Finite Group Databasebeta

← #20255153

Subgroups — #20255153

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#15689932C211yesmaximal, characteristic, complemented
2#15689929C211yesmaximal, characteristic, complemented
3#15689928C211yesmaximal, characteristic, complemented
4#15689927C211yesmaximal, characteristic, complemented
5#15689509C211yesmaximal, characteristic, complemented
6#15689394C211yesmaximal, characteristic, complemented
7#15689392C211yesmaximal, characteristic, complemented
8#15689389C211yesmaximal, characteristic, complemented
9#15689299C211yesmaximal, characteristic, complemented
10#15689298C211yesmaximal, characteristic, complemented
11#15689293C211yesmaximal, characteristic, complemented
12#15689289C211yesmaximal, characteristic, complemented
13#15689244C211yesmaximal, characteristic, complemented
14#15689243C211yesmaximal, characteristic, complemented
15C47×#471C211yesmaximal, characteristic, complemented
16#13094072C2211yescharacteristic, complemented
17#13094070C2211yescharacteristic
18#13094070C2211yescharacteristic, complemented
19#13094069C2211yescharacteristic, complemented
20#13094056—21no—
21#13094055C2211yescharacteristic, complemented
22#13094053—21no—
23#13094052—21no—
24#13094052—21no—
25#13094052C2211yescharacteristic
26#13094052C2211yescharacteristic, complemented
27#13094052C2211yescharacteristic, complemented
28#13094052C2211yescharacteristic, complemented
29#13094051—21no—
30#13094051—21no—
31#13094051—21no—
32#13094050C2211yescharacteristic, complemented
33#13094048—21no—
34#13094047—21no—
35#13094046—21no—
36#13094046C2211yescharacteristic
37#13094045—21no—
38#13094045—21no—
39#13094044C2211yescharacteristic
40C2×#10625336C2211yescharacteristic, complemented
41SD16×D47—21no—
42SD16×D47—21no—
43C2×D376—21no—
44C2×D376C2211yescharacteristic, complemented
45C2×#10625334C2211yescharacteristic, complemented
46D8×D47—21no—
47#13094032C2211yescharacteristic, complemented
48#13094032C2211yescharacteristic, complemented
49#13094030C2211yescharacteristic, complemented
50#13094020C2211yescharacteristic, complemented
51#13094013C2211yescharacteristic, complemented
52#13093959C2211yescharacteristic, complemented
53#13093951C2211yescharacteristic, complemented
54#13093950C2211yescharacteristic, complemented
55#13093950C2211yescharacteristic, complemented
56#13093950C2211yescharacteristic, complemented
57#13093940C2211yescharacteristic, complemented
58#13093940C2211yescharacteristic, complemented
59#13093934C2211yescharacteristic, complemented
60#137×C47C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C47C2211yescharacteristic
62C2×SD16×C47C2211yescharacteristic, complemented
63#131×C47C2211yescharacteristic, complemented
64#108×C47C2211yescharacteristic, complemented
65#101×C47C2211yescharacteristic, complemented
66#100×C47C2211yescharacteristic, complemented
67#41×C47C2311yescharacteristic
68C2×Q8×C47C2311yescharacteristic
69C2×D4×C47C2311yescharacteristic
70C2×C22⋊D47—41no—
71C2×C22⋊D47—41no—
72#10625354—21no—
73#10625354—21no—
74#10625354—21no—
75#10625354—21no—
76Q8×D47—21no—
77Q8×D47—21no—
78#10625352—21no—
79#10625352—21no—
80D4×D47—21no—
81D4×D47—21no—
82D4×D47—21no—
83D4×D47—21no—
84D4×D47—41no—
85D4×D47—41no—
86#10625350—21no—
87#10625350—21no—
88#10625350—41no—
89#10625350C2311yescharacteristic
90#10625350C2311yescharacteristic
91#10625350C2311yescharacteristic
92C2×D188—21no—
93C2×D188—21no—
94C2×D188C2311yescharacteristic
95C2×D188C2311yescharacteristic
96Q16×C47—21no—
97SD16×C47—21no—
98SD16×C47—21no—
99SD16×C47—21no—
100SD16×C47—21no—
101D8×C47—21no—
102M16×C47—21no—
103M16×C47C2311yescharacteristic
104M16×C47C2311yescharacteristic
105M16×C47C2311yescharacteristic
106C2×C8×C47—21no—
107C2×C8×C47C2311yescharacteristic
108#10625337—21no—
109#10625337D411yescharacteristic, complemented
110#10625336—21no—
111#10625336—21no—
