Finite Group Databasebeta

← #20255087

Subgroups — #20255087

Order 6016.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×SD16×D47C212yesmaximal, complemented
2#15689788C211yesmaximal, characteristic, complemented
3D4×D188C211yesmaximal, characteristic
4#15689497C211yesmaximal, characteristic, complemented
5#15689355C212yesmaximal, complemented
6#15689324C211yesmaximal, characteristic, complemented
7#15689272C212yesmaximal, complemented
8#15689263C212yesmaximal, complemented
9C4×#10625335C211yesmaximal, characteristic, complemented
10#15689188C211yesmaximal, characteristic, complemented
11C47×#461C211yesmaximal, characteristic, complemented
12C2×Q8×D47C2212yescomplemented
13C22×D188—21no—
14C2×D4×D47C2212yes—
15C2×#10625325C2212yescomplemented
16C2×#10625335C2211yescharacteristic
17C2×#10625336C2212yescomplemented
18C2×#10625336C2212yescomplemented
19SD16×D47—28no—
20C2×C8×D47C2212yescomplemented
21#13094023—21no—
22#13094021C2211yescharacteristic
23#13094002—22no—
24#13094000C2212yescomplemented
25#13093999C2212yes—
26#13093998—21no—
27#13093994—22no—
28C4×Dic94C2211yescharacteristic, complemented
29C4×D188C2211yescharacteristic
30#13093986—21no—
31#13093955C2211yescharacteristic, complemented
32#13093947C2211yescharacteristic, complemented
33#13093946C2212yescomplemented
34#13093945C2211yescharacteristic
35(C2×D47)⋊C8C2212yescomplemented
36C4×C47⋊C8C2211yescharacteristic, complemented
37C2×SD16×C47C2212yes—
38C4⋊Q8×C47C2211yescharacteristic, complemented
39C4×D4×C47C2211yescharacteristic
40C4⋊C8×C47C2211yescharacteristic, complemented
41#103×C47C2212yescomplemented
42C23×D47—22no—
43C2×Q8×C47C2312yes—
44C2×D4×C47C2311yescharacteristic
45C22×C4×C47—21no—
46C2×C22⋊D47—22no—
47Q8×D47—24no—
48Q8×D47—42no—
49D4×D47—24no—
50D4×D47—42no—
51C2×D188—22no—
52C2×D188—21no—
53C2×D188—21no—
54C2×D188—44no—
55C2×D188D411yescharacteristic
56C2×D188C2312yes—
57C2×C4×D47—22no—
58C2×C4×D47C2312yes—
59C2×Dic94—22no—
60C2×Dic94C2311yescharacteristic
61SD16×C47—24no—
62C2×C8×C47C2312yes—
63C4⋊C4×C47—21no—
64C4⋊C4×C47—21no—
65C4⋊C4×C47C2311yescharacteristic
66C22⋊C4×C47—21no—
67C42×C47C2311yescharacteristic
68#10625336—24no—
69#10625336—42no—
70#10625335D414yescomplemented
71(C2×D47)⋊C4—22no—
72(C2×D47)⋊C4—22no—
73(C2×D47)⋊C4D412yes—
74C4⋊Dic47D411yescharacteristic
75C4⋊Dic47C2311yescharacteristic
76Dic47⋊C4—21no—
77Dic47⋊C4—22no—
78C4×Dic47—21no—
79C2×C47⋊C8C2311yescharacteristic
80C2×C47⋊C8C2311yescharacteristic
81#10625325—24no—
82C8×D47—24no—
83C23×C47—21no—
84C22×D47—22no—
85C22×D47—44no—
86C22×D47—44no—
87C22×D47—82no—
88C22×D47C2×D412yes—
89Q8×C47—22no—
90Q8×C47—22no—
91D4×C47—21no—
92D4×C47C2×D412yes—
93C2×C4×C47—22no—
94C2×C4×C47—21no—
95C2×C4×C47—42no—
96C2×C4×C47C2×D411yescharacteristic
97C2×C4×C47C2×D411yescharacteristic
98C2×C4×C47C2411yescharacteristic
99C22⋊D47—44no—
100C2×Dic47—21no—
101C2×Dic47—21no—
102C2×Dic47C2×D412yes—
103D188—22no—
104D188—22no—
105D188—44no—
106D188—42no—
107D188—81no—
108D188SD1614yescomplemented
109C4×D47—22no—
110C4×D47—22no—
111C4×D47—44no—
112Dic94—21no—
113Dic94—44no—
114Dic94C2×D412yescomplemented
115C8×C47—22no—
116C47⋊C8—21no—
117C47⋊C8C2×D412yescomplemented
118C22×C47—22no—
119C22×C47—41no—
120C22×C47—41no—
121C22×C47C22×D411yescharacteristic
122C2×D47—22no—
123C2×D47—22no—
124C2×D47—42no—
125C2×D47—42no—
126C2×D47—42no—
127C2×D47—88no—
128C2×D47C2×SD1614yescomplemented
129C4×C47—21no—
130C4×C47—42no—
131C4×C47—41no—
132C4×C47C2×SD1612yescomplemented
133C4×C47C22×D411yescharacteristic
134C4×C47H(5,𝔽2)11yescharacteristic
135Dic47—22no—
136Dic47—22no—
137Dic47—41no—
138D4×SD16—471nomaximal, Sylow
139C2×C47—42no—
140C2×C47D4211yescharacteristic
141C2×C47C22×SD1611yescharacteristic
142C2×C47#57711yescharacteristic
143D47—24no—
144D47—82no—
145C22×SD16—472no—
