Finite Group Databasebeta

← #20254402

Subgroups — #20254402

Order 6016.

490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#127×D47C211yesmaximal, characteristic, complemented
2#15689652C211yesmaximal, characteristic, complemented
3#15689513C211yesmaximal, characteristic, complemented
4#15689488C211yesmaximal, characteristic, complemented
5#15689487C211yesmaximal, characteristic, complemented
6#15689321C212yesmaximal, complemented
7#15689316C212yesmaximal, complemented
8#15689272C212yesmaximal, complemented
9#15689255C212yesmaximal, complemented
10#15689178C211yesmaximal, characteristic, complemented
11C47×#496C211yesmaximal, characteristic, complemented
12C2×D4×D47—21no—
13C2×D4×D47—21no—
14C2×D4×D47C2212yes—
15C2×#10625336C2212yescomplemented
16C2×#10625334C2212yescomplemented
17#13094021C2211yescharacteristic
18#13094020—21no—
19#13094020—21no—
20#13094020C2212yes—
21#13094017—21no—
22#13094016C2211yescharacteristic, complemented
23#13094006—21no—
24#13094000C2211yescharacteristic
25#13093995C2211yescharacteristic
26Q8×Dic47C2211yescharacteristic, complemented
27D4×Dic47C2211yescharacteristic, complemented
28(C22⋊D47)⋊C4—21no—
29#13093980—21no—
30C42×D47C2211yescharacteristic
31Dic47⋊C8C2212yescomplemented
32#13093946C2212yescomplemented
33#13093946C2212yescomplemented
34#13093945C2212yescomplemented
35#13093945C2212yescomplemented
36(C2×D47)⋊C8C2212yes—
37#13093935C2211yescharacteristic, complemented
38C2×SD16×C47C2212yescomplemented
39C2×D8×C47C2212yescomplemented
40#127×C47C2211yescharacteristic
41#124×C47C2211yescharacteristic, complemented
42#97×C47C2211yescharacteristic, complemented
43C23×D47—22no—
44C2×Q8×C47C2311yescharacteristic
45C2×D4×C47—21no—
46C2×D4×C47—21no—
47C2×D4×C47C2311yescharacteristic
48C2×D4×C47C2312yes—
49C2×C22⋊D47—21no—
50C2×C22⋊D47—22no—
51C2×C22⋊D47—22no—
52C2×C22⋊D47—22no—
53C22×Dic47—21no—
54D4×D47—42no—
55D4×D47—42no—
56D4×D47—44no—
57D4×D47—44no—
58C2×D188—21no—
59C2×D188—21no—
60C2×D188C2312yes—
61C2×C4×D47D411yescharacteristic
62C2×C4×D47D411yescharacteristic
63C2×C4×D47C2311yescharacteristic
64SD16×C47—42no—
65D8×C47—42no—
66C2×C8×C47C2312yes—
67C22⋊C4×C47—21no—
68C22⋊C4×C47—21no—
69C42×C47C2311yescharacteristic
70C22⋊Dic47—21no—
71C22⋊Dic47—21no—
72#10625336—42no—
73#10625334—42no—
74(C2×D47)⋊C4—21no—
75C4⋊Dic47—21no—
76C4⋊Dic47C2311yescharacteristic
77C4⋊Dic47C2311yescharacteristic
78Dic47⋊C4—21no—
79Dic47⋊C4—21no—
80Dic47⋊C4—21no—
81C4×Dic47—21no—
82C4×Dic47D411yescharacteristic
83C4×Dic47D411yescharacteristic
84C4×Dic47C2311yescharacteristic
85C2×C47⋊C8C2312yes—
86C23×C47—21no—
87C23×C47—22no—
88C22×D47—22no—
89C22×D47—44no—
90C22×D47—44no—
91C22×D47—44no—
92C22×D47C2×D411yescharacteristic
93Q8×C47—22no—
94D4×C47—22no—
95D4×C47—22no—
96D4×C47—22no—
97D4×C47—42no—
98D4×C47—42no—
99C2×C4×C47—21no—
100C2×C4×C47C2×D411yescharacteristic
101C2×C4×C47C2×D411yescharacteristic
102C2×C4×C47C2411yescharacteristic
103C22⋊D47—44no—
104C22⋊D47—44no—
105C22⋊D47—42no—
106C22⋊D47—44no—
107C2×Dic47—21no—
108C2×Dic47—21no—
109C2×Dic47—42no—
110C2×Dic47C2×D411yescharacteristic
111C2×Dic47C2×D411yescharacteristic
112C2×Dic47C2×D411yescharacteristic
113D188—22no—
114D188—22no—
115D188—42no—
116D188—42no—
117C4×D47—22no—
118C4×D47—22no—
119C4×D47—22no—
120C8×C47—22no—
121C47⋊C8—22no—
122C22×C47—42no—
123C22×C47—41no—
124C22×C47—41no—
125C22×C47—42no—
126C22×C47—42no—
127C22×C47—41no—
128C22×C47C22×D411yescharacteristic
129C2×D47—21no—
130C2×D47—21no—
131C2×D47—42no—
132C2×D47—42no—
133C2×D47—42no—
134C2×D47—88no—
135C2×D47AGL(1,ℤ/8)12yes—
136C4×C47—21no—
137C4×C47—21no—
138C4×C47—41no—
139C4×C47H(5,𝔽2)12yes—
140Dic47—21no—
141Dic47—21no—
142Dic47—41no—
143Dic47—41no—
144Dic47AGL(1,ℤ/8)12yes—
145#3217—471nomaximal, Sylow
146C2×C47—82no—
147C2×C47—81no—
148C2×C47#53511yescharacteristic
