Finite Group Databasebeta

← #20253114

Subgroups — #20253114

Order 6016.

466 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689919C211yesmaximal, characteristic, complemented
2C2×#13094048C211yesmaximal, characteristic, complemented
3AGL(1,ℤ/8)×D47C211yesmaximal, characteristic, complemented
4#15689888C211yesmaximal, characteristic, complemented
5#15689392C211yesmaximal, characteristic, complemented
6#15689391C211yesmaximal, characteristic, complemented
7#15689390C211yesmaximal, characteristic, complemented
8#15689387C211yesmaximal, characteristic, complemented
9#15689386C211yesmaximal, characteristic, complemented
10#15689385C211yesmaximal, characteristic, complemented
11#15689384C211yesmaximal, characteristic, complemented
12#15689170C211yesmaximal, characteristic, complemented
13#15689104C211yesmaximal, characteristic, complemented
14#100×D47C211yesmaximal, characteristic, complemented
15C47×#472C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17#41×D47C2211yescharacteristic
18C2×D4×D47C2211yescharacteristic
19#13094057C2211yescharacteristic, complemented
20#13094054C2211yescharacteristic, complemented
21#13094053—21no—
22#13094052C2211yescharacteristic
23#13094051—21no—
24#13094050C2211yescharacteristic
25#13094050C2211yescharacteristic, complemented
26#13094049C2211yescharacteristic
27#13094048—21no—
28#13094048—21no—
29#13094048—21no—
30#13094048—21no—
31#13094048—21no—
32#13094048—21no—
33#13094045—21no—
34#13094043—21no—
35C2×#10625325C2211yescharacteristic, complemented
36C2×#10625335C2211yescharacteristic, complemented
37SD16×D47—21no—
38C2×#10625334C2211yescharacteristic, complemented
39D8×D47—21no—
40#13094032—21no—
41#13094032C2211yescharacteristic, complemented
42#13094031C2211yescharacteristic, complemented
43#13094030—21no—
44#13094030C2211yescharacteristic, complemented
45C2×#10625324—21no—
46C2×#10625324C2211yescharacteristic
47M16×D47—21no—
48M16×D47C2211yescharacteristic
49M16×D47C2211yescharacteristic
50M16×D47C2211yescharacteristic
51#13093960C2211yescharacteristic, complemented
52#13093959C2211yescharacteristic, complemented
53#13093959C2211yescharacteristic, complemented
54#13093942C2211yescharacteristic, complemented
55#13093942C2211yescharacteristic, complemented
56#13093941C2211yescharacteristic, complemented
57#13093941C2211yescharacteristic, complemented
58#13093940C2211yescharacteristic, complemented
59#13093940C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C47C2211yescharacteristic
61AGL(1,ℤ/8)×C47C2211yescharacteristic, complemented
62C2×D8×C47C2211yescharacteristic, complemented
63#131×C47C2211yescharacteristic, complemented
64#108×C47C2211yescharacteristic, complemented
65#100×C47C2211yescharacteristic, complemented
66#100×C47C2211yescharacteristic, complemented
67C23×D47—21no—
68#41×C47C2311yescharacteristic
69C2×D4×C47C2311yescharacteristic
70C2×D4×C47C2311yescharacteristic
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73C22×Dic47—21no—
74#10625354D411yescharacteristic
75Q8×D47D411yescharacteristic
76#10625352—21no—
77#10625352—21no—
78#10625352—21no—
79#10625352—21no—
80#10625352—21no—
81#10625352D411yescharacteristic
82D4×D47—21no—
83D4×D47—21no—
84D4×D47—21no—
85D4×D47—21no—
86D4×D47—21no—
87D4×D47D411yescharacteristic
88#10625350—21no—
89#10625350C2311yescharacteristic
90C2×D188C2311yescharacteristic
91C2×C4×D47—21no—
92C2×C4×D47C2311yescharacteristic
93C2×Dic94C2311yescharacteristic
94SD16×C47—21no—
95SD16×C47—21no—
96D8×C47—21no—
97D8×C47—21no—
98D8×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#10625336—21no—
108#10625335—21no—
109#10625335—21no—
