Finite Group Databasebeta

← #14521857

Subgroups — #14521857

Order 1984.

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
1C31×2−1+4C211yesmaximal, characteristic, complemented
2#11758566C211yesmaximal, characteristic, complemented
3#11758527C213yesmaximal, complemented
4#11758526C213yesmaximal, complemented
5#11758525C211yesmaximal, characteristic, complemented
6#11758519C213yesmaximal, complemented
7C2×#92481C213yesmaximal, complemented
8#41×C31—23no—
9#41×C31C2211yescharacteristic
10#41×C31C2213yescomplemented
11C2×Q8×C31—21no—
12C2×Q8×C31C2213yescomplemented
13#92499—21no—
14D4×D31—23no—
15#92495C2213yes—
16C2×D124C2213yes—
17#92482C2213yescomplemented
18#92481C2213yescomplemented
19#92481C2216yescomplemented
20#92480C2211yescharacteristic, complemented
21#92479C2213yescomplemented
22#92474C2213yescomplemented
23C2×C31⋊C8C2213yescomplemented
24C22×D31—23no—
25Q8×C31—23no—
26Q8×C31D411yescharacteristic
27Q8×C31C2313yes—
28D4×C31—23no—
29D4×C31D413yes—
30D4×C31C2311yescharacteristic
31C2×C4×C31—23no—
32C2×C4×C31—23no—
33C2×C4×C31C2313yes—
34C22⋊D31—23no—
35D124—23no—
36D124C2313yes—
37C4×D31—23no—
38Dic62C2311yescharacteristic
39C31⋊C8C2311yescharacteristic
40C31⋊C8C2313yes—
41C22×C31—21no—
42C22×C31C2×D413yes—
43C2×D31—23no—
44C2×D31—83no—
45C4×C31—23no—
46C4×C31C2×D413yes—
47C4×C31C2411yescharacteristic
48Dic31—21no—
49#577—311nomaximal, Sylow
50C2×C31—23no—
51C2×C31—41no—
52C2×C31C22×D411yescharacteristic
53D31—43no—
542−1+4D3111yescharacteristic, complemented
55H(5,𝔽2)—311no—
56#137—313no—
57AGL(1,ℤ/8)—313no—
58#135—313no—
59C2×SD16—313no—
60#131—311no—
61C31#57711yescharacteristic, complemented, Sylow
62#41—23no—
63#41—313no—
64#41—621no—
65#41C2×D3111yescharacteristic
66#41C2×D3113yescomplemented
67C2×Q8—21no—
68C2×Q8C2×D3113yescomplemented
69C2×D4—313no—
70C2×D4—623no—
71Q16—313no—
72SD16—313no—
73SD16—316no—
74SD16—311no—
75D8—313no—
76M16—313no—
77C2×C8—313no—
78C23—623no—
79Q8—23no—
80Q8—311no—
81Q8C22⋊D3111yescharacteristic
82Q8C22×D3113yes—
83D4—23no—
84D4—313no—
85D4—623no—
86D4—623no—
87D4C22⋊D3113yes—
88D4C22×D3111yescharacteristic
89C2×C4—23no—
90C2×C4—23no—
91C2×C4—623no—
92C2×C4C22×D3113yes—
93C8—311no—
94C8—313no—
95C22—21no—
96C22—623no—
97C22—2483no—
98C22C2×C22⋊D3113yes—
99C4—23no—
100C4—621no—
101C4C2×C22⋊D3113yes—
102C4C23×D3111yescharacteristic
103C2—23no—
104C2—41no—
105C2—1243no—
106C2C22×C22⋊D3111yescharacteristic
subgroupG/H
centerC2C22×C22⋊D31
commutator, cosocleC4×C31C24
FrattiniC4C23×D31
FittingC31×2−1+4C2
socleC2×C31C22×D4
hypercenter2−1+4D31
hypocenterC31#577
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ #41 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. C31×2−1+4C2semidirect
2. #11758566C2semidirect
3. #11758527C2semidirect
4. #11758526C2semidirect
5. #11758525C2semidirect
6. #11758519C2semidirect
7. C2×#92481C2semidirect
10. #41×C31C22semidirect
12. C2×Q8×C31C22semidirect
17. #92482C22semidirect
18. #92481C22semidirect
19. #92481C22semidirect
20. #92480C22semidirect
21. #92479C22semidirect
22. #92474C22semidirect
23. C2×C31⋊C8C22semidirect
54. 2−1+4D31semidirect
61. C31#577semidirect
66. #41C2×D31semidirect
68. C2×Q8C2×D31semidirect

Maximal subgroups

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

subgroupindex
C31×2−1+42
#117585662
#117585272
#117585262
#117585252
#117585192
C2×#924812
#57731