Finite Group Databasebeta

← #20253323

Subgroups — #20253323

Order 6016.

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

normal subgroups only

This group has 462 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#121×D47C211yesmaximal, characteristic
2C2×#13093982C211yesmaximal, characteristic, complemented
3#15689450C212yesmaximal, complemented
4#15689446C212yesmaximal, complemented
5#15689442C211yesmaximal, characteristic, complemented
6#15689439C211yesmaximal, characteristic, complemented
7#15689436C211yesmaximal, characteristic, complemented
8#15689164C212yesmaximal, complemented
9#15689126C212yesmaximal, complemented
10#15689085C211yesmaximal, characteristic, complemented
11C47×#480C211yesmaximal, characteristic, complemented
12C2×D4×D47—21no—
13C2×D4×D47C2211yescharacteristic
14C22×C4×D47C2211yescharacteristic
15C2×#10625324C2212yes—
16#13093999C2211yescharacteristic
17#13093998C2211yescharacteristic
18#13093997—21no—
19#13093996—21no—
20#13093995C2211yescharacteristic
21#13093982—21no—
22#13093982—21no—
23#13093982C2212yes—
24#13093982C2212yescomplemented
25C2×C4⋊Dic47C2211yescharacteristic, complemented
26C4⋊C4×D47C2211yescharacteristic
27C2×(C2×D47)⋊C4—21no—
28C22⋊C4×D47—21no—
29C2×C4×Dic47—21no—
30#13093957C2212yescomplemented
31#13093956C2212yescomplemented
32#13093955C2212yescomplemented
33#13093946C2212yescomplemented
34#13093945C2212yescomplemented
35#13093944C2212yescomplemented
36C22⋊(C47⋊C8)C2211yescharacteristic, complemented
37(C2×D47)⋊C8C2212yescomplemented
38#121×C47C2211yescharacteristic
39C2×C4⋊C4×C47C2211yescharacteristic, complemented
40#107×C47C2212yescomplemented
41#102×C47C2212yescomplemented
42C22⋊C8×C47C2211yescharacteristic, complemented
43C23×D47—21no—
44C23×D47D411yescharacteristic
45C2×D4×C47—21no—
46C2×D4×C47C2311yescharacteristic
47C22×C4×C47—21no—
48C22×C4×C47C2311yescharacteristic
49C2×C22⋊D47—21no—
50C2×C22⋊D47—21no—
51C2×C22⋊D47—21no—
52C22×Dic47—21no—
53C22×Dic47D411yescharacteristic
54D4×D47—24no—
55D4×D47—44no—
56C2×D188—21no—
57C2×D188C2311yescharacteristic
58C2×C4×D47—24no—
59C2×C4×D47—21no—
60C2×C4×D47D411yescharacteristic
61C2×C4×D47D411yescharacteristic
62C2×C4×D47C2311yescharacteristic
63C2×C4×D47C2311yescharacteristic
64C2×C8×C47C2312yes—
65C4⋊C4×C47—21no—
66C4⋊C4×C47C2311yescharacteristic
67C4⋊C4×C47C2312yes—
68C22⋊C4×C47—21no—
69C22⋊Dic47—21no—
70(C2×D47)⋊C4—22no—
71(C2×D47)⋊C4—22no—
72(C2×D47)⋊C4—21no—
73(C2×D47)⋊C4—21no—
74C4⋊Dic47—21no—
75C4⋊Dic47C2312yes—
76C4⋊Dic47C2311yescharacteristic
77Dic47⋊C4—21no—
78C4×Dic47—22no—
79C4×Dic47—22no—
80C2×C47⋊C8C2312yes—
81#10625324—24no—
82C23×C47—21no—
83C23×C47C2×D411yescharacteristic
84C22×D47—22no—
85C22×D47—22no—
86C22×D47—21no—
87C22×D47—41no—
88C22×D47—42no—
89C22×D47—42no—
90C22×D47—42no—
91C22×D47C2×D411yescharacteristic
92C22×D47C2×D411yescharacteristic
93D4×C47—22no—
94D4×C47—42no—
95C2×C4×C47—22no—
96C2×C4×C47—22no—
97C2×C4×C47—21no—
98C2×C4×C47—42no—
99C2×C4×C47C2×D411yescharacteristic
100C2×C4×C47C2411yescharacteristic
101C22⋊D47—42no—
102C22⋊D47—42no—
103C22⋊D47—42no—
104C2×Dic47—22no—
105C2×Dic47—22no—
106C2×Dic47—21no—
107C2×Dic47—42no—
108C2×Dic47C2×D411yescharacteristic
109C2×Dic47C2×D411yescharacteristic
110D188—22no—
111D188—42no—
112C4×D47—22no—
113C4×D47—22no—
114C4×D47—22no—
115C4×D47—42no—
116C4×D47#4114yes—
117C8×C47—22no—
118C47⋊C8—22no—
119C22×C47—21no—
120C22×C47—21no—
121C22×C47—41no—
122C22×C47—41no—
123C22×C47—41no—
124C22×C47AGL(1,ℤ/8)12yes—
125C22×C47C22×D411yescharacteristic
126C2×D47—21no—
127C2×D47—21no—
128C2×D47—21no—
129C2×D47—21no—
130C2×D47—21no—
131C2×D47—44no—
132C2×D47—41no—
133C2×D47—41no—
134C2×D47—41no—
135C2×D47—84no—
136C2×D47#12312yes—
137C4×C47—21no—
138C4×C47—41no—
139C4×C47—42no—
140C4×C47C2×#4112yes—
141Dic47—21no—
142Dic47—41no—
143Dic47—42no—
144Dic47#12312yes—
145#3094—471nomaximal, Sylow
146C2×C47—22no—
