Finite Group Databasebeta

← #20253315

Subgroups — #20253315

Order 6016.

458 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 123 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×C4⋊C4×D47C211yesmaximal, characteristic, complemented
3#15689456C211yesmaximal, characteristic, complemented
4#15689452C212yesmaximal, complemented
5#15689442C211yesmaximal, characteristic, complemented
6#15689441C211yesmaximal, characteristic, complemented
7#15689438C212yesmaximal, complemented
8#15689164C212yesmaximal, complemented
9#15689123C212yesmaximal, complemented
10#15689085C211yesmaximal, characteristic, complemented
11C47×#484C211yesmaximal, characteristic, complemented
12C2×#10625354C2211yescharacteristic
13C22×C4×D47—21no—
14C22×C4×D47C2211yescharacteristic
15C2×#10625324C2212yes—
16#13094009—21no—
17#13094000C2211yescharacteristic
18#13093999C2211yescharacteristic
19#13093998C2211yescharacteristic
20#13093994—21no—
21#13093986—21no—
22(C22⋊D47)⋊C4—21no—
23#13093982C2211yescharacteristic
24C2×C4⋊Dic47C2211yescharacteristic
25C2×Dic47⋊C4—21no—
26C4⋊C4×D47—21no—
27C4⋊C4×D47—21no—
28C4⋊C4×D47C2212yes—
29C4⋊C4×D47C2212yes—
30#13093957C2212yescomplemented
31#13093956C2212yescomplemented
32#13093955C2212yescomplemented
33#13093948C2212yescomplemented
34#13093946C2212yescomplemented
35#13093944C2212yescomplemented
36C22⋊(C47⋊C8)C2211yescharacteristic
37(C2×D47)⋊C8C2212yes—
38C22⋊Q8×C47C2211yescharacteristic
39C2×C4⋊C4×C47C2211yescharacteristic
40#107×C47C2212yescomplemented
41#103×C47C2212yescomplemented
42C22⋊C8×C47C2211yescharacteristic
43C23×D47D411yescharacteristic
44C2×Q8×C47C2311yescharacteristic
45C22×C4×C47—21no—
46C22×C4×C47C2311yescharacteristic
47C2×C22⋊D47—21no—
48C22×Dic47—21no—
49C22×Dic47D411yescharacteristic
50#10625354—24no—
51C2×D188—21no—
52C2×D188—21no—
53C2×D188C2311yescharacteristic
54C2×C4×D47—24no—
55C2×C4×D47—22no—
56C2×C4×D47—22no—
57C2×C4×D47—21no—
58C2×C4×D47—44no—
59C2×C4×D47D411yescharacteristic
60C2×C4×D47D411yescharacteristic
61C2×C4×D47C2311yescharacteristic
62C2×C4×D47C2311yescharacteristic
63C2×C8×C47C2312yes—
64C4⋊C4×C47—21no—
65C4⋊C4×C47—21no—
66C4⋊C4×C47C2312yes—
67C4⋊C4×C47C2311yescharacteristic
68C22⋊C4×C47—21no—
69(C2×D47)⋊C4—21no—
70(C2×D47)⋊C4—21no—
71(C2×D47)⋊C4—21no—
72(C2×D47)⋊C4—21no—
73C4⋊Dic47—21no—
74C4⋊Dic47C2312yes—
75C4⋊Dic47C2311yescharacteristic
76Dic47⋊C4—22no—
77Dic47⋊C4—22no—
78Dic47⋊C4—21no—
79C4×Dic47—21no—
80C2×C47⋊C8C2312yes—
81#10625324—24no—
82C23×C47C2×D411yescharacteristic
83C22×D47—22no—
84C22×D47—22no—
85C22×D47—22no—
86C22×D47—21no—
87C22×D47C2×D411yescharacteristic
88C22×D47C2×D411yescharacteristic
89Q8×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—21no—
92C2×C4×C47—22no—
93C2×C4×C47—21no—
94C2×C4×C47—42no—
95C2×C4×C47C2×D411yescharacteristic
96C2×C4×C47C2411yescharacteristic
97C22⋊D47—42no—
98C2×Dic47—22no—
99C2×Dic47—21no—
100C2×Dic47—22no—
101C2×Dic47—42no—
102C2×Dic47C2×D411yescharacteristic
103C2×Dic47C2×D411yescharacteristic
104D188—22no—
105D188—42no—
106D188—42no—
107C4×D47—22no—
108C4×D47—22no—
109C4×D47—22no—
110C4×D47—44no—
111C4×D47—44no—
112C4×D47—42no—
113C4×D47#4114yes—
114C8×C47—22no—
115C47⋊C8—22no—
116C22×C47—21no—
117C22×C47—21no—
118C22×C47#13712yes—
119C22×C47C22×D411yescharacteristic
120C2×D47—28no—
121C2×D47—21no—
122C2×D47—21no—
123C2×D47—21no—
124C2×D47—21no—
125C2×D47—41no—
126C2×D47—41no—
127C2×D47—41no—
128C2×D47#12312yes—
129C2×D47AGL(1,ℤ/8)12yes—
130C4×C47—21no—
131C4×C47—41no—
132C4×C47—42no—
133C4×C47—41no—
134C4×C47C2×#4112yes—
135Dic47—21no—
136Dic47—42no—
137Dic47—41no—
