Finite Group Databasebeta

← #20254221

Subgroups — #20254221

Order 6016.

414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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#15689636C211yesmaximal, characteristic
2C2×#13094000C211yesmaximal, characteristic, complemented
3#15689462C212yesmaximal, complemented
4#15689456C211yesmaximal, characteristic, complemented
5#15689442C211yesmaximal, characteristic, complemented
6#15689378C212yesmaximal, complemented
7#15689372C212yesmaximal, complemented
8#15689284C212yesmaximal, complemented
9#15689262C211yesmaximal, characteristic, complemented
10#15689085C211yesmaximal, characteristic, complemented
11C47×#451C211yesmaximal, characteristic, complemented
12C2×#10625354C2211yescharacteristic
13C22×C4×D47C2211yescharacteristic
14C2×#10625336C2212yescomplemented
15C2×#10625324C2212yes—
16#13094009—21no—
17#13094000—21no—
18#13094000—21no—
19#13094000C2212yes—
20#13094000C2212yes—
21#13094000C2211yescharacteristic
22#13093999C2211yescharacteristic
23#13093998C2211yescharacteristic
24#13093994—21no—
25#13093986—21no—
26(C22⋊D47)⋊C4—21no—
27#13093982C2211yescharacteristic
28C2×C4⋊Dic47C2211yescharacteristic
29C2×Dic47⋊C4—21no—
30C2×(C2×D47)⋊C4—21no—
31#13093957C2212yescomplemented
32#13093956C2212yescomplemented
33#13093948C2212yescomplemented
34#13093948C2212yescomplemented
35#13093946C2212yescomplemented
36C22⋊(C47⋊C8)C2211yescharacteristic
37(C2×D47)⋊C8C2212yes—
38C22×Q8×C47C2211yescharacteristic
39C2×Q16×C47C2212yescomplemented
40C22⋊Q8×C47C2211yescharacteristic
41#103×C47C2212yescomplemented
42C22⋊C8×C47C2211yescharacteristic
43C23×D47D411yescharacteristic
44C2×Q8×C47—21no—
45C2×Q8×C47—42no—
46C2×Q8×C47C2312yes—
47C2×Q8×C47C2311yescharacteristic
48C22×C4×C47—21no—
49C22×C4×C47C2311yescharacteristic
50C2×C22⋊D47—21no—
51C22×Dic47—21no—
52C22×Dic47D411yescharacteristic
53#10625354—42no—
54C2×D188—21no—
55C2×D188—21no—
56C2×D188C2311yescharacteristic
57C2×C4×D47—21no—
58C2×C4×D47—42no—
59C2×C4×D47D411yescharacteristic
60C2×C4×D47D411yescharacteristic
61C2×C4×D47C2311yescharacteristic
62C2×C4×D47C2311yescharacteristic
63Q16×C47—42no—
64C2×C8×C47C2312yes—
65C4⋊C4×C47—21no—
66C4⋊C4×C47C2311yescharacteristic
67C22⋊C4×C47—21no—
68#10625336—42no—
69(C2×D47)⋊C4—22no—
70(C2×D47)⋊C4—22no—
71(C2×D47)⋊C4—21no—
72(C2×D47)⋊C4—21no—
73(C2×D47)⋊C4—21no—
74(C2×D47)⋊C4—21no—
75C4⋊Dic47—21no—
76C4⋊Dic47C2312yes—
77C4⋊Dic47C2311yescharacteristic
78Dic47⋊C4—22no—
79Dic47⋊C4—22no—
80Dic47⋊C4—21no—
81C4×Dic47—21no—
82C2×C47⋊C8C2312yes—
83#10625324—42no—
84C23×C47C2×D411yescharacteristic
85C22×D47—22no—
86C22×D47—21no—
87C22×D47—41no—
88C22×D47—41no—
89C22×D47C2×D411yescharacteristic
90C22×D47C2×D411yescharacteristic
91Q8×C47—22no—
92Q8×C47—22no—
93Q8×C47—22no—
94Q8×C47—42no—
95C2×C4×C47—22no—
96C2×C4×C47—21no—
97C2×C4×C47—22no—
98C2×C4×C47—21no—
99C2×C4×C47—42no—
100C2×C4×C47C2×D411yescharacteristic
101C2×C4×C47C2411yescharacteristic
102C22⋊D47—42no—
103C2×Dic47—21no—
104C2×Dic47—22no—
105C2×Dic47—41no—
106C2×Dic47—42no—
107C2×Dic47C2×D411yescharacteristic
108C2×Dic47C2×D411yescharacteristic
109D188—22no—
110D188—42no—
111D188—42no—
112C4×D47—22no—
113C4×D47—22no—
114C4×D47—41no—
115C4×D47—41no—
116C4×D47—42no—
117C8×C47—22no—
118C47⋊C8—22no—
119C22×C47—21no—
120C22×C47—21no—
121C22×C47#13712yes—
122C22×C47C22×D411yescharacteristic
123C2×D47—21no—
124C2×D47—21no—
125C2×D47—21no—
126C2×D47—21no—
127C2×D47—21no—
128C2×D47—21no—
129C2×D47—44no—
130C2×D47—41no—
131C2×D47—41no—
132C2×D47—41no—
133C4×C47—21no—
134C4×C47—41no—
135C4×C47—42no—
136C4×C47—41no—
137C4×C47H(5,𝔽2)12yes—
138Dic47—21no—
