Finite Group Databasebeta

← #19148373

Subgroups — #19148373

Order 5504.

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×#13063371C212yesmaximal, complemented
2#14583571C214yesmaximal, complemented
3D4×D172C2112yesmaximal, complemented
4#14583468C216yesmaximal, complemented
5#14583449C213yesmaximal, complemented
6C2×#13063322C213yesmaximal, complemented
7C4×#41×C43C211yesmaximal, characteristic, complemented
8#13063371—216no—
9C2×#10621902C2214yescomplemented
10C2×#10621898C2216yescomplemented
11C22×D172C2216yescomplemented
12C22×D172C22112yescomplemented
13C2×D4×D43C22112yescomplemented
14#13063325C2211yescharacteristic, complemented
15#13063322C22112yescomplemented
16#13063322C2213yescomplemented
17#13063322C2216yescomplemented
18#13063313C2216yescomplemented
19#13063300C22124yescomplemented
20#13063299C22112yescomplemented
21#13063295C22124yescomplemented
22C4×D172C22112yescomplemented
23C2×#41×C43C2211yescharacteristic
24C4×Q8×C43C2212yescomplemented
25C4×D4×C43C2216yescomplemented
26#117×C43C2213yescomplemented
27C2×C42×C43C2213yescomplemented
28C23×D43C23112yes—
29#41×C43D418yescomplemented
30C2×Q8×C43C2311yescharacteristic
31C2×D4×C43C2313yes—
32C22×C4×C43C2316yes—
33C22×C4×C43C2313yes—
34C2×C22⋊D43C23112yes—
35#10621902—216no—
36D4×D43—248no—
37#10621898—224no—
38C2×D172—224no—
39C2×D172—424no—
40C2×D172C23112yes—
41C2×D172C23112yes—
42C2×D172C2316yes—
43C2×D172C23124yes—
44C2×C4×D43C23112yes—
45C2×Dic86C2312yes—
46C4⋊C4×C43C2316yes—
47C22⋊C4×C43C2316yes—
48C42×C43C2311yescharacteristic
49C42×C43C2313yes—
50C42×C43C2316yes—
51(C2×D43)⋊C4C23124yes—
52C4⋊Dic43C2314yes—
53C23×C43C2413yes—
54C22×D43—224no—
55C22×D43—424no—
56C22×D43C24112yes—
57Q8×C43C2×D414yescomplemented
58D4×C43C2×D4112yescomplemented
59C2×C4×C43—212no—
60C2×C4×C43C2×D4112yescomplemented
61C2×C4×C43C2416yes—
62C2×C4×C43C2411yescharacteristic
63C2×C4×C43C2413yes—
64C2×C4×C43C2412yes—
65C22⋊D43—224no—
66C2×Dic43C2414yes—
67D172—212no—
68D172—224no—
69D172—224no—
70D172—424no—
71C4×D43—224no—
72Dic86—24no—
73C22×C43—26no—
74C22×C43C22×D416yes—
75C22×C43C2511yescharacteristic
76C2×D43—212no—
77C2×D43—224no—
78C2×D43—824no—
79C4×C43—26no—
80C4×C43C22×D412yes—
81C4×C43C22×D416yes—
82C4×C43H(5,𝔽2)14yescomplemented
83Dic43—24no—
84#3498—431nomaximal, Sylow
85C2×C43—26no—
86C2×C43C23×D411yescharacteristic
87C2×C43C2×H(5,𝔽2)12yes—
88D43—412no—
89C2×H(5,𝔽2)—432no—
90#550—434no—
91D42—4312no—
92#535—436no—
93#532—433no—
94C2×#127—433no—
95C4×#41D4311yescharacteristic, complemented
96C43#349811yescharacteristic, complemented, Sylow
97H(5,𝔽2)—8616no—
98C2×#41—434no—
99C2×#41—436no—
100C2×#41C2×D4311yescharacteristic
101C22×D4—4312no—
102C22×D4—436no—
103C22×D4—4312no—
104C4⋊Q8—431no—
