Finite Group Databasebeta

← #20252638

Subgroups — #20252638

Order 6016.

806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×#10625350C211yesmaximal, characteristic, complemented
2C2×#13094050C212yesmaximal, complemented
3#15689266C214yesmaximal, complemented
4#15689261C212yesmaximal, complemented
5#15689256C212yesmaximal, complemented
6#15689122C212yesmaximal, complemented
7#15689087C211yesmaximal, characteristic, complemented
8C2×#121×C47C211yesmaximal, characteristic, complemented
9C2×#10625350—21no—
10C2×#10625350—21no—
11C2×#10625350—28no—
12C2×#10625350C2212yes—
13C2×#10625350C2212yescomplemented
14C22×Dic94C2211yescharacteristic, complemented
15C22×D188C2211yescharacteristic, complemented
16C22×C22⋊D47—21no—
17C22×C4×D47—21no—
18#13094050—28no—
19C2×#10625335C2214yescomplemented
20C2×#10625334C2214yescomplemented
21C2×#10625329C2212yescomplemented
22#13093947C2214yescomplemented
23#13093944C2214yescomplemented
24C22⋊(C47⋊C8)C2212yescomplemented
25C22⋊(C47⋊C8)C2212yescomplemented
26C22×D4×C47—21no—
27C22×D4×C47C2211yescharacteristic, complemented
28C23×C4×C47C2211yescharacteristic
29#121×C47—21no—
30#121×C47—21no—
31#121×C47C2212yes—
32#121×C47C2212yescomplemented
33C2×C4⋊C4×C47C2211yescharacteristic, complemented
34C2×C22⋊C4×C47—21no—
35C24×C47—21no—
36C24×C47D411yescharacteristic
37C23×D47—21no—
38C2×D4×C47—22no—
39C2×D4×C47—22no—
40C2×D4×C47—24no—
41C2×D4×C47—21no—
42C2×D4×C47—44no—
43C2×D4×C47C2312yes—
44C22×C4×C47—24no—
45C22×C4×C47—21no—
46C22×C4×C47D411yescharacteristic
47C22×C4×C47D411yescharacteristic
48C22×C4×C47D411yescharacteristic
49C22×C4×C47C2311yescharacteristic
50C22×C4×C47C2311yescharacteristic
51C22×C4×C47C2311yescharacteristic
52C2×C22⋊D47—28no—
53C2×C22⋊D47—22no—
54C2×C22⋊D47—22no—
55C22×Dic47—21no—
56#10625350—28no—
57#10625350—28no—
58#10625350—24no—
59#10625350—24no—
60#10625350—24no—
61#10625350D418yescomplemented
62C2×D188—21no—
63C2×D188—24no—
64C2×D188C2312yes—
65C2×C4×D47—28no—
66C2×C4×D47—22no—
67C2×C4×D47—22no—
68C2×Dic94—21no—
69C2×Dic94—24no—
70C2×Dic94C2312yes—
71C4⋊C4×C47—21no—
72C4⋊C4×C47C2312yes—
73C22⋊C4×C47—22no—
74C22⋊C4×C47—22no—
75#10625335—28no—
76#10625334—28no—
77#10625329—24no—
78C2×C47⋊C8C2314yes—
79C23×C47—22no—
80C23×C47—22no—
81C23×C47—22no—
82C23×C47—41no—
83C23×C47—42no—
84C23×C47—42no—
85C23×C47—42no—
86C23×C47C2×D411yescharacteristic
87C23×C47C2×D411yescharacteristic
88C23×C47C2×D411yescharacteristic
89C22×D47—24no—
90C22×D47—22no—
91C22×D47—42no—
92C22×D47—42no—
93D4×C47—24no—
94D4×C47—44no—
95D4×C47—44no—
96D4×C47—42no—
97C2×C4×C47—22no—
98C2×C4×C47—22no—
99C2×C4×C47—22no—
100C2×C4×C47—22no—
101C2×C4×C47—22no—
102C2×C4×C47—22no—
103C2×C4×C47—42no—
104C2×C4×C47C2×D414yes—
105C2×C4×C47C2×D411yescharacteristic
106C2×C4×C47C2×D411yescharacteristic
107C2×C4×C47C2×D411yescharacteristic
108C2×C4×C47C2411yescharacteristic
109C22⋊D47—28no—
110C22⋊D47—28no—
111C2×Dic47—24no—
112C2×Dic47—22no—
113D188—24no—
114D188—22no—
115D188C2×D414yescomplemented
116C4×D47—28no—
117C4×D47—28no—
118Dic94—24no—
119Dic94—22no—
120Dic94C2×D414yescomplemented
121C47⋊C8—24no—
122C22×C47—21no—
123C22×C47—21no—
124C22×C47—21no—
125C22×C47—21no—
126C22×C47—21no—
127C22×C47—21no—
128C22×C47—21no—
129C22×C47—44no—
130C22×C47—42no—
131C22×C47—42no—
132C22×C47—42no—
133C22×C47—84no—
134C22×C47#12012yes—
135C22×C47AGL(1,ℤ/8)12yescomplemented
136C22×C47C22×D411yescharacteristic
137C2×D47—24no—
138C2×D47—48no—
139C2×D47—42no—
140C2×D47—42no—
141C4×C47—21no—
142C4×C47—21no—
143C4×C47—42no—
144C4×C47#12012yes—
145C4×C47C22×D412yes—
146Dic47—24no—
147#3006—471nomaximal, Sylow
148C2×C47—22no—
149C2×C47—22no—
150C2×C47—41no—
151C2×C47—82no—
152C2×C47C2×#12011yescharacteristic
153C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
154C2×C47#57511yescharacteristic
155D47—44no—
156C22×#41—471no—
157C2×AGL(1,ℤ/8)—472no—
