Finite Group Databasebeta

← #20254204

Subgroups — #20254204

Order 6016.

466 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 121 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, complemented
2C2×#13093998C211yesmaximal, characteristic, complemented
3#15689454C211yesmaximal, characteristic, complemented
4#15689448C212yesmaximal, complemented
5#15689437C211yesmaximal, characteristic, complemented
6#15689376C212yesmaximal, complemented
7#15689369C212yesmaximal, complemented
8#15689276C211yesmaximal, characteristic, complemented
9#15689270C212yesmaximal, complemented
10#15689259C211yesmaximal, characteristic, complemented
11C47×#407C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic, complemented
13C22×D188C2211yescharacteristic
14C22×C22⋊D47—21no—
15C2×#10625325C2212yescomplemented
16C2×D376C2212yescomplemented
17#13094007—21no—
18#13094003C2211yescharacteristic
19#13094003C2211yescharacteristic, complemented
20#13093998—21no—
21#13093998—21no—
22#13093998C2211yescharacteristic
23#13093998C2212yes—
24#13093998C2212yes—
25#13093998C2211yescharacteristic, complemented
26#13093993—21no—
27C4×C22⋊D47—21no—
28C4×C22⋊D47—21no—
29#13093983C2211yescharacteristic, complemented
30C2×C4⋊Dic47C2211yescharacteristic
31C2×(C2×D47)⋊C4—21no—
32#13093958C2212yescomplemented
33#13093956C2212yescomplemented
34#13093949C2212yescomplemented
35#13093946C2212yescomplemented
36#13093946C2212yescomplemented
37#13093946C2212yescomplemented
38C23×C4×C47C2211yescharacteristic
39C2×M16×C47C2212yescomplemented
40C22⋊C8×C47C2211yescharacteristic
41C22⋊C8×C47C2211yescharacteristic
42C22⋊C8×C47C2212yescomplemented
43C24×C47D411yescharacteristic
44C23×D47—21no—
45C22×C4×C47—42no—
46C22×C4×C47D411yescharacteristic
47C22×C4×C47D411yescharacteristic
48C22×C4×C47D411yescharacteristic
49C22×C4×C47C2311yescharacteristic
50C22×C4×C47C2311yescharacteristic
51C22×C4×C47C2311yescharacteristic
52C2×C22⋊D47—21no—
53C2×C22⋊D47—21no—
54C2×C22⋊D47—21no—
55C2×C22⋊D47—22no—
56C2×C22⋊D47—22no—
57C2×C22⋊D47—44no—
58C22×Dic47—21no—
59#10625350—42no—
60C2×D188—21no—
61C2×D188—42no—
62C2×D188C2312yes—
63C2×D188C2311yescharacteristic
64C2×C4×D47—21no—
65C2×Dic94C2311yescharacteristic
66M16×C47—42no—
67C2×C8×C47C2312yes—
68C2×C8×C47C2312yes—
69C22⋊Dic47—21no—
70C22⋊Dic47—21no—
71C22⋊Dic47—21no—
72(C2×D47)⋊C4—22no—
73(C2×D47)⋊C4—22no—
74(C2×D47)⋊C4—21no—
75(C2×D47)⋊C4—21no—
76C4⋊Dic47—21no—
77C4⋊Dic47C2311yescharacteristic
78C4⋊Dic47C2311yescharacteristic
79C4⋊Dic47C2312yes—
80Dic47⋊C4—21no—
81Dic47⋊C4—21no—
82C4×Dic47—21no—
83D376—42no—
84#10625325—42no—
85C23×C47—22no—
86C23×C47—41no—
87C23×C47—41no—
88C23×C47C2×D411yescharacteristic
89C23×C47C2×D411yescharacteristic
90C23×C47C2×D411yescharacteristic
91C22×D47—21no—
92C22×D47—22no—
93C22×D47—42no—
94C22×D47—42no—
95C22×D47—42no—
96C2×C4×C47—22no—
97C2×C4×C47—22no—
98C2×C4×C47—22no—
99C2×C4×C47—41no—
100C2×C4×C47—41no—
101C2×C4×C47—41no—
102C2×C4×C47C2×D411yescharacteristic
103C2×C4×C47C2×D411yescharacteristic
104C2×C4×C47C2×D411yescharacteristic
105C2×C4×C47C2411yescharacteristic
106C22⋊D47—42no—
107C22⋊D47—42no—
108C22⋊D47—44no—
109C22⋊D47—44no—
110C22⋊D47—42no—
111C2×Dic47—21no—
112C2×Dic47—21no—
113C2×Dic47—21no—
114C2×Dic47—22no—
115C2×Dic47—42no—
116D188—22no—
117D188—22no—
118D188—22no—
119D188—42no—
120C4×D47—42no—
121Dic94—22no—
122C8×C47—22no—
123C8×C47—22no—
124C22×C47—21no—
125C22×C47—21no—
126C22×C47—21no—
127C22×C47—21no—
128C22×C47—21no—
129C22×C47—21no—
130C22×C47—21no—
131C22×C47—21no—
132C22×C47—44no—
133C22×C47AGL(1,ℤ/8)12yes—
134C22×C47C22×D411yescharacteristic
135C2×D47—41no—
136C2×D47—42no—
137C2×D47—42no—
138C2×D47—41no—
139C2×D47—41no—
140C2×D47—42no—
141C2×D47—84no—
142C4×C47—21no—
143C4×C47—21no—
144C4×C47—21no—
145C4×C47H(5,𝔽2)12yes—
146Dic47—41no—
147Dic47—42no—
148Dic47—41no—
149Dic47—41no—
150#3194—471nomaximal, Sylow
151C2×C47—22no—
152C2×C47—41no—
