Finite Group Databasebeta

← #20252646

Subgroups — #20252646

Order 6016.

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

normal subgroups only

This group has 754 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
2C2×#13094055C212yesmaximal, complemented
3#15689283C214yesmaximal, complemented
4#15689278C212yesmaximal, complemented
5#15689273C212yesmaximal, complemented
6#15689122C212yesmaximal, complemented
7#15689087C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C47C211yesmaximal, characteristic, complemented
9C2×#10625350—21no—
10C2×#10625350—21no—
11C2×#10625350—28no—
12C2×#10625350C2212yes—
13C2×#10625350C2212yes—
14C22×Dic94C2211yescharacteristic
15C22×D188C2211yescharacteristic
16C22×C22⋊D47—21no—
17C22×C4×D47—21no—
18#13094055—28no—
19C2×#10625337C2214yescomplemented
20C2×#10625336C2214yescomplemented
21C2×#10625329C2212yescomplemented
22#13093947C2214yescomplemented
23#13093944C2214yescomplemented
24C22⋊(C47⋊C8)C2212yes—
25C22⋊(C47⋊C8)C2212yescomplemented
26C22×Q8×C47C2211yescharacteristic, complemented
27C23×C4×C47C2211yescharacteristic
28C22⋊Q8×C47—21no—
29C22⋊Q8×C47—21no—
30C22⋊Q8×C47C2212yes—
31C22⋊Q8×C47C2212yescomplemented
32C2×C4⋊C4×C47—21no—
33C2×C4⋊C4×C47C2211yescharacteristic, complemented
34C2×C22⋊C4×C47—21no—
35C24×C47D411yescharacteristic
36C23×D47—21no—
37C2×Q8×C47—21no—
38C2×Q8×C47—24no—
39C2×Q8×C47C2312yes—
40C22×C4×C47—24no—
41C22×C4×C47—21no—
42C22×C4×C47—21no—
43C22×C4×C47D411yescharacteristic
44C22×C4×C47D411yescharacteristic
45C22×C4×C47D411yescharacteristic
46C22×C4×C47C2311yescharacteristic
47C22×C4×C47C2311yescharacteristic
48C22×C4×C47C2311yescharacteristic
49C2×C22⋊D47—28no—
50C2×C22⋊D47—22no—
51C2×C22⋊D47—22no—
52C22×Dic47—21no—
53#10625350—28no—
54#10625350—28no—
55#10625350—24no—
56#10625350—24no—
57#10625350—24no—
58#10625350D418yes—
59C2×D188—21no—
60C2×D188—24no—
61C2×D188C2312yes—
62C2×C4×D47—28no—
63C2×C4×D47—22no—
64C2×C4×D47—22no—
65C2×Dic94—21no—
66C2×Dic94—24no—
67C2×Dic94C2312yes—
68C4⋊C4×C47—22no—
69C4⋊C4×C47—22no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47C2312yes—
72C22⋊C4×C47—22no—
73C22⋊C4×C47—22no—
74#10625337—28no—
75#10625336—28no—
76#10625329—24no—
77C2×C47⋊C8C2314yes—
78C23×C47—22no—
79C23×C47—22no—
80C23×C47—41no—
81C23×C47C2×D411yescharacteristic
82C23×C47C2×D411yescharacteristic
83C23×C47C2×D411yescharacteristic
84C22×D47—24no—
85C22×D47—22no—
86C22×D47—42no—
87C22×D47—42no—
88Q8×C47—24no—
89Q8×C47—42no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47—22no—
95C2×C4×C47—22no—
96C2×C4×C47—22no—
97C2×C4×C47—42no—
98C2×C4×C47—42no—
99C2×C4×C47C2×D414yes—
100C2×C4×C47C2×D411yescharacteristic
101C2×C4×C47C2×D411yescharacteristic
102C2×C4×C47C2×D411yescharacteristic
103C2×C4×C47C2411yescharacteristic
104C22⋊D47—28no—
105C22⋊D47—28no—
106C2×Dic47—24no—
107C2×Dic47—22no—
108D188—24no—
109D188—22no—
110D188C2×D414yes—
111C4×D47—28no—
112C4×D47—28no—
113Dic94—24no—
114Dic94—22no—
115Dic94C2×D414yes—
116C47⋊C8—24no—
117C22×C47—21no—
118C22×C47—21no—
119C22×C47—21no—
120C22×C47—21no—
121C22×C47—21no—
122C22×C47—21no—
123C22×C47—21no—
124C22×C47—44no—
125C22×C47#12012yes—
126C22×C47#13712yescomplemented
127C22×C47C22×D411yescharacteristic
128C2×D47—24no—
129C2×D47—48no—
130C2×D47—42no—
131C2×D47—42no—
132C4×C47—21no—
133C4×C47—21no—
134C4×C47—42no—
135C4×C47—42no—
136C4×C47#12012yes—
137C4×C47C22×D412yes—
138Dic47—24no—
139#3007—471nomaximal, Sylow
140C2×C47—22no—
141C2×C47—22no—
142C2×C47—41no—
143C2×C47C2×#12011yescharacteristic
144C2×C47C2×#13711yescharacteristic
