Finite Group Databasebeta

← #28389628

Subgroups — #28389628

Order 14464.

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

normal subgroups only

This group has 336 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#20298974C211yesmaximal, characteristic, complemented
2#20298793C212yesmaximal, complemented
3#20298342C211yesmaximal, characteristic, complemented
4D4⋊#11744751C212yesmaximal, complemented
5D42×C113C211yesmaximal, characteristic, complemented
6C2×#14268632—22no—
7C2×#14268632—22no—
8#16813619C2211yescharacteristic, complemented
9C4⋊#11744751C2212yescomplemented
10#16813542—22no—
11C4×#11744751C2211yescharacteristic, complemented
12C22×D4×C113—22no—
13#127×C113C2211yescharacteristic
14#121×C113—22no—
15#120×C113—22no—
16C4×D4×C113C2212yes—
17C2×D452—21no—
18C2×D452—22no—
19#14268632—44no—
20#14268632—44no—
21C2×#11744751—21no—
22C2×#11744751—22no—
23C24×C113—22no—
24C2×D4×C113—24no—
25C2×D4×C113—22no—
26C2×D4×C113—44no—
27C2×D4×C113—44no—
28C2×D4×C113D412yes—
29C2×D4×C113D412yes—
30C22×C4×C113—22no—
31C4⋊C4×C113D412yes—
32C22⋊C4×C113—22no—
33C22⋊C4×C113—22no—
34C42×C113C2311yescharacteristic
35C23×C113—22no—
36C23×C113—22no—
37C23×C113—48no—
38C23×C113—82no—
39C22×D113—41no—
40D4×C113—22no—
41D4×C113—42no—
42D4×C113—48no—
43D4×C113—42no—
44D4×C113—42no—
45D4×C113D814yescomplemented
46C2×C4×C113—22no—
47C2×C4×C113—42no—
48C2×C4×C113—42no—
49C2×C4×C113C2×D411yescharacteristic
50C2×C4×C113C2×D412yes—
51D452—42no—
52D452—42no—
53D452—42no—
54#11744751—22no—
55#11744751—42no—
56C22×C113—24no—
57C22×C113—42no—
58C22×C113—42no—
59C22×C113—44no—
60C22×C113—42no—
61C22×C113—88no—
62C22×C113#12011yescharacteristic
63C2×D113—82no—
64C2×D113—81no—
65C4×C113—21no—
66C4×C113—42no—
67C4×C113C2×D812yes—
68C4×C113AGL(1,ℤ/8)12yes—
69C2×C113—44no—
70C2×C113—82no—
71C2×C113#44712yes—
72C2×C113#45311yescharacteristic
73D113—161no—
74#1619—1131nomaximal, Sylow
75C113#161911yescharacteristic, complemented, Sylow
76D42D11311yescharacteristic, complemented
77#493—1131no—
78#459—1132no—
79#331—1131no—
80D4⋊C8—1132no—
81C22×D4—22no—
82C2×D8—2262no—
83C2×D8—2262no—
84#127—1131no—
85#127C2×D11311yescharacteristic
86#121—22no—
87#120—22no—
88C4×D4C2×D11312yes—
89C4⋊C8—1132no—
90#102—2262no—
91C4×C8—1131no—
92C24—22no—
93C2×D4—24no—
94C2×D4—22no—
95C2×D4—44no—
96C2×D4—44no—
97C2×D4—2262no—
98C2×D4—2261no—
99C2×D4C22⋊D11312yes—
100C2×D4C22⋊D11312yes—
101C22×C4—22no—
102D8—4524no—
103D8—4524no—
104C2×C8—2262no—
105C2×C8—2261no—
106C4⋊C4C22⋊D11312yes—
107C22⋊C4—22no—
108C22⋊C4—22no—
109C42C22×D11311yescharacteristic
110C23—22no—
111C23—22no—
112C23—48no—
113C23—82no—
114C23—4521no—
115D4—22no—
116D4—42no—
117D4—48no—
118D4—42no—
119D4—42no—
120D4—4522no—
121D4—4522no—
122D4—4522no—
123D4#1426863214yescomplemented
124C2×C4—22no—
125C2×C4—42no—
126C2×C4—42no—
127C2×C4C2×C22⋊D11311yescharacteristic
128C2×C4C2×C22⋊D11312yes—
129C8—4522no—
130C8—2262no—
131C22—24no—
132C22—42no—
133C22—42no—
134C22—42no—
135C22—44no—
136C22—88no—
137C22—9041no—
138C22—9042no—
139C22#1681359111yescharacteristic
140C4—21no—
141C4—42no—
142C4C2×#1426863212yes—
143C4#1681364812yes—
144C2—44no—
145C2—82no—
146C2—18081no—
147C2#2029873212yes—
148C2#2029876611yescharacteristic
subgroupG/H
centerC22#16813591
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
FittingD42×C113C2
socleC22×C113#120
hypercenterD42D113
hypocenterC113#1619
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. #20298974C2semidirect
2. #20298793C2semidirect
3. #20298342C2semidirect
4. D4⋊#11744751C2semidirect
5. D42×C113C2semidirect
8. #16813619C22semidirect
9. C4⋊#11744751C22semidirect
11. C4×#11744751C22semidirect
45. D4×C113D8semidirect
75. C113#1619semidirect
76. D42D113semidirect
123. D4#14268632semidirect

Maximal subgroups

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

subgroupindex
#202989742
#202987932
#202983422
D4⋊#117447512
D42×C1132
#1619113