Finite Group Databasebeta

← #471×D47 #20253083

Subgroups — #471×D47 #20253083

Order 6016.

468 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#137×D47C211yesmaximal, characteristic, complemented
2AGL(1,ℤ/8)×D47C211yesmaximal, characteristic
3C2×SD16×D47C211yesmaximal, characteristic, complemented
4#131×D47C211yesmaximal, characteristic, complemented
5#15689389C211yesmaximal, characteristic, complemented
6#15689388C211yesmaximal, characteristic, complemented
7#15689387C211yesmaximal, characteristic, complemented
8#15689386C211yesmaximal, characteristic, complemented
9#15689385C211yesmaximal, characteristic, complemented
10#15689384C211yesmaximal, characteristic, complemented
11#15689383C211yesmaximal, characteristic, complemented
12#108×D47C211yesmaximal, characteristic, complemented
13#101×D47C211yesmaximal, characteristic, complemented
14#100×D47C211yesmaximal, characteristic, complemented
15C47×#471C211yesmaximal, characteristic, complemented
16#41×D47C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18C2×D4×D47C2211yescharacteristic
19#13094057C2211yescharacteristic, complemented
20#13094056—21no—
21#13094055C2211yescharacteristic, complemented
22#13094054C2211yescharacteristic, complemented
23#13094053—21no—
24#13094052C2211yescharacteristic
25#13094051—21no—
26#13094050C2211yescharacteristic
27#13094049C2211yescharacteristic
28#13094048—21no—
29Q16×D47—21no—
30C2×#10625325C2211yescharacteristic, complemented
31C2×#10625335C2211yescharacteristic, complemented
32C2×#10625336C2211yescharacteristic, complemented
33SD16×D47—21no—
34SD16×D47—21no—
35SD16×D47—21no—
36SD16×D47—21no—
37SD16×D47—21no—
38SD16×D47—21no—
39D8×D47—21no—
40#13094032—21no—
41#13094032C2211yescharacteristic, complemented
42#13094031C2211yescharacteristic, complemented
43#13094030—21no—
44#13094030C2211yescharacteristic, complemented
45M16×D47—21no—
46M16×D47C2211yescharacteristic
47M16×D47C2211yescharacteristic
48M16×D47C2211yescharacteristic
49C2×C8×D47—21no—
50C2×C8×D47C2211yescharacteristic
51#13093960C2211yescharacteristic, complemented
52#13093959C2211yescharacteristic, complemented
53#13093959C2211yescharacteristic, complemented
54#13093943C2211yescharacteristic, complemented
55#13093942C2211yescharacteristic, complemented
56#13093942C2211yescharacteristic, complemented
57#13093941C2211yescharacteristic, complemented
58#13093940C2211yescharacteristic, complemented
59#13093940C2211yescharacteristic, 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
67C23×D47—21no—
68#41×C47C2311yescharacteristic
69C2×Q8×C47C2311yescharacteristic
70C2×D4×C47C2311yescharacteristic
71C2×C22⋊D47—21no—
72#10625354D411yescharacteristic
73Q8×D47—21no—
74Q8×D47—21no—
75Q8×D47—21no—
76Q8×D47—21no—
77Q8×D47D411yescharacteristic
78#10625352—21no—
79#10625352D411yescharacteristic
80D4×D47—21no—
