Finite Group Databasebeta

← #20252736

Subgroups — #20252736

Order 6016.

724 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 145 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#15689959C211yesmaximal, characteristic, complemented
2#15689921C212yesmaximal, complemented
3#15689305C212yesmaximal, complemented
4#15689300C212yesmaximal, complemented
5#15689295C212yesmaximal, complemented
6#15689290C212yesmaximal, complemented
7C2×#13093952C212yesmaximal, complemented
8#15689107C211yesmaximal, characteristic, complemented
9C47×#532C211yesmaximal, characteristic, complemented
10#13094072C2212yes—
11#13094071—22no—
12#13094070—22no—
13#13094069—22no—
14#13094069C2212yes—
15C2×#10625350—22no—
16C2×#10625350C2212yes—
17#41×D47—24no—
18#13094055C2214yescomplemented
19#13094054—22no—
20#13094050C2214yescomplemented
21#13094049—22no—
22#13094044—24no—
23C2×#10625329C2212yescomplemented
24#13093952C2214yescomplemented
25#13093952C2214yescomplemented
26#13093943C2212yescomplemented
27#13093941C2212yescomplemented
28C2×#41×C47C2211yescharacteristic
29C2×#41×C47C2211yescharacteristic, complemented
30C4⋊Q8×C47C2211yescharacteristic, complemented
31#127×C47C2211yescharacteristic, complemented
32#124×C47C2211yescharacteristic, complemented
33#124×C47C2211yescharacteristic, complemented
34#121×C47—22no—
35C4×D4×C47—22no—
36C2×C42×C47C2211yescharacteristic, complemented
37#41×C47—22no—
38#41×C47—22no—
39#41×C47—22no—
40#41×C47—22no—
41C2×Q8×C47C2311yescharacteristic
42C2×Q8×C47C2311yescharacteristic
43C2×D4×C47—22no—
44C2×D4×C47—21no—
45C2×D4×C47D412yes—
46C2×D4×C47C2311yescharacteristic
47C2×D4×C47C2311yescharacteristic
48C22×C4×C47—21no—
49C22×C4×C47—21no—
50C22×C4×C47D412yes—
51C22×C4×C47C2311yescharacteristic
52C2×C22⋊D47—24no—
53C2×C22⋊D47—22no—
54#10625354—24no—
55Q8×D47—24no—
56#10625352—28no—
57#10625352—24no—
58D4×D47—28no—
59D4×D47—24no—
60#10625350—24no—
61#10625350—24no—
62#10625350—22no—
63#10625350—24no—
64#10625350—22no—
65#10625350D414yescomplemented
66#10625350C2314yes—
67C2×D188—22no—
68C2×D188D412yescomplemented
69C2×C4×D47—24no—
70C2×C4×D47—22no—
71C2×Dic94—22no—
72C2×Dic94D412yescomplemented
73C4⋊C4×C47—22no—
74C22⋊C4×C47—22no—
75C22⋊C4×C47—22no—
76C42×C47—21no—
77C42×C47C2311yescharacteristic
78C42×C47C2311yescharacteristic
79#10625337—24no—
80#10625336—24no—
81#10625335—24no—
82#10625334—24no—
83#10625329—22no—
84#10625329C2314yes—
85C2×C47⋊C8—22no—
86C23×C47—21no—
87C23×C47C2×D412yes—
88C23×C47C2×D411yescharacteristic
89C22×D47—24no—
90C22×D47—22no—
91Q8×C47—22no—
92Q8×C47—22no—
93D4×C47—24no—
94D4×C47—22no—
95D4×C47—22no—
96D4×C47—44no—
97D4×C47—42no—
98C2×C4×C47—21no—
99C2×C4×C47—22no—
100C2×C4×C47—22no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—42no—
104C2×C4×C47—41no—
105C2×C4×C47—41no—
106C2×C4×C47C2×D412yes—
107C2×C4×C47C2×D412yes—
108C2×C4×C47C2×D412yes—
109C2×C4×C47C2×D411yescharacteristic
110C2×C4×C47C2411yescharacteristic
111C22⋊D47—28no—
112C22⋊D47—24no—
113C22⋊D47—24no—
114C2×Dic47—24no—
115C2×Dic47—22no—
116D188—24no—
117D188—22no—
118D188C2×D414yes—
119C4×D47—28no—
120C4×D47—24no—
121C4×D47—24no—
122Dic94—24no—
123Dic94—22no—
124Dic94C2×D414yes—
125C47⋊C8—24no—
126C22×C47—22no—
127C22×C47—41no—
128C22×C47—42no—
129C22×C47—42no—
130C22×C47—41no—
131C22×C47#12012yes—
132C22×C47C22×D411yescharacteristic
133C2×D47—24no—
134C2×D47—82no—
135C2×D47—84no—
136C4×C47—22no—
137C4×C47—22no—
138C4×C47—41no—
139C4×C47—41no—
140C4×C47#12011yescharacteristic
141C4×C47#12011yescharacteristic
142C4×C47C22×D412yes—
143Dic47—24no—
144#3018—471nomaximal, Sylow
145C2×C47—21no—
146C2×C47—22no—
147C2×C47—42no—
148C2×C47—81no—
149C2×C47C2×#12011yescharacteristic
150D47—44no—
151#585—471no—
152#575—472no—
153#532D4711yescharacteristic, complemented
154#456—472no—
