Finite Group Databasebeta

← #44537528

Subgroups — #44537528

Order 31424.

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#30628383C211yesmaximal, characteristic, complemented
2#30628363C213yesmaximal, complemented
3#30628362C213yesmaximal, complemented
4#30628357C213yesmaximal, complemented
5C2×#21463313C213yesmaximal, complemented
6#30628344C211yesmaximal, characteristic, complemented
7H(5,𝔽2)×C491C211yesmaximal, characteristic, complemented
8#21463329—21no—
9#21463328C2213yescomplemented
10C2×D1964C2213yescomplemented
11D4×D491—23no—
12#21463318C2211yescharacteristic, complemented
13#21463316C2213yescomplemented
14#21463315C2213yescomplemented
15#21463313C2213yescomplemented
16#21463313C2216yescomplemented
17#21463312C2213yescomplemented
18C2×C491⋊C8C2213yescomplemented
19#41×C491—21no—
20#41×C491C2211yescharacteristic
21#41×C491C2213yescomplemented
22C2×D4×C491—23no—
23C2×D4×C491C2213yescomplemented
24C22×D491—23no—
25Dic982C2311yescharacteristic
26D1964—23no—
27D1964C2313yes—
28C22⋊D491—23no—
29C4×D491—23no—
30C491⋊C8C2311yescharacteristic
31C491⋊C8C2313yes—
32C23×C491—23no—
33Q8×C491D411yescharacteristic
34Q8×C491C2311yescharacteristic
35D4×C491—23no—
36D4×C491—23no—
37D4×C491D413yes—
38D4×C491C2313yes—
39C2×C4×C491—23no—
40C2×C4×C491C2313yes—
41C22×C491—23no—
42C22×C491—83no—
43C22×C491C2×D413yes—
44C2×D491—23no—
45C2×D491—83no—
46C4×C491—21no—
47C4×C491C2×D413yes—
48C4×C491C2411yescharacteristic
49Dic491—21no—
50C2×C491—23no—
51C2×C491—43no—
52C2×C491C22×D411yescharacteristic
53D491—43no—
54C491#57611yescharacteristic, complemented, Sylow
55#576—4911nomaximal, Sylow
56H(5,𝔽2)—4911no—
57H(5,𝔽2)D49111yescharacteristic, complemented
58AGL(1,ℤ/8)—4913no—
59AGL(1,ℤ/8)—4913no—
60#135—4913no—
61C2×D8—4913no—
62#131—4911no—
63#41—21no—
64#41—9821no—
65#41—4913no—
66#41C2×D49111yescharacteristic
67#41C2×D49113yescomplemented
68C2×D4—23no—
69C2×D4—9823no—
70C2×D4—4913no—
71C2×D4C2×D49113yescomplemented
72Q16—4911no—
73SD16—4913no—
74SD16—4913no—
75D8—4913no—
76D8—4916no—
77M16—4913no—
78C2×C8—4913no—
79C23—23no—
80C23—9823no—
81Q8—4911no—
82Q8C22⋊D49111yescharacteristic
83Q8C22×D49111yescharacteristic
84D4—23no—
85D4—23no—
86D4—9823no—
87D4—9823no—
88D4—4913no—
89D4C22⋊D49113yes—
90D4C22×D49113yes—
91C2×C4—23no—
92C2×C4—9823no—
93C2×C4C22×D49113yes—
94C8—4911no—
95C8—4913no—
96C22—23no—
97C22—83no—
98C22—39283no—
99C22—9823no—
100C22C2×C22⋊D49113yes—
101C4—21no—
102C4—9821no—
103C4C2×C22⋊D49113yes—
104C4C23×D49111yescharacteristic
105C2—23no—
106C2—43no—
107C2—19643no—
108C2C22×C22⋊D49111yescharacteristic
subgroupG/H
centerC2C22×C22⋊D491
commutator, cosocleC4×C491C24
FrattiniC4C23×D491
FittingH(5,𝔽2)×C491C2
socleC2×C491C22×D4
hypercenterH(5,𝔽2)D491
hypocenterC491#576
LCSG ▷ C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C2 ◁ #41 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #30628383C2semidirect
2. #30628363C2semidirect
3. #30628362C2semidirect
4. #30628357C2semidirect
5. C2×#21463313C2semidirect
6. #30628344C2semidirect
7. H(5,𝔽2)×C491C2semidirect
9. #21463328C22semidirect
10. C2×D1964C22semidirect
12. #21463318C22semidirect
13. #21463316C22semidirect
14. #21463315C22semidirect
15. #21463313C22semidirect
16. #21463313C22semidirect
17. #21463312C22semidirect
18. C2×C491⋊C8C22semidirect
21. #41×C491C22semidirect
23. C2×D4×C491C22semidirect
54. C491#576semidirect
57. H(5,𝔽2)D491semidirect
67. #41C2×D491semidirect
71. C2×D4C2×D491semidirect

Maximal subgroups

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

subgroupindex
#306283832
#306283632
#306283622
#306283572
C2×#214633132
#306283442
H(5,𝔽2)×C4912
#576491