Finite Group Databasebeta

← #20254884

Subgroups — #20254884

Order 6016.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094049C211yesmaximal, characteristic, complemented
2C22×#10625336C211yesmaximal, characteristic, complemented
3D4×D188C211yesmaximal, characteristic, complemented
4#15689513C211yesmaximal, characteristic, complemented
5#15689371C211yesmaximal, characteristic, complemented
6#15689357C211yesmaximal, characteristic, complemented
7#15689335C211yesmaximal, characteristic, complemented
8#15689323C211yesmaximal, characteristic, complemented
9#15689273C211yesmaximal, characteristic, complemented
10#15689268C211yesmaximal, characteristic, complemented
11#15689262C211yesmaximal, characteristic, complemented
12#15689256C211yesmaximal, characteristic, complemented
13#15689221C211yesmaximal, characteristic, complemented
14#15689195C211yesmaximal, characteristic, complemented
15C47×#548C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C2×D4×D47—21no—
19#13094049—24no—
20C2×#10625336—24no—
21C2×#10625336C2211yescharacteristic
22C2×#10625336C2211yescharacteristic
23C2×#10625336C2211yescharacteristic, complemented
24C2×#10625336C2211yescharacteristic, complemented
25C2×#10625336C2211yescharacteristic, complemented
26C2×#10625336C2211yescharacteristic, complemented
27C2×#10625334C2211yescharacteristic
28C2×#10625334C2211yescharacteristic, complemented
29C2×#10625334C2211yescharacteristic, complemented
30C2×#10625329C2211yescharacteristic, complemented
31C22×C47⋊C8C2211yescharacteristic, complemented
32#13094021C2211yescharacteristic
33#13093999—21no—
34#13093998C2211yescharacteristic
35#13093998C2211yescharacteristic
36#13093994—21no—
37#13093994—21no—
38C4×D188C2211yescharacteristic
39#13093957C2211yescharacteristic, complemented
40C4⋊(C47⋊C8)C2211yescharacteristic, complemented
41#13093948C2211yescharacteristic, complemented
42#13093948C2211yescharacteristic, complemented
43#13093945C2211yescharacteristic, complemented
44#13093944C2211yescharacteristic
45#13093944C2211yescharacteristic, complemented
46#13093944C2211yescharacteristic, complemented
47C22⋊(C47⋊C8)C2211yescharacteristic, complemented
48C22⋊(C47⋊C8)C2211yescharacteristic, complemented
49#13093935C2211yescharacteristic, complemented
50C2×#41×C47C2211yescharacteristic, complemented
51C22×Q8×C47C2211yescharacteristic, complemented
52#124×C47—21no—
53#124×C47C2211yescharacteristic, complemented
54C22⋊Q8×C47—21no—
55C22⋊Q8×C47C2211yescharacteristic, complemented
56#121×C47—21no—
57#121×C47C2211yescharacteristic, complemented
58C4×Q8×C47C2211yescharacteristic, complemented
59C4×D4×C47—21no—
60C4×D4×C47C2211yescharacteristic
61C23×D47—21no—
62C23×D47—21no—
63#41×C47—22no—
64#41×C47—41no—
65C2×Q8×C47—21no—
66C2×Q8×C47—22no—
67C2×Q8×C47—41no—
68C2×Q8×C47C2311yescharacteristic
69C2×Q8×C47C2311yescharacteristic
70C2×D4×C47—21no—
71C2×D4×C47—21no—
