Finite Group Databasebeta

← #37566055

Subgroups — #37566055

Order 24256.

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

normal subgroups only

This group has 258 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#27131378C211yesmaximal, characteristic, complemented
2#27131361C213yesmaximal, complemented
3#27131357C213yesmaximal, complemented
4#27131351C213yesmaximal, complemented
5C2×#20258594C213yesmaximal, complemented
6#27131338C211yesmaximal, characteristic, complemented
7H(5,𝔽2)×C379C211yesmaximal, characteristic, complemented
8#20258606C2213yescomplemented
9#20258605—23no—
10C2×Dic758C2213yescomplemented
11Q8×D379—21no—
12#20258596C2213yescomplemented
13#20258594C2213yescomplemented
14#20258594C2216yescomplemented
15#20258593C2211yescharacteristic, complemented
16#20258591C2213yescomplemented
17#20258590C2213yescomplemented
18C2×C379⋊C8C2213yescomplemented
19#41×C379—21no—
20#41×C379C2213yes—
21#41×C379C2211yescharacteristic
22C2×D4×C379—23no—
23C2×D4×C379C2213yes—
24Dic758—23no—
25Dic758C2313yes—
26D1516C2311yescharacteristic
27C22⋊D379—23no—
28C2×Dic379—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—21no—
45C4×C379—21no—
46C4×C379C2×D413yes—
47C4×C379C2411yescharacteristic
48Dic379—23no—
49C2×C379—23no—
50C2×C379—43no—
51C2×C379C22×D411yescharacteristic
52D379—41no—
53C379#57711yescharacteristic, complemented, Sylow
54#577—3791nomaximal, Sylow
552−1+4—3791no—
56H(5,𝔽2)D37911yescharacteristic, complemented
57#137—3793no—
58AGL(1,ℤ/8)—3793no—
59#135—3793no—
60C2×SD16—3793no—
61#131—3791no—
62#41—21no—
63#41—3793no—
64#41—7583no—
65#41C2×D37913yes—
66#41C2×D37911yescharacteristic
67C2×Q8—3793no—
68C2×Q8—7581no—
69C2×D4—23no—
70C2×D4C2×D37913yes—
71Q16—3793no—
72SD16—3791no—
73SD16—3793no—
74SD16—3796no—
75D8—3793no—
76M16—3793no—
77C2×C8—3793no—
78C23—23no—
79Q8—3793no—
80Q8—7583no—
81Q8C22⋊D37911yescharacteristic
82Q8C22×D37911yescharacteristic
83D4—23no—
84D4—23no—
85D4—3791no—
86D4—7583no—
87D4C22⋊D37913yes—
88D4C22×D37913yes—
89C2×C4—23no—
90C2×C4—7583no—
91C2×C4—7583no—
92C2×C4C22×D37913yes—
93C8—3791no—
94C8—3793no—
95C22—23no—
96C22—83no—
97C22—7581no—
98C22C2×C22⋊D37913yes—
99C4—21no—
100C4—7583no—
101C4C2×C22⋊D37913yes—
102C4C23×D37911yescharacteristic
103C2—23no—
104C2—43no—
105C2—15161no—
106C2C22×C22⋊D37911yescharacteristic
subgroupG/H
centerC2C22×C22⋊D379
commutator, cosocleC4×C379C24
FrattiniC4C23×D379
FittingH(5,𝔽2)×C379C2
socleC2×C379C22×D4
hypercenterH(5,𝔽2)D379
hypocenterC379#577
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. #27131378C2semidirect
2. #27131361C2semidirect
3. #27131357C2semidirect
4. #27131351C2semidirect
5. C2×#20258594C2semidirect
6. #27131338C2semidirect
7. H(5,𝔽2)×C379C2semidirect
8. #20258606C22semidirect
10. C2×Dic758C22semidirect
12. #20258596C22semidirect
13. #20258594C22semidirect
14. #20258594C22semidirect
15. #20258593C22semidirect
16. #20258591C22semidirect
17. #20258590C22semidirect
18. C2×C379⋊C8C22semidirect
53. C379#577semidirect
56. H(5,𝔽2)D379semidirect

Maximal subgroups

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

subgroupindex
#271313782
#271313612
#271313572
#271313512
C2×#202585942
#271313382
H(5,𝔽2)×C3792
#577379