Finite Group Databasebeta

← #20257166

Subgroups — #20257166

Order 6016.

1748 conjugacy classes of subgroups; only the 557 normal subgroups are shown.

normal subgroups only

This group has 1748 conjugacy classes of subgroups — too many to draw. Only its 557 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×#13094070C212yesmaximal, complemented
2#15689795C214yesmaximal, complemented
3D4×D188C2112yesmaximal, complemented
4#15689692C216yesmaximal, complemented
5#15689673C213yesmaximal, complemented
6C2×#13094021C213yesmaximal, complemented
7C4×#41×C47C211yesmaximal, characteristic, complemented
8#13094070—216no—
9C2×#10625354C2214yescomplemented
10C2×#10625350C2216yescomplemented
11C22×D188C2216yescomplemented
12C22×D188C22112yescomplemented
13C2×D4×D47C22112yescomplemented
14#13094024C2211yescharacteristic, complemented
15#13094021C22112yescomplemented
16#13094021C2213yescomplemented
17#13094021C2216yescomplemented
18#13094012C2216yescomplemented
19#13093999C22124yescomplemented
20#13093998C22112yescomplemented
21#13093994C22124yescomplemented
22C4×D188C22112yescomplemented
23C2×#41×C47C2211yescharacteristic
24C4×Q8×C47C2212yescomplemented
25C4×D4×C47C2216yescomplemented
26#117×C47C2213yescomplemented
27C2×C42×C47C2213yescomplemented
28C23×D47C23112yes—
29#41×C47D418yescomplemented
30C2×Q8×C47C2311yescharacteristic
31C2×D4×C47C2313yes—
32C22×C4×C47C2316yes—
33C22×C4×C47C2313yes—
34C2×C22⋊D47C23112yes—
35#10625354—216no—
36D4×D47—248no—
37#10625350—224no—
38C2×D188—224no—
39C2×D188—424no—
40C2×D188C23112yes—
41C2×D188C23112yes—
42C2×D188C2316yes—
43C2×D188C23124yes—
44C2×C4×D47C23112yes—
45C2×Dic94C2312yes—
46C4⋊C4×C47C2316yes—
47C22⋊C4×C47C2316yes—
48C42×C47C2311yescharacteristic
49C42×C47C2313yes—
50C42×C47C2316yes—
51(C2×D47)⋊C4C23124yes—
52C4⋊Dic47C2314yes—
53C23×C47C2413yes—
54C22×D47—224no—
55C22×D47—424no—
56C22×D47C24112yes—
57Q8×C47C2×D414yescomplemented
58D4×C47C2×D4112yescomplemented
59C2×C4×C47—212no—
60C2×C4×C47C2×D4112yescomplemented
61C2×C4×C47C2416yes—
62C2×C4×C47C2411yescharacteristic
63C2×C4×C47C2413yes—
64C2×C4×C47C2412yes—
65C22⋊D47—224no—
66C2×Dic47C2414yes—
67D188—212no—
68D188—224no—
69D188—224no—
70D188—424no—
71C4×D47—224no—
72Dic94—24no—
73C22×C47—26no—
74C22×C47C22×D416yes—
75C22×C47C2511yescharacteristic
76C2×D47—212no—
77C2×D47—224no—
78C2×D47—824no—
79C4×C47—26no—
80C4×C47C22×D412yes—
81C4×C47C22×D416yes—
82C4×C47H(5,𝔽2)14yescomplemented
83Dic47—24no—
84#3498—471nomaximal, Sylow
85C2×C47—26no—
86C2×C47C23×D411yescharacteristic
87C2×C47C2×H(5,𝔽2)12yes—
88D47—412no—
89C2×H(5,𝔽2)—472no—
90#550—474no—
91D42—4712no—
92#535—476no—
93#532—473no—
94C2×#127—473no—
95C4×#41D4711yescharacteristic, complemented
96C47#349811yescharacteristic, complemented, Sylow
97H(5,𝔽2)—9416no—
98C2×#41—474no—
99C2×#41—476no—
