Finite Group Databasebeta

← #20253851

Subgroups — #20253851

Order 6016.

572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 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×#13094056C212yesmaximal, complemented
2C2×#13094051C212yesmaximal, complemented
3#15689674C211yesmaximal, characteristic, complemented
4#124×D47C211yesmaximal, characteristic, complemented
5#15689515C211yesmaximal, characteristic, complemented
6#15689513C211yesmaximal, characteristic, complemented
7#15689512C211yesmaximal, characteristic, complemented
8#15689508C212yesmaximal, complemented
9#15689504C212yesmaximal, complemented
10#15689075C211yesmaximal, characteristic, complemented
11C47×#497C211yesmaximal, characteristic, complemented
12C2×#10625354C2212yes—
13C2×Q8×D47C2211yescharacteristic
14C2×D4×D47C2211yescharacteristic
15#13094056—28no—
16#13094051—28no—
17C2×#10625337C2212yescomplemented
18C2×#10625325C2212yescomplemented
19C2×#10625336C2212yes—
20C2×#10625336C2212yescomplemented
21C2×D376C2212yes—
22C2×#10625334C2212yes—
23C2×#10625324C2212yes—
24#13094021C2211yescharacteristic, complemented
25#13094013C2211yescharacteristic
26#13094013C2212yescomplemented
27#13094012C2211yescharacteristic
28#13094011C2211yescharacteristic
29#13094010—22no—
30#13093999—22no—
31#13093986—22no—
32C22⋊C4×D47—22no—
33C42×D47C2211yescharacteristic
34#13093935C2211yescharacteristic, complemented
35C8×Dic47C2212yescomplemented
36C2×Q16×C47C2212yescomplemented
37C2×SD16×C47C2212yes—
38C4⋊Q8×C47C2211yescharacteristic, complemented
39#124×C47C2211yescharacteristic
40#97×C47C2211yescharacteristic, complemented
41C23×D47—21no—
42C2×Q8×C47C2311yescharacteristic
43C2×Q8×C47C2312yes—
44C2×D4×C47C2311yescharacteristic
45C2×C22⋊D47—21no—
46#10625354—24no—
47#10625354—24no—
48Q8×D47—24no—
49D4×D47—24no—
50C2×D188—22no—
51C2×D188—22no—
52C2×D188C2311yescharacteristic
53C2×D188C2312yes—
54C2×C4×D47—21no—
55C2×C4×D47—22no—
56C2×C4×D47D412yes—
57C2×C4×D47C2311yescharacteristic
58C2×Dic94—21no—
59C2×Dic94C2311yescharacteristic
60Q16×C47—24no—
61SD16×C47—24no—
62C2×C8×C47C2312yes—
63C4⋊C4×C47—22no—
64C22⋊C4×C47—22no—
65C42×C47C2311yescharacteristic
66C22⋊Dic47—22no—
67#10625337—24no—
68#10625336—24no—
69#10625336—24no—
70#10625334—24no—
71(C2×D47)⋊C4—22no—
72(C2×D47)⋊C4—22no—
73(C2×D47)⋊C4—24no—
74C4×Dic47D412yes—
75C4×Dic47C2311yescharacteristic
76C2×C47⋊C8C2312yes—
77D376—24no—
78#10625325—24no—
79#10625324D418yescomplemented
80C23×C47—21no—
81C22×D47—21no—
82C22×D47—22no—
83C22×D47—44no—
84C22×D47—42no—
85C22×D47C2×D411yescharacteristic
86Q8×C47—22no—
87Q8×C47—22no—
88Q8×C47—22no—
89D4×C47—22no—
90C2×C4×C47—21no—
91C2×C4×C47—22no—
92C2×C4×C47C2×D412yes—
93C2×C4×C47C2411yescharacteristic
94C22⋊D47—42no—
95C2×Dic47—21no—
96C2×Dic47C2×D412yes—
97C2×Dic47C2×D411yescharacteristic
98D188—22no—
99D188—22no—
100D188—22no—
101D188—44no—
102D188—44no—
103C4×D47—42no—
104C4×D47—42no—
105C4×D47—44no—
106C4×D47C2×D414yes—
107Dic94—22no—
108Dic94—42no—
109C8×C47C2×D414yes—
110C47⋊C8C2×D414yes—
111C22×C47—41no—
112C22×C47—42no—
113C22×C47C22×D411yescharacteristic
114C2×D47—22no—
115C2×D47—42no—
116C2×D47—41no—
117C2×D47—44no—
118C2×D47—42no—
119C2×D47—84no—
120C2×D47#12712yes—
121C4×C47—22no—
122C4×C47—41no—
123C4×C47—42no—
124C4×C47C22×D412yes—
125Dic47—22no—
126Dic47—41no—
127Dic47#12712yes—
128#3153—471nomaximal, Sylow
129C2×C47—81no—
