Finite Group Databasebeta

← #16840565

Subgroups — #16840565

Order 3904.

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#14519823C211yesmaximal, characteristic, complemented
2#14519803C213yesmaximal, complemented
3#14519802C213yesmaximal, complemented
4#14519797C213yesmaximal, complemented
5C2×#11758199C213yesmaximal, complemented
6#14519784C211yesmaximal, characteristic, complemented
7H(5,𝔽2)×C61C211yesmaximal, characteristic, complemented
8#41×C61—21no—
9#41×C61C2211yescharacteristic
10#41×C61C2213yescomplemented
11C2×D4×C61—23no—
12C2×D4×C61C2213yescomplemented
13#11758226—21no—
14D4×D61—23no—
15#11758222C2213yescomplemented
16C2×D244C2213yescomplemented
17#11758202C2211yescharacteristic, complemented
18#11758201C2213yescomplemented
19#11758200C2213yescomplemented
20#11758199C2213yescomplemented
21#11758199C2216yescomplemented
22#11758194C2213yescomplemented
23C2×#92418C2213yescomplemented
24C23×C61—23no—
25C22×D61—23no—
26Q8×C61D411yescharacteristic
27Q8×C61C2311yescharacteristic
28D4×C61—23no—
29D4×C61—23no—
30D4×C61D413yes—
31D4×C61C2313yes—
32C2×C4×C61—23no—
33C2×C4×C61C2313yes—
34C22⋊D61—23no—
35D244—23no—
36D244C2313yes—
37C4×D61—23no—
38Dic122C2311yescharacteristic
39#92418C2311yescharacteristic
40#92418C2313yes—
41C22×C61—23no—
42C22×C61—83no—
43C22×C61C2×D413yes—
44C2×D61—23no—
45C2×D61—83no—
46C4×C61—21no—
47C4×C61C2×D413yes—
48C4×C61C2411yescharacteristic
49Dic61—21no—
50C2×C61—23no—
51C2×C61—43no—
52C2×C61C22×D411yescharacteristic
53D61—43no—
54#576—611nomaximal, Sylow
55C61#57611yescharacteristic, complemented, Sylow
56H(5,𝔽2)—611no—
57H(5,𝔽2)D6111yescharacteristic, complemented
58AGL(1,ℤ/8)—613no—
59AGL(1,ℤ/8)—613no—
60#135—613no—
61C2×D8—613no—
62#131—611no—
63#41—21no—
64#41—613no—
65#41—1221no—
66#41C2×D6111yescharacteristic
67#41C2×D6113yescomplemented
68C2×D4—23no—
69C2×D4—613no—
70C2×D4—1223no—
71C2×D4C2×D6113yescomplemented
72Q16—611no—
73SD16—613no—
74SD16—613no—
75D8—613no—
76D8—616no—
77M16—613no—
78C2×C8—613no—
79C23—23no—
80C23—1223no—
81Q8—611no—
82Q8C22⋊D6111yescharacteristic
83Q8C22×D6111yescharacteristic
84D4—23no—
85D4—23no—
86D4—613no—
87D4—1223no—
88D4—1223no—
89D4C22⋊D6113yes—
90D4C22×D6113yes—
91C2×C4—23no—
92C2×C4—1223no—
93C2×C4C22×D6113yes—
94C8—611no—
95C8—613no—
96C22—23no—
97C22—83no—
98C22—1223no—
99C22—4883no—
100C22C2×C22⋊D6113yes—
101C4—21no—
102C4—1221no—
103C4C2×C22⋊D6113yes—
104C4C23×D6111yescharacteristic
105C2—23no—
106C2—43no—
107C2—2443no—
108C2C22×C22⋊D6111yescharacteristic
subgroupG/H
centerC2C22×C22⋊D61
commutator, cosocleC4×C61C24
FrattiniC4C23×D61
FittingH(5,𝔽2)×C61C2
socleC2×C61C22×D4
hypercenterH(5,𝔽2)D61
hypocenterC61#576
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ #41 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #14519823C2semidirect
2. #14519803C2semidirect
3. #14519802C2semidirect
4. #14519797C2semidirect
5. C2×#11758199C2semidirect
6. #14519784C2semidirect
7. H(5,𝔽2)×C61C2semidirect
10. #41×C61C22semidirect
12. C2×D4×C61C22semidirect
15. #11758222C22semidirect
16. C2×D244C22semidirect
17. #11758202C22semidirect
18. #11758201C22semidirect
19. #11758200C22semidirect
20. #11758199C22semidirect
21. #11758199C22semidirect
22. #11758194C22semidirect
23. C2×#92418C22semidirect
55. C61#576semidirect
57. H(5,𝔽2)D61semidirect
67. #41C2×D61semidirect
71. C2×D4C2×D61semidirect

Maximal subgroups

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

subgroupindex
#145198232
#145198032
#145198022
#145197972
C2×#117581992
#145197842
H(5,𝔽2)×C612
#57661