Finite Group Databasebeta

← #20255351

Subgroups — #20255351

Order 6016.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689777C211yesmaximal, characteristic, complemented
2#15689769C211yesmaximal, characteristic, complemented
3#15689483C211yesmaximal, characteristic, complemented
4#15689454C211yesmaximal, characteristic, complemented
5#15689442C211yesmaximal, characteristic, complemented
6#15689414C211yesmaximal, characteristic, complemented
7#15689376C211yesmaximal, characteristic, complemented
8#15689352C211yesmaximal, characteristic, complemented
9#15689339C211yesmaximal, characteristic, complemented
10#15689270C211yesmaximal, characteristic, complemented
11#15689259C211yesmaximal, characteristic, complemented
12#15689236C211yesmaximal, characteristic, complemented
13#15689125C211yesmaximal, characteristic, complemented
14C2×#13093946C211yesmaximal, characteristic, complemented
15C47×#435C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625352—21no—
18C22×D188C2211yescharacteristic
19C2×#10625325C2211yescharacteristic, complemented
20C2×D376C2211yescharacteristic
21C2×D376C2211yescharacteristic
22#13094024C2211yescharacteristic, complemented
23#13094012C2211yescharacteristic
24#13094009—21no—
25#13094008—21no—
26#13094008—21no—
27#13094004—21no—
28#13094003C2211yescharacteristic
29#13093998C2211yescharacteristic
30#13093998C2211yescharacteristic
31#13093998C2211yescharacteristic, complemented
32#13093997—21no—
33#13093992—21no—
34C4×D188C2211yescharacteristic
35C4×D188C2211yescharacteristic, complemented
36C2×C4⋊Dic47C2211yescharacteristic
37C2×C4⋊Dic47C2211yescharacteristic, complemented
38C22⋊C4×D47—21no—
39#13093956C2211yescharacteristic, complemented
40#13093956C2211yescharacteristic, complemented
41#13093956C2211yescharacteristic, complemented
42#13093949C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic, complemented
52C2×M16×C47C2211yescharacteristic, complemented
53C22×C8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55C4⋊C8×C47C2211yescharacteristic, complemented
56C22⋊C8×C47C2211yescharacteristic
57C22⋊C8×C47C2211yescharacteristic, complemented
58#97×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×D4×C47D411yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C22×Dic47—21no—
68C22×Dic47—21no—
69#10625352—44no—
70#10625350—22no—
71#10625350—41no—
72C2×D188—22no—
73C2×D188—21no—
74C2×D188—41no—
75C2×D188C2311yescharacteristic
76C2×D188C2311yescharacteristic
77C2×D188C2311yescharacteristic
78C2×C4×D47—21no—
79C2×C4×D47—21no—
80C2×C4×D47—21no—
81C2×Dic94—21no—
82C2×Dic94C2311yescharacteristic
83M16×C47—41no—
84C2×C8×C47—41no—
85C2×C8×C47C2311yescharacteristic
86C2×C8×C47C2311yescharacteristic
87C2×C8×C47C2311yescharacteristic
88C2×C8×C47C2311yescharacteristic
89C4⋊C4×C47D411yescharacteristic
90C22⋊C4×C47D411yescharacteristic
91C22⋊C4×C47D411yescharacteristic
92C42×C47C2311yescharacteristic
93C22⋊Dic47—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101C4⋊Dic47—21no—
102C4⋊Dic47—21no—
103C4⋊Dic47—21no—
104C4⋊Dic47C2311yescharacteristic
105C4⋊Dic47C2311yescharacteristic