81D4×D47—21no—
82D4×D47—21no—
83D4×D47—21no—
84D4×D47—21no—
85D4×D47D411yescharacteristic
86#10625350—21no—
87#10625350C2311yescharacteristic
88C2×D188C2311yescharacteristic
89C2×C4×D47—21no—
90C2×C4×D47—21no—
91C2×C4×D47C2311yescharacteristic
92C2×Dic94—21no—
93C2×Dic94C2311yescharacteristic
94Q16×C47—21no—
95SD16×C47—21no—
96SD16×C47—21no—
97SD16×C47—21no—
98SD16×C47—21no—
99D8×C47—21no—
100M16×C47—21no—
101M16×C47C2311yescharacteristic
102M16×C47C2311yescharacteristic
103M16×C47C2311yescharacteristic
104C2×C8×C47—21no—
105C2×C8×C47C2311yescharacteristic
106#10625337—21no—
107#10625337—21no—
108#10625336—21no—
109#10625336—21no—
110#10625336—21no—
111#10625336—21no—
112#10625335—21no—
113#10625335—21no—
114#10625335—21no—
115#10625335—21no—
116#10625334—21no—
117#10625334—21no—
118#10625329—21no—
119#10625329C2311yescharacteristic
120#10625329C2311yescharacteristic
121#10625329C2311yescharacteristic
122C2×C47⋊C8—21no—
123C2×C47⋊C8C2311yescharacteristic
124Dic188—21no—
125D376—21no—
126#10625325—21no—
127#10625325—21no—
128#10625325—21no—
129#10625325—21no—
130#10625324—21no—
131#10625324—21no—
132#10625324—21no—
133#10625324—21no—
134#10625324—21no—
135C8×D47—21no—
136C8×D47—21no—
137C8×D47—21no—
138C8×D47—21no—
139C8×D47—21no—
140C8×D47D411yescharacteristic
141C8×D47D411yescharacteristic
142C8×D47D411yescharacteristic
143C8×D47D411yescharacteristic
144C23×C47—21no—
145C22×D47—21no—
146C22×D47—21no—
147C22×D47—41no—
148C22×D47—41no—
149C22×D47—82no—
150C22×D47#4111yescharacteristic
151Q8×C47—21no—
152Q8×C47—21no—
153Q8×C47C2×D411yescharacteristic
154D4×C47—21no—
155D4×C47—21no—
156D4×C47—21no—
157D4×C47C2×D411yescharacteristic
158C2×C4×C47—21no—
159C2×C4×C47—21no—
160C2×C4×C47C2411yescharacteristic
161C22⋊D47—21no—
162C22⋊D47—21no—
163C22⋊D47—21no—
164C22⋊D47—41no—
165C22⋊D47—41no—
166C2×Dic47—21no—
167C2×Dic47—21no—
168C2×Dic47#4111yescharacteristic
169D188—21no—
170D188—21no—
171D188—21no—
172D188C2×D411yescharacteristic
173C4×D47—21no—
174C4×D47—21no—
175C4×D47—21no—
176C4×D47—41no—
177C4×D47—41no—
178C4×D47C2×D411yescharacteristic
179C4×D47C2×D411yescharacteristic
180C4×D47C2×D411yescharacteristic
181C4×D47C2×D411yescharacteristic
182Dic94—21no—
183Dic94—21no—
184Dic94—21no—
185Dic94—41no—
186Dic94—41no—
187Dic94C2×D411yescharacteristic
188C8×C47—21no—
189C8×C47—21no—
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—41no—
200C22×C47—81no—
201C22×C47C2×#4111yescharacteristic
202C2×D47—22no—
203C2×D47—21no—
204C2×D47—42no—
205C2×D47—41no—
206C2×D47—82no—
207C2×D47—82no—
208C2×D47—81no—
209C2×D47#12111yescharacteristic
210C2×D47#12111yescharacteristic
211C4×C47—21no—
212C4×C47—41no—
213C4×C47C22×D411yescharacteristic
214C4×C47C22×D411yescharacteristic
215Dic47—21no—
216Dic47—41no—
217Dic47#12111yescharacteristic
218Dic47#12111yescharacteristic
219C2×#471—471nomaximal, Sylow
