Finite Group Databasebeta

← #20255155

Subgroups — #20255155

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#15689935C211yesmaximal, characteristic, complemented
2#15689930C211yesmaximal, characteristic, complemented
3#15689928C211yesmaximal, characteristic, complemented
4#15689925C211yesmaximal, characteristic, complemented
5#15689512C211yesmaximal, characteristic, complemented
6#15689394C211yesmaximal, characteristic, complemented
7#15689393C211yesmaximal, characteristic, complemented
8#15689387C211yesmaximal, characteristic, complemented
9#15689386C211yesmaximal, characteristic, complemented
10#15689302C211yesmaximal, characteristic, complemented
11#15689297C211yesmaximal, characteristic, complemented
12#15689292C211yesmaximal, characteristic, complemented
13#15689292C211yesmaximal, characteristic, complemented
14#15689246C211yesmaximal, characteristic, complemented
15C47×#444C211yesmaximal, characteristic, complemented
16#13094071C2211yescharacteristic, complemented
17#13094070C2211yescharacteristic
18#13094070C2211yescharacteristic, complemented
19#13094070C2211yescharacteristic, complemented
20#13094057—21no—
21#13094057C2211yescharacteristic, complemented
22#13094056—21no—
23#13094054C2211yescharacteristic, complemented
24#13094052—21no—
25#13094052—21no—
26#13094052—21no—
27#13094052C2211yescharacteristic
28#13094052C2211yescharacteristic, complemented
29#13094052C2211yescharacteristic, complemented
30#13094051—21no—
31#13094051—21no—
32#13094049C2211yescharacteristic
33#13094049C2211yescharacteristic, complemented
34#13094049C2211yescharacteristic, complemented
35#13094048—21no—
36#13094047—21no—
37#13094046—21no—
38#13094046—21no—
39#13094046C2211yescharacteristic
40#13094045—21no—
41C2×#10625325—21no—
42C2×#10625325C2211yescharacteristic, complemented
43C2×#10625325C2211yescharacteristic, complemented
44SD16×D47—21no—
45C2×D376—21no—
46C2×D376C2211yescharacteristic, complemented
47C2×D376C2211yescharacteristic, complemented
48D8×D47—21no—
49#13094030C2211yescharacteristic, complemented
50#13094030C2211yescharacteristic, complemented
51#13094021C2211yescharacteristic, complemented
52#13094012C2211yescharacteristic, complemented
53#13093960C2211yescharacteristic, complemented
54#13093952C2211yescharacteristic, complemented
55#13093952C2211yescharacteristic, complemented
56#13093942C2211yescharacteristic, complemented
57#13093940C2211yescharacteristic, complemented
58#13093940C2211yescharacteristic, complemented
59#13093940C2211yescharacteristic, complemented
60#135×C47C2211yescharacteristic
61#131×C47C2211yescharacteristic, complemented
62#131×C47C2211yescharacteristic, complemented
63#108×C47C2211yescharacteristic, complemented
64#104×C47C2211yescharacteristic, complemented
65#104×C47C2211yescharacteristic, complemented
66#97×C47C2211yescharacteristic, complemented
67#41×C47C2311yescharacteristic
68#41×C47C2311yescharacteristic
69#10625354—21no—
70#10625354—21no—
71#10625354—21no—
72Q8×D47—21no—
73#10625352—21no—
74#10625352—41no—
75D4×D47—21no—
76D4×D47—21no—
77D4×D47—21no—
78D4×D47—41no—
79D4×D47—41no—
80D4×D47—41no—
81#10625350—21no—
82#10625350—21no—
83#10625350—21no—
84#10625350—21no—
85#10625350C2311yescharacteristic
86#10625350C2311yescharacteristic
87C2×D188—21no—
88C2×D188—21no—
89C2×D188—21no—
90C2×D188—41no—
91C2×D188C2311yescharacteristic
92C2×D188C2311yescharacteristic
93C2×D188C2311yescharacteristic
94C2×Dic94—21no—
95C2×Dic94C2311yescharacteristic
96Q16×C47D411yescharacteristic, complemented
97SD16×C47D411yescharacteristic, complemented
98SD16×C47D411yescharacteristic, complemented
99D8×C47D411yescharacteristic, complemented
100M16×C47—21no—
101M16×C47—21no—
102M16×C47C2311yescharacteristic
103M16×C47C2311yescharacteristic
104C2×C8×C47—21no—
105C2×C8×C47—21no—
106C2×C8×C47C2311yescharacteristic
107C2×C8×C47C2311yescharacteristic
108C42×C47C2311yescharacteristic
109#10625337—21no—
110#10625336—21no—
111#10625336—21no—
112#10625336—21no—
113#10625335—21no—
114#10625334—21no—
115#10625334—21no—
116#10625334—21no—
117(C2×D47)⋊C4—41no—
118#10625329C2311yescharacteristic
119#10625329C2311yescharacteristic
120Dic188—21no—
121Dic188D411yescharacteristic, complemented
122D376—21no—
123D376—21no—
124D376—21no—
125D376—21no—
126D376—21no—
127D376—21no—
128D376—21no—
129D376D411yescharacteristic, complemented
130#10625325—21no—
131#10625325—21no—
132#10625325—21no—
133#10625325—21no—
134#10625325—21no—
135#10625325—21no—
136#10625325—21no—
137#10625325—21no—
138#10625325D411yescharacteristic, complemented
139#10625325D411yescharacteristic, complemented
140#10625324—21no—
141#10625324—21no—
142C8×D47—21no—
143C8×D47—21no—
144C22×D47—21no—
145C22×D47—21no—
146C22×D47—21no—
147C22×D47—41no—
148C22×D47—41no—
149C22×D47—41no—
150Q8×C47C2×D411yescharacteristic
151Q8×C47C2×D411yescharacteristic
152D4×C47—21no—
153D4×C47—21no—
154D4×C47C2×D411yescharacteristic
155D4×C47C2×D411yescharacteristic
156C2×C4×C47—21no—
157C2×C4×C47—21no—
158C2×C4×C47—21no—
