Finite Group Databasebeta

← #20254083

Subgroups — #20254083

Order 6016.

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

normal subgroups only

This group has 410 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#15689671C211yesmaximal, characteristic, complemented
2#15689652C211yesmaximal, characteristic, complemented
3#15689532C211yesmaximal, characteristic, complemented
4#15689487C211yesmaximal, characteristic, complemented
5#15689482C211yesmaximal, characteristic, complemented
6#15689356C212yesmaximal, complemented
7#15689349C212yesmaximal, complemented
8#15689235C212yesmaximal, complemented
9#15689224C212yesmaximal, complemented
10#97×D47C211yesmaximal, characteristic, complemented
11C47×#496C211yesmaximal, characteristic, complemented
12C2×#10625352—21no—
13C2×C8×D47C2212yes—
14#13094024C2211yescharacteristic
15#13094017—21no—
16#13094016C2211yescharacteristic
17#13094011—21no—
18#13094006—21no—
19#13094000C2211yescharacteristic
20#13093995—21no—
21#13093995C2212yes—
22#13093995C2211yescharacteristic
23Q8×Dic47C2211yescharacteristic
24D4×Dic47—21no—
25D4×Dic47C2212yes—
26D4×Dic47C2211yescharacteristic
27(C22⋊D47)⋊C4—21no—
28#13093980—21no—
29C42×D47C2211yescharacteristic
30#13093958C2212yes—
31#13093956C2212yes—
32#13093948C2212yes—
33#13093945C2212yes—
34#13093945C2212yes—
35#13093945C2212yes—
36#13093935C2211yescharacteristic
37#13093934C2212yes—
38C2×SD16×C47C2212yes—
39C2×D8×C47C2212yes—
40#127×C47C2211yescharacteristic
41#124×C47C2211yescharacteristic
42#97×C47C2211yescharacteristic
43C2×Q8×C47C2311yescharacteristic
44C2×D4×C47—21no—
45C2×D4×C47—21no—
46C2×D4×C47C2311yescharacteristic
47C2×D4×C47C2312yes—
48C2×C22⋊D47—21no—
49C2×C22⋊D47—22no—
50C22×Dic47—21no—
51C22×Dic47—22no—
52#10625352—44no—
53C2×C4×D47D411yescharacteristic
54C2×C4×D47D411yescharacteristic
55C2×C4×D47C2311yescharacteristic
56C2×Dic94—21no—
57SD16×C47—24no—
58D8×C47—24no—
59C2×C8×C47C2312yes—
60C22⋊C4×C47—21no—
61C22⋊C4×C47—21no—
62C42×C47C2311yescharacteristic
63C22⋊Dic47—21no—
64C22⋊Dic47—22no—
65C22⋊Dic47—22no—
66C22⋊Dic47—21no—
67(C2×D47)⋊C4—21no—
68C4⋊Dic47—21no—
69C4⋊Dic47—21no—
70C4⋊Dic47C2311yescharacteristic
71C4⋊Dic47C2311yescharacteristic
72C4⋊Dic47C2312yes—
73Dic47⋊C4—21no—
74Dic47⋊C4—21no—
75Dic47⋊C4—21no—
76C4×Dic47—21no—
77C4×Dic47D411yescharacteristic
78C4×Dic47D411yescharacteristic
79C4×Dic47C2311yescharacteristic
80C2×C47⋊C8C2312yes—
81C8×D47—24no—
82C23×C47—21no—
83C23×C47—22no—
84C22×D47C2×D411yescharacteristic
85Q8×C47—22no—
86D4×C47—22no—
87D4×C47—22no—
88D4×C47—22no—
89D4×C47—42no—
90D4×C47—42no—
91C2×C4×C47—21no—
92C2×C4×C47C2×D411yescharacteristic
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47C2411yescharacteristic
95C22⋊D47—44no—
96C22⋊D47—42no—
97C2×Dic47—21no—
98C2×Dic47—21no—
99C2×Dic47—22no—
100C2×Dic47—44no—
101C2×Dic47—42no—
102C2×Dic47C2×D411yescharacteristic
103C2×Dic47C2×D411yescharacteristic
104C2×Dic47C2×D411yescharacteristic
105C4×D47—22no—
106C4×D47—22no—
107C4×D47—41no—
108Dic94—42no—
109C8×C47#4114yescomplemented
110C47⋊C8—22no—
111C22×C47—41no—
112C22×C47—42no—
113C22×C47—42no—
114C22×C47—41no—
115C22×C47—41no—
116C22×C47—42no—
117C22×C47C22×D411yescharacteristic
118C2×D47—21no—
119C2×D47—21no—
120C2×D47AGL(1,ℤ/8)12yes—
121C4×C47—21no—
122C4×C47—21no—
