Finite Group Databasebeta

← #20252654

Subgroups — #20252654

Order 6016.

784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#13094070C211yesmaximal, characteristic, complemented
2C2×#13094050C211yesmaximal, characteristic, complemented
3C22×#10625334C211yesmaximal, characteristic, complemented
4#15689266C214yesmaximal, complemented
5#15689256C214yesmaximal, complemented
6#15689127C211yesmaximal, characteristic, complemented
7#15689117C211yesmaximal, characteristic, complemented
8#15689090C211yesmaximal, characteristic, complemented
9C47×#535C211yesmaximal, characteristic, complemented
10#13094070—24no—
11#13094070—24no—
12C2×#10625354—21no—
13C2×#10625350C2211yescharacteristic
14C2×#10625350C2212yescomplemented
15C22×D188C2211yescharacteristic
16C22×D188C2212yescomplemented
17C2×D4×D47—21no—
18C2×D4×D47—22no—
19#13094050—24no—
20C2×#10625335C2212yescomplemented
21C2×#10625334—24no—
22C2×#10625334C2212yescomplemented
23C2×#10625334C2214yescomplemented
24C2×#10625329C2211yescharacteristic, complemented
25C22×C47⋊C8C2211yescharacteristic, complemented
26#13093947C2212yescomplemented
27#13093944C2212yescomplemented
28#13093944C2214yescomplemented
29C22⋊(C47⋊C8)C2214yescomplemented
30C2×#41×C47C2211yescharacteristic
31C22×D4×C47C2211yescharacteristic, complemented
32#127×C47—21no—
33#124×C47—21no—
34#121×C47C2214yescomplemented
35#120×C47—22no—
36#117×C47C2211yescharacteristic, complemented
37C24×C47—21no—
38C23×D47—21no—
39C23×D47—22no—
40#41×C47—22no—
41#41×C47—22no—
42C2×Q8×C47D411yescharacteristic
43C2×D4×C47—24no—
44C2×D4×C47—22no—
45C2×D4×C47—22no—
46C2×D4×C47—21no—
47C2×D4×C47D412yes—
48C2×D4×C47D411yescharacteristic
49C2×D4×C47C2312yes—
50C22×C4×C47C2312yes—
51C22×C4×C47C2311yescharacteristic
52C2×C22⋊D47—21no—
53C2×C22⋊D47—22no—
54#10625354—28no—
55D4×D47—216no—
56D4×D47—28no—
57#10625350—22no—
58#10625350—24no—
59#10625350—24no—
60#10625350D414yescomplemented
61C2×D188—21no—
62C2×D188—22no—
63C2×D188—22no—
64C2×D188—24no—
65C2×D188—24no—
66C2×D188D414yescomplemented
67C2×D188C2312yes—
68C2×D188C2311yescharacteristic
69C2×C4×D47—21no—
70C2×C4×D47—22no—
71C2×Dic94C2311yescharacteristic
72C4⋊C4×C47C2312yes—
73C22⋊C4×C47—21no—
74C22⋊C4×C47—24no—
75C42×C47—21no—
76#10625335—24no—
77#10625334—28no—
78#10625334—24no—
79#10625329—22no—
80C2×C47⋊C8—22no—
81C2×C47⋊C8C2312yes—
82C2×C47⋊C8C2312yes—
83C23×C47—22no—
84C23×C47—42no—
85C23×C47—82no—
86C23×C47C2×D412yes—
87C23×C47C2×D411yescharacteristic
88C22×D47—21no—
89C22×D47—22no—
90C22×D47—28no—
91C22×D47—24no—
92C22×D47—82no—
93C22×D47—84no—
94Q8×C47—22no—
95D4×C47—24no—
96D4×C47—22no—
97D4×C47—22no—
98D4×C47—22no—
99D4×C47—42no—
100D4×C47—84no—
101C2×C4×C47—22no—
102C2×C4×C47—22no—
103C2×C4×C47—22no—
104C2×C4×C47C2×D412yes—
105C2×C4×C47C2×D412yes—
106C2×C4×C47C2×D412yes—
107C2×C4×C47C2×D411yescharacteristic
108C2×C4×C47C2411yescharacteristic
109C22⋊D47—28no—
110C22⋊D47—24no—
111C2×Dic47—21no—
112D188—28no—
113D188—24no—
114D188—21no—
115D188—22no—
116D188C2×D412yes—
117D188C2×D414yes—
118C4×D47—28no—
119C4×D47—24no—
120Dic94—21no—
121Dic94C2×D412yes—
122C47⋊C8—22no—
123C47⋊C8—22no—
124C22×C47—22no—
125C22×C47—22no—
126C22×C47—24no—
127C22×C47—42no—
128C22×C47—44no—
129C22×C47—84no—
130C22×C47#12012yes—
131C22×C47C22×D411yescharacteristic
132C2×D47—24no—
133C2×D47—22no—
134C2×D47—44no—
135C2×D47—42no—
136C2×D47—84no—
137C2×D47—88no—
138C4×C47—22no—
139C4×C47—42no—
140C4×C47#12012yes—
141C4×C47C22×D411yescharacteristic
142C4×C47C22×D411yescharacteristic
143Dic47—22no—
144#3008—471nomaximal, Sylow
145C2×C47—22no—
146C2×C47—42no—
147C2×C47—82no—
148C2×C47C2×#12011yescharacteristic
149C2×C47#57612yes—
150D47—44no—
151D47—42no—
