Finite Group Databasebeta

← #14521237

Subgroups — #14521237

Order 1984.

198 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 39 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#11758561C211yesmaximal, characteristic, complemented
2#11758514C211yesmaximal, characteristic, complemented
3#11758459C212yesmaximal, complemented
4C31×#99C211yesmaximal, characteristic, complemented
5#11758394C212yesmaximal, complemented
6C23×D31C2211yescharacteristic, complemented
7C2×D4×C31C2211yescharacteristic
8C2×C22⋊D31—21no—
9C2×C22⋊D31—21no—
10C2×C22⋊D31C2212yes—
11#92497—22no—
12D4×D31—22no—
13#92495—21no—
14C2×D124—22no—
15C22⋊C4×C31C2212yescomplemented
16C22⋊Dic31C2211yescharacteristic, complemented
17(C2×D31)⋊C4—21no—
18(C2×D31)⋊C4—22no—
19C23×C31D411yescharacteristic, complemented
20C23×C31C2311yescharacteristic
21C22×D31—22no—
22C22×D31—21no—
23C22×D31—21no—
24C22×D31—42no—
25C22×D31D412yescomplemented
26D4×C31—22no—
27C2×C4×C31—22no—
28C2×C4×C31D411yescharacteristic, complemented
29C22⋊D31—22no—
30C22⋊D31—22no—
31C22⋊D31—22no—
32C22⋊D31—42no—
33C2×Dic31—21no—
34C2×Dic31—21no—
35C2×Dic31D412yescomplemented
36D124—21no—
37D124—44no—
38C4×D31—22no—
39Dic62—21no—
40C22×C31—21no—
41C22×C31—41no—
42C22×C31—41no—
43C22×C31C2×D411yescharacteristic
44C22×C31C2×D412yes—
45C2×D31—24no—
46C2×D31—22no—
47C2×D31—22no—
48C2×D31—41no—
49C2×D31—42no—
50C2×D31—41no—
51C2×D31—42no—
52C2×D31—81no—
53C4×C31—21no—
54C4×C31—42no—
55Dic31—22no—
56Dic31—41no—
57B(4,𝔽2)—311nomaximal, Sylow
58C2×C31—21no—
59C2×C31—22no—
60C2×C31—41no—
61C2×C31#12011yescharacteristic
62D31—42no—
63D31—42no—
64H(5,𝔽2)—311no—
65#120—311no—
66#120—312no—
67#99—312no—
68#99D3111yescharacteristic, complemented
69C31B(4,𝔽2)11yescharacteristic, complemented, Sylow
70C24—311no—
71#41—622no—
72#41—621no—
73C2×D4—312no—
74C2×D4—622no—
75C2×D4—622no—
76C2×D4—621no—
77C2×D4—621no—
78C2×D4C2×D3111yescharacteristic
79C22⋊C4—311no—
80C22⋊C4—622no—
81C22⋊C4—621no—
82C22⋊C4C2×D3112yescomplemented
83C23—312no—
84C23—621no—
85C23—621no—
86C23—622no—
87C23—1242no—
88C23D12411yescharacteristic, complemented
89C23C22×D3111yescharacteristic
90Q8—621no—
91D4—22no—
92D4—621no—
93D4—622no—
94D4—622no—
95D4—622no—
96D4—1244no—
97D4—1242no—
98C2×C4—22no—
99C2×C4—312no—
100C2×C4—622no—
101C2×C4—621no—
102C2×C4—621no—
103C2×C4D12411yescharacteristic, complemented
104C22—21no—
105C22—41no—
106C22—41no—
107C22—624no—
108C22—622no—
109C22—622no—
110C22—1242no—
111C22—1242no—
112C22—1241no—
113C22—1241no—
114C22—2481no—
115C22C2×D12411yescharacteristic
116C22D4×D3112yes—
117C4—21no—
118C4—42no—
119C4—622no—
120C4—1241no—
121C2—22no—
122C2—21no—
123C2—41no—
124C2—1242no—
125C2—1242no—
126C2#1175845911yescharacteristic
subgroupG/H
centerC2#11758459
commutator, cosocleC23×C31C23
FrattiniC23C22×D31
FittingC31×#99C2
socleC2×C31#120
hypercenter#99D31
hypocenterC31B(4,𝔽2)
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
1. #11758561C2semidirect
2. #11758514C2semidirect
3. #11758459C2semidirect
4. C31×#99C2semidirect
5. #11758394C2semidirect
6. C23×D31C22semidirect
15. C22⋊C4×C31C22semidirect
16. C22⋊Dic31C22semidirect
19. C23×C31D4semidirect
25. C22×D31D4semidirect
28. C2×C4×C31D4semidirect
35. C2×Dic31D4semidirect
68. #99D31semidirect
69. C31B(4,𝔽2)semidirect
82. C22⋊C4C2×D31semidirect
88. C23D124semidirect
103. C2×C4D124semidirect

Maximal subgroups

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

subgroupindex
#117585612
#117585142
#117584592
C31×#992
#117583942
B(4,𝔽2)31