112#10625336—21no—
113#10625336D411yescharacteristic, complemented
114#10625335—21no—
115#10625335D411yescharacteristic, complemented
116#10625334—21no—
117#10625334—21no—
118#10625334—21no—
119#10625334D411yescharacteristic, complemented
120(C2×D47)⋊C4—41no—
121C4×Dic47C2311yescharacteristic
122#10625329C2311yescharacteristic
123C2×C47⋊C8C2311yescharacteristic
124Dic188D411yescharacteristic, complemented
125D376—21no—
126D376—21no—
127D376—21no—
128D376—21no—
129D376—21no—
130D376—21no—
131D376D411yescharacteristic, complemented
132#10625325—21no—
133#10625325—21no—
134#10625325—21no—
135#10625325—21no—
136#10625325D411yescharacteristic, complemented
137#10625325D411yescharacteristic, complemented
138#10625324—21no—
139#10625324—21no—
140#10625324—21no—
141C8×D47—21no—
142C8×D47—21no—
143C8×D47—21no—
144C23×C47—21no—
145C22×D47—21no—
146C22×D47—21no—
147C22×D47—41no—
148C22×D47—41no—
149C22×D47—41no—
150Q8×C47—21no—
151Q8×C47—21no—
152Q8×C47C2×D411yescharacteristic
153D4×C47—21no—
154D4×C47—21no—
155D4×C47—21no—
156D4×C47C2×D411yescharacteristic
157C2×C4×C47—21no—
158C2×C4×C47—21no—
159C2×C4×C47C2411yescharacteristic
160C22⋊D47—21no—
161C22⋊D47—21no—
162C22⋊D47—21no—
163C22⋊D47—41no—
164C22⋊D47—41no—
165C22⋊D47—41no—
166C22⋊D47—41no—
167C22⋊D47—82no—
168C2×Dic47—21no—
169C2×Dic47—41no—
170D188—21no—
171D188—21no—
172D188—21no—
173D188—21no—
174D188—41no—
175D188—41no—
176D188—41no—
177D188C2×D411yescharacteristic
178D188C2×D411yescharacteristic
179D188C2×D411yescharacteristic
180C4×D47—21no—
181C4×D47—21no—
182C4×D47—21no—
183C4×D47—41no—
184C4×D47—41no—
185C4×D47—41no—
186C4×D47—41no—
187Dic94—41no—
188Dic94C2×D411yescharacteristic
189Dic94C2×D411yescharacteristic
190Dic94C2×D411yescharacteristic
191C8×C47—21no—
192C8×C47—21no—
193C8×C47—21no—
194C8×C47C2×D411yescharacteristic
195C8×C47C2×D411yescharacteristic
196C47⋊C8—21no—
197C47⋊C8C2×D411yescharacteristic
198C47⋊C8C2×D411yescharacteristic
199C22×C47—21no—
200C22×C47—41no—
201C22×C47—81no—
202C22×C47H(5,𝔽2)11yescharacteristic
203C2×D47—21no—
204C2×D47—21no—
205C2×D47—21no—
206C2×D47—41no—
207C2×D47—41no—
208C2×D47—81no—
209C2×D47—81no—
210C2×D47—161no—
211C2×D47—161no—
212C2×D47—161no—
213C4×C47—21no—
214C4×C47—41no—
215C4×C47C22×D411yescharacteristic
216C4×C47C22×D411yescharacteristic
217Dic47—21no—
218Dic47—21no—
219Dic47—21no—
220Dic47—41no—
221#3288—471nomaximal, Sylow
222C2×C47—21no—
223C2×C47—41no—
224C2×C47—81no—
225C2×C47D4211yescharacteristic
226D47—41no—
227D47—41no—
228D47—41no—
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#471D4711yescharacteristic, complemented
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)—471no—
250H(5,𝔽2)—471no—
251#137—471no—
252#137—941no—
253#137—941no—
254#137C2×D4711yescharacteristic, complemented
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)—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)—941no—
266AGL(1,ℤ/8)C2×D4711yescharacteristic
267#135—471no—
268#135—471no—
269#135—941no—
270#135—941no—
271#135—941no—
272#135—941no—
273C2×SD16—471no—
274C2×SD16—941no—
275C2×SD16—941no—
276C2×SD16C2×D4711yescharacteristic, complemented
277C2×D8—471no—
278C2×D8—471no—
279C2×D8—941no—
280C2×D8—941no—
281#131—471no—
282#131—471no—
283#131—471no—
284#131C2×D4711yescharacteristic, complemented
285#127—471no—
286#124—471no—
287#108—471no—
288#108C2×D4711yescharacteristic, complemented
289#104—471no—
290#104—471no—
291#104—471no—
292#104—471no—
293#101C2×D4711yescharacteristic, complemented
294#100—471no—
295#100—471no—
296#100C2×D4711yescharacteristic, complemented
297#97—471no—
298#41—471no—
299#41—471no—
300#41—471no—
301#41—941no—
302#41—941no—
303#41—941no—
304#41—941no—
305#41—941no—
306#41—941no—
307#41—941no—
308#41—941no—
309#41—1881no—
310#41C22×D4711yescharacteristic
311C2×Q8—941no—
312C2×Q8—941no—
313C2×Q8C22×D4711yescharacteristic
314C2×D4—471no—