72C2×D4×C47D411yescharacteristic
73C2×D4×C47C2311yescharacteristic
74C22×C4×C47—21no—
75C22×C4×C47—21no—
76C22×C4×C47C2311yescharacteristic
77C22×C4×C47C2311yescharacteristic
78C2×C22⋊D47—21no—
79C2×C22⋊D47—21no—
80D4×D47—44no—
81C2×D188—22no—
82C2×D188—22no—
83C2×D188—21no—
84C2×D188—21no—
85C2×D188—21no—
86C2×D188—21no—
87C2×D188—41no—
88C2×D188—41no—
89C2×D188C2311yescharacteristic
90C2×D188C2311yescharacteristic
91C2×D188C2311yescharacteristic
92C2×C4×D47—21no—
93C4⋊C4×C47—21no—
94C4⋊C4×C47—21no—
95C4⋊C4×C47D411yescharacteristic
96C4⋊C4×C47C2311yescharacteristic
97C22⋊C4×C47—21no—
98C22⋊C4×C47—21no—
99C22⋊C4×C47—21no—
100C22⋊C4×C47—21no—
101C22⋊C4×C47D411yescharacteristic
102C22⋊C4×C47D411yescharacteristic
103C42×C47—21no—
104C42×C47C2311yescharacteristic
105#10625336—22no—
106#10625336—22no—
107#10625336—22no—
108#10625336—22no—
109#10625336—41no—
110#10625336D414yescomplemented
111#10625334—22no—
112#10625334—22no—
113#10625334—41no—
114(C2×D47)⋊C4—21no—
115(C2×D47)⋊C4—21no—
116(C2×D47)⋊C4—21no—
117C4⋊Dic47C2311yescharacteristic
118#10625329—22no—
119C2×C47⋊C8—22no—
120C2×C47⋊C8C2311yescharacteristic
121C2×C47⋊C8C2311yescharacteristic
122C2×C47⋊C8C2311yescharacteristic
123C2×C47⋊C8C2311yescharacteristic
124C23×C47—21no—
125C23×C47C2×D411yescharacteristic
126C23×C47C2×D411yescharacteristic
127C22×D47—21no—
128C22×D47—21no—
129C22×D47—21no—
130C22×D47—42no—
131C22×D47—42no—
132C22×D47—42no—
133C22×D47—42no—
134C22×D47—81no—
135C22×D47—81no—
136Q8×C47—21no—
137Q8×C47—21no—
138Q8×C47—21no—
139Q8×C47—42no—
140Q8×C47C2×D412yescomplemented
141D4×C47—22no—
142D4×C47—21no—
143D4×C47—21no—
144D4×C47—42no—
145D4×C47—42no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—21no—
150C2×C4×C47—21no—
151C2×C4×C47—21no—
152C2×C4×C47—21no—
153C2×C4×C47—42no—
154C2×C4×C47—42no—
155C2×C4×C47C2×D411yescharacteristic
156C2×C4×C47C2×D411yescharacteristic
157C2×C4×C47C2×D411yescharacteristic
158C2×C4×C47C2×D411yescharacteristic
159C2×C4×C47C2411yescharacteristic
160C22⋊D47—42no—
161C22⋊D47—42no—
162C2×Dic47—21no—
163D188—21no—
164D188—21no—
165D188—21no—
166D188—21no—
167D188—21no—
168D188—42no—
169D188—42no—
170D188—42no—
171D188—81no—
172D188C2×D412yes—
173C4×D47—42no—
174C47⋊C8—21no—
175C47⋊C8—21no—
176C47⋊C8—21no—
177C47⋊C8C2×D412yescomplemented
178C22×C47—21no—
179C22×C47—21no—
180C22×C47—21no—
181C22×C47—21no—
182C22×C47—21no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47AGL(1,ℤ/8)12yescomplemented
187C22×C47C22×D411yescharacteristic
188C2×D47—22no—
189C2×D47—41no—
190C2×D47—41no—
191C2×D47—41no—
192C2×D47—41no—
193C2×D47—41no—
194C2×D47—41no—
195C2×D47—41no—
196C2×D47—41no—
197C2×D47—84no—
198C2×D47—84no—
199C4×C47—21no—
200C4×C47—21no—
201C4×C47—22no—
202C4×C47—21no—
203C4×C47—21no—
204C4×C47—41no—
205C4×C47—41no—
206C4×C47C22×D411yescharacteristic
207C4×C47H(5,𝔽2)11yescharacteristic
208Dic47—41no—
209#3265—471nomaximal, Sylow
