Finite Group Databasebeta

← #20254887

Subgroups — #20254887

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×#13094048C211yesmaximal, characteristic, complemented
2C22×#10625335C211yesmaximal, characteristic, complemented
3#15689779C211yesmaximal, characteristic, complemented
4D4×C22⋊D47C211yesmaximal, characteristic, complemented
5#15689511C211yesmaximal, characteristic, complemented
6#15689368C211yesmaximal, characteristic, complemented
7#15689357C211yesmaximal, characteristic, complemented
8#15689336C211yesmaximal, characteristic, complemented
9#15689322C211yesmaximal, characteristic, complemented
10#15689275C211yesmaximal, characteristic, complemented
11#15689265C211yesmaximal, characteristic, complemented
12#15689264C211yesmaximal, characteristic, complemented
13#15689220C211yesmaximal, characteristic, complemented
14#15689191C211yesmaximal, characteristic, complemented
15C47×#447C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic, complemented
17C22×Dic94C2211yescharacteristic, complemented
18C22×C22⋊D47—21no—
19C2×D4×D47C2211yescharacteristic
20#13094048—24no—
21C2×#10625325C2211yescharacteristic, complemented
22C2×#10625325C2211yescharacteristic, complemented
23C2×#10625335—24no—
24C2×#10625335C2211yescharacteristic
25C2×#10625335C2211yescharacteristic
26C2×#10625335C2211yescharacteristic, complemented
27C2×#10625335C2211yescharacteristic, complemented
28C2×#10625334C2211yescharacteristic, complemented
29C2×#10625324C2211yescharacteristic, complemented
30C22×C47⋊C8C2211yescharacteristic, complemented
31#13094020C2211yescharacteristic
32#13094011C2211yescharacteristic, complemented
33#13094010—21no—
34#13094004C2211yescharacteristic, complemented
35#13094001—21no—
36#13093998C2211yescharacteristic
37#13093996—21no—
38#13093996—21no—
39#13093995C2211yescharacteristic
40#13093993—21no—
41#13093992—21no—
42#13093989C2211yescharacteristic, complemented
43D4×Dic47—21no—
44D4×Dic47C2211yescharacteristic
45C4×C22⋊D47C2211yescharacteristic
46#13093957C2211yescharacteristic, complemented
47Dic47⋊C8C2211yescharacteristic, complemented
48#13093949C2211yescharacteristic, complemented
49#13093949C2211yescharacteristic, complemented
50#13093945C2211yescharacteristic, complemented
51#13093944C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic, complemented
53#13093934C2211yescharacteristic, complemented
54C22×D4×C47C2211yescharacteristic
55C2×D8×C47C2211yescharacteristic
56C2×D8×C47C2211yescharacteristic, complemented
57#121×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic
59#102×C47C2211yescharacteristic, complemented
60C22⋊C8×C47C2211yescharacteristic, complemented
61C24×C47—21no—
62C23×D47—21no—
63C2×D4×C47—22no—
64C2×D4×C47—21no—
65C2×D4×C47—21no—
66C2×D4×C47—41no—
67C2×D4×C47C2311yescharacteristic
68C2×D4×C47C2311yescharacteristic
69C2×D4×C47C2311yescharacteristic
70C22×C4×C47C2311yescharacteristic
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73C2×C22⋊D47—21no—
74C2×C22⋊D47—21no—
75C2×C22⋊D47—21no—
76C2×C22⋊D47—21no—
77C2×C22⋊D47—44no—
78C2×C22⋊D47D411yescharacteristic
79C22×Dic47—21no—
80C22×Dic47—21no—
81C22×Dic47—21no—
82#10625352—22no—
83#10625352—41no—
84D4×D47—22no—
85D4×D47—41no—
86C2×D188C2311yescharacteristic
87C2×C4×D47C2311yescharacteristic
88C2×Dic94—22no—
89C2×Dic94—21no—
90C2×Dic94—41no—
91C2×Dic94C2311yescharacteristic
92C2×Dic94C2311yescharacteristic
93D8×C47—22no—
94D8×C47—41no—
95C2×C8×C47C2311yescharacteristic
96C2×C8×C47C2311yescharacteristic
97C4⋊C4×C47C2311yescharacteristic
98C22⋊C4×C47—21no—
99C22⋊Dic47—21no—
100C22⋊Dic47—21no—
101C22⋊Dic47—21no—
102C22⋊Dic47—21no—
103C22⋊Dic47D411yescharacteristic
104#10625335—22no—
105#10625335—22no—
106#10625335—22no—
