Finite Group Databasebeta

← #16845035

Subgroups — #16845035

Order 3968.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#14521797C211yesmaximal, characteristic
2#14521419C211yesmaximal, characteristic, complemented
3#14521409C212yesmaximal, complemented
4#14520788C212yesmaximal, complemented
5C31×#330C211yesmaximal, characteristic, complemented
6C31×#125C2211yescharacteristic
7#11758473—22no—
8#11758472—22no—
9#11758471—22no—
10#11758452C2212yes—
11#11758446C2211yescharacteristic
12C31×#97C2212yes—
13#11758409—22no—
14#11758404—22no—
15#11758398—22no—
16#11758391C2211yescharacteristic
17C2×D124—22no—
18C2×D124D412yes—
19C2×C4×D31—22no—
20C2×Dic62—21no—
21C2×Dic62D412yes—
22C2×C8×C31—22no—
23C4⋊C4×C31—22no—
24C4⋊C4×C31D412yes—
25C42×C31C2311yescharacteristic
26(C2×D31)⋊C4—22no—
27(C2×D31)⋊C4—22no—
28(C2×D31)⋊C4—22no—
29C4⋊Dic31—22no—
30Dic31⋊C4—22no—
31C2×C31⋊C8—21no—
32C22×D31—22no—
33C2×C4×C31—22no—
34C2×C4×C31C2×D411yescharacteristic
35C2×C4×C31C2×D412yes—
36C2×Dic31—22no—
37C2×Dic31—41no—
38D124—42no—
39D124—82no—
40C4×D31—82no—
41Dic62—42no—
42Dic62—42no—
43C8×C31—42no—
44C31⋊C8—41no—
45#1662—311nomaximal, Sylow
46C22×C31#12011yescharacteristic
47C2×D31—42no—
48C2×D31—42no—
49C2×D31—42no—
50C4×C31—21no—
51C4×C31—22no—
52C4×C31—42no—
53Dic31—42no—
54Dic31—81no—
55#562—311no—
56#491—311no—
57#489—312no—
58#330D3111yescharacteristic, complemented
59#329—312no—
60C2×C31#45411yescharacteristic
61C2×C31#45512yes—
62D31—82no—
63C4⋊Q8—311no—
64#125C2×D3111yescharacteristic
65#124—312no—
66#123—622no—
67C22⋊Q8—622no—
68#121—622no—
69#103—622no—
70#103—622no—
71#102—622no—
72#97—311no—
73#97C2×D3112yes—
74C31#166211yescharacteristic, complemented, Sylow
75C2×Q8—312no—
76C2×Q8—621no—
77C2×D4—312no—
78C2×D4—622no—
79C22×C4—622no—
80C2×C8—22no—
81C2×C8—621no—
82C4⋊C4—22no—
83C4⋊C4—622no—
84C4⋊C4—622no—
85C4⋊C4D12412yes—
86C22⋊C4—622no—
87C22⋊C4—622no—
88C22⋊C4—622no—
89C42C22×D3111yescharacteristic
90C23—622no—
91Q8—1242no—
92Q8—1242no—
93D4—1242no—
94D4—2482no—
95C2×C4—22no—
96C2×C4—622no—
97C2×C4—1241no—
98C2×C4—2482no—
99C2×C4C2×D12411yescharacteristic
100C2×C4D4×D3112yes—
101C8—42no—
102C8—1241no—
103C22—1242no—
104C22—1242no—
105C22—1242no—
106C22#1175845911yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—1242no—
111C4—2481no—
112C2—2482no—
113C2#1452122411yescharacteristic
114C2#1452122812yes—
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#330C2
socleC22×C31#120
prime radical#14521797C2
hypercenter#330D31
hypocenterC31#1662
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #14521419C2semidirect
3. #14521409C2semidirect
4. #14520788C2semidirect
5. C31×#330C2semidirect
58. #330D31semidirect
74. C31#1662semidirect

Maximal subgroups

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

subgroupindex
#145217972
#145214192
#145214092
#145207882
C31×#3302
#166231