106C4⋊Dic47C2311yescharacteristic
107C4⋊Dic47C2311yescharacteristic
108Dic47⋊C4—21no—
109D376—22no—
110D376—41no—
111#10625325—41no—
112C23×C47C2×D411yescharacteristic
113C23×C47C2×D411yescharacteristic
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—21no—
117C22×D47—42no—
118C22×D47—42no—
119C22×D47—81no—
120D4×C47—22no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—42no—
131C22⋊D47—42no—
132C22⋊D47—42no—
133C22⋊D47—81no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—42no—
140C2×Dic47—42no—
141D188—21no—
142D188—21no—
143D188—21no—
144D188—21no—
145D188—21no—
146D188—42no—
147D188#4112yescomplemented
148C4×D47—42no—
149C4×D47—42no—
150C4×D47—81no—
151Dic94—21no—
152Dic94—21no—
153Dic94—42no—
154C8×C47—21no—
155C8×C47—21no—
156C8×C47—21no—
157C8×C47—21no—
158C22×C47—21no—
159C22×C47—21no—
160C22×C47—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47AGL(1,ℤ/8)12yes—
164C22×C47C22×D411yescharacteristic
165C2×D47—22no—
166C2×D47—41no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—41no—
172C2×D47—41no—
173C2×D47—41no—
174C2×D47—84no—
175C4×C47—21no—
176C4×C47—21no—
177C4×C47—21no—
178C4×C47—21no—
179C4×C47C2×#4111yescharacteristic
180C4×C47H(5,𝔽2)11yescharacteristic
181Dic47—41no—
182Dic47—41no—
183Dic47—41no—
184Dic47—41no—
185Dic47—41no—
186#3306—471nomaximal, Sylow
187C2×C47—22no—
188C2×C47—41no—
189C2×C47#54611yescharacteristic
190C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C47#57711yescharacteristic
192D47—42no—
193D47—81no—
194D47—81no—
195#547—471no—
196#546—471no—
197#489—471no—
198#483—471no—
199#481—471no—
200#476—471no—
201#469—471no—
202#465—471no—
203#463—471no—
204#449—471no—
205#447—471no—
206#442—471no—
207#435D4711yescharacteristic, complemented
208#417—471no—
209C2×#102—471no—
210C47#330611yescharacteristic, complemented, Sylow
211C2×#41—471no—
212C2×#41—941no—
213C22×D4—471no—
214C2×SD16—471no—
215C2×D8—471no—
216C2×D8—471no—
217C2×M16C2×D4711yescharacteristic, complemented
218C22×C8C2×D4711yescharacteristic
219C4⋊Q8—471no—
220#124—471no—
221#123—941no—
222#123—941no—
223#123—941no—
224C22⋊Q8—471no—
225C22⋊Q8—941no—
226#121—471no—
227#121—471no—
228#121—471no—
229#121—941no—
230#120—941no—
231C4×D4—471no—
232C4×D4—471no—
233C4×D4C2×D4711yescharacteristic
234C2×C4⋊C4—471no—
235C2×C4⋊C4—471no—
236C2×C22⋊C4—941no—
237#106—471no—
238#106—471no—
239#106—471no—
240C4⋊C8C2×D4711yescharacteristic, complemented
241#103—471no—
242#103—471no—
243#103—471no—
244#102—471no—
245#102—471no—
246#102—471no—
247#102—471no—
248#102—471no—
249#102—471no—
250#102—471no—
251C22⋊C8C2×D4711yescharacteristic
252C22⋊C8C2×D4711yescharacteristic, complemented
253#97C2×D4711yescharacteristic, complemented
254C24—941no—
255#41—942no—
256#41—1881no—
257#41—1884no—
258C2×Q8—471no—
259C2×Q8—941no—
260C2×D4—471no—
261C2×D4—471no—
262C2×D4—471no—
263C2×D4—942no—
264C2×D4—941no—
265C2×D4—941no—
266C2×D4—941no—
267C2×D4—941no—
268C2×D4—941no—
269C2×D4—1881no—
270C2×D4D18811yescharacteristic
271C22×C4—941no—
272C22×C4—941no—
273C22×C4—941no—
274C22×C4—941no—
275C22×C4—941no—
276C22×C4C22×D4711yescharacteristic
