Finite Group Databasebeta

← #46855804

Subgroups — #46855804

Order 35008.

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#31776048C211yesmaximal, characteristic, complemented
2#31776028C213yesmaximal, complemented
3#31776027C213yesmaximal, complemented
4#31776022C213yesmaximal, complemented
5C2×#22576761C213yesmaximal, complemented
6#31776009C211yesmaximal, characteristic, complemented
7H(5,𝔽2)×C547C211yesmaximal, characteristic, complemented
8#22576777—21no—
9#22576776C2213yescomplemented
10C2×D2188C2213yescomplemented
11D4×D547—23no—
12#22576766C2211yescharacteristic, complemented
13#22576764C2213yescomplemented
14#22576763C2213yescomplemented
15#22576761C2213yescomplemented
16#22576761C2216yescomplemented
17#22576760C2213yescomplemented
18C2×C547⋊C8C2213yescomplemented
19#41×C547—21no—
20#41×C547C2211yescharacteristic
21#41×C547C2213yescomplemented
22C2×D4×C547—23no—
23C2×D4×C547C2213yescomplemented
24C22×D547—23no—
25Dic1094C2311yescharacteristic
26D2188—23no—
27D2188C2313yes—
28C22⋊D547—23no—
29C4×D547—23no—
30C547⋊C8C2311yescharacteristic
31C547⋊C8C2313yes—
32C23×C547—23no—
33Q8×C547D411yescharacteristic
34Q8×C547C2311yescharacteristic
35D4×C547—23no—
36D4×C547—23no—
37D4×C547D413yes—
38D4×C547C2313yes—
39C2×C4×C547—23no—
40C2×C4×C547C2313yes—
41C22×C547—23no—
42C22×C547—83no—
43C22×C547C2×D413yes—
44C2×D547—23no—
45C2×D547—83no—
46C4×C547—21no—
47C4×C547C2×D413yes—
48C4×C547C2411yescharacteristic
49Dic547—21no—
50C2×C547—23no—
51C2×C547—43no—
52C2×C547C22×D411yescharacteristic
53D547—43no—
54C547#57611yescharacteristic, complemented, Sylow
55#576—5471nomaximal, Sylow
56H(5,𝔽2)—5471no—
57H(5,𝔽2)D54711yescharacteristic, complemented
58AGL(1,ℤ/8)—5473no—
59AGL(1,ℤ/8)—5473no—
60#135—5473no—
61C2×D8—5473no—
62#131—5471no—
63#41—21no—
64#41—5473no—
65#41—10941no—
66#41C2×D54711yescharacteristic
67#41C2×D54713yescomplemented
68C2×D4—23no—
69C2×D4—5473no—
70C2×D4—10943no—
71C2×D4C2×D54713yescomplemented
72Q16—5471no—
73SD16—5473no—
74SD16—5473no—
75D8—5473no—
76D8—5476no—
77M16—5473no—
78C2×C8—5473no—
79C23—23no—
80C23—10943no—
81Q8—5471no—
82Q8C22⋊D54711yescharacteristic
83Q8C22×D54711yescharacteristic
84D4—23no—
85D4—23no—
86D4—5473no—
87D4—10943no—
88D4—10943no—
89D4C22⋊D54713yes—
90D4C22×D54713yes—
91C2×C4—23no—
92C2×C4—10943no—
93C2×C4C22×D54713yes—
94C8—5471no—
95C8—5473no—
96C22—23no—
97C22—83no—
98C22—43763no—
99C22—10943no—
100C22C2×C22⋊D54713yes—
101C4—21no—
102C4—10941no—
103C4C2×C22⋊D54713yes—
104C4C23×D54711yescharacteristic
105C2—23no—
106C2—43no—
107C2—21883no—
108C2C22×C22⋊D54711yescharacteristic
subgroupG/H
centerC2C22×C22⋊D547
commutator, cosocleC4×C547C24
FrattiniC4C23×D547
FittingH(5,𝔽2)×C547C2
socleC2×C547C22×D4
hypercenterH(5,𝔽2)D547
hypocenterC547#576
LCSG ▷ C4×C547 ▷ C2×C547 ▷ C547
UCSC1 ◁ C2 ◁ #41 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #31776048C2semidirect
2. #31776028C2semidirect
3. #31776027C2semidirect
4. #31776022C2semidirect
5. C2×#22576761C2semidirect
6. #31776009C2semidirect
7. H(5,𝔽2)×C547C2semidirect
9. #22576776C22semidirect
10. C2×D2188C22semidirect
12. #22576766C22semidirect
13. #22576764C22semidirect
14. #22576763C22semidirect
15. #22576761C22semidirect
16. #22576761C22semidirect
17. #22576760C22semidirect
18. C2×C547⋊C8C22semidirect
21. #41×C547C22semidirect
23. C2×D4×C547C22semidirect
54. C547#576semidirect
57. H(5,𝔽2)D547semidirect
67. #41C2×D547semidirect
71. C2×D4C2×D547semidirect

Maximal subgroups

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

subgroupindex
#317760482
#317760282
#317760272
#317760222
C2×#225767612
#317760092
H(5,𝔽2)×C5472
#576547