Finite Group Databasebeta

← #20253773

Subgroups — #20253773

Order 6016.

400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689678C211yesmaximal, characteristic, complemented
2#124×D47C211yesmaximal, characteristic
3#15689485C211yesmaximal, characteristic, complemented
4#15689483C211yesmaximal, characteristic, complemented
5#15689482C211yesmaximal, characteristic, complemented
6#15689479C212yesmaximal, complemented
7#15689476C212yesmaximal, complemented
8#15689130C212yesmaximal, complemented
9#15689126C212yesmaximal
10#15689075C211yesmaximal, characteristic, complemented
11C47×#489C211yesmaximal, characteristic, complemented
12C2×Q8×D47C2211yescharacteristic
13C2×D4×D47C2211yescharacteristic
14C2×#10625324C2212yes—
15#13094024C2211yescharacteristic, complemented
16#13094015C2212yescomplemented
17#13094013C2211yescharacteristic
18#13094012C2211yescharacteristic
19#13094011C2211yescharacteristic
20#13094010—21no—
21#13094010—21no—
22#13094004—21no—
23#13094000—21no—
24Q8×Dic47—21no—
25#13093989—21no—
26#13093982C2212yes—
27C22⋊C4×D47—21no—
28C22⋊C4×D47—21no—
29C42×D47C2211yescharacteristic
30#13093949C2212yescomplemented
31#13093948C2212yescomplemented
32#13093947C2212yescomplemented
33#13093946C2212yes—
34#13093945C2212yes—
35#13093944C2212yes—
36#13093935C2211yescharacteristic, complemented
37C8×Dic47C2212yescomplemented
38C4⋊Q8×C47C2211yescharacteristic, complemented
39#124×C47C2211yescharacteristic
40#103×C47C2212yescomplemented
41#102×C47C2212yes—
42#97×C47C2211yescharacteristic, complemented
43C23×D47—21no—
44C2×Q8×C47—21no—
45C2×Q8×C47C2311yescharacteristic
46C2×D4×C47C2311yescharacteristic
47C2×C22⋊D47—21no—
48Q8×D47—24no—
49D4×D47—24no—
50C2×D188C2311yescharacteristic
51C2×C4×D47—21no—
52C2×C4×D47D411yescharacteristic
53C2×C4×D47D411yescharacteristic
54C2×C4×D47C2311yescharacteristic
55C2×Dic94—21no—
56C2×Dic94—21no—
57C2×Dic94C2311yescharacteristic
58C2×C8×C47C2312yes—
59C4⋊C4×C47—21no—
60C4⋊C4×C47C2312yes—
61C22⋊C4×C47—21no—
62C22⋊C4×C47—21no—
63C42×C47C2311yescharacteristic
64C22⋊Dic47—21no—
65C22⋊Dic47—21no—
66(C2×D47)⋊C4—22no—
67(C2×D47)⋊C4—21no—
68(C2×D47)⋊C4—21no—
69(C2×D47)⋊C4—21no—
70(C2×D47)⋊C4—21no—
71C4⋊Dic47—21no—
72C4⋊Dic47—22no—
73C4⋊Dic47C2312yes—
74Dic47⋊C4—22no—
75C4×Dic47—22no—
76C4×Dic47D411yescharacteristic
77C4×Dic47D411yescharacteristic
78C4×Dic47C2311yescharacteristic
79C2×C47⋊C8C2312yes—
80#10625324—24no—
81C23×C47—21no—
82C22×D47—21no—
83C22×D47—42no—
84C22×D47—42no—
85C22×D47—42no—
86C22×D47C2×D411yescharacteristic
87Q8×C47—22no—
88Q8×C47—42no—
89D4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—21no—
92C2×C4×C47C2×D411yescharacteristic
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47C2411yescharacteristic
95C22⋊D47—42no—
96C2×Dic47—22no—
97C2×Dic47—21no—
98C2×Dic47C2×D411yescharacteristic
99C2×Dic47C2×D411yescharacteristic
100C2×Dic47C2×D411yescharacteristic
101D188—22no—
102C4×D47—41no—
103C4×D47—41no—
104C4×D47—42no—
105C4×D47#4114yes—
106Dic94—22no—
107Dic94—42no—
108Dic94—42no—
109C8×C47—22no—
110C47⋊C8—22no—
111C22×C47—41no—
112C22×C47—41no—
113C22×C47—41no—
114C22×C47C22×D411yescharacteristic
115C2×D47—21no—
116C2×D47—21no—
117C2×D47—41no—
118C2×D47—41no—
119C2×D47—41no—
120C2×D47—84no—
121C2×D47#12412yes—
122C4×C47—21no—
123C4×C47—21no—
124C4×C47—41no—
125C4×C47—42no—
126C4×C47C2×#4112yes—
127Dic47—21no—
128Dic47—21no—
129Dic47—41no—
130Dic47—42no—
131Dic47#12412yes—
