Finite Group Databasebeta

← #20255350

Subgroups — #20255350

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#15689774C211yesmaximal, characteristic, complemented
2#15689761C211yesmaximal, characteristic, complemented
3#15689484C211yesmaximal, characteristic, complemented
4#15689452C211yesmaximal, characteristic, complemented
5#15689441C211yesmaximal, characteristic, complemented
6#15689411C211yesmaximal, characteristic, complemented
7#15689376C211yesmaximal, characteristic, complemented
8#15689355C211yesmaximal, characteristic, complemented
9#15689341C211yesmaximal, characteristic, complemented
10#15689268C211yesmaximal, characteristic, complemented
11#15689258C211yesmaximal, characteristic, complemented
12#15689232C211yesmaximal, characteristic, complemented
13#15689192C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#417C211yesmaximal, characteristic, complemented
16C2×#10625350—21no—
17C2×D4×D47C2211yescharacteristic
18C2×#10625336C2211yescharacteristic, complemented
19C2×D376C2211yescharacteristic
20C2×#10625334C2211yescharacteristic
21C2×C8×D47C2211yescharacteristic
22#13094023C2211yescharacteristic, complemented
23#13094013C2211yescharacteristic
24#13094009—21no—
25#13094007—21no—
26#13094007—21no—
27#13094002—21no—
28#13094000C2211yescharacteristic
29#13093999C2211yescharacteristic
30#13093998C2211yescharacteristic
31#13093998C2211yescharacteristic, complemented
32#13093996—21no—
33#13093992—21no—
34D4×Dic47C2211yescharacteristic
35#13093986C2211yescharacteristic, complemented
36C4×C22⋊D47C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic
38C2×(C2×D47)⋊C4—21no—
39#13093956C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41#13093955C2211yescharacteristic, complemented
42Dic47⋊C8C2211yescharacteristic, complemented
43#13093948C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic, complemented
46#13093945C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic
51#13093934C2211yescharacteristic, complemented
52C2×#41×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic, complemented
54C2×C4⋊C4×C47C2211yescharacteristic, complemented
55#103×C47C2211yescharacteristic, complemented
56#103×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C23×D47—21no—
60#41×C47—22no—
61#41×C47—41no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47C2311yescharacteristic
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47D411yescharacteristic
72C22×Dic47—21no—
73D4×D47—22no—
74D4×D47—41no—
75#10625350—44no—
76C2×D188—21no—
77C2×D188C2311yescharacteristic
78C2×D188C2311yescharacteristic
79C2×C4×D47—21no—
80C2×C4×D47—21no—
81C2×C4×D47C2311yescharacteristic
82C2×Dic94—21no—
83M16×C47—41no—
84C2×C8×C47C2311yescharacteristic
85C2×C8×C47C2311yescharacteristic
86C4⋊C4×C47—21no—
87C4⋊C4×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C22⋊Dic47—21no—
90C22⋊Dic47D411yescharacteristic
91#10625336—41no—
92#10625334—22no—
93(C2×D47)⋊C4—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)⋊C4D411yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102C4⋊Dic47C2311yescharacteristic
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106Dic47⋊C4D411yescharacteristic
107C4×Dic47C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110D376—41no—
111C8×D47—41no—
112C23×C47—21no—
113C23×C47C2×D411yescharacteristic
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—42no—
117C22×D47—42no—
118C22×D47—81no—
119C22×D47C2×D411yescharacteristic
120Q8×C47—21no—
121Q8×C47—21no—
122D4×C47—21no—
123D4×C47—42no—
124D4×C47#4112yescomplemented
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—42no—
131C2×C4×C47—42no—
132C2×C4×C47C2×D411yescharacteristic
133C2×C4×C47C2411yescharacteristic
134C22⋊D47—22no—
135C22⋊D47—42no—
136C22⋊D47—42no—
137C22⋊D47—81no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—81no—
141C2×Dic47C2×D411yescharacteristic
142C2×Dic47C2×D411yescharacteristic
143C2×Dic47C2×D411yescharacteristic
144D188—21no—
145D188—21no—
146D188—21no—
147D188—21no—
148D188—42no—
149C4×D47—21no—
150C4×D47—21no—
151C4×D47—42no—
152C4×D47—42no—
153Dic94—42no—
154C8×C47—21no—
155C8×C47—21no—
156C47⋊C8—21no—
157C47⋊C8—21no—
158C22×C47—22no—
159C22×C47—21no—
160C22×C47—21no—
161C22×C47—21no—
162C22×C47—41no—
163C22×C47—41no—
164C22×C47C22×D411yescharacteristic
165C2×D47—21no—
166C2×D47—21no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—41no—
172C2×D47—41no—
173C2×D47—84no—
174C2×D47AGL(1,ℤ/8)12yes—
175C4×C47—21no—
176C4×C47—41no—
177C4×C47—41no—
178C4×C47—41no—
179C4×C47C2×#4111yescharacteristic
180C4×C47H(5,𝔽2)11yescharacteristic
181Dic47—21no—