110#10625335—21no—
111#10625335—21no—
112#10625335—21no—
113#10625334—21no—
114#10625334—21no—
115#10625334—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—
135#10625324D411yescharacteristic
136#10625324D411yescharacteristic
137#10625324D411yescharacteristic
138#10625324D411yescharacteristic
139C8×D47—21no—
140C8×D47—21no—
141C8×D47—21no—
142C8×D47—21no—
143C8×D47—21no—
144C23×C47—21no—
145C23×C47—21no—
146C22×D47—21no—
147C22×D47—21no—
148C22×D47—41no—
149C22×D47—41no—
150C22×D47—82no—
151C22×D47#4111yescharacteristic
152Q8×C47C2×D411yescharacteristic
153D4×C47—21no—
154D4×C47—21no—
155D4×C47—21no—
156D4×C47—21no—
157D4×C47—21no—
158D4×C47C2×D411yescharacteristic
159C2×C4×C47—21no—
160C2×C4×C47C2411yescharacteristic
161C22⋊D47—21no—
162C22⋊D47—21no—
163C22⋊D47—21no—
164C22⋊D47—41no—
165C22⋊D47—41no—
166C22⋊D47—41no—
167C22⋊D47—41no—
168C2×Dic47—21no—
169C2×Dic47—21no—
170C2×Dic47—41no—
171C2×Dic47—41no—
172C2×Dic47#4111yescharacteristic
173D188—21no—
174D188—21no—
175D188—21no—
176D188C2×D411yescharacteristic
177C4×D47—21no—
178C4×D47—21no—
179C4×D47—21no—
180C4×D47C2×D411yescharacteristic
181C4×D47C2×D411yescharacteristic
182C4×D47C2×D411yescharacteristic
183C4×D47C2×D411yescharacteristic
184Dic94—21no—
185Dic94—21no—
186Dic94—21no—
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—41no—
201C22×C47—81no—
202C22×C47—81no—
203C22×C47C2×#4111yescharacteristic
204C2×D47—21no—
205C2×D47—41no—
206C2×D47—41no—
207C2×D47—81no—
208C2×D47—82no—
209C2×D47—82no—
210C2×D47—81no—
211C2×D47#12111yescharacteristic
212C2×D47#12111yescharacteristic
213C4×C47—21no—
214C4×C47C22×D411yescharacteristic
215C4×C47C22×D411yescharacteristic
216Dic47—21no—
217Dic47—41no—
218Dic47#12111yescharacteristic
219Dic47#12111yescharacteristic
220#3068—471nomaximal, Sylow
221C2×C47—21no—
222C2×C47—41no—
223C2×C47—81no—
224C2×C47—81no—
225C2×C47C2×#12111yescharacteristic
226D47—21no—
227D47—21no—
228D47—41no—
229D47—81no—
230#575—471no—
231C2×AGL(1,ℤ/8)—471no—
232C2×AGL(1,ℤ/8)—471no—
233#568—471no—
234#472—471no—
235#472—471no—
236#472—471no—
237#472D4711yescharacteristic, complemented
238#471—471no—
239#471—471no—
240#471—471no—
241#471—471no—
242#430—471no—
243#413—471no—
244C2×#100—471no—
245C47#306811yescharacteristic, complemented, Sylow
246C2×#41—471no—
247C2×#41—471no—
248C22×D4—471no—
249#137—471no—
250#137—471no—
251#137—941no—
252AGL(1,ℤ/8)—471no—
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)—941no—
259AGL(1,ℤ/8)—941no—
260AGL(1,ℤ/8)—941no—
261AGL(1,ℤ/8)—941no—
262AGL(1,ℤ/8)—941no—
263AGL(1,ℤ/8)C2×D4711yescharacteristic
264AGL(1,ℤ/8)C2×D4711yescharacteristic, complemented
265#135—941no—
266#135—941no—
267C2×SD16—471no—
268C2×SD16—471no—
269C2×SD16—941no—
270C2×D8—471no—
271C2×D8—941no—
272C2×D8C2×D4711yescharacteristic, complemented
273#131—471no—
274#131—471no—
275#131—471no—
276#131—941no—
277#131—941no—
278#131C2×D4711yescharacteristic, complemented
279C2×M16—471no—
280C2×M16—471no—
281C2×M16—471no—
282C2×M16—471no—
283C2×M16—941no—
284C2×M16—941no—
285#108—471no—
286#108—471no—
287#108—471no—
288#108C2×D4711yescharacteristic, complemented
289#101—471no—
290#101—471no—
291#100—471no—
292#100—471no—
293#100—471no—
294#100—471no—
295#100C2×D4711yescharacteristic, complemented
296#100C2×D4711yescharacteristic, complemented
297C24—941no—
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#41C22×D4711yescharacteristic
308C2×Q8—471no—
309C2×Q8—471no—
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×D4—941no—
319C2×D4C22×D4711yescharacteristic
320C2×D4C22×D4711yescharacteristic
321C22×C4—471no—
322C22×C4—941no—
