Finite Group Databasebeta

← #28389688

Subgroups — #28389688

Order 14464.

314 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 57 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#20299233C211yesmaximal, characteristic
2#20298885C212yesmaximal, complemented
3#20298342C211yesmaximal, characteristic, complemented
4#20298327C212yesmaximal, complemented
5#492×C113C211yesmaximal, characteristic, complemented
6C2×D4×D113—22no—
7#16813593—22no—
8#16813590—22no—
9C4×D452C2212yes—
10#16813553—22no—
11C4⋊#11744751C2212yescomplemented
12#16813542—22no—
13C2×SD16×C113—22no—
14C4⋊Q8×C113C2211yescharacteristic, complemented
15#127×C113C2211yescharacteristic
16C4×C8×C113C2211yescharacteristic, complemented
17C23×D113—22no—
18C2×D452D412yes—
19C2×C22⋊D113—24no—
20D4×D113—44no—
21D4×D113—44no—
22C2×C4×D113—22no—
23C2×#11744751—22no—
24C4⋊Dic113D412yes—
25C22⋊Dic113—22no—
26#14268624—22no—
27C2×Q8×C113—21no—
28C2×D4×C113—22no—
29C2×D4×C113D412yes—
30SD16×C113—44no—
31C2×C8×C113—21no—
32C4⋊C4×C113—22no—
33C42×C113C2311yescharacteristic
34C23×C113—22no—
35C22×D113—22no—
36C22×D113—48no—
37C22×D113—82no—
38Q8×C113—42no—
39D4×C113—42no—
40D4×C113—42no—
41D4×C113—42no—
42C2×C4×C113—41no—
43C2×C4×C113C2×D412yes—
44C2×C4×C113C2×D411yescharacteristic
45C22⋊D113—48no—
46C2×Dic113—22no—
47D452—22no—
48D452SD1614yescomplemented
49C4×D113—42no—
50C4×D113—42no—
51C8×C113—22no—
52#11744751—42no—
53C22×C113—44no—
54C22×C113—42no—
55C22×C113#12011yescharacteristic
56C2×D113—24no—
57C2×D113—42no—
58C2×D113—42no—
59C2×D113—88no—
60C4×C113—21no—
61C4×C113—81no—
62C4×C113C2×SD1612yes—
63C4×C113AGL(1,ℤ/8)12yes—
64Dic113—42no—
65C2×C113—82no—
66C2×C113#45012yes—
67C2×C113#45311yescharacteristic
68D113—44no—
69#1629—1131nomaximal, Sylow
70C113#162911yescharacteristic, complemented, Sylow
71D42—1131no—
72#492D11311yescharacteristic, complemented
73#476—1132no—
74#331—1131no—
75D4⋊C8—1132no—
76C22×D4—2262no—
77C2×SD16—22no—
78C4⋊Q8C2×D11311yescharacteristic, complemented
79#127C2×D11311yescharacteristic
80#121—2262no—
81#120—2262no—
82C4×D4—1132no—
83#106—2262no—
84C4⋊C8—1132no—
85#102—2262no—
86C4×C8C2×D11311yescharacteristic, complemented
87C24—2262no—
88C2×Q8—21no—
89C2×D4—22no—
90C2×D4—1132no—
91C2×D4—4524no—
92C2×D4—4524no—
93C2×D4—2264no—
94C2×D4C22⋊D11312yes—
95C22×C4—2262no—
96SD16—44no—
97C2×C8—21no—
98C2×C8—2262no—
99C4⋊C4—22no—
100C4⋊C4—1132no—
101C22⋊C4—2262no—
102C22⋊C4—2262no—
103C42C22×D11311yescharacteristic
104C23—22no—
105C23—9042no—
106C23—4528no—
107C23—2262no—
108Q8—42no—
109D4—42no—
110D4—42no—
111D4—42no—
112D4—1134no—
113D4—4528no—
114D4—2262no—
115C2×C4—41no—
116C2×C4—4522no—
117C2×C4—4522no—
118C2×C4—2262no—
119C2×C4D4×D11312yes—
120C2×C4C2×C22⋊D11311yescharacteristic
121C8—22no—
122C8—4522no—
123C22—42no—
124C22—44no—
125C22—9048no—
126C22—4522no—
127C22—4522no—
128C22—2264no—
129C22#1681359011yescharacteristic
130C4—21no—
131C4—81no—
132C4—4522no—
133C4SD16×D11312yes—
134C4#1681364912yes—
135C2—82no—
136C2—4524no—
137C2#2029874712yes—
138C2#2029876511yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#492×C113C2
socleC22×C113#120
prime radical#20299233C2
hypercenter#492D113
hypocenterC113#1629
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. #20298885C2semidirect
3. #20298342C2semidirect
4. #20298327C2semidirect
5. #492×C113C2semidirect
11. C4⋊#11744751C22semidirect
14. C4⋊Q8×C113C22semidirect
16. C4×C8×C113C22semidirect
48. D452SD16semidirect
70. C113#1629semidirect
72. #492D113semidirect
78. C4⋊Q8C2×D113semidirect
86. C4×C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992332
#202988852
#202983422
#202983272
#492×C1132
#1629113