Finite Group Databasebeta

← #37566047

Subgroups — #37566047

Order 24256.

268 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 107 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#27131377C211yesmaximal, characteristic, complemented
2#27131357C213yesmaximal, complemented
3#27131356C213yesmaximal, complemented
4#27131351C213yesmaximal, complemented
5C2×#20258591C213yesmaximal, complemented
6#27131338C211yesmaximal, characteristic, complemented
7H(5,𝔽2)×C379C211yesmaximal, characteristic, complemented
8#20258607—21no—
9#20258606C2213yescomplemented
10C2×D1516C2213yescomplemented
11D4×D379—23no—
12#20258596C2211yescharacteristic, complemented
13#20258594C2213yescomplemented
14#20258593C2213yescomplemented
15#20258591C2213yescomplemented
16#20258591C2216yescomplemented
17#20258590C2213yescomplemented
18C2×C379⋊C8C2213yescomplemented
19#41×C379—21no—
20#41×C379C2211yescharacteristic
21#41×C379C2213yescomplemented
22C2×D4×C379—23no—
23C2×D4×C379C2213yescomplemented
24C22×D379—23no—
25Dic758C2311yescharacteristic
26D1516—23no—
27D1516C2313yes—
28C22⋊D379—23no—
29C4×D379—23no—
30C379⋊C8C2311yescharacteristic
31C379⋊C8C2313yes—
32C23×C379—23no—
33Q8×C379D411yescharacteristic
34Q8×C379C2311yescharacteristic
35D4×C379—23no—
36D4×C379—23no—
37D4×C379D413yes—
38D4×C379C2313yes—
39C2×C4×C379—23no—
40C2×C4×C379C2313yes—
41C22×C379—23no—
42C22×C379—83no—
43C22×C379C2×D413yes—
44C2×D379—23no—
45C2×D379—83no—
46C4×C379—21no—
47C4×C379C2×D413yes—
48C4×C379C2411yescharacteristic
49Dic379—21no—
50C2×C379—23no—
51C2×C379—43no—
52C2×C379C22×D411yescharacteristic
53D379—43no—
54C379#57611yescharacteristic, complemented, Sylow
55#576—3791nomaximal, Sylow
56H(5,𝔽2)—3791no—
57H(5,𝔽2)D37911yescharacteristic, complemented
58AGL(1,ℤ/8)—3793no—
59AGL(1,ℤ/8)—3793no—
60#135—3793no—
61C2×D8—3793no—
62#131—3791no—
63#41—21no—
64#41—3793no—
65#41—7581no—
66#41C2×D37911yescharacteristic
67#41C2×D37913yescomplemented
68C2×D4—23no—
69C2×D4—3793no—
70C2×D4—7583no—
71C2×D4C2×D37913yescomplemented
72Q16—3791no—
73SD16—3793no—
74SD16—3793no—
75D8—3793no—
76D8—3796no—
77M16—3793no—
78C2×C8—3793no—
79C23—23no—
80C23—7583no—
81Q8—3791no—
82Q8C22⋊D37911yescharacteristic
83Q8C22×D37911yescharacteristic
84D4—23no—
85D4—23no—
86D4—3793no—
87D4—7583no—
88D4—7583no—
89D4C22⋊D37913yes—
90D4C22×D37913yes—
91C2×C4—23no—
92C2×C4—7583no—
93C2×C4C22×D37913yes—
94C8—3791no—
95C8—3793no—
96C22—23no—
97C22—83no—
98C22—30323no—
99C22—7583no—
100C22C2×C22⋊D37913yes—
101C4—21no—
102C4—7581no—
103C4C2×C22⋊D37913yes—
104C4C23×D37911yescharacteristic
105C2—23no—
106C2—43no—
107C2—15163no—
108C2C22×C22⋊D37911yescharacteristic
subgroupG/H
centerC2C22×C22⋊D379
commutator, cosocleC4×C379C24
FrattiniC4C23×D379
FittingH(5,𝔽2)×C379C2
socleC2×C379C22×D4
hypercenterH(5,𝔽2)D379
hypocenterC379#576
LCSG ▷ C4×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C2 ◁ #41 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #27131377C2semidirect
2. #27131357C2semidirect
3. #27131356C2semidirect
4. #27131351C2semidirect
5. C2×#20258591C2semidirect
6. #27131338C2semidirect
7. H(5,𝔽2)×C379C2semidirect
9. #20258606C22semidirect
10. C2×D1516C22semidirect
12. #20258596C22semidirect
13. #20258594C22semidirect
14. #20258593C22semidirect
15. #20258591C22semidirect
16. #20258591C22semidirect
17. #20258590C22semidirect
18. C2×C379⋊C8C22semidirect
21. #41×C379C22semidirect
23. C2×D4×C379C22semidirect
54. C379#576semidirect
57. H(5,𝔽2)D379semidirect
67. #41C2×D379semidirect
71. C2×D4C2×D379semidirect

Maximal subgroups

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

subgroupindex
#271313772
#271313572
#271313562
#271313512
C2×#202585912
#271313382
H(5,𝔽2)×C3792
#576379