Finite Group Databasebeta

← #19133887

Subgroups — #19133887

Order 5504.

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

normal subgroups only

This group has 230 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#14583647C211yesmaximal, characteristic, complemented
2#14583286C212yesmaximal, complemented
3#14582641C211yesmaximal, characteristic, complemented
4#14582638C212yesmaximal, complemented
5C43×#490C211yesmaximal, characteristic, complemented
6C2×#10621883—22no—
7C2×#10621882—22no—
8#13063313C2212yes—
9#13063310—22no—
10#13063303—22no—
11#13063300—22no—
12#13063236C2212yes—
13#127×C43C2211yescharacteristic
14#125×C43C2211yescharacteristic
15#102×C43—22no—
16#97×C43C2211yescharacteristic
17C2×D4×C43—21no—
18C2×D4×C43—22no—
19C2×D172—22no—
20C2×D172D412yes—
21C2×C4×D43—22no—
22C2×Dic86D412yes—
23C2×C8×C43—21no—
24C4⋊C4×C43—22no—
25C4⋊C4×C43D412yes—
26C42×C43C2311yescharacteristic
27#10621883—44no—
28#10621882—44no—
29(C2×D43)⋊C4—22no—
30(C2×D43)⋊C4—22no—
31(C2×D43)⋊C4—22no—
32Dic43⋊C4—22no—
33C2×C43⋊C8—22no—
34C23×C43—41no—
35C22×D43—22no—
36D4×C43—42no—
37D4×C43—42no—
38D4×C43—42no—
39C2×C4×C43—22no—
40C2×C4×C43C2×D412yes—
41C2×C4×C43C2×D411yescharacteristic
42C2×Dic43—22no—
43D172—42no—
44D172—82no—
45C4×D43—82no—
46Dic86—42no—
47C8×C43—41no—
48C43⋊C8—24no—
49C22×C43—82no—
50C22×C43—81no—
51C22×C43#12011yescharacteristic
52C2×D43—42no—
53C2×D43—42no—
54C2×D43—42no—
55C4×C43—22no—
56C4×C43—21no—
57C4×C43—42no—
58Dic43—42no—
59#1656—431nomaximal, Sylow
60C2×C43—161no—
61C2×C43#45312yes—
62C2×C43#45411yescharacteristic
63D43—82no—
64#562—431no—
65#496—432no—
66#490D4311yescharacteristic, complemented
67#330—431no—
68#329—432no—
69C43#165611yescharacteristic, complemented, Sylow
70C2×SD16—862no—
71C2×D8—862no—
72#127C2×D4311yescharacteristic
73#125C2×D4311yescharacteristic
74#124—432no—
75#123—862no—
76C22⋊Q8—862no—
77#121—862no—
78#102—22no—
79#97—432no—
80#97C2×D4311yescharacteristic
81C2×Q8—432no—
82C2×D4—22no—
83C2×D4—21no—
84C2×D4—432no—
85C2×D4—862no—
86C22×C4—862no—
87SD16—1724no—
88D8—1724no—
89C2×C8—21no—
90C2×C8—862no—
91C4⋊C4—22no—
92C4⋊C4—862no—
93C4⋊C4C22⋊D4312yes—
94C22⋊C4—862no—
95C22⋊C4—862no—
96C22⋊C4—862no—
97C42C22×D4311yescharacteristic
98C23—41no—
99C23—862no—
100Q8—1722no—
101D4—42no—
102D4—42no—
103D4—42no—
104D4—3442no—
105D4—1722no—
106C2×C4—22no—
107C2×C4—862no—
108C2×C4—3442no—
109C2×C4D4×D4312yes—
110C2×C4C2×C22⋊D4311yescharacteristic
111C8—41no—
112C8—864no—
113C22—82no—
114C22—81no—
115C22—1722no—
116C22—1722no—
117C22—1722no—
118C22#1306329311yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—1722no—
123C2—161no—
124C2—3442no—
125C2#1458306512yes—
126C2#1458307111yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#490C2
socleC22×C43#120
hypercenter#490D43
hypocenterC43#1656
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #14583647C2semidirect
2. #14583286C2semidirect
3. #14582641C2semidirect
4. #14582638C2semidirect
5. C43×#490C2semidirect
66. #490D43semidirect
69. C43#1656semidirect