145C2×C47#57511yescharacteristic
146D47—44no—
147C22×#41—471no—
148C2×#137—472no—
149C2×C22⋊Q8D4711yescharacteristic, complemented
150#452—474no—
151#451—472no—
152#450—472no—
153#417—472no—
154#407—471no—
155C47#300711yescharacteristic, complemented, Sylow
156C2×#41—472no—
157C2×#41—472no—
158C2×#41—948no—
159C2×#41—941no—
160C2×#41—941no—
161C22×Q8—471no—
162C22×Q8C2×D4711yescharacteristic, complemented
163C22×D4—471no—
164C22×D4—941no—
165C23×C4—941no—
166C23×C4C2×D4711yescharacteristic
167#137—948no—
168C2×Q16—474no—
169C2×SD16—474no—
170C2×M16—472no—
171C22⋊Q8—21no—
172C22⋊Q8—21no—
173C22⋊Q8C2×D4712yes—
174C22⋊Q8C2×D4712yescomplemented
175C2×C4⋊C4—21no—
176C2×C4⋊C4C2×D4711yescharacteristic, complemented
177C2×C22⋊C4—21no—
178#103—474no—
179#102—474no—
180C22⋊C8—472no—
181C22⋊C8—472no—
182C24—941no—
183C24C22⋊D4711yescharacteristic
184#41—478no—
185#41—944no—
186#41—944no—
187#41—948no—
188#41—948no—
189#41—944no—
190C2×Q8—21no—
191C2×Q8—24no—
192C2×Q8—472no—
193C2×Q8—944no—
194C2×Q8—941no—
195C2×Q8C22×D4712yes—
196C2×D4—472no—
197C2×D4—944no—
198C2×D4—948no—
199C2×D4—942no—
200C2×D4—942no—
201C2×D4—941no—
202C22×C4—24no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—948no—
206C22×C4—941no—
207C22×C4—942no—
208C22×C4—942no—
209C22×C4C22⋊D4711yescharacteristic
210C22×C4C22⋊D4711yescharacteristic
211C22×C4C22⋊D4711yescharacteristic
212C22×C4C22×D4711yescharacteristic
213C22×C4C22×D4711yescharacteristic
214C22×C4C22×D4711yescharacteristic
215Q16—948no—
216SD16—948no—
217M16—944no—
218C2×C8—474no—
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—21no—
222C4⋊C4C22×D4712yes—
223C22⋊C4—22no—
224C22⋊C4—22no—
225C23—22no—
226C23—22no—
227C23—41no—
228C23—944no—
229C23—942no—
230C23—1882no—
231C23—1882no—
232C23C2×C22⋊D4711yescharacteristic
233C23C2×C22⋊D4711yescharacteristic
234C23C2×C22⋊D4711yescharacteristic
235Q8—24no—
236Q8—42no—
237Q8—474no—
238Q8—944no—
239Q8—942no—
240D4—474no—
241D4—944no—
242D4—948no—
243D4—948no—
244D4—942no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—948no—
255C2×C4—944no—
256C2×C4—942no—
257C2×C4—948no—
258C2×C4D4×D4714yes—
259C2×C4C2×C22⋊D4711yescharacteristic
260C2×C4C2×C22⋊D4711yescharacteristic
261C2×C4C2×C22⋊D4711yescharacteristic
262C2×C4C23×D4711yescharacteristic
263C8—944no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—44no—
272C22—944no—
273C22—1888no—
274C22—1882no—
275C22—1882no—
276C22#1309399212yes—
277C22#1309405512yescomplemented
278C22C22×C22⋊D4711yescharacteristic
279C4—21no—
280C4—21no—
281C4—42no—
282C4—42no—
283C4—944no—
284C4#1309399212yes—
285C4C2×D4×D4712yes—
286C2—22no—
287C2—22no—
288C2—41no—
289C2—1884no—
290C2C2×#1309399211yescharacteristic
291C2C2×#1309405511yescharacteristic
292C2#1568992111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×C22⋊Q8×C47C2
socleC22×C47C22×D4
hypercenterC2×C22⋊Q8D47
hypocenterC47#3007
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#13094055C2semidirect
3. #15689283C2semidirect
4. #15689278C2semidirect
5. #15689273C2semidirect
6. #15689122C2semidirect
7. #15689087C2semidirect
8. C2×C22⋊Q8×C47C2semidirect
19. C2×#10625337C22semidirect
20. C2×#10625336C22semidirect
21. C2×#10625329C22semidirect
22. #13093947C22semidirect
23. #13093944C22semidirect
25. C22⋊(C47⋊C8)C22semidirect
26. C22×Q8×C47C22semidirect
31. C22⋊Q8×C47C22semidirect
33. C2×C4⋊C4×C47C22semidirect
126. C22×C47#137semidirect
149. C2×C22⋊Q8D47semidirect
155. C47#3007semidirect
162. C22×Q8C2×D47semidirect
174. C22⋊Q8C2×D47semidirect
176. C2×C4⋊C4C2×D47semidirect
277. C22#13094055semidirect