132#3140—471nomaximal, Sylow
133C2×C47—81no—
134C2×C47C2×#12411yescharacteristic
135C2×C47#57511yescharacteristic
136C2×C47#57511yescharacteristic
137D47—22no—
138D47—81no—
139#533—471no—
140C2×#124—471no—
141#489—471no—
142#489—471no—
143#489—471no—
144#489D4711yescharacteristic, complemented
145#488—472no—
146#488—472no—
147#419—472no—
148#418—472no—
149C4×M16—471no—
150C47#314011yescharacteristic, complemented, Sylow
151C22×Q8—471no—
152C22×D4—471no—
153C2×M16—472no—
154C4⋊Q8—471no—
155C4⋊Q8C2×D4711yescharacteristic, complemented
156#125—472no—
157#124—471no—
158#124—471no—
159#124—471no—
160#124—941no—
161#124—941no—
162#124C2×D4711yescharacteristic
163C22⋊Q8—941no—
164C22⋊Q8—941no—
165C4×Q8—941no—
166C4×Q8—941no—
167#117—472no—
168C2×C22⋊C4—941no—
169C2×C22⋊C4—941no—
170C2×C42—471no—
171#103—472no—
172#103—472no—
173#103—472no—
174#103C2×D4712yescomplemented
175#102—472no—
176#102—472no—
177#102—472no—
178#102C2×D4712yes—
179#97—471no—
180#97C2×D4711yescharacteristic, complemented
181C4×C8—472no—
182C24—941no—
183C2×Q8—21no—
184C2×Q8—471no—
185C2×Q8—941no—
186C2×Q8—944no—
187C2×Q8—941no—
188C2×Q8C22×D4711yescharacteristic
189C2×D4—471no—
190C2×D4—944no—
191C2×D4—941no—
192C2×D4C22×D4711yescharacteristic
193C22×C4—471no—
194C22×C4—471no—
195C22×C4—471no—
196C22×C4—941no—
197M16—944no—
198C2×C8—472no—
199C2×C8C22×D4712yes—
200C4⋊C4—21no—
201C4⋊C4—472no—
202C4⋊C4—942no—
203C4⋊C4—942no—
204C4⋊C4—941no—
205C4⋊C4C22×D4712yes—
206C22⋊C4—21no—
207C22⋊C4—21no—
208C22⋊C4—941no—
209C22⋊C4—941no—
210C22⋊C4—942no—
211C22⋊C4—941no—
212C22⋊C4—941no—
213C22⋊C4—941no—
214C22⋊C4—941no—
215C42—471no—
216C42—471no—
217C42—471no—
218C42—942no—
219C42C22×D4711yescharacteristic
220C23—21no—
221C23—471no—
222C23—941no—
223C23—1882no—
224C23—1882no—
225C23—1882no—
226Q8—22no—
227Q8—42no—
228Q8—942no—
229Q8—1882no—
230Q8—1882no—
231D4—22no—
232D4—942no—
233D4—1882no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—471no—
237C2×C4—474no—
238C2×C4—471no—
239C2×C4—471no—
240C2×C4—942no—
241C2×C4—941no—
242C2×C4—1881no—
243C2×C4—1881no—
244C2×C4—1882no—
245C2×C4D4×D4711yescharacteristic
246C2×C4D4×D4711yescharacteristic
247C2×C4C23×D4711yescharacteristic
248C8—22no—
249C8—942no—
250C22—41no—
251C22—41no—
252C22—41no—
253C22—472no—
254C22—941no—
255C22—941no—
256C22—3764no—
257C22—1881no—
258C22—1881no—
259C22—1881no—
260C22C2×D4×D4711yescharacteristic
261C4—21no—
262C4—21no—
263C4—41no—
264C4—42no—
265C4—472no—
266C4—941no—
267C4—941no—
268C4—1881no—
269C4—1882no—
270C4#41×D4712yes—
271C2—81no—
272C2—942no—
273C2—3761no—
274C2#124×D4711yescharacteristic
275C2#1568991911yescharacteristic
276C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#489C2
socleC22×C47C22×D4
hypercenter#489D47
hypocenterC47#3140
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #15689678C2semidirect
3. #15689485C2semidirect
4. #15689483C2semidirect
5. #15689482C2semidirect
6. #15689479C2semidirect
7. #15689476C2semidirect
8. #15689130C2semidirect
10. #15689075C2semidirect
11. C47×#489C2semidirect
15. #13094024C22semidirect
16. #13094015C22semidirect
30. #13093949C22semidirect
31. #13093948C22semidirect
32. #13093947C22semidirect
36. #13093935C22semidirect
37. C8×Dic47C22semidirect
38. C4⋊Q8×C47C22semidirect
40. #103×C47C22semidirect
42. #97×C47C22semidirect
144. #489D47semidirect
150. C47#3140semidirect
155. C4⋊Q8C2×D47semidirect
174. #103C2×D47semidirect
180. #97C2×D47semidirect