155#455—472no—
156#454—472no—
157#453—472no—
158C2×#104—472no—
159#413—471no—
160C47#301811yescharacteristic, complemented, Sylow
1612−1+4—472no—
1622−1+4—942no—
163H(5,𝔽2)—472no—
164H(5,𝔽2)—942no—
165H(5,𝔽2)—942no—
166C2×#41—472no—
167C2×#41—944no—
168C2×#41—942no—
169C2×#41C2×D4711yescharacteristic
170C2×#41C2×D4711yescharacteristic, complemented
171#137—474no—
172#137—942no—
173AGL(1,ℤ/8)—474no—
174AGL(1,ℤ/8)—942no—
175#135—944no—
176C2×M16—472no—
177C4⋊Q8C2×D4711yescharacteristic, complemented
178#127C2×D4711yescharacteristic, complemented
179#124C2×D4711yescharacteristic, complemented
180#124C2×D4711yescharacteristic, complemented
181#121—22no—
182C4×D4—22no—
183C2×C42C2×D4711yescharacteristic, complemented
184#104—474no—
185#104—474no—
186#101—472no—
187#100—472no—
188#41—22no—
189#41—22no—
190#41—22no—
191#41—22no—
192#41—474no—
193#41—474no—
194#41—944no—
195#41—944no—
196#41—944no—
197#41—948no—
198#41—944no—
199#41—942no—
200#41—942no—
201#41—944no—
202C2×Q8—472no—
203C2×Q8—942no—
204C2×Q8—944no—
205C2×Q8C22×D4711yescharacteristic
206C2×Q8C22×D4711yescharacteristic
207C2×D4—22no—
208C2×D4—21no—
209C2×D4—472no—
210C2×D4—942no—
211C2×D4—944no—
212C2×D4—948no—
213C2×D4—942no—
214C2×D4—944no—
215C2×D4C22⋊D4712yes—
216C2×D4C22×D4711yescharacteristic
217C2×D4C22×D4711yescharacteristic
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—944no—
221C22×C4—942no—
222C22×C4C22⋊D4712yes—
223C22×C4C22×D4711yescharacteristic
224Q16—944no—
225SD16—944no—
226SD16—944no—
227D8—944no—
228M16—474no—
229M16—942no—
230C2×C8—942no—
231C4⋊C4—22no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C42—21no—
235C42C22×D4711yescharacteristic
236C42C22×D4711yescharacteristic
237C23—21no—
238C23—944no—
239C23—942no—
240C23C2×C22⋊D4712yes—
241C23C2×C22⋊D4711yescharacteristic
242Q8—22no—
243Q8—22no—
244Q8—474no—
245Q8—944no—
246Q8—942no—
247D4—24no—
248D4—22no—
249D4—22no—
250D4—44no—
251D4—42no—
252D4—474no—
253D4—944no—
254D4—948no—
255D4—944no—
256D4—944no—
257D4—942no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—948no—
267C2×C4—944no—
268C2×C4—942no—
269C2×C4—944no—
270C2×C4—944no—
271C2×C4D4×D4712yes—
272C2×C4D4×D4712yes—
273C2×C4C2×C22⋊D4712yes—
274C2×C4C2×C22⋊D4711yescharacteristic
275C2×C4C23×D4711yescharacteristic
276C8—944no—
277C22—22no—
278C22—41no—
279C22—42no—
280C22—42no—
281C22—41no—
282C22—944no—
283C22—3762no—
284C22—3764no—
285C22#1309399212yes—
286C22C22×C22⋊D4711yescharacteristic
287C4—22no—
288C4—22no—
289C4—41no—
290C4—41no—
291C4—944no—
292C4#1309399211yescharacteristic
293C4#1309399211yescharacteristic
294C4C2×D4×D4712yes—
295C2—21no—
296C2—22no—
297C2—42no—
298C2—81no—
299C2—1884no—
300C2C2×#1309399211yescharacteristic
subgroupG/H
centerC4#13093992
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#532C2
socleC2×C47C2×#120
hypercenter#532D47
hypocenterC47#3018
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #15689959C2semidirect
2. #15689921C2semidirect
3. #15689305C2semidirect
4. #15689300C2semidirect
5. #15689295C2semidirect
6. #15689290C2semidirect
7. C2×#13093952C2semidirect
8. #15689107C2semidirect
9. C47×#532C2semidirect
18. #13094055C22semidirect
20. #13094050C22semidirect
23. C2×#10625329C22semidirect
24. #13093952C22semidirect
25. #13093952C22semidirect
26. #13093943C22semidirect
27. #13093941C22semidirect
29. C2×#41×C47C22semidirect
30. C4⋊Q8×C47C22semidirect
31. #127×C47C22semidirect
32. #124×C47C22semidirect
33. #124×C47C22semidirect
36. C2×C42×C47C22semidirect
65. #10625350D4semidirect
68. C2×D188D4semidirect
72. C2×Dic94D4semidirect
153. #532D47semidirect
160. C47#3018semidirect
170. C2×#41C2×D47semidirect
177. C4⋊Q8C2×D47semidirect
178. #127C2×D47semidirect
179. #124C2×D47semidirect
180. #124C2×D47semidirect
183. C2×C42C2×D47semidirect