107#10625335D414yescomplemented
108#10625334—22no—
109(C2×D47)⋊C4—21no—
110(C2×D47)⋊C4—21no—
111(C2×D47)⋊C4D411yescharacteristic
112C4⋊Dic47—21no—
113C4⋊Dic47C2311yescharacteristic
114Dic47⋊C4—21no—
115Dic47⋊C4D411yescharacteristic
116C4×Dic47—21no—
117C4×Dic47C2311yescharacteristic
118C2×C47⋊C8—22no—
119C2×C47⋊C8C2311yescharacteristic
120C2×C47⋊C8C2311yescharacteristic
121#10625325—22no—
122#10625325—41no—
123#10625324—22no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47—42no—
128C23×C47—42no—
129C23×C47—81no—
130C23×C47C2×D411yescharacteristic
131C22×D47—21no—
132C22×D47—42no—
133C22×D47—42no—
134C22×D47—81no—
135C22×D47C2×D411yescharacteristic
136D4×C47—21no—
137D4×C47—21no—
138D4×C47—21no—
139D4×C47—21no—
140D4×C47—21no—
141D4×C47—42no—
142D4×C47—42no—
143D4×C47C2×D412yes—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47C2×D411yescharacteristic
148C2×C4×C47C2411yescharacteristic
149C22⋊D47—22no—
150C22⋊D47—42no—
151C22⋊D47—42no—
152C22⋊D47—42no—
153C22⋊D47—42no—
154C22⋊D47—42no—
155C22⋊D47—81no—
156C2×Dic47—21no—
157C2×Dic47—21no—
158C2×Dic47—21no—
159C2×Dic47—42no—
160C2×Dic47—42no—
161C2×Dic47—42no—
162C2×Dic47C2×D411yescharacteristic
163C2×Dic47C2×D411yescharacteristic
164C2×Dic47C2×D411yescharacteristic
165D188—21no—
166D188—21no—
167C4×D47—21no—
168C4×D47—21no—
169Dic94—21no—
170Dic94—21no—
171Dic94—21no—
172Dic94—42no—
173Dic94C2×D412yescomplemented
174C8×C47—21no—
175C8×C47—21no—
176C47⋊C8—21no—
177C47⋊C8C2×D412yescomplemented
178C22×C47—21no—
179C22×C47—21no—
180C22×C47—22no—
181C22×C47—41no—
182C22×C47—41no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47—41no—
187C22×C47—41no—
188C22×C47—41no—
189C22×C47—84no—
190C22×C47AGL(1,ℤ/8)12yescomplemented
191C22×C47C22×D411yescharacteristic
192C2×D47—21no—
193C2×D47—21no—
194C2×D47—21no—
195C2×D47—41no—
196C2×D47—41no—
197C2×D47—41no—
198C2×D47—84no—
199C4×C47—21no—
200C4×C47—41no—
201C4×C47C22×D411yescharacteristic
202C4×C47H(5,𝔽2)11yescharacteristic
203Dic47—22no—
204Dic47—21no—
205Dic47—21no—
206Dic47—21no—
207Dic47—41no—
208Dic47—41no—
209#3265—471nomaximal, Sylow
210C2×C47—22no—
211C2×C47—42no—
212C2×C47—81no—
213C2×C47—81no—
214C2×C47D4211yescharacteristic
215C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
216C2×C47#57711yescharacteristic
217D47—41no—
218D47—81no—
219C2×AGL(1,ℤ/8)—471no—
220C22×SD16—471no—
221#548—471no—
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#447D4711yescharacteristic, complemented
232#440—471no—
233#435—471no—
234C47#326511yescharacteristic, complemented, Sylow
235C2×#41—471no—
236C22×Q8—471no—
237C22×D4—471no—
238C22×D4—941no—
239C22×D4C2×D4711yescharacteristic
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×D8C2×D4711yescharacteristic
250C2×D8C2×D4711yescharacteristic, complemented
251C2×M16—471no—
252C22×C8—471no—
253#127—471no—
254#124—471no—
255#124—941no—
256C22⋊Q8—471no—
257C22⋊Q8—941no—
258#121—471no—
259#121—471no—
260#121—941no—
261#121—941no—
262#121C2×D4711yescharacteristic, complemented
263#120—941no—
264#120—941no—
265C4×Q8—471no—
266C4×D4—471no—
267C4×D4—471no—
268C4×D4—941no—
269#107—471no—
270C4⋊C8—471no—
271#103—471no—
272#103—471no—
273#102—471no—
274#102—471no—
275#102C2×D4711yescharacteristic
276#102C2×D4711yescharacteristic, complemented
277C22⋊C8—471no—
278C22⋊C8C2×D4711yescharacteristic, complemented
279#97—471no—
280C24—21no—
281C24—941no—
282#41—942no—
283#41—1881no—
284C2×Q8—471no—
285C2×Q8—471no—
286C2×Q8—942no—
287C2×Q8—941no—
288C2×Q8—1881no—
289C2×D4—22no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—41no—
293C2×D4—471no—
294C2×D4—471no—
295C2×D4—941no—
296C2×D4—941no—
297C2×D4—941no—
298C2×D4—942no—
299C2×D4—941no—
300C2×D4—941no—
301C2×D4—941no—
302C2×D4—1881no—
