Finite Group Databasebeta

← #20255168

Subgroups — #20255168

Order 6016.

454 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689938C211yesmaximal, characteristic, complemented
2#15689930C211yesmaximal, characteristic, complemented
3#15689926C211yesmaximal, characteristic, complemented
4#15689504C211yesmaximal, characteristic, complemented
5#15689396C211yesmaximal, characteristic, complemented
6#15689391C211yesmaximal, characteristic, complemented
7#15689386C211yesmaximal, characteristic, complemented
8#15689383C211yesmaximal, characteristic, complemented
9#15689301C211yesmaximal, characteristic, complemented
10#15689299C211yesmaximal, characteristic, complemented
11#15689296C211yesmaximal, characteristic, complemented
12#15689294C211yesmaximal, characteristic, complemented
13#15689240C211yesmaximal, characteristic, complemented
14#15689238C211yesmaximal, characteristic, complemented
15C47×#577C211yesmaximal, characteristic, complemented
16#13094071C2211yescharacteristic, complemented
17#13094070C2211yescharacteristic
18#13094056—21no—
19#13094055—21no—
20#13094055C2211yescharacteristic, complemented
21#13094054—21no—
22#13094054C2211yescharacteristic
23#13094054C2211yescharacteristic, complemented
24#13094050—21no—
25#13094050C2211yescharacteristic
26#13094049—21no—
27#13094049C2211yescharacteristic
28#13094049C2211yescharacteristic, complemented
29#13094048—21no—
30#13094045—21no—
31#13094044—21no—
32#13094044—21no—
33#13094044C2211yescharacteristic
34C2×#10625337—21no—
35C2×#10625337C2211yescharacteristic, complemented
36C2×#10625325C2211yescharacteristic, complemented
37SD16×D47—21no—
38C2×#10625334—21no—
39C2×#10625334C2211yescharacteristic
40#13094031C2211yescharacteristic
41#13094031C2211yescharacteristic, complemented
42#13094030C2211yescharacteristic, complemented
43#13094013C2211yescharacteristic, complemented
44#13094011C2211yescharacteristic, complemented
45#13093960C2211yescharacteristic, complemented
46#13093959C2211yescharacteristic, complemented
47#13093951C2211yescharacteristic
48#13093951C2211yescharacteristic, complemented
49#13093951C2211yescharacteristic, complemented
50#13093950C2211yescharacteristic, complemented
51#13093943C2211yescharacteristic, complemented
52#13093942C2211yescharacteristic, complemented
53#13093941C2211yescharacteristic, complemented
54#13093940C2211yescharacteristic, complemented
55C8×Dic47C2211yescharacteristic, complemented
562−1+4×C47C2211yescharacteristic, complemented
57H(5,𝔽2)×C47C2211yescharacteristic
58#137×C47—21no—
59#137×C47C2211yescharacteristic
60AGL(1,ℤ/8)×C47—21no—
61AGL(1,ℤ/8)×C47C2211yescharacteristic, complemented
62#135×C47—21no—
63#135×C47C2211yescharacteristic
64C2×SD16×C47—21no—
65C2×SD16×C47C2211yescharacteristic, complemented
66#131×C47C2211yescharacteristic, complemented
67#41×C47—21no—
68#41×C47—21no—
69#41×C47—21no—
70#41×C47—21no—
71#41×C47—41no—
72#41×C47C2311yescharacteristic
73#41×C47C2311yescharacteristic
74#41×C47C2311yescharacteristic
75C2×Q8×C47—21no—
76C2×Q8×C47—21no—
77C2×Q8×C47C2311yescharacteristic
78C2×D4×C47—21no—
79C2×D4×C47—21no—
80C2×D4×C47—41no—
81C2×D4×C47C2311yescharacteristic
82#10625354—21no—
83Q8×D47—21no—
84#10625352—21no—
85#10625352—41no—
86D4×D47—21no—
87D4×D47—41no—
88#10625350—21no—
89#10625350—21no—
90#10625350C2311yescharacteristic
91C2×D188—21no—
92C2×D188C2311yescharacteristic
93C2×Dic94—21no—
94C2×Dic94C2311yescharacteristic
95Q16×C47—21no—
96Q16×C47D411yescharacteristic
97SD16×C47—21no—
98SD16×C47—21no—
99SD16×C47—21no—
100SD16×C47—21no—
101SD16×C47D411yescharacteristic
102SD16×C47D411yescharacteristic
103D8×C47—21no—
104D8×C47D411yescharacteristic
105M16×C47—21no—
106M16×C47C2311yescharacteristic
107C2×C8×C47—21no—
