Finite Group Databasebeta

← #20254325

Subgroups — #20254325

Order 6016.

488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 125 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#127×D47C211yesmaximal, characteristic
3#15689497C211yesmaximal, characteristic, complemented
4#15689470C211yesmaximal, characteristic, complemented
5#15689469C211yesmaximal, characteristic, complemented
6#15689321C214yesmaximal, complemented
7#15689272C214yesmaximal, complemented
8#15689174C211yesmaximal, characteristic, complemented
9C47×#492C211yesmaximal, characteristic, complemented
10C2×D4×D47—21no—
11C2×D4×D47—21no—
12C2×D4×D47C2212yes—
13C2×#10625336C2214yescomplemented
14#13094024C2211yescharacteristic, complemented
15#13094021C2211yescharacteristic
16#13094020—21no—
17#13094020—21no—
18#13094020C2212yes—
19#13094015—21no—
20#13094004—21no—
21#13094000C2212yes—
22Q8×Dic47C2212yescomplemented
23#13093989—21no—
24#13093982—21no—
25C42×D47C2211yescharacteristic
26Dic47⋊C8C2212yescomplemented
27#13093946C2214yescomplemented
28#13093945C2214yescomplemented
29(C2×D47)⋊C8C2212yes—
30C4×C47⋊C8C2211yescharacteristic, complemented
31C2×SD16×C47C2214yescomplemented
32C4⋊Q8×C47C2211yescharacteristic, complemented
33#127×C47C2211yescharacteristic
34C4×C8×C47C2211yescharacteristic, complemented
35C23×D47—22no—
36C2×Q8×C47C2312yes—
37C2×D4×C47—21no—
38C2×D4×C47—21no—
39C2×D4×C47C2312yes—
40C2×C22⋊D47—22no—
41C2×C22⋊D47—22no—
42C2×C22⋊D47—22no—
43D4×D47—44no—
44D4×D47—44no—
45D4×D47—44no—
46C2×D188—21no—
47C2×D188—21no—
48C2×D188C2312yes—
49C2×C4×D47D411yescharacteristic
50C2×C4×D47D411yescharacteristic
51C2×C4×D47C2311yescharacteristic
52C2×Dic94—21no—
53SD16×C47—44no—
54C2×C8×C47C2312yes—
55C4⋊C4×C47—21no—
56C4⋊C4×C47—21no—
57C42×C47C2311yescharacteristic
58#10625336—44no—
59(C2×D47)⋊C4—22no—
60C4⋊Dic47—21no—
61C4⋊Dic47—22no—
62C4⋊Dic47C2312yes—
63Dic47⋊C4—22no—
64C4×Dic47—22no—
65C4×Dic47D411yescharacteristic
66C4×Dic47D411yescharacteristic
67C4×Dic47C2311yescharacteristic
68C2×C47⋊C8C2312yes—
69C23×C47—22no—
70C22×D47—22no—
71C22×D47—44no—
72C22×D47—44no—
73C22×D47—44no—
74C22×D47C2×D411yescharacteristic
75Q8×C47—24no—
76D4×C47—24no—
77D4×C47—42no—
78D4×C47—42no—
79C2×C4×C47—22no—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2411yescharacteristic
83C22⋊D47—44no—
84C22⋊D47—44no—
85C22⋊D47—44no—
86C2×Dic47—22no—
87C2×Dic47C2×D411yescharacteristic
88C2×Dic47C2×D411yescharacteristic
89C2×Dic47C2×D411yescharacteristic
90D188—24no—
91D188—42no—
92D188—42no—
93C4×D47—22no—
94C4×D47—22no—
95C4×D47SD1614yescomplemented
96Dic94—42no—
97C8×C47—22no—
98C47⋊C8—22no—
99C22×C47—42no—
100C22×C47—42no—
101C22×C47—42no—
102C22×C47C22×D411yescharacteristic
103C2×D47—21no—
104C2×D47—21no—
105C2×D47—42no—
106C2×D47—42no—
107C2×D47—42no—
108C2×D47—88no—
109C2×D47C2×SD1612yes—
110C4×C47—42no—
111C4×C47C2×SD1612yes—
112C4×C47AGL(1,ℤ/8)12yes—
113C4×C47H(5,𝔽2)12yes—
114Dic47—21no—
115Dic47—21no—
116Dic47—42no—
117Dic47C2×SD1612yes—
118#3208—471nomaximal, Sylow
119C2×C47—82no—
120C2×C47#53511yescharacteristic
121C2×C47C22×SD1611yescharacteristic
