Finite Group Databasebeta

← #28389690

Subgroups — #28389690

Order 14464.

314 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 65 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#20298970C211yesmaximal, characteristic, complemented
2#20298888C212yesmaximal, complemented
3#20298342C211yesmaximal, characteristic, complemented
4D4⋊#11744751C212yesmaximal, complemented
5D42×C113C211yesmaximal, characteristic
6C2×#14268635—22no—
7#16813622C2211yescharacteristic, complemented
8#16813553—22no—
9C4⋊#11744751C2212yescomplemented
10#16813543—22no—
11C4×#11744751C2211yescharacteristic, complemented
12C22×D4×C113—22no—
13#127×C113C2211yescharacteristic
14#121×C113—22no—
15#120×C113—22no—
16C4×D4×C113C2212yes—
17C2×Dic226—21no—
18#14268635—44no—
19C2×#11744751—21no—
20C2×#11744751—22no—
21C4⋊Dic113—22no—
22C24×C113—22no—
23C2×D4×C113—24no—
24C2×D4×C113—22no—
25C2×D4×C113—44no—
26C2×D4×C113—44no—
27C2×D4×C113D412yes—
28C2×D4×C113D412yes—
29C22×C4×C113—22no—
30C4⋊C4×C113D412yes—
31C22⋊C4×C113—22no—
32C22⋊C4×C113—22no—
33C42×C113C2311yescharacteristic
34C23×C113—22no—
35C23×C113—22no—
36C23×C113—48no—
37C23×C113—82no—
38D4×C113—22no—
39D4×C113—42no—
40D4×C113—48no—
41D4×C113—42no—
42D4×C113—42no—
43D4×C113SD1614yescomplemented
44C2×C4×C113—22no—
45C2×C4×C113—42no—
46C2×C4×C113—42no—
47C2×C4×C113C2×D411yescharacteristic
48C2×C4×C113C2×D412yes—
49C2×Dic113—41no—
50Dic226—42no—
51#11744751—22no—
52#11744751—42no—
53C22×C113—24no—
54C22×C113—42no—
55C22×C113—42no—
56C22×C113—44no—
57C22×C113—42no—
58C22×C113—88no—
59C22×C113#12011yescharacteristic
60C4×C113—21no—
61C4×C113—42no—
62C4×C113C2×SD1612yes—
63C4×C113AGL(1,ℤ/8)12yes—
64Dic113—81no—
65C2×C113—44no—
66C2×C113—82no—
67C2×C113#45012yes—
68C2×C113#45311yescharacteristic
69#1629—1131nomaximal, Sylow
70C113#162911yescharacteristic, complemented, Sylow
71D42D11311yescharacteristic
72#492—1131no—
73#476—1132no—
74#331—1131no—
75D4⋊C8—1132no—
76C22×D4—22no—
77C2×SD16—2262no—
78C4⋊Q8—1131no—
79#127C2×D11311yescharacteristic
80#121—22no—
81#120—22no—
82C4×D4C2×D11312yes—
83#106—2262no—
84C4⋊C8—1132no—
85#102—2262no—
86C4×C8—1131no—
87C24—22no—
88C2×Q8—2261no—
89C2×D4—24no—
90C2×D4—22no—
91C2×D4—44no—
92C2×D4—44no—
93C2×D4C22⋊D11312yes—
94C2×D4C22⋊D11312yes—
95C22×C4—22no—
96SD16—4524no—
97C2×C8—2262no—
98C2×C8—2261no—
99C4⋊C4—2262no—
100C4⋊C4C22⋊D11312yes—
101C22⋊C4—22no—
102C22⋊C4—22no—
103C42C22×D11311yescharacteristic
104C23—22no—
105C23—22no—
106C23—48no—
107C23—82no—
108Q8—4522no—
109D4—22no—
110D4—42no—
111D4—48no—
112D4—42no—
113D4—42no—
114D4#1426863514yescomplemented
115C2×C4—22no—
116C2×C4—42no—
117C2×C4—42no—
118C2×C4—4521no—
119C2×C4C2×C22⋊D11311yescharacteristic
120C2×C4C2×C22⋊D11312yes—
121C8—4522no—
122C8—2262no—
123C22—24no—
124C22—42no—
125C22—42no—
126C22—42no—
127C22—44no—
128C22—88no—
129C22#1681359111yescharacteristic
130C4—21no—
131C4—42no—
132C4—9041no—
133C4C2×#1426863512yes—
134C4#1681364812yes—
135C2—44no—
136C2—82no—
137C2#2029874912yes—
138C2#2029876611yescharacteristic
subgroupG/H
centerC22#16813591
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting, prime radicalD42×C113C2
socleC22×C113#120
hypercenterD42D113
hypocenterC113#1629
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #20298970C2semidirect
2. #20298888C2semidirect
3. #20298342C2semidirect
4. D4⋊#11744751C2semidirect
7. #16813622C22semidirect
9. C4⋊#11744751C22semidirect
11. C4×#11744751C22semidirect
43. D4×C113SD16semidirect
70. C113#1629semidirect
114. D4#14268635semidirect

Maximal subgroups

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

subgroupindex
#202989702
#202988882
#202983422
D4⋊#117447512
D42×C1132
#1629113