Finite Group Databasebeta

← #20254171

Subgroups — #20254171

Order 6016.

420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689634C211yesmaximal, characteristic
2C2×#13094003C211yesmaximal, characteristic, complemented
3#15689465C212yesmaximal, complemented
4#15689454C211yesmaximal, characteristic, complemented
5#15689437C211yesmaximal, characteristic, complemented
6#15689364C212yesmaximal, complemented
7#15689352C212yesmaximal, complemented
8#15689287C212yesmaximal, complemented
9#15689281C211yesmaximal, characteristic, complemented
10#15689264C211yesmaximal, characteristic, complemented
11C2×C22⋊C8×C47C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13C22×Dic94C2211yescharacteristic
14C2×Dic188C2212yescomplemented
15C2×#10625325C2212yescomplemented
16#13094007—21no—
17#13094003—21no—
18#13094003—21no—
19#13094003C2211yescharacteristic
20#13094003C2212yes—
21#13094003C2212yes—
22#13094003C2211yescharacteristic
23#13093998C2211yescharacteristic
24#13093998C2211yescharacteristic
25#13093993—21no—
26C4×C22⋊D47—21no—
27C4×C22⋊D47—21no—
28#13093983C2211yescharacteristic
29C2×C4⋊Dic47C2211yescharacteristic
30C2×Dic47⋊C4—21no—
31C2×C22⋊Dic47—21no—
32#13093958C2212yescomplemented
33#13093956C2212yescomplemented
34#13093949C2212yescomplemented
35#13093949C2212yescomplemented
36#13093949C2212yescomplemented
37#13093946C2212yescomplemented
38C23×C4×C47C2211yescharacteristic
39C22×C8×C47C2212yes—
40C22⋊C8×C47C2211yescharacteristic
41C22⋊C8×C47C2211yescharacteristic
42C22⋊C8×C47C2212yes—
43C24×C47D411yescharacteristic
44C22×C4×C47—42no—
45C22×C4×C47D411yescharacteristic
46C22×C4×C47D411yescharacteristic
47C22×C4×C47D411yescharacteristic
48C22×C4×C47C2311yescharacteristic
49C22×C4×C47C2311yescharacteristic
50C22×C4×C47C2311yescharacteristic
51C2×C22⋊D47—21no—
52C2×C22⋊D47—21no—
53C2×C22⋊D47—21no—
54C22×Dic47—21no—
55C22×Dic47—21no—
56#10625350—42no—
57C2×D188C2311yescharacteristic
58C2×C4×D47—21no—
59C2×Dic94—21no—
60C2×Dic94—42no—
61C2×Dic94C2312yes—
62C2×Dic94C2311yescharacteristic
63C2×C8×C47—42no—
64C2×C8×C47C2312yes—
65C2×C8×C47C2312yes—
66C22⋊Dic47—22no—
67C22⋊Dic47—22no—
68C22⋊Dic47—21no—
69C22⋊Dic47—21no—
70C22⋊Dic47—21no—
71(C2×D47)⋊C4—21no—
72(C2×D47)⋊C4—21no—
73C4⋊Dic47—21no—
74C4⋊Dic47C2312yes—
75C4⋊Dic47C2311yescharacteristic
76C4⋊Dic47C2311yescharacteristic
77Dic47⋊C4—22no—
78Dic47⋊C4—22no—
79Dic47⋊C4—21no—
80Dic47⋊C4—21no—
81C4×Dic47—21no—
82Dic188—42no—
83#10625325—42no—
84C23×C47—22no—
85C23×C47—22no—
86C23×C47—41no—
87C23×C47C2×D411yescharacteristic
88C23×C47C2×D411yescharacteristic
89C23×C47C2×D411yescharacteristic
90C22×D47—21no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47—41no—
95C2×C4×C47—41no—
96C2×C4×C47—41no—
97C2×C4×C47C2×D411yescharacteristic
98C2×C4×C47C2×D411yescharacteristic
99C2×C4×C47C2×D411yescharacteristic
100C2×C4×C47C2411yescharacteristic
101C22⋊D47—42no—
102C22⋊D47—42no—
103C22⋊D47—42no—
104C2×Dic47—21no—
105C2×Dic47—21no—
106C2×Dic47—22no—
107C2×Dic47—22no—
108C2×Dic47—21no—
109C2×Dic47—42no—
110C2×Dic47—42no—
111D188—22no—
112C4×D47—42no—
113Dic94—22no—
114Dic94—22no—
115Dic94—22no—
116Dic94—42no—
117C8×C47—22no—
118C8×C47—22no—
119C22×C47—21no—
120C22×C47—21no—
121C22×C47—21no—
122C22×C47—21no—
123C22×C47—21no—
124C22×C47—21no—
125C22×C47—21no—
126C22×C47—44no—
127C22×C47#13512yes—
128C22×C47#13712yes—
129C22×C47C22×D411yescharacteristic
130C2×D47—41no—
131C2×D47—41no—
132C2×D47—41no—
133C4×C47—21no—
134C4×C47—21no—
135C4×C47—21no—
136C4×C47H(5,𝔽2)12yes—
137Dic47—42no—