147C2×C47—81no—
148C2×C47C2×#12311yescharacteristic
149C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
150C2×C47#57511yescharacteristic
151D47—22no—
152D47—41no—
153D47—81no—
154C2×#121—471no—
155C2×#117—471no—
156#482—472no—
157#482—472no—
158#481—471no—
159#481—471no—
160#480—471no—
161#480D4711yescharacteristic, complemented
162#428—472no—
163#418—472no—
164#407—471no—
165C47#309411yescharacteristic, complemented, Sylow
166C22×D4—471no—
167C22×D4—941no—
168C23×C4—471no—
169C2×M16—472no—
170#121—471no—
171#121—471no—
172#121—471no—
173#121—941no—
174#121—941no—
175#121C2×D4711yescharacteristic
176#117—472no—
177#117—472no—
178#117—941no—
179#117—941no—
180C2×C4⋊C4—471no—
181C2×C4⋊C4—471no—
182C2×C4⋊C4C2×D4711yescharacteristic, complemented
183C2×C22⋊C4—941no—
184C2×C22⋊C4—941no—
185C2×C42—941no—
186#107—472no—
187#107C2×D4712yescomplemented
188#106—472no—
189#106—472no—
190#102—472no—
191#102—472no—
192#102—472no—
193#102C2×D4712yescomplemented
194C22⋊C8—471no—
195C22⋊C8—472no—
196C22⋊C8C2×D4711yescharacteristic, complemented
197C24—471no—
198C24—941no—
199C2×D4—21no—
200C2×D4—471no—
201C2×D4—941no—
202C2×D4—944no—
203C2×D4—941no—
204C2×D4—941no—
205C2×D4—941no—
206C2×D4—1884no—
207C2×D4C22×D4711yescharacteristic
208C22×C4—21no—
209C22×C4—471no—
210C22×C4—471no—
211C22×C4—471no—
212C22×C4—471no—
213C22×C4—471no—
214C22×C4—944no—
215C22×C4—941no—
216C22×C4—941no—
217C22×C4C22×D4711yescharacteristic
218M16—944no—
219C2×C8—472no—
220C2×C8C22×D4712yes—
221C4⋊C4—21no—
222C4⋊C4—472no—
223C4⋊C4—471no—
224C4⋊C4—941no—
225C4⋊C4—941no—
226C4⋊C4C22×D4712yes—
227C4⋊C4C22×D4711yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—941no—
230C22⋊C4—942no—
231C22⋊C4—942no—
232C22⋊C4—941no—
233C22⋊C4—941no—
234C42—942no—
235C42—942no—
236C23—21no—
237C23—471no—
238C23—471no—
239C23—942no—
240C23—942no—
241C23—941no—
242C23—1881no—
243C23—1882no—
244C23—1882no—
245C23—1882no—
246C23D4×D4711yescharacteristic
247D4—22no—
248D4—42no—
249D4—942no—
250D4—1882no—
251D4—1882no—
252D4—1882no—
253D4—1882no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—471no—
259C2×C4—474no—
260C2×C4—471no—
261C2×C4—942no—
262C2×C4—942no—
263C2×C4—942no—
264C2×C4—942no—
265C2×C4—942no—
266C2×C4—941no—
267C2×C4—1882no—
268C2×C4—1882no—
269C2×C4D4×D4711yescharacteristic
270C2×C4C23×D4711yescharacteristic
271C8—22no—
272C8—942no—
273C22—21no—
274C22—21no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—472no—
279C22—941no—
280C22—941no—
281C22—941no—
282C22—941no—
283C22—941no—
284C22—3764no—
285C22—1884no—
286C22—1881no—
287C22—1881no—
288C22—1881no—
289C22#1309404812yes—
290C22C2×D4×D4711yescharacteristic
291C4—21no—
292C4—42no—
293C4—41no—
294C4—472no—
295C4—941no—
296C4—1881no—
297C4—1882no—
298C4#41×D4712yes—
299C2—22no—
300C2—81no—
301C2—942no—
302C2—3761no—
303C2—1881no—
304C2#123×D4711yescharacteristic
305C2C2×#1309404811yescharacteristic
306C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#480C2
socleC22×C47C22×D4
hypercenter#480D47
hypocenterC47#3094
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#13093982C2semidirect
3. #15689450C2semidirect
4. #15689446C2semidirect
5. #15689442C2semidirect
6. #15689439C2semidirect
7. #15689436C2semidirect
8. #15689164C2semidirect
9. #15689126C2semidirect
10. #15689085C2semidirect
11. C47×#480C2semidirect
24. #13093982C22semidirect
25. C2×C4⋊Dic47C22semidirect
30. #13093957C22semidirect
31. #13093956C22semidirect
32. #13093955C22semidirect
33. #13093946C22semidirect
34. #13093945C22semidirect
35. #13093944C22semidirect
36. C22⋊(C47⋊C8)C22semidirect
37. (C2×D47)⋊C8C22semidirect
39. C2×C4⋊C4×C47C22semidirect
40. #107×C47C22semidirect
41. #102×C47C22semidirect
42. C22⋊C8×C47C22semidirect
161. #480D47semidirect
165. C47#3094semidirect
182. C2×C4⋊C4C2×D47semidirect
187. #107C2×D47semidirect
193. #102C2×D47semidirect
196. C22⋊C8C2×D47semidirect