303C2×D4—1884no—
304C2×D4C22×D4711yescharacteristic
305C2×D4C22×D4711yescharacteristic
306C2×D4C22×D4711yescharacteristic
307C22×C4—471no—
308C22×C4—941no—
309C22×C4—941no—
310C22×C4—941no—
311C22×C4C22×D4711yescharacteristic
312SD16—474no—
313SD16—942no—
314SD16—942no—
315SD16—942no—
316SD16—942no—
317SD16—1881no—
318D8—22no—
319D8—41no—
320D8—942no—
321M16—942no—
322C2×C8—471no—
323C2×C8—471no—
324C2×C8—942no—
325C2×C8C22×D4711yescharacteristic
326C2×C8C22×D4711yescharacteristic
327C4⋊C4—471no—
328C4⋊C4—471no—
329C4⋊C4—941no—
330C4⋊C4—941no—
331C4⋊C4C22×D4711yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—471no—
334C22⋊C4—471no—
335C22⋊C4—941no—
336C22⋊C4—941no—
337C22⋊C4—941no—
338C22⋊C4—941no—
339C22⋊C4—941no—
340C22⋊C4—941no—
341C42—471no—
342C42—941no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—42no—
347C23—42no—
348C23—81no—
349C23—471no—
350C23—941no—
351C23—3761no—
352C23—1882no—
353C23—1882no—
354C23D4×D4711yescharacteristic
355Q8—472no—
356Q8—941no—
357Q8—941no—
358Q8—941no—
359Q8—1882no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—42no—
366D4—42no—
367D4—942no—
368D4—941no—
369D4—941no—
370D4—3761no—
371D4—1882no—
372D4—1882no—
373D4—1882no—
374D4—1882no—
375D4—1882no—
376D4D4×D4712yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—471no—
381C2×C4—471no—
382C2×C4—471no—
383C2×C4—941no—
384C2×C4—941no—
385C2×C4—941no—
386C2×C4—941no—
387C2×C4—941no—
388C2×C4—1882no—
389C2×C4—1882no—
390C2×C4—1882no—
391C2×C4D4×D4711yescharacteristic
392C2×C4C23×D4711yescharacteristic
393C8—21no—
394C8—21no—
395C8—472no—
396C8—941no—
397C22—21no—
398C22—21no—
399C22—22no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—84no—
409C22—941no—
410C22—941no—
411C22—941no—
412C22—3764no—
413C22—1881no—
414C22—1881no—
415C22—1881no—
416C22#1309404812yescomplemented
417C22C2×D4×D4711yescharacteristic
418C4—21no—
419C4—41no—
420C4—941no—
421C4—942no—
422C4—941no—
423C4—941no—
424C4—1881no—
425C4—1881no—
426C4C2×D4×D4711yescharacteristic
427C4#1309406911yescharacteristic
428C2—22no—
429C2—42no—
430C2—81no—
431C2—81no—
432C2—3761no—
433C2—1881no—
434C2#1568975511yescharacteristic
435C2C2×#1309404811yescharacteristic
436C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#447C2
socleC22×C47C22×D4
hypercenter#447D47
hypocenterC47#3265
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#13094048C2semidirect
2. C22×#10625335C2semidirect
3. #15689779C2semidirect
4. D4×C22⋊D47C2semidirect
5. #15689511C2semidirect
6. #15689368C2semidirect
7. #15689357C2semidirect
8. #15689336C2semidirect
9. #15689322C2semidirect
10. #15689275C2semidirect
11. #15689265C2semidirect
12. #15689264C2semidirect
13. #15689220C2semidirect
14. #15689191C2semidirect
15. C47×#447C2semidirect
16. C2×#10625352C22semidirect
17. C22×Dic94C22semidirect
21. C2×#10625325C22semidirect
22. C2×#10625325C22semidirect
26. C2×#10625335C22semidirect
27. C2×#10625335C22semidirect
28. C2×#10625334C22semidirect
29. C2×#10625324C22semidirect
30. C22×C47⋊C8C22semidirect
32. #13094011C22semidirect
34. #13094004C22semidirect
42. #13093989C22semidirect
46. #13093957C22semidirect
47. Dic47⋊C8C22semidirect
48. #13093949C22semidirect
49. #13093949C22semidirect
50. #13093945C22semidirect
51. #13093944C22semidirect
52. (C2×D47)⋊C8C22semidirect
53. #13093934C22semidirect
56. C2×D8×C47C22semidirect
57. #121×C47C22semidirect
59. #102×C47C22semidirect
60. C22⋊C8×C47C22semidirect
107. #10625335D4semidirect
173. Dic94C2×D4semidirect
177. C47⋊C8C2×D4semidirect
190. C22×C47AGL(1,ℤ/8)semidirect
231. #447D47semidirect
234. C47#3265semidirect
250. C2×D8C2×D47semidirect
262. #121C2×D47semidirect
276. #102C2×D47semidirect
278. C22⋊C8C2×D47semidirect
416. C22#13094048semidirect