Finite Group Databasebeta

← #20253484

Subgroups — #20253484

Order 6016.

444 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 119 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#15689675C211yesmaximal, characteristic, complemented
2C2×#13093986C211yesmaximal, characteristic
3#15689458C211yesmaximal, characteristic, complemented
4#15689402C212yesmaximal, complemented
5#15689327C212yesmaximal, complemented
6#15689276C211yesmaximal, characteristic
7#15689273C211yesmaximal, characteristic
8#15689226C212yesmaximal, complemented
9#15689222C212yesmaximal, complemented
10#15689177C211yesmaximal, characteristic, complemented
11C47×#484C211yesmaximal, characteristic, complemented
12C22×D188C2211yescharacteristic
13C22×C4×D47—21no—
14C2×#10625325C2212yes—
15C2×#10625336C2212yes—
16#13094023C2211yescharacteristic, complemented
17#13094022C2211yescharacteristic, complemented
18#13094014—21no—
19#13094003C2211yescharacteristic
20#13094001—21no—
21Q8×Dic47C2211yescharacteristic, complemented
22#13093989—21no—
23#13093989C2211yescharacteristic, complemented
24#13093986—21no—
25#13093986—21no—
26#13093986C2212yes—
27#13093986C2212yes—
28#13093980—21no—
29C2×(C2×D47)⋊C4—21no—
30C2×C4×Dic47C2211yescharacteristic
31#13093957C2212yescomplemented
32Dic47⋊C8C2212yescomplemented
33#13093947C2212yescomplemented
34#13093946C2212yes—
35#13093944C2212yes—
36C22⋊(C47⋊C8)C2211yescharacteristic
37#13093934C2212yescomplemented
38C22⋊Q8×C47C2211yescharacteristic
39C2×C4⋊C4×C47C2211yescharacteristic
40#107×C47C2212yescomplemented
41#103×C47C2212yescomplemented
42C22⋊C8×C47C2211yescharacteristic
43C23×D47—21no—
44C2×Q8×C47C2311yescharacteristic
45C22×C4×C47—21no—
46C22×C4×C47C2311yescharacteristic
47C22×Dic47D411yescharacteristic
48C22×Dic47D411yescharacteristic
49C2×D188—21no—
50C2×D188—24no—
51C2×D188C2312yes—
52C2×C4×D47—22no—
53C2×C4×D47—22no—
54C2×C4×D47—44no—
55C2×Dic94—21no—
56C2×Dic94C2311yescharacteristic
57C2×C8×C47C2312yes—
58C4⋊C4×C47—21no—
59C4⋊C4×C47—21no—
60C4⋊C4×C47C2312yes—
61C4⋊C4×C47C2311yescharacteristic
62C22⋊C4×C47—21no—
63C22⋊Dic47—21no—
64#10625336—24no—
65(C2×D47)⋊C4—22no—
66(C2×D47)⋊C4—22no—
67C4⋊Dic47—21no—
68C4⋊Dic47C2311yescharacteristic
69Dic47⋊C4—21no—
70Dic47⋊C4—21no—
71Dic47⋊C4—21no—
72Dic47⋊C4—21no—
73Dic47⋊C4—21no—
74C4×Dic47—21no—
75C4×Dic47—21no—
76C4×Dic47D411yescharacteristic
77C4×Dic47D411yescharacteristic
78C4×Dic47C2311yescharacteristic
79C4×Dic47C2311yescharacteristic
80C2×C47⋊C8C2312yes—
81#10625325—24no—
82C23×C47C2×D411yescharacteristic
83C22×D47—24no—
84C22×D47—22no—
85C22×D47—42no—
86C22×D47—42no—
87Q8×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—21no—
90C2×C4×C47—21no—
91C2×C4×C47—22no—
92C2×C4×C47—42no—
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47C2411yescharacteristic
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—21no—
98C2×Dic47—21no—
99C2×Dic47C2×D411yescharacteristic
100C2×Dic47C2×D411yescharacteristic
101C2×Dic47C2×D411yescharacteristic
102C2×Dic47C2×D411yescharacteristic
103D188—24no—
104D188—22no—
105D188#4114yes—
106C4×D47—44no—
107C4×D47—44no—
108Dic94—22no—
109Dic94—42no—
110C8×C47—22no—
111C47⋊C8—22no—
112C22×C47—21no—
113C22×C47—21no—
114C22×C47#13712yes—
115C22×C47C22×D411yescharacteristic
116C2×D47—24no—
117C2×D47—48no—
118C2×D47—42no—
119C2×D47—42no—
120C4×C47—21no—
121C4×C47—41no—
122C4×C47—41no—
123C4×C47—42no—
124C4×C47C2×#4112yes—
125Dic47—21no—
126Dic47—21no—