108C2×C8×C47C2311yescharacteristic
109C22⋊Dic47—41no—
110#10625337—21no—
111#10625337—21no—
112#10625337—21no—
113#10625337—21no—
114#10625337—21no—
115#10625337D411yescharacteristic
116#10625336—21no—
117#10625336—21no—
118#10625336—21no—
119#10625336D411yescharacteristic
120#10625335—21no—
121#10625335—21no—
122#10625335—21no—
123#10625335D411yescharacteristic
124#10625334—21no—
125#10625334—21no—
126#10625334—21no—
127#10625334—21no—
128#10625334—21no—
129#10625334D411yescharacteristic
130(C2×D47)⋊C4—41no—
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—41no—
146C22×D47—21no—
147C22×D47—41no—
148Q8×C47—21no—
149Q8×C47—21no—
150Q8×C47—41no—
151Q8×C47C2×D411yescharacteristic
152Q8×C47C2×D411yescharacteristic
153Q8×C47C2×D411yescharacteristic
154D4×C47—21no—
155D4×C47—21no—
156D4×C47—21no—
157D4×C47—21no—
158D4×C47—21no—
159D4×C47—41no—
160D4×C47—41no—
161D4×C47—41no—
162D4×C47C2×D411yescharacteristic
163D4×C47C2×D411yescharacteristic
164D4×C47C2×D411yescharacteristic
165C2×C4×C47—21no—
166C2×C4×C47—21no—
167C2×C4×C47—21no—
168C2×C4×C47—21no—
169C2×C4×C47—41no—
170C2×C4×C47—41no—
171C2×C4×C47—41no—
172C2×C4×C47C2411yescharacteristic
173C22⋊D47—21no—
174C22⋊D47—41no—
175C22⋊D47—41no—
176C2×Dic47—21no—
177C2×Dic47—21no—
178C2×Dic47—41no—
179D188—21no—
180D188—21no—
181D188—41no—
182D188C2×D411yescharacteristic
183C4×D47—21no—
184C4×D47—41no—
185C4×D47—41no—
186Dic94—21no—
187Dic94—21no—
188Dic94—41no—
189Dic94C2×D411yescharacteristic
190C8×C47—21no—
191C8×C47C2×D411yescharacteristic
192C8×C47C2×D411yescharacteristic
193C47⋊C8—21no—
194C47⋊C8—21no—
195C47⋊C8—21no—
196C47⋊C8C2×D411yescharacteristic
197C47⋊C8C2×D411yescharacteristic
198C22×C47—21no—
199C22×C47—21no—
200C22×C47—21no—
201C22×C47—41no—
202C22×C47—81no—
203C22×C47—161no—
204C22×C47H(5,𝔽2)11yescharacteristic
205C2×D47—21no—
206C2×D47—41no—
207C2×D47—81no—
208C2×D47—161no—
209C4×C47—21no—
210C4×C47—21no—
211C4×C47—21no—
212C4×C47—41no—
213C4×C47C22×D411yescharacteristic
214C4×C47C22×D411yescharacteristic
215Dic47—21no—
216Dic47—41no—
217Dic47—41no—
218#3290—471nomaximal, Sylow
219C2×C47—21no—
220C2×C47—41no—
221C2×C47—41no—
222C2×C47—41no—
223C2×C47—81no—
224C2×C47D4211yescharacteristic
225D47—41no—
226D47—81no—
227#578—471no—
228#577—471no—
229#577D4711yescharacteristic, complemented
230#576—471no—
231#495—471no—
232#473—471no—
233#472—471no—
234#471—471no—
235#471—471no—
236#455—471no—
237#455—471no—
238#454—471no—
239#454—471no—
240#443—471no—
241#443—471no—
242C47#329011yescharacteristic, complemented, Sylow
2432−1+4—471no—
2442−1+4C2×D4711yescharacteristic, complemented
245H(5,𝔽2)—471no—
246H(5,𝔽2)C2×D4711yescharacteristic
247#137—21no—
248#137—471no—
249#137—471no—
250#137—471no—
251#137—941no—
252#137—941no—
253#137—941no—
254#137C2×D4711yescharacteristic
255AGL(1,ℤ/8)—21no—
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)C2×D4711yescharacteristic, complemented
263#135—21no—
264#135—471no—
265#135—941no—
266#135—941no—
267#135—941no—
268#135C2×D4711yescharacteristic
269C2×Q16—471no—
270C2×Q16—941no—
271C2×SD16—21no—
272C2×SD16—471no—
273C2×SD16—941no—
274C2×SD16C2×D4711yescharacteristic, complemented
275C2×D8—471no—
276C2×D8—941no—
277#131—471no—
278#131—471no—
279#131—471no—
280#131C2×D4711yescharacteristic, complemented
281#124—471no—
282#124—471no—
283#108—471no—
284#108—471no—
285#104—471no—
286#104—471no—
287#104—471no—
288#104—471no—
289#101—471no—
290#101—471no—
291#100—471no—
292#100—471no—
293C4×C8—471no—
294#41—21no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—41no—
299#41—471no—
300#41—941no—
301#41—941no—
302#41—941no—
303#41—941no—
304#41—1881no—
305#41C22×D4711yescharacteristic
306#41C22×D4711yescharacteristic
307#41C22×D4711yescharacteristic