210C2×C47—22no—
211C2×C47—41no—
212C2×C47—81no—
213C2×C47D4211yescharacteristic
214C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
215C2×C47#57711yescharacteristic
216D47—42no—
217D47—81no—
218D47—81no—
219C2×AGL(1,ℤ/8)—471no—
220C22×SD16—471no—
221#548D4711yescharacteristic, complemented
222D42—471no—
223#496—471no—
224#468—471no—
225#466—471no—
226#463—471no—
227#460—471no—
228#450—471no—
229#449—471no—
230#448—471no—
231#447—471no—
232#440—471no—
233#435—471no—
234C47#326511yescharacteristic, complemented, Sylow
235C2×#41C2×D4711yescharacteristic, complemented
236C22×Q8C2×D4711yescharacteristic, complemented
237C22×D4—471no—
238C22×D4—471no—
239C22×D4—941no—
240AGL(1,ℤ/8)—944no—
241C2×SD16—471no—
242C2×SD16—471no—
243C2×SD16—471no—
244C2×SD16—471no—
245C2×SD16—471no—
246C2×SD16—471no—
247C2×SD16—944no—
248C2×D8—471no—
249C2×D8—471no—
250C2×D8—471no—
251C2×M16—471no—
252C22×C8—471no—
253#127—471no—
254#124—21no—
255#124C2×D4711yescharacteristic, complemented
256C22⋊Q8—21no—
257C22⋊Q8C2×D4711yescharacteristic, complemented
258#121—21no—
259#121—471no—
260#121—471no—
261#121—941no—
262#121C2×D4711yescharacteristic, complemented
263#120—941no—
264#120—941no—
265C4×Q8C2×D4711yescharacteristic, complemented
266C4×D4—21no—
267C4×D4—471no—
268C4×D4C2×D4711yescharacteristic
269#107—471no—
270C4⋊C8—471no—
271#103—471no—
272#103—471no—
273#102—471no—
274#102—471no—
275#102—471no—
276#102—471no—
277C22⋊C8—471no—
278C22⋊C8—471no—
279#97—471no—
280C24—941no—
281C24—941no—
282#41—22no—
283#41—41no—
284C2×Q8—21no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8C22×D4711yescharacteristic
288C2×Q8C22×D4711yescharacteristic
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—471no—
292C2×D4—471no—
293C2×D4—471no—
294C2×D4—942no—
295C2×D4—942no—
296C2×D4—941no—
297C2×D4—941no—
298C2×D4—941no—
299C2×D4—941no—
300C2×D4—941no—
301C2×D4—941no—
302C2×D4—1881no—
303C2×D4—1881no—
304C2×D4—1884no—
305C2×D4C22⋊D4711yescharacteristic
306C2×D4C22×D4711yescharacteristic
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—941no—
310C22×C4C22×D4711yescharacteristic
311C22×C4C22×D4711yescharacteristic
312SD16—474no—
313SD16—942no—
314SD16—942no—
315SD16—942no—
316SD16—942no—
317SD16—1881no—
318D8—942no—
319D8—942no—
320D8—1881no—
321M16—942no—
322C2×C8—471no—
323C2×C8—471no—
324C2×C8—471no—
325C2×C8—471no—
326C2×C8—942no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—471no—
330C4⋊C4C22⋊D4711yescharacteristic
331C4⋊C4C22×D4711yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—941no—
337C22⋊C4—941no—
338C22⋊C4—941no—
339C22⋊C4C22⋊D4711yescharacteristic
340C22⋊C4C22⋊D4711yescharacteristic
341C42—21no—
342C42C22×D4711yescharacteristic
343C23—21no—
344C23—941no—
345C23—941no—
346C23—941no—
347C23—3761no—
348C23—3761no—
349C23—1882no—
350C23—1882no—
351C23—1882no—
352C23—1882no—
353C23C2×C22⋊D4711yescharacteristic
