Finite Group Databasebeta

← #14583701

Subgroups — #14583701

Order 2752.

268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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#13063371C212yesmaximal, complemented
2#13063352C214yesmaximal, complemented
3#13063350C212yesmaximal, complemented
4#13063348C212yesmaximal, complemented
5C2×D344C211yesmaximal, characteristic, complemented
6D8×D43C212yesmaximal, complemented
7#13063331C211yesmaximal, characteristic, complemented
8#135×C43C211yesmaximal, characteristic, complemented
9#41×C43C2212yescomplemented
10#10621902C2214yescomplemented
11D4×D43—24no—
12D4×D43C2214yescomplemented
13#10621898—22no—
14#10621898C2211yescharacteristic
15C2×D172—22no—
16C2×D172C2212yescomplemented
17Q16×C43C2211yescharacteristic, complemented
18SD16×C43C2212yescomplemented
19D8×C43C2211yescharacteristic, complemented
20C2×C8×C43C2211yescharacteristic, complemented
21#10621884C2214yescomplemented
22#10621882C2214yescomplemented
23#10621877C2211yescharacteristic, complemented
24D344C2212yescomplemented
25D344C2212yescomplemented
26#10621872C2212yescomplemented
27C8×D43C2212yescomplemented
28C22×D43—22no—
29C22×D43—24no—
30Q8×C43C2312yes—
31D4×C43—22no—
32D4×C43C2312yes—
33C2×C4×C43—22no—
34C2×C4×C43C2311yescharacteristic
35C22⋊D43—24no—
36C22⋊D43D412yes—
37D172—24no—
38D172—22no—
39D172D411yescharacteristic
40D172C2314yes—
41C4×D43—24no—
42C4×D43C2312yes—
43Dic86D411yescharacteristic
44C8×C43C2311yescharacteristic
45C8×C43C2311yescharacteristic
46C43⋊C8C2312yes—
47C22×C43—22no—
48C22×C43C2×D411yescharacteristic
49C2×D43—24no—
50C2×D43—84no—
51C2×D43—82no—
52C2×D43C2×D412yes—
53C4×C43—22no—
54C4×C43C2×D411yescharacteristic
55C4×C43C2411yescharacteristic
56Dic43C2×D412yes—
57C2×C43—21no—
58C2×C43—42no—
59C2×C43C22×D411yescharacteristic
60D43—22no—
61D43—44no—
62#576—431nomaximal, Sylow
63C43#57611yescharacteristic, complemented, Sylow
64H(5,𝔽2)—432no—
65AGL(1,ℤ/8)—432no—
66AGL(1,ℤ/8)—434no—
67#135—432no—
68#135D4311yescharacteristic, complemented
69C2×D8—432no—
70C2×D8—431no—
71#131—431no—
72#41—431no—
73#41—434no—
74#41—862no—
75#41C2×D4312yescomplemented
76C2×D4—434no—
77C2×D4—432no—
78C2×D4—862no—
79C2×D4—864no—
80Q16C2×D4311yescharacteristic, complemented
81SD16—434no—
82SD16C2×D4312yescomplemented
83D8—434no—
84D8—432no—
85D8—432no—
86D8C2×D4311yescharacteristic, complemented
87M16—431no—
88M16—432no—
89C2×C8—432no—
90C2×C8C2×D4311yescharacteristic, complemented
91C23—864no—
92C23—862no—
93Q8—431no—
94Q8C22×D4312yes—
95D4—22no—
96D4—432no—
97D4—431no—
98D4—434no—
99D4—864no—
100D4—864no—
101D4—862no—
102D4C22×D4312yes—
103C2×C4—22no—
104C2×C4—432no—
105C2×C4—864no—
106C2×C4C22×D4311yescharacteristic
107C8—432no—
108C8C22×D4311yescharacteristic
109C8C22×D4311yescharacteristic
110C22—22no—
111C22—432no—
112C22—864no—
113C22—3442no—
114C22—3444no—
115C22D4×D4311yescharacteristic
116C4—22no—
117C4—432no—
118C4D4×D4311yescharacteristic
119C4C23×D4311yescharacteristic
120C2—21no—
121C2—42no—
122C2—862no—
123C2—1724no—
124C2C2×D4×D4311yescharacteristic
subgroupG/H
centerC2C2×D4×D43
commutator, cosocleC4×C43C24
FrattiniC4C23×D43
Fitting#135×C43C2
socleC2×C43C22×D4
hypercenter#135D43
hypocenterC43#576
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #13063371C2semidirect
2. #13063352C2semidirect
3. #13063350C2semidirect
4. #13063348C2semidirect
5. C2×D344C2semidirect
6. D8×D43C2semidirect
7. #13063331C2semidirect
8. #135×C43C2semidirect
9. #41×C43C22semidirect
10. #10621902C22semidirect
12. D4×D43C22semidirect
16. C2×D172C22semidirect
17. Q16×C43C22semidirect
18. SD16×C43C22semidirect
19. D8×C43C22semidirect
20. C2×C8×C43C22semidirect
21. #10621884C22semidirect
22. #10621882C22semidirect
23. #10621877C22semidirect
24. D344C22semidirect
25. D344C22semidirect
26. #10621872C22semidirect
27. C8×D43C22semidirect
63. C43#576semidirect
68. #135D43semidirect
75. #41C2×D43semidirect
80. Q16C2×D43semidirect
82. SD16C2×D43semidirect
86. D8C2×D43semidirect
90. C2×C8C2×D43semidirect

Maximal subgroups

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

subgroupindex
#130633712
#130633522
#130633502
#130633482
C2×D3442
D8×D432
#130633312
#135×C432
#57643