139Dic47—21no—
140Dic47—41no—
141Dic47—42no—
142#3196—471nomaximal, Sylow
143C2×C47—22no—
144C2×C47#53411yescharacteristic
145C2×C47C2×#13711yescharacteristic
146C2×C47#57511yescharacteristic
147D47—41no—
148D47—41no—
149D47—81no—
150#525—471no—
151C2×C22⋊Q8—471no—
152#485—472no—
153#484—471no—
154#481—471no—
155#470—472no—
156#468—472no—
157#452—472no—
158#451D4711yescharacteristic, complemented
159#448—471no—
160#407—471no—
161C47#319611yescharacteristic, complemented, Sylow
162C2×#41—471no—
163C22×Q8C2×D4711yescharacteristic
164C23×C4—471no—
165C2×Q16C2×D4712yescomplemented
166C2×SD16—472no—
167C2×M16—472no—
168#123—941no—
169C22⋊Q8—472no—
170C22⋊Q8—472no—
171C22⋊Q8—471no—
172C22⋊Q8—941no—
173C22⋊Q8—941no—
174C22⋊Q8C2×D4711yescharacteristic
175#121—471no—
176#121—471no—
177#120—941no—
178C4×D4—941no—
179C4×D4—941no—
180#117—471no—
181C2×C4⋊C4—471no—
182C2×C4⋊C4—941no—
183C2×C22⋊C4—941no—
184#107—472no—
185#106—472no—
186#103—472no—
187#103—472no—
188#103C2×D4712yescomplemented
189#102—472no—
190C22⋊C8—471no—
191C22⋊C8—472no—
192C22⋊C8C2×D4711yescharacteristic
193C24—471no—
194#41—1882no—
195C2×Q8—21no—
196C2×Q8—42no—
197C2×Q8C22×D4711yescharacteristic
198C2×Q8C22×D4712yes—
199C2×D4—471no—
200C2×D4—941no—
201C2×D4—941no—
202C2×D4—941no—
203C22×C4—21no—
204C22×C4—471no—
205C22×C4—471no—
206C22×C4—471no—
207C22×C4—471no—
208C22×C4—471no—
209C22×C4—941no—
210C22×C4—941no—
211C22×C4—1882no—
212C22×C4C22×D4711yescharacteristic
213Q16—42no—
214SD16—1882no—
215M16—1882no—
216C2×C8—472no—
217C2×C8C22×D4712yes—
218C4⋊C4—21no—
219C4⋊C4—472no—
220C4⋊C4—471no—
221C4⋊C4—942no—
222C4⋊C4—942no—
223C4⋊C4—941no—
224C4⋊C4—941no—
225C4⋊C4C22×D4711yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—941no—
228C22⋊C4—942no—
229C22⋊C4—942no—
230C22⋊C4—941no—
231C22⋊C4—941no—
232C22⋊C4—941no—
233C42—941no—
234C23—471no—
235C23—471no—
236C23—942no—
237C23—941no—
238C23—1881no—
239C23—1881no—
240C23D4×D4711yescharacteristic
241Q8—22no—
242Q8—22no—
243Q8—22no—
244Q8—42no—
245D4—942no—
246D4—1882no—
247D4—1882no—
248D4—1882no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—471no—
255C2×C4—471no—
256C2×C4—942no—
257C2×C4—942no—
258C2×C4—941no—
259C2×C4—942no—
260C2×C4—1881no—
261C2×C4—1881no—
262C2×C4—1882no—
263C2×C4—1881no—
264C2×C4—1882no—
265C2×C4D4×D4711yescharacteristic
266C2×C4C23×D4711yescharacteristic
267C8—22no—
268C8—942no—
269C22—21no—
270C22—21no—
271C22—941no—
272C22—941no—
273C22—941no—
274C22—941no—
275C22—941no—
276C22—941no—
277C22—1884no—
278C22—1881no—
279C22—1881no—
280C22—1881no—
281C22#1309405612yes—
282C22C2×D4×D4711yescharacteristic
283C4—21no—
284C4—41no—
285C4—42no—
286C4—41no—
287C4—941no—
288C4—941no—
289C4—1881no—
290C4—1882no—
291C4#1309406912yes—
292C2—22no—
293C2—3761no—
294C2—1881no—
295C2—1881no—
296C2#1568968311yescharacteristic
297C2C2×#1309405611yescharacteristic
298C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#451C2
socleC22×C47C22×D4
hypercenter#451D47
hypocenterC47#3196
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. C2×#13094000C2semidirect
3. #15689462C2semidirect
4. #15689456C2semidirect
5. #15689442C2semidirect
6. #15689378C2semidirect
7. #15689372C2semidirect
8. #15689284C2semidirect
9. #15689262C2semidirect
10. #15689085C2semidirect
11. C47×#451C2semidirect
14. C2×#10625336C22semidirect
31. #13093957C22semidirect
32. #13093956C22semidirect
33. #13093948C22semidirect
34. #13093948C22semidirect
35. #13093946C22semidirect
39. C2×Q16×C47C22semidirect
41. #103×C47C22semidirect
158. #451D47semidirect
161. C47#3196semidirect
165. C2×Q16C2×D47semidirect
188. #103C2×D47semidirect