354C23C2×C22⋊D4711yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—21no—
358Q8—42no—
359Q8D4×D4712yescomplemented
360D4—22no—
361D4—21no—
362D4—21no—
363D4—42no—
364D4—42no—
365D4—472no—
366D4—941no—
367D4—941no—
368D4—941no—
369D4—941no—
370D4—941no—
371D4—3761no—
372D4—1882no—
373D4—1882no—
374D4—1882no—
375D4—1882no—
376D4—1882no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—941no—
387C2×C4—1882no—
388C2×C4C2×C22⋊D4711yescharacteristic
389C2×C4C2×C22⋊D4711yescharacteristic
390C2×C4C2×C22⋊D4711yescharacteristic
391C2×C4C2×C22⋊D4711yescharacteristic
392C2×C4C23×D4711yescharacteristic
393C8—472no—
394C8—941no—
395C8—941no—
396C8—941no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—942no—
406C22—3764no—
407C22—3764no—
408C22—1881no—
409C22—1881no—
410C22—1881no—
411C22—1881no—
412C22—1881no—
413C22—1881no—
414C22—1881no—
415C22—1881no—
416C22#1309404912yescomplemented
417C22C22×C22⋊D4711yescharacteristic
418C4—21no—
419C4—21no—
420C4—22no—
421C4—21no—
422C4—21no—
423C4—41no—
424C4—41no—
425C4—1881no—
426C4C2×D4×D4711yescharacteristic
427C4#1309406911yescharacteristic
428C2—22no—
429C2—41no—
430C2—81no—
431C2—3761no—
432C2—3761no—
433C2—1882no—
434C2D4×C22⋊D4711yescharacteristic
435C2C2×#1309404911yescharacteristic
436C2#1568993111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#548C2
socleC22×C47C22×D4
hypercenter#548D47
hypocenterC47#3265
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#13094049C2semidirect
2. C22×#10625336C2semidirect
3. D4×D188C2semidirect
4. #15689513C2semidirect
5. #15689371C2semidirect
6. #15689357C2semidirect
7. #15689335C2semidirect
8. #15689323C2semidirect
9. #15689273C2semidirect
10. #15689268C2semidirect
11. #15689262C2semidirect
12. #15689256C2semidirect
13. #15689221C2semidirect
14. #15689195C2semidirect
15. C47×#548C2semidirect
23. C2×#10625336C22semidirect
24. C2×#10625336C22semidirect
25. C2×#10625336C22semidirect
26. C2×#10625336C22semidirect
28. C2×#10625334C22semidirect
29. C2×#10625334C22semidirect
30. C2×#10625329C22semidirect
31. C22×C47⋊C8C22semidirect
39. #13093957C22semidirect
40. C4⋊(C47⋊C8)C22semidirect
41. #13093948C22semidirect
42. #13093948C22semidirect
43. #13093945C22semidirect
45. #13093944C22semidirect
46. #13093944C22semidirect
47. C22⋊(C47⋊C8)C22semidirect
48. C22⋊(C47⋊C8)C22semidirect
49. #13093935C22semidirect
50. C2×#41×C47C22semidirect
51. C22×Q8×C47C22semidirect
53. #124×C47C22semidirect
55. C22⋊Q8×C47C22semidirect
57. #121×C47C22semidirect
58. C4×Q8×C47C22semidirect
110. #10625336D4semidirect
140. Q8×C47C2×D4semidirect
177. C47⋊C8C2×D4semidirect
186. C22×C47AGL(1,ℤ/8)semidirect
221. #548D47semidirect
234. C47#3265semidirect
235. C2×#41C2×D47semidirect
236. C22×Q8C2×D47semidirect
255. #124C2×D47semidirect
257. C22⋊Q8C2×D47semidirect
262. #121C2×D47semidirect
265. C4×Q8C2×D47semidirect
359. Q8D4×D47semidirect
416. C22#13094049semidirect