138Dic47#12312yes—
139#3092—471nomaximal, Sylow
140C2×C47—22no—
141C2×C47C2×#12311yescharacteristic
142C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
143C2×C47C2×#13711yescharacteristic
144D47—22no—
145D47—22no—
146D47—81no—
147#525—471no—
148C22×C4⋊C4—471no—
149#484—471no—
150#484D4711yescharacteristic, complemented
151#483—472no—
152#481—471no—
153#481—471no—
154#480—472no—
155#428—472no—
156#417—472no—
157#407—471no—
158C47#309211yescharacteristic, complemented, Sylow
159C2×#41—471no—
160C23×C4—471no—
161C23×C4—941no—
162C2×M16—472no—
163#123—941no—
164C22⋊Q8—471no—
165C22⋊Q8C2×D4711yescharacteristic
166#121—471no—
167#121—471no—
168#120—941no—
169C4×D4—941no—
170C4×D4—941no—
171#117—471no—
172C2×C4⋊C4—471no—
173C2×C4⋊C4—472no—
174C2×C4⋊C4—472no—
175C2×C4⋊C4—941no—
176C2×C4⋊C4—941no—
177C2×C4⋊C4—941no—
178C2×C4⋊C4C2×D4711yescharacteristic
179#107—472no—
180#107C2×D4712yescomplemented
181#106—472no—
182#106—472no—
183#103—472no—
184#103C2×D4712yescomplemented
185#102—472no—
186#102—472no—
187C22⋊C8—471no—
188C22⋊C8—472no—
189C22⋊C8C2×D4711yescharacteristic
190C24—471no—
191#41—944no—
192C2×Q8C22×D4711yescharacteristic
193C2×D4—471no—
194C2×D4—941no—
195C2×D4—941no—
196C2×D4—941no—
197C22×C4—21no—
198C22×C4—471no—
199C22×C4—471no—
200C22×C4—471no—
201C22×C4—471no—
202C22×C4—471no—
203C22×C4—944no—
204C22×C4—941no—
205C22×C4—942no—
206C22×C4—942no—
207C22×C4—941no—
208C22×C4—1884no—
209C22×C4C22×D4711yescharacteristic
210M16—944no—
211C2×C8—472no—
212C2×C8C22×D4712yes—
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—472no—
216C4⋊C4—471no—
217C4⋊C4—942no—
218C4⋊C4—942no—
219C4⋊C4—941no—
220C4⋊C4—941no—
221C4⋊C4C22×D4712yes—
222C4⋊C4C22×D4711yescharacteristic
223C22⋊C4—21no—
224C22⋊C4—941no—
225C22⋊C4—941no—
226C22⋊C4—941no—
227C22⋊C4—941no—
228C42—941no—
229C23—471no—
230C23—471no—
231C23—942no—
232C23—942no—
233C23—942no—
234C23—941no—
235C23D4×D4711yescharacteristic
236Q8—22no—
237D4—942no—
238D4—1882no—
239D4—1882no—
240D4—1882no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—42no—
246C2×C4—471no—
247C2×C4—474no—
248C2×C4—471no—
249C2×C4—942no—
250C2×C4—942no—
251C2×C4—942no—
252C2×C4—942no—
253C2×C4—941no—
254C2×C4—942no—
255C2×C4—1882no—
256C2×C4—1884no—
257C2×C4—1884no—
258C2×C4—1882no—
259C2×C4D4×D4711yescharacteristic
260C2×C4C23×D4711yescharacteristic
261C8—22no—
262C8—942no—
263C22—21no—
264C22—21no—
265C22—472no—
266C22—472no—
267C22—948no—
268C22—941no—
269C22—941no—
270C22—941no—
271C22—941no—
272C22—1881no—
273C22—1881no—
274C22—1881no—
275C22#1309405612yes—
276C22C2×D4×D4711yescharacteristic
277C4—21no—
278C4—41no—
279C4—42no—
280C4—41no—
281C4—472no—
282C4—941no—
283C4—1882no—
284C4—1881no—
285C4#41×D4712yes—
286C2—22no—
287C2—942no—
288C2—942no—
289C2—3761no—
290C2#123×D4711yescharacteristic
291C2AGL(1,ℤ/8)×D4711yescharacteristic
292C2C2×#1309405611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#484C2
socleC22×C47C22×D4
hypercenter#484D47
hypocenterC47#3092
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D47C2semidirect
3. #15689456C2semidirect
4. #15689452C2semidirect
5. #15689442C2semidirect
6. #15689441C2semidirect
7. #15689438C2semidirect
8. #15689164C2semidirect
9. #15689123C2semidirect
10. #15689085C2semidirect
11. C47×#484C2semidirect
30. #13093957C22semidirect
31. #13093956C22semidirect
32. #13093955C22semidirect
33. #13093948C22semidirect
34. #13093946C22semidirect
35. #13093944C22semidirect
40. #107×C47C22semidirect
41. #103×C47C22semidirect
150. #484D47semidirect
158. C47#3092semidirect
180. #107C2×D47semidirect
184. #103C2×D47semidirect