Finite Group Databasebeta

← #20254997

Subgroups — #20254997

Order 6016.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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×#13094051C212yesmaximal, complemented
2#15689766C212yesmaximal, complemented
3#15689366C212yesmaximal, complemented
4#15689335C212yesmaximal, complemented
5#15689284C212yesmaximal, complemented
6#15689255C212yesmaximal, complemented
7C4×D376C211yesmaximal, characteristic, complemented
8#15689202C211yesmaximal, characteristic, complemented
9C47×#495C211yesmaximal, characteristic, complemented
10C2×#10625354C2212yes—
11C2×D4×D47C2212yescomplemented
12#13094051—28no—
13C2×#10625336C2212yescomplemented
14C2×D376C2211yescharacteristic
15C2×#10625334C2212yes—
16C2×#10625324C2212yescomplemented
17#13094006—22no—
18#13094000C2212yescomplemented
19#13093997—22no—
20#13093995C2212yes—
21#13093994—22no—
22C4×D188C2211yescharacteristic
23C4×D188C2212yescomplemented
24C22⋊C4×D47—22no—
25#13093958C2211yescharacteristic, complemented
26C4⋊(C47⋊C8)C2211yescharacteristic, complemented
27#13093948C2212yescomplemented
28#13093946C2212yescomplemented
29#13093945C2212yescomplemented
30(C2×D47)⋊C8C2212yescomplemented
31C2×Q16×C47C2211yescharacteristic, complemented
32C2×SD16×C47C2212yescomplemented
33C2×D8×C47C2211yescharacteristic
34#124×C47C2212yescomplemented
35C4×C8×C47C2211yescharacteristic, complemented
36C23×D47—22no—
37C2×Q8×C47C2312yes—
38C2×D4×C47C2312yes—
39C2×C22⋊D47—22no—
40C2×C22⋊D47—22no—
41#10625354—24no—
42#10625354—42no—
43D4×D47—24no—
44D4×D47—42no—
45C2×D188—22no—
46C2×D188D411yescharacteristic
47C2×D188C2312yes—
48C2×C4×D47—22no—
49C2×C4×D47—22no—
50C2×C4×D47C2312yes—
51Q16×C47—41no—
52SD16×C47—24no—
53D8×C47—41no—
54C2×C8×C47C2311yescharacteristic
55C2×C8×C47C2311yescharacteristic
56C22⋊C4×C47—22no—
57C22⋊C4×C47—22no—
58C42×C47C2311yescharacteristic
59C22⋊Dic47—22no—
60#10625336—24no—
61#10625334—24no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—22no—
64(C2×D47)⋊C4D412yes—
65C4⋊Dic47D411yescharacteristic
66C4⋊Dic47C2312yes—
67Dic47⋊C4—22no—
68C2×C47⋊C8C2312yes—
69D376D414yescomplemented
70#10625324—24no—
71C23×C47—22no—
72C22×D47—22no—
73C22×D47—44no—
74C22×D47—44no—
75C22×D47—82no—
76C22×D47C2×D412yes—
77Q8×C47—22no—
78Q8×C47—22no—
79D4×C47—22no—
80D4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2411yescharacteristic
85C22⋊D47—44no—
86C22⋊D47—82no—
87C2×Dic47—22no—
88C2×Dic47C2×D412yes—
89D188—22no—
90D188—41no—
91D188—44no—
92D188C2×D414yes—
93C4×D47—22no—
94C4×D47—22no—
95C4×D47—44no—
96C4×D47—82no—
97C8×C47—21no—
98C8×C47C2×D412yes—
99C47⋊C8—22no—
100C22×C47—42no—
101C22×C47—42no—
102C22×C47—42no—
103C22×C47C22×D411yescharacteristic
104C2×D47—22no—
105C2×D47—24no—
106C2×D47—22no—
107C2×D47—22no—
108C2×D47—42no—
109C2×D47—42no—
110C2×D47—88no—
111C4×C47—21no—
112C4×C47—21no—
113C4×C47—42no—
114C4×C47C22×D411yescharacteristic
115C4×C47H(5,𝔽2)11yescharacteristic
116Dic47—22no—
117Dic47—42no—
118#3273—471nomaximal, Sylow
119C2×C47—82no—
120C2×C47D4211yescharacteristic
121C2×C47#57511yescharacteristic
122C2×C47#57611yescharacteristic
123D47—42no—
124D47—44no—
125C2×AGL(1,ℤ/8)—472no—
126#546—472no—
127#495D4711yescharacteristic, complemented