220C2×C47—21no—
221C2×C47—41no—
222C2×C47—81no—
223C2×C47C2×#12111yescharacteristic
224D47—21no—
225D47—41no—
226D47—81no—
227D47#47112yesdirect product factor
228C2×#137—471no—
229C2×AGL(1,ℤ/8)—471no—
230C22×SD16—471no—
231C2×#131—471no—
232#471—471no—
233#471—471no—
234#471—471no—
235#471—471no—
236#471—471no—
237#471—471no—
238#471—471no—
239#471D4711yescharacteristic, direct product factor
240C2×#108—471no—
241C2×#101—471no—
242C2×#100—471no—
243C47C2×#47111yescharacteristic, complemented, Sylow
244C2×#41—471no—
245C22×Q8—471no—
246C22×D4—471no—
247#137—471no—
248#137—471no—
249#137—471no—
250#137—941no—
251#137—941no—
252#137C2×D4711yescharacteristic, complemented
253AGL(1,ℤ/8)—471no—
254AGL(1,ℤ/8)—471no—
255AGL(1,ℤ/8)—471no—
256AGL(1,ℤ/8)—941no—
257AGL(1,ℤ/8)—941no—
258AGL(1,ℤ/8)C2×D4711yescharacteristic
259C2×Q16—941no—
260C2×SD16—471no—
261C2×SD16—471no—
262C2×SD16—471no—
263C2×SD16—941no—
264C2×SD16—941no—
265C2×SD16—941no—
266C2×SD16—941no—
267C2×SD16—941no—
268C2×SD16—941no—
269C2×SD16C2×D4711yescharacteristic, complemented
270C2×D8—941no—
271#131—471no—
272#131—471no—
273#131—471no—
274#131—941no—
275#131—941no—
276#131C2×D4711yescharacteristic, complemented
277C2×M16—471no—
278C2×M16—471no—
279C2×M16—471no—
280C2×M16—941no—
281C22×C8—471no—
282C22×C8—941no—
283#108—471no—
284#108—471no—
285#108—471no—
286#108C2×D4711yescharacteristic, complemented
287#101—471no—
288#101—471no—
289#101—471no—
290#101C2×D4711yescharacteristic, complemented
291#100—471no—
292#100—471no—
293#100—471no—
294#100C2×D4711yescharacteristic, complemented
295C24—941no—
296#41—471no—
297#41—471no—
298#41—471no—
299#41—941no—
300#41—941no—
301#41C22×D4711yescharacteristic
302C2×Q8—471no—
303C2×Q8—471no—
304C2×Q8—941no—
305C2×Q8—941no—
306C2×Q8—941no—
307C2×Q8—941no—
308C2×Q8—941no—
309C2×Q8C22×D4711yescharacteristic
310C2×D4—471no—
311C2×D4—471no—
312C2×D4—941no—
313C2×D4—941no—
314C2×D4—941no—
315C2×D4—941no—
316C2×D4—941no—
317C2×D4—941no—
318C2×D4C22×D4711yescharacteristic
319C22×C4—471no—
320C22×C4—941no—
321C22×C4—941no—
322Q16—21no—
323Q16—941no—
324Q16—941no—
325Q16—941no—
326SD16—21no—
327SD16—21no—
328SD16—21no—
329SD16—21no—
330SD16—941no—
331SD16—941no—
332SD16—941no—
333SD16—941no—
334SD16—941no—
335SD16—941no—
336SD16—941no—
337SD16—941no—
338SD16—941no—
339SD16—941no—
340SD16—941no—
341SD16—941no—
342D8—21no—
343D8—941no—
344D8—941no—
345D8—941no—
346M16—21no—
347M16—471no—
348M16—471no—
349M16—471no—
350M16—941no—
351M16—941no—
352M16—941no—
353M16—941no—
354M16—941no—
355M16—941no—
356M16C22×D4711yescharacteristic
357M16C22×D4711yescharacteristic
358M16C22×D4711yescharacteristic
359C2×C8—21no—
360C2×C8—471no—
361C2×C8—471no—
362C2×C8—471no—
363C2×C8—471no—
364C2×C8—471no—
365C2×C8—941no—
366C2×C8—941no—
367C2×C8—941no—
368C2×C8—941no—
369C2×C8—941no—
