Finite Group Databasebeta

← #120×D43 #14583383

Subgroups — #120×D43 #14583383

Order 2752.

662 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C24×D43C211yesmaximal, characteristic, complemented
2C2×D4×D43C213yesmaximal, complemented
3#13063295C213yesmaximal, complemented
4#13063294C211yesmaximal, characteristic, complemented
5#13063293C213yesmaximal, complemented
6C22⋊C4×D43C213yesmaximal, complemented
7#120×C43C211yesmaximal, characteristic, complemented
8C24×C43C2211yescharacteristic, complemented
9C23×D43—212no—
10C23×D43C2213yes—
11C23×D43C2213yescomplemented
12C23×D43C2211yescharacteristic, complemented
13C2×D4×C43C2213yescomplemented
14C2×C22⋊D43C2213yescomplemented
15C2×C22⋊D43C2213yescomplemented
16D4×D43—212no—
17C2×D172C2213yescomplemented
18C2×C4×D43C2213yescomplemented
19C22⋊C4×C43C2213yescomplemented
20C22⋊Dic43C2213yescomplemented
21(C2×D43)⋊C4C2216yescomplemented
22C23×C43—26no—
23C23×C43C2313yes—
24C23×C43C2311yescharacteristic, complemented
25C22×D43—232no—
26C22×D43—26no—
27C22×D43—212no—
28C22×D43—212no—
29C22×D43—26no—
30C22×D43D4112yescomplemented
31C22×D43C2313yes—
32C22×D43C2311yescharacteristic
33C22×D43C2311yescharacteristic, complemented
34D4×C43—26no—
35C2×C4×C43C2313yescomplemented
36C22⋊D43—26no—
37C22⋊D43—26no—
38C2×Dic43C2313yescomplemented
39D172—26no—
40C4×D43—26no—
41C22×C43—28no—
42C22×C43—26no—
43C22×C43—23no—
44C22×C43C2×D416yescomplemented
45C22×C43C2411yescharacteristic
46C2×D43—224no—
47C2×D43—26no—
48C2×D43—224no—
49C2×D43—23no—
50C2×D43—44no—
51C2×D43C2×D416yes—
52C2×D43C2×D416yescomplemented
53C4×C43—23no—
54Dic43—23no—
55C2×C43—26no—
56C2×C43—41no—
57C2×C43C22×D413yes—
58D43—26no—
59D43—41no—
60D43#12014yesdirect product factor
61C2×#120—431nomaximal, Sylow
62C43C2×#12011yescharacteristic, complemented, Sylow
63C25—431no—
64C22×D4—433no—
65#120—431no—
66#120—433no—
67#120—433no—
68#120D4311yescharacteristic, direct product factor
69C2×C22⋊C4—433no—
70C24—433no—
71C24—433no—
72C24—431no—
73C24—8612no—
74C24C2×D4311yescharacteristic, complemented
75C2×D4—433no—
76C2×D4—433no—
77C2×D4—433no—
78C2×D4—8612no—
79C2×D4C2×D4313yescomplemented
80C22×C4—433no—
81C22⋊C4—433no—
82C22⋊C4—436no—
83C22⋊C4C2×D4313yescomplemented
84C23—26no—
85C23—431no—
86C23—4312no—
87C23—433no—
88C23—431no—
89C23—8612no—
90C23—8612no—
91C23—866no—
92C23—8632no—
93C23—866no—
94C23C22×D4313yes—
95C23C22×D4311yescharacteristic, complemented
96D4—26no—
97D4—866no—
98D4—866no—
99D4—866no—
100C2×C4—433no—
101C2×C4—866no—
102C2×C4C22×D4313yescomplemented
103C22—28no—
104C22—26no—
105C22—23no—
106C22—436no—
107C22—436no—
108C22—8624no—
109C22—8624no—
110C22—866no—
111C22—863no—
112C22—1724no—
113C22D4×D4316yescomplemented
114C22C23×D4311yescharacteristic
115C4—23no—
116C4—863no—
117C2—26no—
118C2—41no—
119C2—434no—
120C2—866no—
121C2—1721no—
122C2C2×D4×D4313yes—
subgroupG/H
center, FrattiniC22C23×D43
commutator, socle, cosocleC22×C43C24
Fitting#120×C43C2
hypercenter#120D43
hypocenterC43C2×#120
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C24×D43C2semidirect
2. C2×D4×D43C2semidirect
3. #13063295C2semidirect
4. #13063294C2semidirect
5. #13063293C2semidirect
6. C22⋊C4×D43C2semidirect
7. #120×C43C2semidirect
8. C24×C43C22semidirect
11. C23×D43C22semidirect
12. C23×D43C22semidirect
13. C2×D4×C43C22semidirect
14. C2×C22⋊D43C22semidirect
15. C2×C22⋊D43C22semidirect
17. C2×D172C22semidirect
18. C2×C4×D43C22semidirect
19. C22⋊C4×C43C22semidirect
20. C22⋊Dic43C22semidirect
21. (C2×D43)⋊C4C22semidirect
24. C23×C43C23semidirect
30. C22×D43D4semidirect
33. C22×D43C23semidirect
35. C2×C4×C43C23semidirect
38. C2×Dic43C23semidirect
44. C22×C43C2×D4semidirect
52. C2×D43C2×D4semidirect
60. D43#120direct (N × H)
62. C43C2×#120semidirect
68. #120D43direct (N × H)
74. C24C2×D43semidirect
79. C2×D4C2×D43semidirect
83. C22⋊C4C2×D43semidirect
95. C23C22×D43semidirect
102. C2×C4C22×D43semidirect
113. C22D4×D43semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C24×D432
C2×D4×D432
#130632952
#130632942
#130632932
C22⋊C4×D432
#120×C432
C2×#12043