100C2×#41C2×D4711yescharacteristic
101C22×D4—4712no—
102C22×D4—476no—
103C22×D4—4712no—
104C4⋊Q8—471no—
105#127—473no—
106#127—476no—
107#127—4712no—
108#124—476no—
109#121—4712no—
110#121—4724no—
111#120—4724no—
112C4×Q8C2×D4712yescomplemented
113C4×D4—4712no—
114C4×D4C2×D4716yescomplemented
115#117C2×D4713yescomplemented
116C2×C42C2×D4713yescomplemented
117C24—4712no—
118#41—9416no—
119#41—9424no—
120#41D18818yescomplemented
121C2×Q8—472no—
122C2×Q8C22×D4711yescharacteristic
123C2×D4—4712no—
124C2×D4—4712no—
125C2×D4—4712no—
126C2×D4—476no—
127C2×D4—4724no—
128C2×D4—9448no—
129C2×D4—9424no—
130C2×D4—18824no—
131C2×D4C22×D4713yes—
132C22×C4—4712no—
133C22×C4C22×D4716yes—
134C22×C4C22×D4713yes—
135C4⋊C4—474no—
136C4⋊C4C22×D4716yes—
137C22⋊C4—4724no—
138C22⋊C4C22×D4716yes—
139C42C22×D4711yescharacteristic
140C42C22×D4713yes—
141C42C22×D4716yes—
142C23—4712no—
143C23—9424no—
144C23—18824no—
145C23C23×D4713yes—
146Q8—944no—
147Q8C2×D18814yescomplemented
148D4—9424no—
149D4—9424no—
150D4—9412no—
151D4—9424no—
152D4—18824no—
153D4C2×D188112yescomplemented
154C2×C4—212no—
155C2×C4—474no—
156C2×C4—9424no—
157C2×C4C2×D188112yescomplemented
158C2×C4C23×D4716yes—
159C2×C4C23×D4711yescharacteristic
160C2×C4C23×D4713yes—
161C2×C4C23×D4712yes—
162C22—26no—
163C22—9412no—
164C22—9424no—
165C22—37624no—
166C22C22×D18816yes—
167C22C24×D4711yescharacteristic
168C4—26no—
169C4—944no—
170C4C22×D18816yes—
171C4C22×D18812yes—
172C4#1309407014yescomplemented
173C2—26no—
174C2—18812no—
175C2C23×D18811yescharacteristic
176C2C2×#1309407012yes—
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC4×#41×C47C2
hypercenterC4×#41D47
hypocenterC47#3498
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#13094070C2semidirect
2. #15689795C2semidirect
3. D4×D188C2semidirect
4. #15689692C2semidirect
5. #15689673C2semidirect
6. C2×#13094021C2semidirect
7. C4×#41×C47C2semidirect
9. C2×#10625354C22semidirect
10. C2×#10625350C22semidirect
11. C22×D188C22semidirect
12. C22×D188C22semidirect
13. C2×D4×D47C22semidirect
14. #13094024C22semidirect
15. #13094021C22semidirect
16. #13094021C22semidirect
17. #13094021C22semidirect
18. #13094012C22semidirect
19. #13093999C22semidirect
20. #13093998C22semidirect
21. #13093994C22semidirect
22. C4×D188C22semidirect
24. C4×Q8×C47C22semidirect
25. C4×D4×C47C22semidirect
26. #117×C47C22semidirect
27. C2×C42×C47C22semidirect
29. #41×C47D4semidirect
57. Q8×C47C2×D4semidirect
58. D4×C47C2×D4semidirect
60. C2×C4×C47C2×D4semidirect
82. C4×C47H(5,𝔽2)semidirect
95. C4×#41D47semidirect
96. C47#3498semidirect
112. C4×Q8C2×D47semidirect
114. C4×D4C2×D47semidirect
115. #117C2×D47semidirect
116. C2×C42C2×D47semidirect
120. #41D188semidirect
147. Q8C2×D188semidirect
153. D4C2×D188semidirect
157. C2×C4C2×D188semidirect
172. C4#13094070semidirect