138Dic47—41no—
139Dic47—42no—
140Dic47—41no—
141Dic47—41no—
142#3190—471nomaximal, Sylow
143C2×C47—22no—
144C2×C47—22no—
145C2×C47—41no—
146C2×C47#53411yescharacteristic
147C2×C47C2×#13511yescharacteristic
148C2×C47C2×#13711yescharacteristic
149D47—81no—
150#525—471no—
151C2×C22⋊Q8—471no—
152#485—472no—
153#483—471no—
154#480—471no—
155#467—472no—
156#465—472no—
157#452—472no—
158#451—471no—
159#448—471no—
160C2×C22⋊C8D4711yescharacteristic, complemented
161C47#319011yescharacteristic, complemented, Sylow
162C2×#41—471no—
163C22×Q8—471no—
164C23×C4C2×D4711yescharacteristic
165C2×Q16—472no—
166C2×SD16—472no—
167C22×C8C2×D4712yes—
168#123—941no—
169C22⋊Q8—472no—
170C22⋊Q8—472no—
171C22⋊Q8—471no—
172C22⋊Q8—471no—
173C22⋊Q8—941no—
174C22⋊Q8—941no—
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#103—472no—
189#102—472no—
190C22⋊C8C2×D4711yescharacteristic
191C22⋊C8C2×D4711yescharacteristic
192C22⋊C8C2×D4712yes—
193C24D18811yescharacteristic
194#41—1882no—
195C2×Q8—472no—
196C2×Q8—471no—
197C2×Q8—941no—
198C2×Q8—1882no—
199C2×D4—471no—
200C2×D4—941no—
201C2×D4—941no—
202C2×D4—941no—
203C22×C4—42no—
204C22×C4—941no—
205C22×C4—941no—
206C22×C4—941no—
207C22×C4D18811yescharacteristic
208C22×C4D18811yescharacteristic
209C22×C4D18811yescharacteristic
210C22×C4C22×D4711yescharacteristic
211C22×C4C22×D4711yescharacteristic
212C22×C4C22×D4711yescharacteristic
213Q16—1882no—
214SD16—1882no—
215C2×C8—42no—
216C2×C8C22×D4712yes—
217C2×C8C22×D4712yes—
218C4⋊C4—472no—
219C4⋊C4—471no—
220C4⋊C4—471no—
221C4⋊C4—942no—
222C4⋊C4—942no—
223C4⋊C4—941no—
224C4⋊C4—941no—
225C4⋊C4—941no—
226C22⋊C4—942no—
227C22⋊C4—942no—
228C22⋊C4—941no—
229C22⋊C4—941no—
230C22⋊C4—941no—
231C22⋊C4—941no—
232C22⋊C4—941no—
233C42—941no—
234C23—22no—
235C23—22no—
236C23—41no—
237C23—941no—
238C23C2×D18811yescharacteristic
239C23C2×D18811yescharacteristic
240C23C2×D18811yescharacteristic
241Q8—942no—
242Q8—942no—
243Q8—942no—
244Q8—1882no—
245D4—942no—
246D4—1882no—
247D4—1882no—
248D4—1882no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—941no—
256C2×C4—941no—
257C2×C4—942no—
258C2×C4—941no—
259C2×C4—942no—
260C2×C4—1882no—
261C2×C4—1882no—
262C2×C4—1882no—
263C2×C4C2×D18811yescharacteristic
264C2×C4C2×D18811yescharacteristic
265C2×C4C2×D18811yescharacteristic
266C2×C4C23×D4711yescharacteristic
267C8—22no—
268C8—22no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—44no—
277C22—1881no—
278C22—1881no—
279C22—1881no—
280C22#1309404612yes—
281C22#1309405712yes—
282C22C22×D18811yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—1882no—
287C4—1881no—
288C4—1881no—
289C4—1881no—
290C4—1882no—
291C4#1309406912yes—
292C2—22no—
293C2—22no—
294C2—41no—
295C2—3761no—
296C2#1568968511yescharacteristic
297C2C2×#1309404611yescharacteristic
298C2C2×#1309405711yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×C22⋊C8×C47C2
socleC22×C47C22×D4
hypercenterC2×C22⋊C8D47
hypocenterC47#3190
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#13094003C2semidirect
3. #15689465C2semidirect
4. #15689454C2semidirect
5. #15689437C2semidirect
6. #15689364C2semidirect
7. #15689352C2semidirect
8. #15689287C2semidirect
9. #15689281C2semidirect
10. #15689264C2semidirect
11. C2×C22⋊C8×C47C2semidirect
14. C2×Dic188C22semidirect
15. C2×#10625325C22semidirect
32. #13093958C22semidirect
33. #13093956C22semidirect
34. #13093949C22semidirect
35. #13093949C22semidirect
36. #13093949C22semidirect
37. #13093946C22semidirect
160. C2×C22⋊C8D47semidirect
161. C47#3190semidirect