159C2×C4×C47C2411yescharacteristic
160C22⋊D47—21no—
161C22⋊D47—21no—
162C22⋊D47—41no—
163C22⋊D47—41no—
164C22⋊D47—41no—
165C22⋊D47—41no—
166C2×Dic47—21no—
167C2×Dic47—41no—
168D188—21no—
169D188—21no—
170D188—21no—
171D188—21no—
172D188—21no—
173D188—21no—
174D188—41no—
175D188—41no—
176D188—41no—
177D188—82no—
178D188C2×D411yescharacteristic
179D188C2×D411yescharacteristic
180C4×D47—21no—
181C4×D47—21no—
182C4×D47—41no—
183C4×D47—41no—
184C4×D47—41no—
185C4×D47—41no—
186Dic94—21no—
187Dic94—21no—
188Dic94—41no—
189Dic94C2×D411yescharacteristic
190Dic94C2×D411yescharacteristic
191C8×C47—21no—
192C8×C47—21no—
193C8×C47C2×D411yescharacteristic
194C8×C47C2×D411yescharacteristic
195C8×C47C2×D411yescharacteristic
196C8×C47C2×D411yescharacteristic
197C47⋊C8—21no—
198C47⋊C8—21no—
199C22×C47—21no—
200C22×C47—21no—
201C22×C47H(5,𝔽2)11yescharacteristic
202C2×D47—21no—
203C2×D47—21no—
204C2×D47—41no—
205C2×D47—41no—
206C2×D47—41no—
207C2×D47—81no—
208C2×D47—81no—
209C2×D47—81no—
210C2×D47—161no—
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×C47D4211yescharacteristic
226D47—41no—
227D47—41no—
228D47—81no—
229D47—81no—
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#453—471no—
244#444—471no—
245#444D4711yescharacteristic, complemented
246C47#328811yescharacteristic, complemented, Sylow
2472−1+4—471no—
248H(5,𝔽2)—471no—
249H(5,𝔽2)—471no—
250H(5,𝔽2)—471no—
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)—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)—941no—
266AGL(1,ℤ/8)—941no—
267#135—471no—
268#135—941no—
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—471no—
278C2×D8—471no—
279C2×D8—941no—
280C2×D8—941no—
281#131—471no—
282#131—471no—
283#131C2×D4711yescharacteristic, complemented
284#131C2×D4711yescharacteristic, complemented
285#127—471no—
286#124—471no—
287#108—471no—
288#108C2×D4711yescharacteristic, complemented
289#104—471no—
290#104—471no—
291#104C2×D4711yescharacteristic, complemented
292#104C2×D4711yescharacteristic, complemented
293#101—471no—
294#100—471no—
295#100—471no—
296#100—471no—
297#97C2×D4711yescharacteristic, complemented
298#41—471no—
299#41—471no—
300#41—941no—
301#41—941no—
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—471no—
315C2×D4—471no—
316C2×D4—471no—
317C2×D4—941no—
318C2×D4—941no—
319C2×D4—941no—
320C2×D4—941no—
321C2×D4—941no—
322C2×D4—941no—
323C2×D4—1881no—
324C2×D4—1881no—
325C2×D4—1881no—
326C2×D4—1881no—
327Q16—471no—
328Q16—941no—
329Q16—941no—
330Q16D18811yescharacteristic, complemented
331SD16—471no—
332SD16—471no—
333SD16—941no—
334SD16—941no—
335SD16—941no—
336SD16—941no—
337SD16—941no—
338SD16—941no—
339SD16—941no—
340SD16—941no—
341SD16—941no—
342SD16—941no—
343SD16—941no—
344SD16—941no—
345SD16D18811yescharacteristic, complemented
346SD16D18811yescharacteristic, complemented
347D8—471no—
348D8—941no—
349D8—941no—
350D8—941no—
351D8—941no—
352D8—941no—
353D8—941no—
354D8—941no—
355D8—941no—
356D8—941no—
357D8—941no—
358D8D18811yescharacteristic, complemented
359M16—21no—
360M16—21no—
361M16—471no—
362M16—471no—
363M16—941no—
364M16—941no—
365M16C22×D4711yescharacteristic
366M16C22×D4711yescharacteristic
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—941no—
370C2×C8—941no—
371C2×C8C22×D4711yescharacteristic
372C2×C8C22×D4711yescharacteristic
373C22⋊C4—1881no—
374C42C22×D4711yescharacteristic
375C23—941no—
376C23—941no—
377C23—941no—
378C23—1881no—
379C23—1881no—
380C23—1881no—
381Q8—471no—
382Q8—471no—
383Q8—941no—
384Q8—941no—
385Q8—1881no—
386Q8C2×D18811yescharacteristic
387Q8C2×D18811yescharacteristic
388D4—21no—
389D4—21no—
390D4—471no—
391D4—471no—
392D4—941no—
393D4—941no—
394D4—941no—
395D4—941no—
396D4—941no—
397D4—941no—
398D4—941no—
399D4—941no—
400D4—3762no—
401D4—1881no—
402D4—1881no—
403D4—1881no—
404D4—1881no—
405D4—1881no—
406D4—1881no—
407D4—1881no—
408D4C2×D18811yescharacteristic
409D4C2×D18811yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—941no—
414C2×C4—941no—
415C2×C4—941no—
416C2×C4—1881no—
417C2×C4—1881no—
418C2×C4—1881no—
419C2×C4—1881no—
420C2×C4—1881no—
421C2×C4C23×D4711yescharacteristic
422C8—21no—
423C8—21no—
424C8—941no—
425C8—941no—
426C8C2×D18811yescharacteristic
427C8C2×D18811yescharacteristic
428C8D4×D4711yescharacteristic
429C8D4×D4711yescharacteristic
430C22—21no—
431C22—21no—
432C22—941no—
433C22—941no—
434C22—3761no—
435C22—3761no—
436C22—3761no—
437C22—1881no—
438C22—1881no—
439C22—1881no—
440C22—7521no—
441C22—7521no—
442C22—7521no—
443C22#1309407011yescharacteristic
444C4—21no—
445C4—21no—
446C4—41no—
447C4—941no—
448C4—941no—
449C4—1881no—
450C4C2×D4×D4711yescharacteristic
451C4C22×D18811yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—3761no—
456C2—3761no—
457C2—3761no—
458C2—1881no—
459C2—1881no—
460C2D4×D18811yescharacteristic
subgroupG/H
centerC2D4×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#444C2
socleC2×C47D42
hypercenter#444D47
hypocenterC47#3288
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #444