149C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
150C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
151D47—22no—
152D47—82no—
153C2×#127—471no—
154#529—471no—
155#496—471no—
156#496D4711yescharacteristic, complemented
157#490—471no—
158#490—471no—
159#460—472no—
160#459—472no—
161#450—472no—
162#447—472no—
163#432—471no—
164C47#321711yescharacteristic, complemented, Sylow
165C22×D4—472no—
166C22×D4—941no—
167C22×D4—941no—
168C2×SD16—472no—
169C2×SD16C2×D4712yescomplemented
170C2×D8—472no—
171C2×D8C2×D4712yescomplemented
172#127—472no—
173#127—471no—
174#127—941no—
175#127—941no—
176#127C2×D4711yescharacteristic
177#126—941no—
178#125—471no—
179#124C2×D4711yescharacteristic, complemented
180#123—941no—
181C22⋊Q8—471no—
182#121—471no—
183C4×Q8—471no—
184C4×D4—471no—
185C4×D4—941no—
186#117—941no—
187C2×C42—471no—
188C4⋊C8—472no—
189#102—472no—
190#102—472no—
191#102—472no—
192#102—472no—
193C22⋊C8—472no—
194#97—471no—
195#97C2×D4711yescharacteristic, complemented
196C24—942no—
197C2×Q8C22×D4711yescharacteristic
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—472no—
201C2×D4—942no—
202C2×D4—942no—
203C2×D4—942no—
204C2×D4—941no—
205C2×D4—941no—
206C2×D4—941no—
207C2×D4—1882no—
208C2×D4—1882no—
209C2×D4—1884no—
210C2×D4—1884no—
211C2×D4C22×D4712yes—
212C2×D4C22×D4711yescharacteristic
213C22×C4—471no—
214C22×C4—471no—
215C22×C4—471no—
216C22×C4—941no—
217SD16—42no—
218SD16—1882no—
219D8—42no—
220D8—1882no—
221C2×C8—472no—
222C2×C8C22×D4712yes—
223C4⋊C4—471no—
224C4⋊C4—471no—
225C4⋊C4—941no—
226C4⋊C4—941no—
227C4⋊C4—941no—
228C4⋊C4—941no—
229C22⋊C4—21no—
230C22⋊C4—21no—
231C22⋊C4—941no—
232C22⋊C4—941no—
233C22⋊C4—941no—
234C42—471no—
235C42—471no—
236C42—471no—
237C42—941no—
238C42C22×D4711yescharacteristic
239C23—21no—
240C23—22no—
241C23—471no—
242C23—942no—
243C23—1884no—
244C23—1884no—
245C23—1884no—
246Q8—22no—
247D4—22no—
248D4—22no—
249D4—22no—
250D4—42no—
251D4—42no—
252D4—942no—
253D4—942no—
254D4—1882no—
255D4—1882no—
256D4—1884no—
257D4—1884no—
258D4—1884no—
259D4—1882no—
260C2×C4—21no—
261C2×C4—471no—
262C2×C4—471no—
263C2×C4—471no—
264C2×C4—942no—
265C2×C4—942no—
266C2×C4—942no—
267C2×C4—941no—
268C2×C4—941no—
269C2×C4—1882no—
270C2×C4D4×D4711yescharacteristic
271C2×C4D4×D4711yescharacteristic
272C2×C4C23×D4711yescharacteristic
273C8—22no—
274C8—942no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—41no—
279C22—42no—
280C22—41no—
281C22—472no—
282C22—941no—
283C22—941no—
284C22—3768no—
285C22—1882no—
286C22—1882no—
287C22—1882no—
288C22C2×D4×D4711yescharacteristic
289C4—21no—
290C4—21no—
291C4—41no—
292C4—472no—
293C4—941no—
294C4—941no—
295C4—1881no—
296C4—1881no—
297C4#1309406912yes—
298C2—82no—
299C2—81no—
300C2—942no—
301C2—3762no—
302C2#1568968611yescharacteristic
303C2AGL(1,ℤ/8)×D4711yescharacteristic
304C2AGL(1,ℤ/8)×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#496C2
socleC22×C47C22×D4
hypercenter#496D47
hypocenterC47#3217
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #127×D47C2semidirect
2. #15689652C2semidirect
3. #15689513C2semidirect
4. #15689488C2semidirect
5. #15689487C2semidirect
6. #15689321C2semidirect
7. #15689316C2semidirect
8. #15689272C2semidirect
9. #15689255C2semidirect
10. #15689178C2semidirect
11. C47×#496C2semidirect
15. C2×#10625336C22semidirect
16. C2×#10625334C22semidirect
22. #13094016C22semidirect
26. Q8×Dic47C22semidirect
27. D4×Dic47C22semidirect
31. Dic47⋊C8C22semidirect
32. #13093946C22semidirect
33. #13093946C22semidirect
34. #13093945C22semidirect
35. #13093945C22semidirect
37. #13093935C22semidirect
38. C2×SD16×C47C22semidirect
39. C2×D8×C47C22semidirect
41. #124×C47C22semidirect
42. #97×C47C22semidirect
156. #496D47semidirect
164. C47#3217semidirect
169. C2×SD16C2×D47semidirect
171. C2×D8C2×D47semidirect
179. #124C2×D47semidirect
195. #97C2×D47semidirect