182Dic47—21no—
183Dic47—21no—
184Dic47—41no—
185Dic47—41no—
186#3306—471nomaximal, Sylow
187C2×C47—42no—
188C2×C47—41no—
189C2×C47#54611yescharacteristic
190C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C47#57711yescharacteristic
192D47—22no—
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#435—471no—
208#417D4711yescharacteristic, complemented
209C2×#102—471no—
210C47#330611yescharacteristic, complemented, Sylow
211C2×#41—941no—
212C2×#41C2×D4711yescharacteristic
213C22×D4—471no—
214C2×SD16—471no—
215C2×D8—471no—
216C2×D8—471no—
217C2×M16C2×D4711yescharacteristic, complemented
218C22×C8—471no—
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×D4—471no—
234C2×C4⋊C4—471no—
235C2×C4⋊C4C2×D4711yescharacteristic, complemented
236C2×C22⋊C4—941no—
237#106—471no—
238#106—471no—
239#106—471no—
240C4⋊C8—471no—
241#103—471no—
242#103C2×D4711yescharacteristic, complemented
243#103C2×D4711yescharacteristic, complemented
244#102—471no—
245#102—471no—
246#102—471no—
247#102—471no—
248#102—471no—
249#102C2×D4711yescharacteristic
250#102C2×D4711yescharacteristic
251C22⋊C8—471no—
252C22⋊C8—471no—
253#97—471no—
254C24—941no—
255#41—22no—
256#41—41no—
257#41—1884no—
258C2×Q8—941no—
259C2×Q8C22×D4711yescharacteristic
260C2×D4—21no—
261C2×D4—471no—
262C2×D4—471no—
263C2×D4—471no—
264C2×D4—941no—
265C2×D4—941no—
266C2×D4—942no—
267C2×D4—941no—
268C2×D4—941no—
269C2×D4—1881no—
270C2×D4C22×D4711yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—471no—
274C22×C4—941no—
275C22×C4—941no—
276C22×C4—941no—
277C22×C4C22×D4711yescharacteristic
278SD16—1881no—
279D8—942no—
280D8—1881no—
281M16—41no—
282C2×C8—471no—
283C2×C8—471no—
284C2×C8—1881no—
285C2×C8C22×D4711yescharacteristic
286C2×C8C22×D4711yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—471no—
289C4⋊C4—471no—
290C4⋊C4—471no—
291C4⋊C4—941no—
292C4⋊C4—941no—
293C4⋊C4—941no—
294C4⋊C4C22×D4711yescharacteristic
295C4⋊C4C22×D4711yescharacteristic
296C22⋊C4—471no—
297C22⋊C4—471no—
298C22⋊C4—941no—
299C22⋊C4—941no—
300C22⋊C4—941no—
301C22⋊C4—941no—
302C22⋊C4—941no—
303C22⋊C4—941no—
304C22⋊C4—941no—
305C22⋊C4—941no—
306C42—471no—
307C23—21no—
308C23—471no—
309C23—941no—
310C23—941no—
311C23—3761no—
312C23—1882no—
313C23—1882no—
314C23D4×D4711yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—1882no—
318D4—21no—
319D4—42no—
320D4—942no—
321D4—941no—
322D4—941no—
323D4—941no—
324D4—941no—
325D4—3761no—
326D4—1882no—
327D4—1882no—
328D4—1882no—
329D4#1062535012yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—471no—
338C2×C4—471no—
339C2×C4—471no—
340C2×C4—941no—
341C2×C4—941no—
342C2×C4—941no—
343C2×C4—941no—
344C2×C4—3761no—
345C2×C4—1882no—
346C2×C4—1882no—
347C2×C4D4×D4711yescharacteristic
348C2×C4C23×D4711yescharacteristic
349C8—21no—
350C8—21no—
351C8—941no—
352C8—941no—
353C22—21no—
354C22—22no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—472no—
360C22—941no—
361C22—941no—
362C22—3764no—
363C22—1881no—
364C22—1881no—
365C22—1881no—
366C22—1881no—
367C22—1881no—
368C22—1881no—
369C22C2×D4×D4711yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—941no—
375C4—941no—
376C4—941no—
377C4—1881no—
378C4—1881no—
379C4C2×#1062535011yescharacteristic
380C4#1309406911yescharacteristic
381C2—41no—
382C2—42no—
383C2—942no—
384C2—3761no—
385C2—3761no—
386C2#1568976311yescharacteristic
387C2AGL(1,ℤ/8)×D4711yescharacteristic
388C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#417C2
socleC22×C47C22×D4
hypercenter#417D47
hypocenterC47#3306
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #15689774C2semidirect
2. #15689761C2semidirect
3. #15689484C2semidirect
4. #15689452C2semidirect
5. #15689441C2semidirect
6. #15689411C2semidirect
7. #15689376C2semidirect
8. #15689355C2semidirect
9. #15689341C2semidirect
10. #15689268C2semidirect
11. #15689258C2semidirect
12. #15689232C2semidirect
13. #15689192C2semidirect
14. #102×D47C2semidirect
15. C47×#417C2semidirect
18. C2×#10625336C22semidirect
22. #13094023C22semidirect
31. #13093998C22semidirect
35. #13093986C22semidirect
39. #13093956C22semidirect
40. #13093955C22semidirect
41. #13093955C22semidirect
42. Dic47⋊C8C22semidirect
43. #13093948C22semidirect
45. #13093946C22semidirect
49. C22⋊(C47⋊C8)C22semidirect
51. #13093934C22semidirect
53. C2×M16×C47C22semidirect
54. C2×C4⋊C4×C47C22semidirect
55. #103×C47C22semidirect
56. #103×C47C22semidirect
124. D4×C47#41semidirect
208. #417D47semidirect
210. C47#3306semidirect
217. C2×M16C2×D47semidirect
235. C2×C4⋊C4C2×D47semidirect
242. #103C2×D47semidirect
243. #103C2×D47semidirect
329. D4#10625350semidirect