158C2×#121D4711yescharacteristic, complemented
159#449—474no—
160#448—472no—
161#447—472no—
162#417—472no—
163#407—471no—
164C47#300611yescharacteristic, complemented, Sylow
165C2×#41—472no—
166C2×#41—472no—
167C2×#41—948no—
168C2×#41—941no—
169C2×#41—941no—
170C22×Q8—471no—
171C22×D4—21no—
172C22×D4—471no—
173C22×D4—941no—
174C22×D4C2×D4711yescharacteristic, complemented
175C23×C4—941no—
176C23×C4C2×D4711yescharacteristic
177AGL(1,ℤ/8)—948no—
178C2×SD16—474no—
179C2×D8—474no—
180C2×M16—472no—
181#121—21no—
182#121—21no—
183#121C2×D4712yes—
184#121C2×D4712yescomplemented
185C2×C4⋊C4C2×D4711yescharacteristic, complemented
186C2×C22⋊C4—21no—
187#103—474no—
188#102—474no—
189C22⋊C8—472no—
190C22⋊C8—472no—
191C24—21no—
192C24—941no—
193C24C22⋊D4711yescharacteristic
194#41—478no—
195#41—944no—
196#41—944no—
197#41—948no—
198#41—948no—
199#41—944no—
200C2×Q8—472no—
201C2×Q8—944no—
202C2×Q8—941no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—24no—
206C2×D4—21no—
207C2×D4—44no—
208C2×D4—472no—
209C2×D4—944no—
210C2×D4—948no—
211C2×D4—942no—
212C2×D4—942no—
213C2×D4—941no—
214C2×D4C22×D4712yes—
215C22×C4—24no—
216C22×C4—21no—
217C22×C4—948no—
218C22×C4—941no—
219C22×C4—942no—
220C22×C4—942no—
221C22×C4C22⋊D4711yescharacteristic
222C22×C4C22⋊D4711yescharacteristic
223C22×C4C22⋊D4711yescharacteristic
224C22×C4C22×D4711yescharacteristic
225C22×C4C22×D4711yescharacteristic
226C22×C4C22×D4711yescharacteristic
227SD16—948no—
228D8—948no—
229M16—944no—
230C2×C8—474no—
231C4⋊C4—21no—
232C4⋊C4C22×D4712yes—
233C22⋊C4—22no—
234C22⋊C4—22no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—41no—
239C23—42no—
240C23—42no—
241C23—42no—
242C23—944no—
243C23—942no—
244C23—1882no—
245C23—1882no—
246C23C2×C22⋊D4711yescharacteristic
247C23C2×C22⋊D4711yescharacteristic
248C23C2×C22⋊D4711yescharacteristic
249Q8—474no—
250Q8—944no—
251Q8—942no—
252D4—24no—
253D4—44no—
254D4—44no—
255D4—42no—
256D4—474no—
257D4—944no—
258D4—948no—
259D4—948no—
260D4—942no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—42no—
268C2×C4—948no—
269C2×C4—944no—
270C2×C4—942no—
271C2×C4—948no—
272C2×C4D4×D4714yes—
273C2×C4C2×C22⋊D4711yescharacteristic
274C2×C4C2×C22⋊D4711yescharacteristic
275C2×C4C2×C22⋊D4711yescharacteristic
276C2×C4C23×D4711yescharacteristic
277C8—944no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—44no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—84no—
290C22—944no—
291C22—1888no—
292C22—1882no—
293C22—1882no—
294C22#1309399212yes—
295C22#1309405012yescomplemented
296C22C22×C22⋊D4711yescharacteristic
297C4—21no—
298C4—21no—
299C4—42no—
300C4—944no—
301C4#1309399212yes—
302C4C2×D4×D4712yes—
303C2—22no—
304C2—22no—
305C2—41no—
306C2—82no—
307C2—1884no—
308C2C2×#1309399211yescharacteristic
309C2C2×#1309405011yescharacteristic
310C2#1568992111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#121×C47C2
socleC22×C47C22×D4
hypercenterC2×#121D47
hypocenterC47#3006
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#10625350C2semidirect
2. C2×#13094050C2semidirect
3. #15689266C2semidirect
4. #15689261C2semidirect
5. #15689256C2semidirect
6. #15689122C2semidirect
7. #15689087C2semidirect
8. C2×#121×C47C2semidirect
13. C2×#10625350C22semidirect
14. C22×Dic94C22semidirect
15. C22×D188C22semidirect
19. C2×#10625335C22semidirect
20. C2×#10625334C22semidirect
21. C2×#10625329C22semidirect
22. #13093947C22semidirect
23. #13093944C22semidirect
24. C22⋊(C47⋊C8)C22semidirect
25. C22⋊(C47⋊C8)C22semidirect
27. C22×D4×C47C22semidirect
32. #121×C47C22semidirect
33. C2×C4⋊C4×C47C22semidirect
61. #10625350D4semidirect
115. D188C2×D4semidirect
120. Dic94C2×D4semidirect
135. C22×C47AGL(1,ℤ/8)semidirect
158. C2×#121D47semidirect
164. C47#3006semidirect
174. C22×D4C2×D47semidirect
184. #121C2×D47semidirect
185. C2×C4⋊C4C2×D47semidirect
295. C22#13094050semidirect