323C22×C4—941no—
324Q16—941no—
325Q16—941no—
326SD16—21no—
327SD16—21no—
328SD16—941no—
329SD16—941no—
330SD16—941no—
331SD16—941no—
332SD16—941no—
333SD16—941no—
334SD16—941no—
335SD16—941no—
336SD16—941no—
337SD16—941no—
338D8—21no—
339D8—21no—
340D8—21no—
341D8—21no—
342D8—941no—
343D8—941no—
344D8—941no—
345D8—941no—
346D8—941no—
347D8—941no—
348M16—21no—
349M16—471no—
350M16—471no—
351M16—471no—
352M16—471no—
353M16—471no—
354M16—471no—
355M16—471no—
356M16—941no—
357M16—941no—
358M16—941no—
359M16—941no—
360M16—941no—
361M16—941no—
362M16C22×D4711yescharacteristic
363M16C22×D4711yescharacteristic
364M16C22×D4711yescharacteristic
365C2×C8—21no—
366C2×C8—471no—
367C2×C8—941no—
368C2×C8—941no—
369C2×C8—941no—
370C2×C8—941no—
371C2×C8—941no—
372C2×C8—941no—
373C2×C8C22×D4711yescharacteristic
374C23—21no—
375C23—21no—
376C23—471no—
377C23—941no—
378C23—941no—
379C23—3762no—
380C23—1881no—
381C23—1881no—
382Q8—471no—
383Q8—941no—
384Q8—941no—
385Q8—941no—
386Q8D4×D4711yescharacteristic
387D4—21no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—471no—
393D4—941no—
394D4—941no—
395D4—941no—
396D4—941no—
397D4—941no—
398D4—941no—
399D4—1881no—
400D4—1881no—
401D4—1881no—
402D4—1881no—
403D4D4×D4711yescharacteristic
404C2×C4—21no—
405C2×C4—471no—
406C2×C4—471no—
407C2×C4—471no—
408C2×C4—471no—
409C2×C4—471no—
410C2×C4—941no—
411C2×C4—941no—
412C2×C4—941no—
413C2×C4—941no—
414C2×C4—941no—
415C2×C4—1881no—
416C2×C4—1881no—
417C2×C4C23×D4711yescharacteristic
418C8—21no—
419C8—21no—
420C8—21no—
421C8—471no—
422C8—471no—
423C8—941no—
424C8—941no—
425C8—941no—
426C8D4×D4711yescharacteristic
427C8D4×D4711yescharacteristic
428C22—21no—
429C22—41no—
430C22—41no—
431C22—81no—
432C22—81no—
433C22—471no—
434C22—471no—
435C22—941no—
436C22—3761no—
437C22—3761no—
438C22—3762no—
439C22—3762no—
440C22—1881no—
441C22—1881no—
442C22#41×D4711yescharacteristic
443C4—21no—
444C4—471no—
445C4—471no—
446C4—941no—
447C4—1881no—
448C4C2×D4×D4711yescharacteristic
449C4C2×D4×D4711yescharacteristic
450C2—21no—
451C2—41no—
452C2—81no—
453C2—81no—
454C2—941no—
455C2—941no—
456C2—3761no—
457C2—1881no—
458C2#121×D4711yescharacteristic
subgroupG/H
centerC2#121×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#472C2
socleC2×C47C2×#121
hypercenter#472D47
hypocenterC47#3068
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #15689919C2semidirect
2. C2×#13094048C2semidirect
3. AGL(1,ℤ/8)×D47C2semidirect
4. #15689888C2semidirect
5. #15689392C2semidirect
6. #15689391C2semidirect
7. #15689390C2semidirect
8. #15689387C2semidirect
9. #15689386C2semidirect
10. #15689385C2semidirect
11. #15689384C2semidirect
12. #15689170C2semidirect
13. #15689104C2semidirect
14. #100×D47C2semidirect
15. C47×#472C2semidirect
19. #13094057C22semidirect
20. #13094054C22semidirect
25. #13094050C22semidirect
35. C2×#10625325C22semidirect
36. C2×#10625335C22semidirect
38. C2×#10625334C22semidirect
41. #13094032C22semidirect
42. #13094031C22semidirect
44. #13094030C22semidirect
51. #13093960C22semidirect
52. #13093959C22semidirect
53. #13093959C22semidirect
54. #13093942C22semidirect
55. #13093942C22semidirect
56. #13093941C22semidirect
57. #13093941C22semidirect
58. #13093940C22semidirect
59. #13093940C22semidirect
61. AGL(1,ℤ/8)×C47C22semidirect
62. C2×D8×C47C22semidirect
63. #131×C47C22semidirect
64. #108×C47C22semidirect
65. #100×C47C22semidirect
66. #100×C47C22semidirect
237. #472D47semidirect
245. C47#3068semidirect
264. AGL(1,ℤ/8)C2×D47semidirect
272. C2×D8C2×D47semidirect
278. #131C2×D47semidirect
288. #108C2×D47semidirect
295. #100C2×D47semidirect
296. #100C2×D47semidirect