122C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
123D47—22no—
124D47—82no—
125#533—471no—
126C2×#127—471no—
127#492—471no—
128#492D4711yescharacteristic, complemented
129#486—471no—
130#486—471no—
131#460—474no—
132#450—474no—
133#431—471no—
134C47#320811yescharacteristic, complemented, Sylow
135C22×D4—472no—
136C22×D4—941no—
137C22×D4—941no—
138C2×SD16—474no—
139C2×SD16C2×D4714yescomplemented
140C4⋊Q8—471no—
141C4⋊Q8C2×D4711yescharacteristic, complemented
142#127—472no—
143#127—471no—
144#127—941no—
145#127—941no—
146#127C2×D4711yescharacteristic
147#125—941no—
148C22⋊Q8—472no—
149C22⋊Q8—941no—
150C4×Q8—472no—
151C4×Q8—941no—
152#117—941no—
153C2×C42—471no—
154C4⋊C8—472no—
155#102—474no—
156#102—474no—
157C22⋊C8—472no—
158C4×C8—471no—
159C4×C8C2×D4711yescharacteristic, complemented
160C24—942no—
161C2×Q8—941no—
162C2×Q8C22×D4712yes—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—472no—
166C2×D4—942no—
167C2×D4—942no—
168C2×D4—942no—
169C2×D4—941no—
170C2×D4—941no—
171C2×D4—1884no—
172C2×D4—1884no—
173C2×D4—1884no—
174C2×D4C22×D4712yes—
175C22×C4—471no—
176C22×C4—471no—
177C22×C4—471no—
178SD16—44no—
179SD16—1884no—
180C2×C8—472no—
181C2×C8C22×D4712yes—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—472no—
185C4⋊C4—942no—
186C4⋊C4—942no—
187C4⋊C4—941no—
188C22⋊C4—942no—
189C42—471no—
190C42—471no—
191C42—471no—
192C42—942no—
193C42C22×D4711yescharacteristic
194C23—22no—
195C23—471no—
196C23—942no—
197C23—1884no—
198C23—1884no—
199C23—1884no—
200Q8—24no—
201Q8—1882no—
202D4—24no—
203D4—42no—
204D4—42no—
205D4—944no—
206D4—1884no—
207D4—1884no—
208D4—1884no—
209D4—1882no—
210D4—1882no—
211C2×C4—22no—
212C2×C4—471no—
213C2×C4—474no—
214C2×C4—471no—
215C2×C4—471no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—942no—
219C2×C4D4×D4711yescharacteristic
220C2×C4D4×D4711yescharacteristic
221C2×C4C23×D4711yescharacteristic
222C8—22no—
223C8—942no—
224C22—42no—
225C22—42no—
226C22—42no—
227C22—472no—
228C22—941no—
229C22—941no—
230C22—3768no—
231C22—1882no—
232C22—1882no—
233C22—1882no—
234C22C2×D4×D4711yescharacteristic
235C4—42no—
236C4—472no—
237C4—941no—
238C4—941no—
239C4—1882no—
240C4SD16×D4712yes—
241C4#1309405112yes—
242C4#1309406912yes—
243C2—82no—
244C2—942no—
245C2—3762no—
246C2#1568968611yescharacteristic
247C2C2×SD16×D4711yescharacteristic
248C2C2×#1309405111yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#492C2
socleC22×C47C22×D4
hypercenter#492D47
hypocenterC47#3208
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #15689678C2semidirect
3. #15689497C2semidirect
4. #15689470C2semidirect
5. #15689469C2semidirect
6. #15689321C2semidirect
7. #15689272C2semidirect
8. #15689174C2semidirect
9. C47×#492C2semidirect
13. C2×#10625336C22semidirect
14. #13094024C22semidirect
22. Q8×Dic47C22semidirect
26. Dic47⋊C8C22semidirect
27. #13093946C22semidirect
28. #13093945C22semidirect
30. C4×C47⋊C8C22semidirect
31. C2×SD16×C47C22semidirect
32. C4⋊Q8×C47C22semidirect
34. C4×C8×C47C22semidirect
95. C4×D47SD16semidirect
128. #492D47semidirect
134. C47#3208semidirect
139. C2×SD16C2×D47semidirect
141. C4⋊Q8C2×D47semidirect
159. C4×C8C2×D47semidirect