315C2×D4—471no—
316C2×D4—941no—
317C2×D4—941no—
318C2×D4—941no—
319C2×D4—941no—
320C2×D4—941no—
321C2×D4—941no—
322C2×D4—1881no—
323C2×D4—1881no—
324C2×D4—1881no—
325C2×D4—1881no—
326C2×D4C22×D4711yescharacteristic
327Q16—21no—
328Q16—471no—
329Q16—471no—
330Q16—941no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—21no—
335SD16—471no—
336SD16—471no—
337SD16—471no—
338SD16—471no—
339SD16—941no—
340SD16—941no—
341SD16—941no—
342SD16—941no—
343SD16—941no—
344SD16—941no—
345SD16—941no—
346SD16—941no—
347D8—21no—
348D8—471no—
349D8—471no—
350D8—941no—
351D8—941no—
352D8—941no—
353D8—941no—
354D8—941no—
355D8—941no—
356D8—941no—
357D8—941no—
358D8—941no—
359M16—21no—
360M16—471no—
361M16—941no—
362M16—941no—
363M16—941no—
364M16C22×D4711yescharacteristic
365M16C22×D4711yescharacteristic
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—941no—
377C23—941no—
378C23—1881no—
379C23—1881no—
380C23—1881no—
381Q8—21no—
382Q8—21no—
383Q8—471no—
384Q8—471no—
385Q8—471no—
386Q8—1881no—
387Q8D4×D4711yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—471no—
392D4—471no—
393D4—471no—
394D4—941no—
395D4—941no—
396D4—941no—
397D4—941no—
398D4—941no—
399D4—941no—
400D4—941no—
401D4—3762no—
402D4—1881no—
403D4—1881no—
404D4—1881no—
405D4—1881no—
406D4—1881no—
407D4—1881no—
408D4—1881no—
409D4D4×D4711yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—941no—
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—21no—
425C8—471no—
426C8—471no—
427C8—941no—
428C8D4×D4711yescharacteristic
429C8D4×D4711yescharacteristic
430C22—21no—
431C22—41no—
432C22—81no—
433C22—941no—
434C22—941no—
435C22—941no—
436C22—3761no—
437C22—3761no—
438C22—1881no—
439C22—1881no—
440C22—7521no—
441C22—7521no—
442C22—7521no—
443C22#1309407011yescharacteristic
444C4—21no—
445C4—41no—
446C4—941no—
447C4—941no—
448C4—941no—
449C4—1881no—
450C4C2×D4×D4711yescharacteristic
451C4C2×D4×D4711yescharacteristic
452C2—21no—
453C2—41no—
454C2—81no—
455C2—3761no—
456C2—3761no—
457C2—1881no—
458C2—1881no—
459C2—1881no—
460C2#1568975711yescharacteristic
subgroupG/H
centerC2#15689757
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#471C2
socleC2×C47D42
hypercenter#471D47
hypocenterC47#3288
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #15689932C2semidirect
2. #15689929C2semidirect
3. #15689928C2semidirect
4. #15689927C2semidirect
5. #15689509C2semidirect
6. #15689394C2semidirect
7. #15689392C2semidirect
8. #15689389C2semidirect
9. #15689299C2semidirect
10. #15689298C2semidirect
11. #15689293C2semidirect
12. #15689289C2semidirect
13. #15689244C2semidirect
14. #15689243C2semidirect
15. C47×#471C2semidirect
16. #13094072C22semidirect
18. #13094070C22semidirect
19. #13094069C22semidirect
21. #13094055C22semidirect
26. #13094052C22semidirect
27. #13094052C22semidirect
28. #13094052C22semidirect
32. #13094050C22semidirect
40. C2×#10625336C22semidirect
44. C2×D376C22semidirect
45. C2×#10625334C22semidirect
47. #13094032C22semidirect
48. #13094032C22semidirect
49. #13094030C22semidirect
50. #13094020C22semidirect
51. #13094013C22semidirect
52. #13093959C22semidirect
53. #13093951C22semidirect
54. #13093950C22semidirect
55. #13093950C22semidirect
56. #13093950C22semidirect
57. #13093940C22semidirect
58. #13093940C22semidirect
59. #13093934C22semidirect
60. #137×C47C22semidirect
62. C2×SD16×C47C22semidirect
63. #131×C47C22semidirect
64. #108×C47C22semidirect
65. #101×C47C22semidirect
66. #100×C47C22semidirect
109. #10625337D4semidirect
113. #10625336D4semidirect
115. #10625335D4semidirect
119. #10625334D4semidirect
124. Dic188D4semidirect
131. D376D4semidirect
136. #10625325D4semidirect
137. #10625325D4semidirect
239. #471D47semidirect
246. C47#3288semidirect
254. #137C2×D47semidirect
276. C2×SD16C2×D47semidirect
284. #131C2×D47semidirect
288. #108C2×D47semidirect
293. #101C2×D47semidirect
296. #100C2×D47semidirect