123C4×C47—41no—
124C4×C47C2×#4112yes—
125Dic47—21no—
126Dic47—21no—
127Dic47—21no—
128Dic47—42no—
129Dic47—41no—
130Dic47—41no—
131#3180—471nomaximal, Sylow
132C2×C47—82no—
133C2×C47—81no—
134C2×C47#53211yescharacteristic
135C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
136C2×C47#57511yescharacteristic
137D47—22no—
138#532—471no—
139#529—471no—
140#501—471no—
141#496D4711yescharacteristic, complemented
142#490—471no—
143#489—471no—
144#466—472no—
145#465—472no—
146#442—472no—
147#440—472no—
148C2×#97—471no—
149C47#318011yescharacteristic, complemented, Sylow
150C2×#41—941no—
151C2×SD16C2×D4712yes—
152C2×D8C2×D4712yes—
153C22×C8—472no—
154C4⋊Q8—471no—
155#127C2×D4711yescharacteristic
156#126—941no—
157#125—471no—
158#124—941no—
159#124C2×D4711yescharacteristic
160#123—941no—
161C22⋊Q8—471no—
162#121—471no—
163#121—472no—
164#121—941no—
165C4×Q8—471no—
166C4×D4—471no—
167C4×D4—472no—
168C4×D4—941no—
169C4×D4—941no—
170#117—941no—
171C2×C42—471no—
172#107—472no—
173#106—472no—
174#103—472no—
175#102—472no—
176#102—472no—
177#102—472no—
178#97—472no—
179#97—471no—
180#97C2×D4711yescharacteristic
181#41—1884no—
182C2×Q8—941no—
183C2×Q8C22×D4711yescharacteristic
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—941no—
187C2×D4—942no—
188C2×D4C22×D4711yescharacteristic
189C2×D4C22×D4712yes—
190C22×C4—471no—
191C22×C4—471no—
192C22×C4—471no—
193C22×C4—941no—
194C22×C4—942no—
195SD16—24no—
196D8—24no—
197C2×C8—472no—
198C2×C8—944no—
199C2×C8C22×D4712yes—
200C4⋊C4—471no—
201C4⋊C4—471no—
202C4⋊C4—472no—
203C4⋊C4—941no—
204C4⋊C4—941no—
205C4⋊C4—941no—
206C4⋊C4—941no—
207C4⋊C4—941no—
208C22⋊C4—21no—
209C22⋊C4—21no—
210C22⋊C4—941no—
211C22⋊C4—941no—
212C22⋊C4—942no—
213C22⋊C4—941no—
214C22⋊C4—942no—
215C42—471no—
216C42—471no—
217C42—471no—
218C42—941no—
219C42C22×D4711yescharacteristic
220C23—21no—
221C23—22no—
222C23—471no—
223Q8—22no—
224Q8—1882no—
225D4—22no—
226D4—22no—
227D4—22no—
228D4—42no—
229D4—42no—
230D4—1882no—
231D4—1884no—
232C2×C4—21no—
233C2×C4—471no—
234C2×C4—471no—
235C2×C4—471no—
236C2×C4—942no—
237C2×C4—942no—
238C2×C4—941no—
239C2×C4—941no—
240C2×C4—942no—
241C2×C4—1881no—
242C2×C4—1882no—
243C2×C4—1884no—
244C2×C4D4×D4711yescharacteristic
245C2×C4D4×D4711yescharacteristic
246C2×C4C23×D4711yescharacteristic
247C8—942no—
248C8#1062535214yescomplemented
249C22—42no—
250C22—41no—
251C22—41no—
252C22—42no—
253C22—41no—
254C22—42no—
255C22—472no—
256C22—941no—
257C22—941no—
258C22C2×D4×D4711yescharacteristic
259C4—21no—
260C4—21no—
261C4—41no—
262C4—941no—
263C4—941no—
264C4—941no—
265C4—1882no—
266C4—1881no—
267C4—1881no—
268C4C2×#1062535212yes—
269C2—82no—
270C2—81no—
271C2—942no—
272C2#1568967111yescharacteristic
273C2AGL(1,ℤ/8)×D4711yescharacteristic
274C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#496C2
socleC22×C47C22×D4
hypercenter#496D47
hypocenterC47#3180
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #15689671C2semidirect
2. #15689652C2semidirect
3. #15689532C2semidirect
4. #15689487C2semidirect
5. #15689482C2semidirect
6. #15689356C2semidirect
7. #15689349C2semidirect
8. #15689235C2semidirect
9. #15689224C2semidirect
10. #97×D47C2semidirect
11. C47×#496C2semidirect
109. C8×C47#41semidirect
141. #496D47semidirect
149. C47#3180semidirect
248. C8#10625352semidirect