Finite Group Databasebeta

← #20252657

Subgroups — #20252657

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×#13094069C211yesmaximal, characteristic, complemented
2C2×#13094052C211yesmaximal, characteristic, complemented
3C22×#10625334C211yesmaximal, characteristic, complemented
4#15689692C211yesmaximal, characteristic, complemented
5#15689269C214yesmaximal, complemented
6#15689258C214yesmaximal, complemented
7#15689117C211yesmaximal, characteristic, complemented
8#15689091C211yesmaximal, characteristic, complemented
9C47×#418C211yesmaximal, characteristic, complemented
10#13094069—24no—
11#13094069—24no—
12C2×#10625350C2211yescharacteristic
13C2×#10625350C2211yescharacteristic
14C2×#10625352—21no—
15C2×#10625352C2212yescomplemented
16C22×D188C2211yescharacteristic, complemented
17C22×C22⋊D47—22no—
18C2×D4×D47—21no—
19C2×D4×D47C2212yescomplemented
20#13094052—24no—
21C2×#10625325C2212yescomplemented
22C2×D376C2212yescomplemented
23C2×#10625334—24no—
24C2×#10625334C2214yescomplemented
25C22×C47⋊C8C2211yescharacteristic, complemented
26#13094021—21no—
27#13094012—21no—
28#13093999C2214yescomplemented
29#13093994—22no—
30#13093947C2212yescomplemented
31#13093944C2212yescomplemented
32(C2×D47)⋊C8C2214yescomplemented
33C22×D4×C47C2211yescharacteristic
34C2×M16×C47C2211yescharacteristic, complemented
35#117×C47C2211yescharacteristic, complemented
36#102×C47C2214yescomplemented
37C24×C47—21no—
38C23×D47—22no—
39C23×D47—21no—
40C2×D4×C47—21no—
41C2×D4×C47—22no—
42C2×D4×C47D414yescomplemented
43C2×D4×C47C2312yes—
44C22×C4×C47C2311yescharacteristic
45C2×C22⋊D47—216no—
46C2×C22⋊D47—21no—
47C2×C22⋊D47—22no—
48C2×C22⋊D47—22no—
49C2×C22⋊D47D412yes—
50C22×Dic47—22no—
51#10625352—28no—
52#10625352—24no—
53#10625352—24no—
54D4×D47—28no—
55D4×D47—24no—
56D4×D47—24no—
57#10625350—22no—
58#10625350—22no—
59#10625350—22no—
60#10625350D414yescomplemented
61C2×D188—22no—
62C2×D188—22no—
63C2×D188—21no—
64C2×D188—24no—
65C2×D188D411yescharacteristic
66C2×D188C2312yes—
67C2×D188C2311yescharacteristic
68C2×C4×D47—21no—
69C2×C4×D47C2312yes—
70C2×Dic94D411yescharacteristic
71C2×Dic94C2311yescharacteristic
72M16×C47—22no—
73C2×C8×C47C2312yes—
74C4⋊C4×C47C2312yes—
75C22⋊C4×C47—21no—
76C42×C47—21no—
77#10625334—28no—
78(C2×D47)⋊C4—24no—
79C2×C47⋊C8—22no—
80C2×C47⋊C8C2312yes—
81D376—24no—
82#10625325—24no—
83C23×C47—22no—
84C23×C47—24no—
85C23×C47—82no—
86C23×C47C2×D411yescharacteristic
87C22×D47—21no—
88C22×D47—28no—
89C22×D47—22no—
90C22×D47—42no—
91C22×D47—84no—
92C22×D47—82no—
93C22×D47C2×D412yes—
94D4×C47—24no—
95D4×C47—22no—
96D4×C47C2×D414yes—
97C2×C4×C47—22no—
98C2×C4×C47C2×D412yes—
99C2×C4×C47C2×D411yescharacteristic
100C2×C4×C47C2×D412yes—
101C2×C4×C47C2411yescharacteristic
102C22⋊D47—28no—
103C22⋊D47—28no—
104C22⋊D47—24no—
105C22⋊D47—24no—
106C2×Dic47—28no—
107C2×Dic47—21no—
108C2×Dic47C2×D412yes—
109D188—22no—
110D188—21no—
111D188—22no—
112D188—22no—
113D188—42no—
114D188—84no—
115D188C2×D412yes—
116C4×D47—24no—
117C4×D47—22no—
118C4×D47—22no—
119Dic94—22no—
120Dic94—21no—
121Dic94C2×D412yes—
122C8×C47—22no—
123C47⋊C8—22no—
124C22×C47—22no—
125C22×C47—24no—
126C22×C47—44no—
127C22×C47—84no—
128C22×C47#12012yes—
129C22×C47C22×D411yescharacteristic
130C2×D47—22no—
131C2×D47—22no—
132C2×D47—24no—
133C2×D47—42no—
134C2×D47—42no—
135C2×D47—44no—
136C2×D47—88no—
137C2×D47—84no—
138C4×C47—42no—
139C4×C47#12012yes—
140C4×C47C22×D411yescharacteristic
141C4×C47C22×D411yescharacteristic
142Dic47—22no—
143Dic47—22no—
144#3008—471nomaximal, Sylow
145C2×C47—22no—
146C2×C47—44no—
147C2×C47C2×#12011yescharacteristic
148C2×C47#57612yes—