105#127—433no—
106#127—436no—
107#127—4312no—
108#124—436no—
109#121—4312no—
110#121—4324no—
111#120—4324no—
112C4×Q8C2×D4312yescomplemented
113C4×D4—4312no—
114C4×D4C2×D4316yescomplemented
115#117C2×D4313yescomplemented
116C2×C42C2×D4313yescomplemented
117C24—4312no—
118#41—8616no—
119#41—8624no—
120#41D17218yescomplemented
121C2×Q8—432no—
122C2×Q8C22×D4311yescharacteristic
123C2×D4—4312no—
124C2×D4—4312no—
125C2×D4—4312no—
126C2×D4—436no—
127C2×D4—4324no—
128C2×D4—8648no—
129C2×D4—8624no—
130C2×D4—17224no—
131C2×D4C22×D4313yes—
132C22×C4—4312no—
133C22×C4C22×D4316yes—
134C22×C4C22×D4313yes—
135C4⋊C4—434no—
136C4⋊C4C22×D4316yes—
137C22⋊C4—4324no—
138C22⋊C4C22×D4316yes—
139C42C22×D4311yescharacteristic
140C42C22×D4313yes—
141C42C22×D4316yes—
142C23—4312no—
143C23—8624no—
144C23—17224no—
145C23C23×D4313yes—
146Q8—864no—
147Q8C2×D17214yescomplemented
148D4—8624no—
149D4—8624no—
150D4—8612no—
151D4—8624no—
152D4—17224no—
153D4C2×D172112yescomplemented
154C2×C4—212no—
155C2×C4—434no—
156C2×C4—8624no—
157C2×C4C2×D172112yescomplemented
158C2×C4C23×D4316yes—
159C2×C4C23×D4311yescharacteristic
160C2×C4C23×D4313yes—
161C2×C4C23×D4312yes—
162C22—26no—
163C22—8612no—
164C22—8624no—
165C22—34424no—
166C22C22×D17216yes—
167C22C24×D4311yescharacteristic
168C4—26no—
169C4—864no—
170C4C22×D17216yes—
171C4C22×D17212yes—
172C4#1306337114yescomplemented
173C2—26no—
174C2—17212no—
175C2C23×D17211yescharacteristic
176C2C2×#1306337112yes—
subgroupG/H
center, FrattiniC22C24×D43
commutator, socleC22×C43C25
FittingC4×#41×C43C2
hypercenterC4×#41D43
hypocenterC43#3498
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#13063371C2semidirect
2. #14583571C2semidirect
3. D4×D172C2semidirect
4. #14583468C2semidirect
5. #14583449C2semidirect
6. C2×#13063322C2semidirect
7. C4×#41×C43C2semidirect
9. C2×#10621902C22semidirect
10. C2×#10621898C22semidirect
11. C22×D172C22semidirect
12. C22×D172C22semidirect
13. C2×D4×D43C22semidirect
14. #13063325C22semidirect
15. #13063322C22semidirect
16. #13063322C22semidirect
17. #13063322C22semidirect
18. #13063313C22semidirect
19. #13063300C22semidirect
20. #13063299C22semidirect
21. #13063295C22semidirect
22. C4×D172C22semidirect
24. C4×Q8×C43C22semidirect
25. C4×D4×C43C22semidirect
26. #117×C43C22semidirect
27. C2×C42×C43C22semidirect
29. #41×C43D4semidirect
57. Q8×C43C2×D4semidirect
58. D4×C43C2×D4semidirect
60. C2×C4×C43C2×D4semidirect
82. C4×C43H(5,𝔽2)semidirect
95. C4×#41D43semidirect
96. C43#3498semidirect
112. C4×Q8C2×D43semidirect
114. C4×D4C2×D43semidirect
115. #117C2×D43semidirect
116. C2×C42C2×D43semidirect
120. #41D172semidirect
147. Q8C2×D172semidirect
153. D4C2×D172semidirect
157. C2×C4C2×D172semidirect
172. C4#13063371semidirect