146D4×Q8—471no—
147D42—471no—
148#492—471no—
149#465—472no—
150#461D4711yescharacteristic, complemented
151#460—471no—
152#450—472no—
153#448—472no—
154C4×SD16—471no—
155C8×D4—471no—
156C47D4×SD1611yescharacteristic, complemented, Sylow
157C22×Q8—472no—
158C22×D4—472no—
159C22×D4—941no—
160C2×SD16—471no—
161C2×SD16—472no—
162C2×SD16—472no—
163C2×SD16—472no—
164C2×SD16—948no—
165C2×SD16C2×D4712yes—
166C22×C8—472no—
167C4⋊Q8—941no—
168C4⋊Q8C2×D4711yescharacteristic, complemented
169#127—471no—
170C22⋊Q8—472no—
171C22⋊Q8—942no—
172#121—472no—
173#121—941no—
174#120—942no—
175C4×Q8—471no—
176C4×D4—471no—
177C4×D4—941no—
178C4×D4C2×D4711yescharacteristic
179#106—471no—
180C4⋊C8C2×D4711yescharacteristic, complemented
181#103—471no—
182#103C2×D4712yescomplemented
183#102—471no—
184#102—472no—
185C22⋊C8—472no—
186C4×C8—471no—
187C24—942no—
188C2×Q8—471no—
189C2×Q8—942no—
190C2×Q8—944no—
191C2×Q8—1882no—
192C2×Q8C22×D4712yes—
193C2×D4—471no—
194C2×D4—472no—
195C2×D4—942no—
196C2×D4—942no—
197C2×D4—944no—
198C2×D4—941no—
199C2×D4—941no—
200C2×D4—1884no—
201C2×D4—1882no—
202C2×D4C22×D4711yescharacteristic
203C22×C4—21no—
204C22×C4—472no—
205C22×C4—942no—
206SD16—24no—
207SD16—474no—
208SD16—944no—
209SD16—944no—
210SD16—1882no—
211C2×C8—471no—
212C2×C8—471no—
213C2×C8—944no—
214C2×C8C22×D4712yes—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—471no—
218C4⋊C4—471no—
219C4⋊C4—942no—
220C4⋊C4—941no—
221C4⋊C4C22×D4711yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—472no—
224C22⋊C4—942no—
225C22⋊C4—942no—
226C42—941no—
227C42C22×D4711yescharacteristic
228C23—21no—
229C23—472no—
230C23—942no—
231C23—3762no—
232C23—1884no—
233C23—1884no—
234Q8—22no—
235Q8—22no—
236Q8—472no—
237Q8—941no—
238Q8—1884no—
239D4—21no—
240D4—474no—
241D4—942no—
242D4—942no—
243D4—3761no—
244D4—1884no—
245D4—1884no—
246D4—1882no—
247D4D4×D4712yes—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—42no—
251C2×C4—472no—
252C2×C4—941no—
253C2×C4—942no—
254C2×C4—942no—
255C2×C4—941no—
256C2×C4—1884no—
257C2×C4D4×D4711yescharacteristic
258C2×C4D4×D4711yescharacteristic
259C2×C4C23×D4711yescharacteristic
260C8—22no—
261C8—472no—
262C8—941no—
263C22—22no—
264C22—41no—
265C22—41no—
266C22—474no—
267C22—942no—
268C22—942no—
269C22—3768no—
270C22—1882no—
271C22—1882no—
272C22—1882no—
273C22C2×D4×D4711yescharacteristic
274C4—21no—
275C4—42no—
276C4—41no—
277C4—942no—
278C4—942no—
279C4—1881no—
280C4SD16×D4712yescomplemented
281C4C2×D4×D4711yescharacteristic
282C4#1309407011yescharacteristic
283C2—42no—
284C2—944no—
285C2—3762no—
286C2#1568975711yescharacteristic
287C2C2×SD16×D4711yescharacteristic
288C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#461C2
socleC22×C47C22×D4
hypercenter#461D47
hypocenterC47D4×SD16
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D47C2semidirect
2. #15689788C2semidirect
4. #15689497C2semidirect
5. #15689355C2semidirect
6. #15689324C2semidirect
7. #15689272C2semidirect
8. #15689263C2semidirect
9. C4×#10625335C2semidirect
10. #15689188C2semidirect
11. C47×#461C2semidirect
12. C2×Q8×D47C22semidirect
15. C2×#10625325C22semidirect
17. C2×#10625336C22semidirect
18. C2×#10625336C22semidirect
20. C2×C8×D47C22semidirect
24. #13094000C22semidirect
28. C4×Dic94C22semidirect
31. #13093955C22semidirect
32. #13093947C22semidirect
33. #13093946C22semidirect
35. (C2×D47)⋊C8C22semidirect
36. C4×C47⋊C8C22semidirect
38. C4⋊Q8×C47C22semidirect
40. C4⋊C8×C47C22semidirect
41. #103×C47C22semidirect
70. #10625335D4semidirect
108. D188SD16semidirect
114. Dic94C2×D4semidirect
117. C47⋊C8C2×D4semidirect
128. C2×D47C2×SD16semidirect
132. C4×C47C2×SD16semidirect
150. #461D47semidirect
156. C47D4×SD16semidirect
168. C4⋊Q8C2×D47semidirect
180. C4⋊C8C2×D47semidirect
182. #103C2×D47semidirect
280. C4SD16×D47semidirect