153C2×C47—41no—
154C2×C47#53411yescharacteristic
155C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
156C2×C47#57511yescharacteristic
157D47—81no—
158D47—82no—
159#525—471no—
160C2×#121—471no—
161#483—471no—
162#482—472no—
163#480—471no—
164#469—472no—
165#468—472no—
166#450—471no—
167#449—472no—
168#447—471no—
169#407D4711yescharacteristic, complemented
170C47#319411yescharacteristic, complemented, Sylow
171C2×#41—471no—
172C22×D4—471no—
173C22×D4—941no—
174C23×C4C2×D4711yescharacteristic
175C2×SD16—472no—
176C2×D8—472no—
177C2×M16C2×D4712yescomplemented
178#123—941no—
179C22⋊Q8—471no—
180C22⋊Q8—471no—
181#121—472no—
182#121—472no—
183#121—471no—
184#121—471no—
185#121—941no—
186#121—941no—
187#120—941no—
188C4×D4—941no—
189C4×D4—941no—
190#117—471no—
191C2×C4⋊C4—471no—
192C2×C22⋊C4—941no—
193#107—472no—
194#106—472no—
195#103—472no—
196#102—472no—
197#102—472no—
198#102—472no—
199C22⋊C8C2×D4711yescharacteristic
200C22⋊C8C2×D4711yescharacteristic
201C22⋊C8C2×D4712yescomplemented
202C24—941no—
203C24D18811yescharacteristic
204#41—1882no—
205C2×Q8—471no—
206C2×D4—471no—
207C2×D4—472no—
208C2×D4—941no—
209C2×D4—941no—
210C2×D4—941no—
211C2×D4—942no—
212C2×D4—942no—
213C2×D4—941no—
214C2×D4—1882no—
215C2×D4—1884no—
216C22×C4—42no—
217C22×C4—941no—
218C22×C4—941no—
219C22×C4D18811yescharacteristic
220C22×C4D18811yescharacteristic
221C22×C4D18811yescharacteristic
222C22×C4C22×D4711yescharacteristic
223C22×C4C22×D4711yescharacteristic
224C22×C4C22×D4711yescharacteristic
225SD16—1882no—
226D8—1882no—
227M16—42no—
228C2×C8C22×D4712yes—
229C2×C8C22×D4712yes—
230C4⋊C4—471no—
231C4⋊C4—471no—
232C4⋊C4—472no—
233C4⋊C4—941no—
234C4⋊C4—941no—
235C4⋊C4—941no—
236C22⋊C4—941no—
237C22⋊C4—941no—
238C22⋊C4—941no—
239C22⋊C4—942no—
240C22⋊C4—942no—
241C22⋊C4—941no—
242C22⋊C4—941no—
243C42—941no—
244C23—22no—
245C23—41no—
246C23—41no—
247C23—941no—
248C23—942no—
249C23—1882no—
250C23—1882no—
251C23—1882no—
252C23C2×D18811yescharacteristic
253C23C2×D18811yescharacteristic
254C23C2×D18811yescharacteristic
255Q8—942no—
256D4—942no—
257D4—942no—
258D4—942no—
259D4—1882no—
260D4—1882no—
261D4—1884no—
262D4—1884no—
263D4—1882no—
264D4—1882no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—941no—
272C2×C4—941no—
273C2×C4—942no—
274C2×C4—941no—
275C2×C4—1882no—
276C2×C4—1882no—
277C2×C4C2×D18811yescharacteristic
278C2×C4C2×D18811yescharacteristic
279C2×C4C2×D18811yescharacteristic
280C2×C4C23×D4711yescharacteristic
281C8—22no—
282C8—22no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—44no—
292C22—3764no—
293C22—1882no—
294C22—1881no—
295C22—1881no—
296C22—1882no—
297C22—1881no—
298C22—1882no—
299C22#1309405212yes—
300C22C22×D18811yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—1882no—
305C4—1881no—
306C4—1881no—
307C4—1881no—
308C4#1309406912yes—
309C2—22no—
310C2—41no—
311C2—41no—
312C2—3762no—
313C2—3761no—
314C2#1568968511yescharacteristic
315C2C2×#1309405211yescharacteristic
316C2#1568992311yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#407C2
socleC22×C47C22×D4
hypercenter#407D47
hypocenterC47#3194
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #15689634C2semidirect
2. C2×#13093998C2semidirect
3. #15689454C2semidirect
4. #15689448C2semidirect
5. #15689437C2semidirect
6. #15689376C2semidirect
7. #15689369C2semidirect
8. #15689276C2semidirect
9. #15689270C2semidirect
10. #15689259C2semidirect
11. C47×#407C2semidirect
12. C2×#10625350C22semidirect
15. C2×#10625325C22semidirect
16. C2×D376C22semidirect
19. #13094003C22semidirect
25. #13093998C22semidirect
29. #13093983C22semidirect
32. #13093958C22semidirect
33. #13093956C22semidirect
34. #13093949C22semidirect
35. #13093946C22semidirect
36. #13093946C22semidirect
37. #13093946C22semidirect
39. C2×M16×C47C22semidirect
42. C22⋊C8×C47C22semidirect
169. #407D47semidirect
170. C47#3194semidirect
177. C2×M16C2×D47semidirect
201. C22⋊C8C2×D47semidirect