277C22×C4C22×D4711yescharacteristic
278SD16—1881no—
279D8—942no—
280D8—1881no—
281M16—41no—
282C2×C8—41no—
283C2×C8C22×D4711yescharacteristic
284C2×C8C22×D4711yescharacteristic
285C2×C8C22×D4711yescharacteristic
286C2×C8C22×D4711yescharacteristic
287C4⋊C4—471no—
288C4⋊C4—471no—
289C4⋊C4—471no—
290C4⋊C4—471no—
291C4⋊C4—941no—
292C4⋊C4—941no—
293C4⋊C4—941no—
294C4⋊C4—941no—
295C4⋊C4D18811yescharacteristic
296C22⋊C4—941no—
297C22⋊C4—941no—
298C22⋊C4—941no—
299C22⋊C4—941no—
300C22⋊C4—941no—
301C22⋊C4—941no—
302C22⋊C4—941no—
303C22⋊C4—941no—
304C22⋊C4D18811yescharacteristic
305C22⋊C4D18811yescharacteristic
306C42C22×D4711yescharacteristic
307C23—941no—
308C23—941no—
309C23—941no—
310C23—3761no—
311C23—1882no—
312C23—1882no—
313C23C2×D18811yescharacteristic
314C23C2×D18811yescharacteristic
315Q8—941no—
316Q8—941no—
317Q8—1882no—
318D4—22no—
319D4—472no—
320D4—941no—
321D4—941no—
322D4—941no—
323D4—941no—
324D4—941no—
325D4—3761no—
326D4—1882no—
327D4—1882no—
328D4—1882no—
329D4—1882no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—941no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—941no—
338C2×C4—941no—
339C2×C4—3761no—
340C2×C4—1882no—
341C2×C4—1882no—
342C2×C4—1882no—
343C2×C4—1882no—
344C2×C4C2×D18811yescharacteristic
345C2×C4C2×D18811yescharacteristic
346C2×C4C2×D18811yescharacteristic
347C2×C4C2×D18811yescharacteristic
348C2×C4C23×D4711yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—942no—
359C22—3764no—
360C22—1881no—
361C22—1881no—
362C22—1881no—
363C22—1881no—
364C22—1881no—
365C22—1881no—
366C22—1881no—
367C22—1881no—
368C22#1309405212yes—
369C22C22×D18811yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—1881no—
375C4—1881no—
376C4—1881no—
377C4—1881no—
378C4—1881no—
379C4#41×D4711yescharacteristic
380C4#1309406911yescharacteristic
381C2—22no—
382C2—41no—
383C2—3761no—
384C2—3761no—
385C2—1882no—
386C2#1568976811yescharacteristic
387C2C2×#1309405211yescharacteristic
388C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#435C2
socleC22×C47C22×D4
hypercenter#435D47
hypocenterC47#3306
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #15689777C2semidirect
2. #15689769C2semidirect
3. #15689483C2semidirect
4. #15689454C2semidirect
5. #15689442C2semidirect
6. #15689414C2semidirect
7. #15689376C2semidirect
8. #15689352C2semidirect
9. #15689339C2semidirect
10. #15689270C2semidirect
11. #15689259C2semidirect
12. #15689236C2semidirect
13. #15689125C2semidirect
14. C2×#13093946C2semidirect
15. C47×#435C2semidirect
19. C2×#10625325C22semidirect
22. #13094024C22semidirect
31. #13093998C22semidirect
35. C4×D188C22semidirect
37. C2×C4⋊Dic47C22semidirect
39. #13093956C22semidirect
40. #13093956C22semidirect
41. #13093956C22semidirect
42. #13093949C22semidirect
43. #13093949C22semidirect
44. #13093949C22semidirect
51. #13093946C22semidirect
52. C2×M16×C47C22semidirect
55. C4⋊C8×C47C22semidirect
57. C22⋊C8×C47C22semidirect
58. #97×C47C22semidirect
147. D188#41semidirect
207. #435D47semidirect
210. C47#3306semidirect
217. C2×M16C2×D47semidirect
240. C4⋊C8C2×D47semidirect
252. C22⋊C8C2×D47semidirect
253. #97C2×D47semidirect