128#468—472no—
129#463—472no—
130#452—472no—
131#447—472no—
132C4×D8—471no—
133#436—471no—
134C47#327311yescharacteristic, complemented, Sylow
135C2×#41—472no—
136C22×D4—472no—
137AGL(1,ℤ/8)—948no—
138C2×Q16C2×D4711yescharacteristic, complemented
139C2×SD16—472no—
140C2×SD16C2×D4712yescomplemented
141C2×D8—472no—
142C2×D8—471no—
143C2×D8C2×D4711yescharacteristic
144C2×M16—472no—
145#124C2×D4712yescomplemented
146#123—942no—
147C22⋊Q8—472no—
148#121—472no—
149#121—942no—
150#120—942no—
151C4×D4—471no—
152C4×D4—472no—
153C2×C22⋊C4—942no—
154#107—471no—
155C4⋊C8—471no—
156#103—472no—
157#102—472no—
158#102—472no—
159C22⋊C8—472no—
160C4×C8C2×D4711yescharacteristic, complemented
161C24—942no—
162#41—944no—
163#41—1882no—
164C2×Q8C22×D4712yes—
165C2×D4—471no—
166C2×D4—472no—
167C2×D4—942no—
168C2×D4—942no—
169C2×D4—944no—
170C2×D4—942no—
171C2×D4—1882no—
172C2×D4C22×D4712yes—
173C22×C4—472no—
174C22×C4—942no—
175C22×C4—942no—
176Q16—41no—
177SD16—24no—
178SD16—944no—
179D8—41no—
180D8—474no—
181D8—944no—
182M16—944no—
183C2×C8—472no—
184C2×C8C22×D4711yescharacteristic
185C2×C8C22×D4711yescharacteristic
186C4⋊C4—471no—
187C4⋊C4—472no—
188C4⋊C4—942no—
189C22⋊C4—22no—
190C22⋊C4—22no—
191C22⋊C4—472no—
192C22⋊C4—942no—
193C22⋊C4—942no—
194C22⋊C4—942no—
195C42C22×D4711yescharacteristic
196C23—22no—
197C23—472no—
198C23—942no—
199C23—3762no—
200C23—1884no—
201C23—1884no—
202Q8—22no—
203Q8—22no—
204D4—22no—
205D4—22no—
206D4—474no—
207D4—942no—
208D4—3762no—
209D4—1881no—
210D4—1884no—
211D4—1884no—
212C2×C4—22no—
213C2×C4—472no—
214C2×C4—942no—
215C2×C4—942no—
216C2×C4—942no—
217C2×C4—3762no—
218C2×C4—1884no—
219C2×C4D4×D4711yescharacteristic
220C2×C4D4×D4711yescharacteristic
221C2×C4C23×D4711yescharacteristic
222C8—21no—
223C8—942no—
224C8D4×D4712yes—
225C22—42no—
226C22—42no—
227C22—42no—
228C22—942no—
229C22—944no—
230C22—942no—
231C22—942no—
232C22—3768no—
233C22—1882no—
234C22—1882no—
235C22C2×D4×D4711yescharacteristic
236C4—21no—
237C4—21no—
238C4—42no—
239C4—942no—
240C4—1882no—
241C4C2×D4×D4711yescharacteristic
242C4#1309406911yescharacteristic
243C2—82no—
244C2—1882no—
245C2—1884no—
246C2#1568975811yescharacteristic
247C2#1568992011yescharacteristic
248C2#1568992511yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#495C2
socleC22×C47C22×D4
hypercenter#495D47
hypocenterC47#3273
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#13094051C2semidirect
2. #15689766C2semidirect
3. #15689366C2semidirect
4. #15689335C2semidirect
5. #15689284C2semidirect
6. #15689255C2semidirect
7. C4×D376C2semidirect
8. #15689202C2semidirect
9. C47×#495C2semidirect
11. C2×D4×D47C22semidirect
13. C2×#10625336C22semidirect
16. C2×#10625324C22semidirect
18. #13094000C22semidirect
23. C4×D188C22semidirect
25. #13093958C22semidirect
26. C4⋊(C47⋊C8)C22semidirect
27. #13093948C22semidirect
28. #13093946C22semidirect
29. #13093945C22semidirect
30. (C2×D47)⋊C8C22semidirect
31. C2×Q16×C47C22semidirect
32. C2×SD16×C47C22semidirect
34. #124×C47C22semidirect
35. C4×C8×C47C22semidirect
69. D376D4semidirect
127. #495D47semidirect
134. C47#3273semidirect
138. C2×Q16C2×D47semidirect
140. C2×SD16C2×D47semidirect
145. #124C2×D47semidirect
160. C4×C8C2×D47semidirect