152C2×H(5,𝔽2)—471no—
153C2×AGL(1,ℤ/8)—471no—
154C22×D8—471no—
155#535D4711yescharacteristic, complemented
156#449—474no—
157#447—474no—
158#418—471no—
159#416—471no—
160#408—471no—
161C47#300811yescharacteristic, complemented, Sylow
162H(5,𝔽2)—944no—
163H(5,𝔽2)—944no—
164C2×#41—471no—
165C2×#41—472no—
166C2×#41—941no—
167C2×#41C2×D4711yescharacteristic
168C22×D4—471no—
169C22×D4—472no—
170C22×D4—942no—
171C22×D4—941no—
172C22×D4C2×D4711yescharacteristic, complemented
173AGL(1,ℤ/8)—944no—
174C2×SD16—472no—
175C2×D8—474no—
176C2×D8—472no—
177C2×D8—944no—
178C2×M16—471no—
179C22×C8—471no—
180#127—21no—
181#124—21no—
182#121C2×D4714yescomplemented
183#120—22no—
184#117C2×D4711yescharacteristic, complemented
185#103—472no—
186#102—472no—
187#102—474no—
188C22⋊C8—474no—
189C24—21no—
190C24—942no—
191C24—941no—
192#41—22no—
193#41—22no—
194#41—474no—
195#41—944no—
196#41—944no—
197#41—948no—
198#41—942no—
199C2×Q8—471no—
200C2×Q8C22⋊D4711yescharacteristic
201C2×D4—24no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—21no—
205C2×D4—474no—
206C2×D4—472no—
207C2×D4—471no—
208C2×D4—944no—
209C2×D4—944no—
210C2×D4—9416no—
211C2×D4—948no—
212C2×D4—942no—
213C2×D4—941no—
214C2×D4—942no—
215C2×D4—942no—
216C2×D4—941no—
217C2×D4C22⋊D4712yes—
218C2×D4C22⋊D4711yescharacteristic
219C2×D4C22×D4712yes—
220C22×C4—942no—
221C22×C4—941no—
222C22×C4C22×D4712yes—
223C22×C4C22×D4711yescharacteristic
224SD16—944no—
225D8—948no—
226D8—944no—
227M16—942no—
228C2×C8—472no—
229C2×C8—472no—
230C2×C8—942no—
231C4⋊C4C22×D4712yes—
232C22⋊C4—21no—
233C22⋊C4—24no—
234C42—21no—
235C23—22no—
236C23—42no—
237C23—82no—
238C23—948no—
239C23—944no—
240C23—942no—
241C23—941no—
242C23—3762no—
243C23—3764no—
244C23C2×C22⋊D4712yes—
245C23C2×C22⋊D4711yescharacteristic
246Q8—22no—
247Q8—472no—
248Q8—941no—
249D4—24no—
250D4—22no—
251D4—22no—
252D4—22no—
253D4—42no—
254D4—84no—
255D4—474no—
256D4—472no—
257D4—948no—
258D4—948no—
259D4—944no—
260D4—944no—
261D4—941no—
262D4—942no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—948no—
267C2×C4—941no—
268C2×C4—944no—
269C2×C4D4×D4712yes—
270C2×C4D4×D4712yes—
271C2×C4C2×C22⋊D4712yes—
272C2×C4C2×C22⋊D4711yescharacteristic
273C2×C4C23×D4711yescharacteristic
274C8—942no—
275C8—942no—
276C22—22no—
277C22—22no—
278C22—24no—
279C22—42no—
280C22—44no—
281C22—84no—
282C22—944no—
283C22—942no—
284C22—3764no—
285C22—3768no—
286C22—1884no—
287C22—1882no—
288C22#1309399212yes—
289C22C22×C22⋊D4711yescharacteristic
290C4—22no—
291C4—42no—
292C4—942no—
293C4#1309399212yes—
294C4C2×D4×D4711yescharacteristic
295C4C2×D4×D4711yescharacteristic
296C2—22no—
297C2—42no—
298C2—82no—
299C2—1884no—
300C2—1882no—
301C2C2×#1309399211yescharacteristic
302C2#1568992612yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#535C2
socleC22×C47C22×D4
hypercenter#535D47
hypocenterC47#3008
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#13094070C2semidirect
2. C2×#13094050C2semidirect
3. C22×#10625334C2semidirect
4. #15689266C2semidirect
5. #15689256C2semidirect
6. #15689127C2semidirect
7. #15689117C2semidirect
8. #15689090C2semidirect
9. C47×#535C2semidirect
14. C2×#10625350C22semidirect
16. C22×D188C22semidirect
20. C2×#10625335C22semidirect
22. C2×#10625334C22semidirect
23. C2×#10625334C22semidirect
24. C2×#10625329C22semidirect
25. C22×C47⋊C8C22semidirect
26. #13093947C22semidirect
27. #13093944C22semidirect
28. #13093944C22semidirect
29. C22⋊(C47⋊C8)C22semidirect
31. C22×D4×C47C22semidirect
34. #121×C47C22semidirect
36. #117×C47C22semidirect
60. #10625350D4semidirect
66. C2×D188D4semidirect
155. #535D47semidirect
161. C47#3008semidirect
172. C22×D4C2×D47semidirect
182. #121C2×D47semidirect
184. #117C2×D47semidirect