149D47—42no—
150D47—42no—
151D47—82no—
152C2×H(5,𝔽2)—471no—
153C2×AGL(1,ℤ/8)—471no—
154C22×D8—471no—
155#535—471no—
156#449—474no—
157#447—474no—
158#418D4711yescharacteristic, complemented
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—471no—
167C2×#41—941no—
168C22×D4—472no—
169C22×D4—471no—
170C22×D4—941no—
171C22×D4—942no—
172C22×D4C2×D4711yescharacteristic
173AGL(1,ℤ/8)—944no—
174C2×SD16—472no—
175C2×D8—474no—
176C2×D8—472no—
177C2×D8—944no—
178C2×M16C2×D4711yescharacteristic, complemented
179C22×C8—471no—
180#127—941no—
181#124—941no—
182#121—474no—
183#120—942no—
184#117C2×D4711yescharacteristic, complemented
185#103—472no—
186#102—472no—
187#102C2×D4714yescomplemented
188C22⋊C8—474no—
189C24—21no—
190C24—942no—
191C24—941no—
192#41—474no—
193#41—944no—
194#41—948no—
195#41—944no—
196#41—942no—
197#41—942no—
198#41—942no—
199C2×Q8—471no—
200C2×Q8—471no—
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—472no—
204C2×D4—471no—
205C2×D4—471no—
206C2×D4—472no—
207C2×D4—944no—
208C2×D4—942no—
209C2×D4—944no—
210C2×D4—948no—
211C2×D4—942no—
212C2×D4—9416no—
213C2×D4—941no—
214C2×D4—944no—
215C2×D4—942no—
216C2×D4—942no—
217C2×D4—941no—
218C2×D4D18814yescomplemented
219C2×D4C22×D4712yes—
220C22×C4—472no—
221C22×C4—942no—
222C22×C4—941no—
223C22×C4C22×D4711yescharacteristic
224SD16—944no—
225D8—944no—
226D8—948no—
227M16—22no—
228C2×C8—472no—
229C2×C8—942no—
230C2×C8C22×D4712yes—
231C4⋊C4C22×D4712yes—
232C22⋊C4—21no—
233C22⋊C4—944no—
234C42—21no—
235C23—22no—
236C23—24no—
237C23—82no—
238C23—472no—
239C23—948no—
240C23—941no—
241C23—942no—
242C23—3762no—
243C23—3764no—
244C23—1882no—
245C23D4×D4711yescharacteristic
246Q8—472no—
247Q8—942no—
248Q8—941no—
249D4—24no—
250D4—22no—
251D4—472no—
252D4—948no—
253D4—948no—
254D4—944no—
255D4—944no—
256D4—942no—
257D4—942no—
258D4—941no—
259D4—942no—
260D4—3764no—
261D4—1882no—
262D4C2×D18814yes—
263C2×C4—22no—
264C2×C4—472no—
265C2×C4—948no—
266C2×C4—941no—
267C2×C4—944no—
268C2×C4—942no—
269C2×C4—942no—
270C2×C4C2×D18812yes—
271C2×C4D4×D4711yescharacteristic
272C2×C4D4×D4712yes—
273C2×C4C23×D4711yescharacteristic
274C8—22no—
275C8—942no—
276C22—22no—
277C22—24no—
278C22—44no—
279C22—84no—
280C22—942no—
281C22—942no—
282C22—944no—
283C22—3764no—
284C22—3768no—
285C22—1882no—
286C22—1884no—
287C22—1882no—
288C22#1309399412yes—
289C22C2×D4×D4711yescharacteristic
290C4—42no—
291C4—942no—
292C4—942no—
293C4#1309399412yes—
294C4C2×D4×D4711yescharacteristic
295C4C22×D18811yescharacteristic
296C2—22no—
297C2—44no—
298C2—3762no—
299C2—1882no—
300C2—1882no—
301C2C2×#1309399411yescharacteristic
302C2#1568992712yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#418C2
socleC22×C47C22×D4
hypercenter#418D47
hypocenterC47#3008
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#13094069C2semidirect
2. C2×#13094052C2semidirect
3. C22×#10625334C2semidirect
4. #15689692C2semidirect
5. #15689269C2semidirect
6. #15689258C2semidirect
7. #15689117C2semidirect
8. #15689091C2semidirect
9. C47×#418C2semidirect
15. C2×#10625352C22semidirect
16. C22×D188C22semidirect
19. C2×D4×D47C22semidirect
21. C2×#10625325C22semidirect
22. C2×D376C22semidirect
24. C2×#10625334C22semidirect
25. C22×C47⋊C8C22semidirect
28. #13093999C22semidirect
30. #13093947C22semidirect
31. #13093944C22semidirect
32. (C2×D47)⋊C8C22semidirect
34. C2×M16×C47C22semidirect
35. #117×C47C22semidirect
36. #102×C47C22semidirect
42. C2×D4×C47D4semidirect
60. #10625350D4semidirect
158. #418D47semidirect
161. C47#3008semidirect
178. C2×M16C2×D47semidirect
184. #117C2×D47semidirect
187. #102C2×D47semidirect
218. C2×D4D188semidirect