127Dic47—21no—
128Dic47—41no—
129Dic47—41no—
130Dic47AGL(1,ℤ/8)12yes—
131#3110—471nomaximal, Sylow
132C2×C47—22no—
133C2×C47#52511yescharacteristic
134C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
135C2×C47C2×#13711yescharacteristic
136D47—44no—
137#533—471no—
138C2×C4×D4—471no—
139#484—471no—
140#484D4711yescharacteristic, complemented
141#474—472no—
142#461—472no—
143#450—471no—
144#450—471no—
145#440—472no—
146#440—472no—
147#432—471no—
148C47#311011yescharacteristic, complemented, Sylow
149C22×D4—471no—
150C23×C4—941no—
151C2×SD16—472no—
152C2×SD16—472no—
153C4⋊Q8—471no—
154C4⋊Q8—471no—
155#125—941no—
156C22⋊Q8—471no—
157C22⋊Q8—941no—
158C22⋊Q8C2×D4711yescharacteristic
159C4×Q8—471no—
160C4×Q8—471no—
161C4×Q8—941no—
162C4×D4—472no—
163C4×D4—472no—
164C4×D4—941no—
165C4×D4—941no—
166#117—941no—
167C2×C4⋊C4C2×D4711yescharacteristic
168C2×C22⋊C4—941no—
169C2×C42—471no—
170#107—472no—
171#107C2×D4712yescomplemented
172C4⋊C8—472no—
173#103—472no—
174#103C2×D4712yescomplemented
175#102—472no—
176#102—472no—
177C22⋊C8—471no—
178C22⋊C8C2×D4711yescharacteristic
179#97—472no—
180C24—941no—
181C2×Q8—471no—
182C2×Q8—941no—
183C2×Q8C22×D4711yescharacteristic
184C2×D4—472no—
185C2×D4—944no—
186C2×D4—941no—
187C22×C4—21no—
188C22×C4—471no—
189C22×C4—471no—
190C22×C4—942no—
191C22×C4—942no—
192C22×C4—1884no—
193C22×C4C22×D4711yescharacteristic
194SD16—944no—
195SD16—944no—
196C2×C8—472no—
197C2×C8C22×D4712yes—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—471no—
201C4⋊C4—941no—
202C4⋊C4—941no—
203C4⋊C4—941no—
204C4⋊C4—941no—
205C4⋊C4—941no—
206C4⋊C4—941no—
207C4⋊C4C22×D4711yescharacteristic
208C4⋊C4C22×D4712yes—
209C22⋊C4—21no—
210C22⋊C4—942no—
211C22⋊C4—942no—
212C22⋊C4—941no—
213C42—471no—
214C42—471no—
215C42—471no—
216C42—471no—
217C42—941no—
218C42—941no—
219C23—944no—
220C23—942no—
221C23—1882no—
222C23—1882no—
223C23D4×D4711yescharacteristic
224Q8—22no—
225Q8—942no—
226Q8—1882no—
227D4—474no—
228D4—944no—
229D4—942no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—471no—
236C2×C4—471no—
237C2×C4—471no—
238C2×C4—471no—
239C2×C4—942no—
240C2×C4—942no—
241C2×C4—941no—
242C2×C4—941no—
243C2×C4—1884no—
244C2×C4—1884no—
245C2×C4D4×D4711yescharacteristic
246C2×C4C23×D4711yescharacteristic
247C8—22no—
248C8—942no—
249C22—21no—
250C22—21no—
251C22—944no—
252C22—1888no—
253C22—1882no—
254C22—1882no—
255C22#1309405612yes—
256C22C2×D4×D4711yescharacteristic
257C4—21no—
258C4—41no—
259C4—42no—
260C4—41no—
261C4—472no—
262C4—941no—
263C4—941no—
264C4—941no—
265C4—1881no—
266C4—1881no—
267C4#41×D4712yes—
268C2—22no—
269C2—1884no—
270C2#1568963111yescharacteristic
271C2AGL(1,ℤ/8)×D4711yescharacteristic
272C2C2×#1309405611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#484C2
socleC22×C47C22×D4
hypercenter#484D47
hypocenterC47#3110
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
1. #15689675C2semidirect
3. #15689458C2semidirect
4. #15689402C2semidirect
5. #15689327C2semidirect
8. #15689226C2semidirect
9. #15689222C2semidirect
10. #15689177C2semidirect
11. C47×#484C2semidirect
16. #13094023C22semidirect
17. #13094022C22semidirect
21. Q8×Dic47C22semidirect
23. #13093989C22semidirect
31. #13093957C22semidirect
32. Dic47⋊C8C22semidirect
33. #13093947C22semidirect
37. #13093934C22semidirect
40. #107×C47C22semidirect
41. #103×C47C22semidirect
140. #484D47semidirect
148. C47#3110semidirect
171. #107C2×D47semidirect
174. #103C2×D47semidirect