Complements

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

NH ≅ G/Ntype
1. #15689935C2semidirect
2. #15689930C2semidirect
3. #15689928C2semidirect
4. #15689925C2semidirect
5. #15689512C2semidirect
6. #15689394C2semidirect
7. #15689393C2semidirect
8. #15689387C2semidirect
9. #15689386C2semidirect
10. #15689302C2semidirect
11. #15689297C2semidirect
12. #15689292C2semidirect
13. #15689292C2semidirect
14. #15689246C2semidirect
15. C47×#444C2semidirect
16. #13094071C22semidirect
18. #13094070C22semidirect
19. #13094070C22semidirect
21. #13094057C22semidirect
23. #13094054C22semidirect
28. #13094052C22semidirect
29. #13094052C22semidirect
33. #13094049C22semidirect
34. #13094049C22semidirect
42. C2×#10625325C22semidirect
43. C2×#10625325C22semidirect
46. C2×D376C22semidirect
47. C2×D376C22semidirect
49. #13094030C22semidirect
50. #13094030C22semidirect
51. #13094021C22semidirect
52. #13094012C22semidirect
53. #13093960C22semidirect
54. #13093952C22semidirect
55. #13093952C22semidirect
56. #13093942C22semidirect
57. #13093940C22semidirect
58. #13093940C22semidirect
59. #13093940C22semidirect
61. #131×C47C22semidirect
62. #131×C47C22semidirect
63. #108×C47C22semidirect
64. #104×C47C22semidirect
65. #104×C47C22semidirect
66. #97×C47C22semidirect
96. Q16×C47D4semidirect
97. SD16×C47D4semidirect
98. SD16×C47D4semidirect
99. D8×C47D4semidirect
121. Dic188D4semidirect
129. D376D4semidirect
138. #10625325D4semidirect
139. #10625325D4semidirect
245. #444D47semidirect
246. C47#3288semidirect
283. #131C2×D47semidirect
284. #131C2×D47semidirect
288. #108C2×D47semidirect
291. #104C2×D47semidirect
292. #104C2×D47semidirect
297. #97C2×D47semidirect
330. Q16D188semidirect
345. SD16D188semidirect
346. SD16D188semidirect
358. D8D188semidirect