130C2×C47C2×#12711yescharacteristic
131C2×C47#57512yes—
132D47—22no—
133D47—82no—
134D47—81no—
135C2×#137—472no—
136C2×AGL(1,ℤ/8)—472no—
137#532—471no—
138C2×#124—471no—
139#497—471no—
140#497D4711yescharacteristic, complemented
141#496—471no—
142#496—471no—
143#495—472no—
144#495—472no—
145C4×M16—471no—
146C47#315311yescharacteristic, complemented, Sylow
147C2×#41—472no—
148C22×Q8—471no—
149C22×D4—471no—
150#137—948no—
151AGL(1,ℤ/8)—948no—
152C2×Q16—472no—
153C2×Q16C2×D4712yescomplemented
154C2×SD16—472no—
155C2×SD16—472no—
156C2×SD16—472no—
157C2×SD16C2×D4712yes—
158C2×D8—472no—
159C2×D8—472no—
160C2×M16—472no—
161C4⋊Q8C2×D4711yescharacteristic, complemented
162#127—471no—
163#124—471no—
164#124—472no—
165#124—471no—
166#124—471no—
167#124—942no—
168#124C2×D4711yescharacteristic
169#121—942no—
170C4×D4—942no—
171C2×C22⋊C4—942no—
172C2×C42—471no—
173#97—471no—
174#97C2×D4711yescharacteristic, complemented
175C4×C8—472no—
176C24—941no—
177#41—944no—
178#41—944no—
179C2×Q8—471no—
180C2×Q8—941no—
181C2×Q8—944no—
182C2×Q8C22×D4711yescharacteristic
183C2×Q8C22×D4712yes—
184C2×D4—471no—
185C2×D4—472no—
186C2×D4—942no—
187C2×D4—944no—
188C2×D4—941no—
189C2×D4—942no—
190C2×D4C22×D4711yescharacteristic
191C22×C4—471no—
192C22×C4—472no—
193C22×C4—942no—
194C22×C4—941no—
195Q16—24no—
196Q16—944no—
197SD16—24no—
198SD16—944no—
199SD16—944no—
200SD16—944no—
201D8—944no—
202D8—944no—
203M16—478no—
204C2×C8—472no—
205C2×C8C22×D4712yes—
206C4⋊C4—22no—
207C22⋊C4—22no—
208C22⋊C4—942no—
209C22⋊C4—944no—
210C22⋊C4—942no—
211C22⋊C4—942no—
212C42—472no—
213C42—471no—
214C42C22×D4711yescharacteristic
215C23—21no—
216C23—471no—
217C23—941no—
218C23—942no—
219C23—1882no—
220C23—1884no—
221Q8—22no—
222Q8—22no—
223Q8—22no—
224Q8—942no—
225Q8—1882no—
226D4—22no—
227D4—942no—
228D4—942no—
229D4—942no—
230D4—1884no—
231D4—1884no—
232D4—1882no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—471no—
236C2×C4—474no—
237C2×C4—472no—
238C2×C4—941no—
239C2×C4—1882no—
240C2×C4—1884no—
241C2×C4—1882no—
242C2×C4D4×D4712yes—
243C2×C4C23×D4711yescharacteristic
244C8—474no—
245C8D4×D4714yes—
246C22—41no—
247C22—42no—
248C22—472no—
249C22—942no—
250C22—3764no—
251C22—1882no—
252C22—1881no—
253C22—1884no—
254C22—1882no—
255C22C2×D4×D4711yescharacteristic
256C4—22no—
257C4—42no—
258C4—41no—
259C4—472no—
260C4—942no—
261C4—1881no—
262C4C2×D4×D4712yes—
263C2—81no—
264C2—942no—
265C2—3761no—
266C2—3762no—
267C2#127×D4711yescharacteristic
268C2#1568992212yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#497C2
socleC22×C47C22×D4
hypercenter#497D47
hypocenterC47#3153
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×#13094056C2semidirect
2. C2×#13094051C2semidirect
3. #15689674C2semidirect
4. #124×D47C2semidirect
5. #15689515C2semidirect
6. #15689513C2semidirect
7. #15689512C2semidirect
8. #15689508C2semidirect
9. #15689504C2semidirect
10. #15689075C2semidirect
11. C47×#497C2semidirect
17. C2×#10625337C22semidirect
18. C2×#10625325C22semidirect
20. C2×#10625336C22semidirect
24. #13094021C22semidirect
26. #13094013C22semidirect
34. #13093935C22semidirect
35. C8×Dic47C22semidirect
36. C2×Q16×C47C22semidirect
38. C4⋊Q8×C47C22semidirect
40. #97×C47C22semidirect
79. #10625324D4semidirect
140. #497D47semidirect
146. C47#3153semidirect
153. C2×Q16C2×D47semidirect
161. C4⋊Q8C2×D47semidirect
174. #97C2×D47semidirect