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—471no—
311C2×Q8—941no—
312C2×Q8—941no—
313C2×Q8C22×D4711yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—471no—
318C2×D4—941no—
319C2×D4—941no—
320C2×D4—1881no—
321C2×D4C22×D4711yescharacteristic
322Q16—21no—
323Q16—471no—
324Q16—941no—
325Q16—941no—
326Q16—941no—
327Q16—941no—
328Q16—941no—
329Q16C22⋊D4711yescharacteristic
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—471no—
335SD16—471no—
336SD16—941no—
337SD16—941no—
338SD16—941no—
339SD16—941no—
340SD16—941no—
341SD16—941no—
342SD16—941no—
343SD16—941no—
344SD16C22⋊D4711yescharacteristic
345SD16C22⋊D4711yescharacteristic
346D8—21no—
347D8—471no—
348D8—941no—
349D8—941no—
350D8—941no—
351D8—941no—
352D8—941no—
353D8C22⋊D4711yescharacteristic
354M16—21no—
355M16—471no—
356M16—471no—
357M16—471no—
358M16—941no—
359M16—941no—
360M16—941no—
361M16C22×D4711yescharacteristic
362C2×C8—21no—
363C2×C8—471no—
364C2×C8—941no—
365C2×C8—941no—
366C2×C8—941no—
367C2×C8C22×D4711yescharacteristic
368C22⋊C4—1881no—
369C22⋊C4—1881no—
370C42—471no—
371C23—21no—
372C23—41no—
373C23—941no—
374C23—1881no—
375Q8—21no—
376Q8—21no—
377Q8—41no—
378Q8—471no—
379Q8—941no—
380Q8—941no—
381Q8—1881no—
382Q8D4×D4711yescharacteristic
383Q8C2×C22⋊D4711yescharacteristic
384Q8C2×C22⋊D4711yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—41no—
391D4—41no—
392D4—41no—
393D4—471no—
394D4—941no—
395D4—941no—
396D4—941no—
397D4—1881no—
398D4—1881no—
399D4—1881no—
400D4D4×D4711yescharacteristic
401D4C2×C22⋊D4711yescharacteristic
402D4C2×C22⋊D4711yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—941no—
411C2×C4—941no—
412C2×C4—941no—
413C2×C4—1881no—
414C2×C4—1881no—
415C2×C4—1881no—
416C2×C4C23×D4711yescharacteristic
417C8—21no—
418C8—471no—
419C8—471no—
420C8—941no—
421C8—941no—
422C8—941no—
423C8C2×C22⋊D4711yescharacteristic
424C8C2×C22⋊D4711yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—41no—
429C22—81no—
430C22—161no—
431C22—941no—
432C22—3761no—
433C22—1881no—
434C22—7521no—
435C22#1309406911yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—41no—
440C4—941no—
441C4—1881no—
442C4—1881no—
443C4C2×D4×D4711yescharacteristic
444C4C22×C22⋊D4711yescharacteristic
445C2—21no—
446C2—41no—
447C2—41no—
448C2—41no—
449C2—81no—
450C2—3761no—
451C2—1881no—
452C2D4×C22⋊D4711yescharacteristic
subgroupG/H
centerC2D4×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#577C2
socleC2×C47D42
hypercenter#577D47
hypocenterC47#3290
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #15689938C2semidirect
2. #15689930C2semidirect
3. #15689926C2semidirect
4. #15689504C2semidirect
5. #15689396C2semidirect
6. #15689391C2semidirect
7. #15689386C2semidirect
8. #15689383C2semidirect
9. #15689301C2semidirect
10. #15689299C2semidirect
11. #15689296C2semidirect
12. #15689294C2semidirect
13. #15689240C2semidirect
14. #15689238C2semidirect
15. C47×#577C2semidirect
16. #13094071C22semidirect
20. #13094055C22semidirect
23. #13094054C22semidirect
28. #13094049C22semidirect
35. C2×#10625337C22semidirect
36. C2×#10625325C22semidirect
41. #13094031C22semidirect
42. #13094030C22semidirect
43. #13094013C22semidirect
44. #13094011C22semidirect
45. #13093960C22semidirect
46. #13093959C22semidirect
48. #13093951C22semidirect
49. #13093951C22semidirect
50. #13093950C22semidirect
51. #13093943C22semidirect
52. #13093942C22semidirect
53. #13093941C22semidirect
54. #13093940C22semidirect
55. C8×Dic47C22semidirect
56. 2−1+4×C47C22semidirect
61. AGL(1,ℤ/8)×C47C22semidirect
65. C2×SD16×C47C22semidirect
66. #131×C47C22semidirect
229. #577D47semidirect
242. C47#3290semidirect
244. 2−1+4C2×D47semidirect
262. AGL(1,ℤ/8)C2×D47semidirect
274. C2×SD16C2×D47semidirect
280. #131C2×D47semidirect