370C2×C8—941no—
371C2×C8C22×D4711yescharacteristic
372C23—21no—
373C23—471no—
374C23—941no—
375C23—941no—
376C23—3762no—
377C23—1881no—
378C23—1881no—
379Q8—21no—
380Q8—21no—
381Q8—471no—
382Q8—941no—
383Q8—941no—
384Q8—941no—
385Q8—1881no—
386Q8—1881no—
387Q8D4×D4711yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—471no—
392D4—941no—
393D4—941no—
394D4—941no—
395D4—941no—
396D4—941no—
397D4—941no—
398D4—1881no—
399D4—1881no—
400D4D4×D4711yescharacteristic
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—471no—
404C2×C4—471no—
405C2×C4—471no—
406C2×C4—471no—
407C2×C4—471no—
408C2×C4—941no—
409C2×C4—941no—
410C2×C4—941no—
411C2×C4—941no—
412C2×C4—941no—
413C2×C4—1881no—
414C2×C4—1881no—
415C2×C4C23×D4711yescharacteristic
416C8—21no—
417C8—21no—
418C8—21no—
419C8—471no—
420C8—471no—
421C8—941no—
422C8—941no—
423C8—941no—
424C8D4×D4711yescharacteristic
425C8D4×D4711yescharacteristic
426C22—21no—
427C22—41no—
428C22—81no—
429C22—471no—
430C22—471no—
431C22—942no—
432C22—941no—
433C22—3761no—
434C22—3762no—
435C22—3762no—
436C22—1882no—
437C22—1881no—
438C22#41×D4711yescharacteristic
439C4—21no—
440C4—41no—
441C4—471no—
442C4—471no—
443C4—941no—
444C4—1881no—
445C4C2×D4×D4711yescharacteristic
446C4C2×D4×D4711yescharacteristic
447C2—21no—
448C2—41no—
449C2—81no—
450C2—472no—
451C2—941no—
452C2—3761no—
453C2—1881no—
454C2#121×D4711yescharacteristic
subgroupG/H
centerC2#121×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#471C2
socleC2×C47C2×#121
hypercenter#471D47
hypocenterC47C2×#471
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. #137×D47C2semidirect
3. C2×SD16×D47C2semidirect
4. #131×D47C2semidirect
5. #15689389C2semidirect
6. #15689388C2semidirect
7. #15689387C2semidirect
8. #15689386C2semidirect
9. #15689385C2semidirect
10. #15689384C2semidirect
11. #15689383C2semidirect
12. #108×D47C2semidirect
13. #101×D47C2semidirect
14. #100×D47C2semidirect
15. C47×#471C2semidirect
19. #13094057C22semidirect
21. #13094055C22semidirect
22. #13094054C22semidirect
30. C2×#10625325C22semidirect
31. C2×#10625335C22semidirect
32. C2×#10625336C22semidirect
41. #13094032C22semidirect
42. #13094031C22semidirect
44. #13094030C22semidirect
51. #13093960C22semidirect
52. #13093959C22semidirect
53. #13093959C22semidirect
54. #13093943C22semidirect
55. #13093942C22semidirect
56. #13093942C22semidirect
57. #13093941C22semidirect
58. #13093940C22semidirect
59. #13093940C22semidirect
60. #137×C47C22semidirect
62. C2×SD16×C47C22semidirect
63. #131×C47C22semidirect
64. #108×C47C22semidirect
65. #101×C47C22semidirect
66. #100×C47C22semidirect
227. D47#471direct (N × H)
239. #471D47direct (N × H)
243. C47C2×#471semidirect
252. #137C2×D47semidirect
269. C2×SD16C2×D47semidirect
276. #131C2×D47semidirect
286. #108C2×D47semidirect
290. #101C2×D47semidirect
294. #100C2×D47semidirect