453D4711yescharacteristic, complemented
244#444—471no—
245#444—471no—
246C47#328811yescharacteristic, complemented, Sylow
2472−1+4—471no—
248H(5,𝔽2)—471no—
249H(5,𝔽2)—471no—
250H(5,𝔽2)C2×D4711yescharacteristic, complemented
251#137—471no—
252#137—471no—
253#137—941no—
254#137—941no—
255AGL(1,ℤ/8)—471no—
256AGL(1,ℤ/8)—471no—
257AGL(1,ℤ/8)—471no—
258AGL(1,ℤ/8)—471no—
259AGL(1,ℤ/8)—941no—
260AGL(1,ℤ/8)—941no—
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—471no—
268#135—471no—
269#135—941no—
270#135—941no—
271#135—941no—
272#135—941no—
273C2×SD16—471no—
274C2×SD16—471no—
275C2×SD16—941no—
276C2×SD16—941no—
277C2×D8—471no—
278C2×D8—471no—
279C2×D8—941no—
280C2×D8—941no—
281#131—471no—
282#131—471no—
283#131—471no—
284#131—471no—
285#127C2×D4711yescharacteristic, complemented
286#124—471no—
287#108—471no—
288#108—471no—
289#104—471no—
290#104—471no—
291#104C2×D4711yescharacteristic, complemented
292#104C2×D4711yescharacteristic, complemented
293#101—471no—
294#100—471no—
295#100—471no—
296#100C2×D4711yescharacteristic, complemented
297#97—471no—
298#41—21no—
299#41—21no—
300#41—471no—
301#41—471no—
302#41—941no—
303#41—941no—
304#41—941no—
305#41—941no—
306#41—941no—
307#41—941no—
308#41—1881no—
309#41C22×D4711yescharacteristic
310#41C22×D4711yescharacteristic
311C2×Q8—471no—
312C2×Q8—941no—
313C2×Q8—941no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—471no—
319C2×D4—941no—
320C2×D4—941no—
321C2×D4—941no—
322C2×D4—941no—
323C2×D4—1881no—
324C2×D4—1881no—
325C2×D4C22×D4711yescharacteristic
326C2×D4C22×D4711yescharacteristic
327Q16—471no—
328Q16—471no—
329Q16—941no—
330Q16—941no—
331SD16—21no—
332SD16—21no—
333SD16—471no—
334SD16—471no—
335SD16—471no—
336SD16—471no—
337SD16—941no—
338SD16—941no—
339SD16—941no—
340SD16—941no—
341SD16—941no—
342SD16—941no—
343SD16—941no—
344SD16—941no—
345SD16—941no—
346SD16—941no—
347D8—21no—
348D8—21no—
349D8—471no—
350D8—471no—
351D8—941no—
352D8—941no—
353D8—941no—
354D8—941no—
355D8—941no—
356D8—941no—
357D8—941no—
358D8—941no—
359M16—471no—
360M16—471no—
361M16—941no—
362M16—941no—
363M16—941no—
364M16—941no—
365M16C22×D4711yescharacteristic
366M16C22×D4711yescharacteristic
367C2×C8—471no—
368C2×C8—471no—
369C2×C8—941no—
370C2×C8—941no—
371C2×C8—941no—
372C2×C8—941no—
373C22⋊C4—1881no—
374C42C22×D4711yescharacteristic
375C23—21no—
376C23—21no—
377C23—41no—
378C23—941no—
379C23—1881no—
380C23—1881no—
381Q8—471no—
382Q8—471no—
383Q8—941no—
384Q8—941no—
385Q8—1881no—
386Q8D4×D4711yescharacteristic
387Q8D4×D4711yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—21no—
394D4—41no—
395D4—41no—
396D4—82no—
397D4—471no—
398D4—471no—
399D4—941no—
400D4—941no—
401D4—941no—
402D4—941no—
403D4—1881no—
404D4—1881no—
405D4—1881no—
406D4—1881no—
407D4—1881no—
408D4D4×D4711yescharacteristic
409D4D4×D4711yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—941no—
415C2×C4—941no—
416C2×C4—941no—
417C2×C4—1881no—
418C2×C4—1881no—
419C2×C4—1881no—
420C2×C4—1881no—
421C2×C4C23×D4711yescharacteristic
422C8—21no—
423C8—21no—
424C8—471no—
425C8—471no—
426C8—471no—
427C8—471no—
428C8—941no—
429C8—941no—
430C22—21no—
431C22—21no—
432C22—41no—
433C22—41no—
434C22—81no—
435C22—81no—
436C22—161no—
437C22—941no—
438C22—941no—
439C22—3761no—
440C22—1881no—
441C22—7521no—
442C22—7521no—
443C22#1309406911yescharacteristic
444C4—21no—
445C4—21no—
446C4—41no—
447C4—941no—
448C4—941no—
449C4—1881no—
450C4C2×D4×D4711yescharacteristic
451C4C2×D4×D4711yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—81no—
456C2—81no—
457C2—3761no—
458C2—1881no—
459C2—1881no—
460C2#1568975511yescharacteristic
subgroupG/H
centerC2#15689755
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#453C2
socleC2×C47D42
hypercenter#453D47
hypocenterC47#3288
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #15689934C2semidirect
2. #15689933C2semidirect
3. #15689927C2semidirect
4. #15689926C2semidirect
5. #15689510C2semidirect
6. #15689392C2semidirect
7. #15689391C2semidirect
8. #15689385C2semidirect
9. #15689384C2semidirect
10. #15689302C2semidirect
11. #15689297C2semidirect
12. #15689290C2semidirect
13. #15689242C2semidirect
14. #15689242C2semidirect
15. C47×#453C2semidirect
16. #13094071C22semidirect
18. #13094069C22semidirect
19. #13094057C22semidirect
21. #13094054C22semidirect
23. #13094052C22semidirect
28. #13094050C22semidirect
30. #13094049C22semidirect
40. C2×#10625335C22semidirect
41. C2×#10625335C22semidirect
44. C2×#10625334C22semidirect
45. C2×#10625334C22semidirect
47. #13094032C22semidirect
48. #13094032C22semidirect
49. #13094031C22semidirect
50. #13094031C22semidirect
51. #13094012C22semidirect
52. #13093959C22semidirect
53. #13093959C22semidirect
54. #13093952C22semidirect
55. #13093952C22semidirect
56. #13093942C22semidirect
57. #13093941C22semidirect
58. #13093940C22semidirect
59. #13093935C22semidirect
60. H(5,𝔽2)×C47C22semidirect
62. AGL(1,ℤ/8)×C47C22semidirect
63. #127×C47C22semidirect
64. #104×C47C22semidirect
65. #104×C47C22semidirect
66. #100×C47C22semidirect
104. #10625337D4semidirect
105. #10625337D4semidirect
107. #10625336D4semidirect
108. #10625336D4semidirect
116. #10625335D4semidirect
117. #10625335D4semidirect
125. #10625334D4semidirect
126. #10625334D4semidirect
243. #453D47semidirect
246. C47#3288semidirect
250. H(5,𝔽2)C2×D47semidirect
266. AGL(1,ℤ/8)C2×D47semidirect
285. #127C2×D47semidirect
291. #104C2×D47semidirect
292. #104C2×D47semidirect
296. #100C2×D47semidirect