Finite Group Databasebeta

← #19132435

Subgroups — #19132435

Order 5504.

208 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C2×C4⋊(C43⋊C8)C211yesmaximal, characteristic
2C4×C4⋊Dic43C211yesmaximal, characteristic
3C2×C4×C8×C43C211yesmaximal, characteristic
4C22×C43⋊C8—21no—
5C2×C4⋊Dic43C412yes—
6C2×C4×Dic43—21no—
7C4⋊(C43⋊C8)—21no—
8C4⋊(C43⋊C8)C412yescomplemented
9C43⋊#95—21no—
10C22×C8×C43—21no—
11C2×C42×C43C2211yescharacteristic
12C4×C8×C43—21no—
13C4×C8×C43C412yescomplemented
14C22×C4×C43C2×C411yescharacteristic
15C22×C4×C43D411yescharacteristic
16C22×C4×C43D411yescharacteristic
17C22×Dic43—22no—
18C2×C8×C43—24no—
19C2×C8×C43—22no—
20C42×C43C2×C411yescharacteristic
21C42×C43C2×C411yescharacteristic
22C42×C43D411yescharacteristic
23C42×C43Q811yescharacteristic
24C4⋊Dic43—22no—
25C4⋊Dic43C814yescomplemented
26C4×Dic43—41no—
27C4×Dic43—41no—
28C2×C43⋊C8—22no—
29C2×C43⋊C8—41no—
30C2×C43⋊C8—41no—
31C23×C43C22⋊C411yescharacteristic
32C2×C4×C43—22no—
33C2×C4×C43C4211yescharacteristic
34C2×C4×C43C22⋊C411yescharacteristic
35C2×C4×C43C22⋊C411yescharacteristic
36C2×C4×C43C4⋊C411yescharacteristic
37C2×C4×C43C4⋊C411yescharacteristic
38C2×C4×C43C4⋊C411yescharacteristic
39C2×C4×C43C2×C812yes—
40C2×C4×C43M1612yes—
41C2×C4×C43D811yescharacteristic
42C2×C4×C43SD1611yescharacteristic
43C2×C4×C43SD1611yescharacteristic
44C2×C4×C43Q1611yescharacteristic
45C2×Dic43—24no—
46C2×Dic43—42no—
47C2×Dic43—42no—
48C8×C43—24no—
49C43⋊C8—42no—
50C22×C43#9511yescharacteristic
51C22×C43C22⋊C812yes—
52C22×C43#10211yescharacteristic
53C22×C43#10311yescharacteristic
54C22×C43#10412yes—
55C4×C43—21no—
56C4×C43—21no—
57C4×C43C4×C811yescharacteristic
58C4×C43#9711yescharacteristic
59C4×C43#10211yescharacteristic
60C4×C43#10311yescharacteristic
61C4×C43C4⋊C812yes—
62C4×C43#10611yescharacteristic
63C4×C43#10711yescharacteristic
64Dic43—44no—
65#1279—431nomaximal, Sylow
66C2×C43D4⋊C812yes—
67C2×C43Q8⋊C812yes—
68C2×C43#33611yescharacteristic
69C2×C43#33911yescharacteristic
70C2×C43#34011yescharacteristic
71C2×C4⋊C8—431no—
72C2×C4×C8D4311yescharacteristic
73C4×C4⋊C4—431no—
74C43#127911yescharacteristic, complemented, Sylow
75C22×C8—21no—
76C22×C8—861no—
77C2×C4⋊C4—432no—
78C2×C42—861no—
79C2×C42C2×D4311yescharacteristic
80C4⋊C8—432no—
81C4⋊C8—861no—
82C4×C8—21no—
83C4×C8Dic4312yescomplemented
84#95—861no—
85C22×C4—862no—
86C22×C4C4×D4311yescharacteristic
87C22×C4D17211yescharacteristic
88C22×C4C22⋊D4311yescharacteristic
89C2×C8—24no—
90C2×C8—22no—
91C2×C8—862no—
92C2×C8—1721no—
93C2×C8—1721no—
94C4⋊C4—434no—
95C4⋊C4—862no—
96C42—1721no—
97C42—1721no—
98C42Dic8611yescharacteristic
99C42C4×D4311yescharacteristic
100C42C2×Dic4311yescharacteristic
101C42C22⋊D4311yescharacteristic
102C23(C2×D43)⋊C411yescharacteristic
103C2×C4—22no—
104C2×C4—864no—
105C2×C4—1722no—
106C2×C4—1722no—
107C2×C4C8×D4312yes—
108C2×C4#1062187212yes—
109C2×C4#1062187311yescharacteristic
110C2×C4#1062187311yescharacteristic
111C2×C4D34411yescharacteristic
112C2×C4Dic17211yescharacteristic
113C2×C4C4×Dic4311yescharacteristic
114C2×C4Dic43⋊C411yescharacteristic
115C2×C4Dic43⋊C411yescharacteristic
116C2×C4C4⋊Dic4311yescharacteristic
117C2×C4(C2×D43)⋊C411yescharacteristic
118C2×C4C22⋊Dic4311yescharacteristic
119C8—24no—
120C8—1722no—
121C22C43⋊#9511yescharacteristic
122C22(C2×D43)⋊C812yes—
123C22#1306324711yescharacteristic
124C22#1306325011yescharacteristic
125C22#1306325312yes—
126C4—21no—
127C4—21no—
128C4—1724no—
129C4C8×Dic4311yescharacteristic
130C4#1306323511yescharacteristic
131C4#1306324711yescharacteristic
132C4#1306325011yescharacteristic
133C4Dic43⋊C812yes—
134C4#1306325711yescharacteristic
135C4#1306325911yescharacteristic
136C2#1458262812yes—
137C2#1458263112yes—
138C2#1458265311yescharacteristic
139C2#1458265911yescharacteristic
140C2#1458266211yescharacteristic
subgroupG/H
centerC22×C4D172
commutatorC4×C43C4×C8
FrattiniC2×C42C2×D43
FittingC2×C4×C8×C43C2
socleC23×C43C22⋊C4
hypercenterC2×C4×C8D43
hypocenterC43#1279
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
8. C4⋊(C43⋊C8)C4semidirect
13. C4×C8×C43C4semidirect
25. C4⋊Dic43C8semidirect
74. C43#1279semidirect
83. C4×C8Dic43semidirect