Finite Group Databasebeta

← #19133888

Subgroups — #19133888

Order 5504.

230 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 49 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#14583289C212yesmaximal, complemented
2#14583265C211yesmaximal, characteristic, complemented
3#14582641C211yesmaximal, characteristic, complemented
4#14582639C212yesmaximal, complemented
5C43×#562C211yesmaximal, characteristic, complemented
6C2×#10621884—22no—
7C2×#10621882—22no—
8#13063322C2211yescharacteristic
9#13063245—22no—
10#13063236C2211yescharacteristic
11#13063236C2212yes—
12#125×C43C2211yescharacteristic
13#124×C43C2212yes—
14#123×C43—22no—
15C22⋊Q8×C43—22no—
16#121×C43—22no—
17C2×Q8×C43D412yes—
18C2×D4×C43—22no—
19C2×D4×C43D412yes—
20C22×C4×C43—22no—
21C2×D172—21no—
22C2×D172—22no—
23C4⋊C4×C43—22no—
24C4⋊C4×C43—22no—
25C4⋊C4×C43D412yes—
26C22⋊C4×C43—22no—
27C22⋊C4×C43—22no—
28C22⋊C4×C43—22no—
29C42×C43C2311yescharacteristic
30#10621884—44no—
31#10621882—44no—
32C2×C43⋊C8—22no—
33C2×C43⋊C8—21no—
34C23×C43—22no—
35C22×D43—41no—
36Q8×C43—42no—
37D4×C43—42no—
38D4×C43—82no—
39C2×C4×C43—22no—
40C2×C4×C43—22no—
41C2×C4×C43—82no—
42C2×C4×C43C2×D411yescharacteristic
43C2×C4×C43C2×D412yes—
44D172—42no—
45D172—42no—
46D172—42no—
47C43⋊C8—24no—
48C43⋊C8—41no—
49C22×C43—42no—
50C22×C43—42no—
51C22×C43—42no—
52C22×C43#12011yescharacteristic
53C2×D43—82no—
54C2×D43—81no—
55C4×C43—22no—
56C4×C43—21no—
57C4×C43—42no—
58C4×C43—42no—
59#1656—431nomaximal, Sylow
60C2×C43—82no—
61C2×C43#45312yes—
62C2×C43#45411yescharacteristic
63D43—161no—
64#562D4311yescharacteristic, complemented
65#496—432no—
66#490—431no—
67#330—431no—
68#329—432no—
69C43#165611yescharacteristic, complemented, Sylow
70C2×SD16—862no—
71C2×D8—862no—
72#127—431no—
73#125C2×D4311yescharacteristic
74#124C2×D4312yes—
75#123—22no—
76C22⋊Q8—22no—
77#121—22no—
78#102—862no—
79#97—431no—
80#97—432no—
81C2×Q8C22⋊D4312yes—
82C2×D4—22no—
83C2×D4—861no—
84C2×D4—862no—
85C2×D4C22⋊D4312yes—
86C22×C4—22no—
87SD16—1724no—
88D8—1724no—
89C2×C8—862no—
90C2×C8—861no—
91C4⋊C4—22no—
92C4⋊C4—22no—
93C4⋊C4C22⋊D4312yes—
94C22⋊C4—22no—
95C22⋊C4—22no—
96C22⋊C4—22no—
97C42C22×D4311yescharacteristic
98C23—22no—
99C23—1721no—
100Q8—42no—
101D4—42no—
102D4—82no—
103D4—1722no—
104D4—1722no—
105D4—1722no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—82no—
109C2×C4C2×C22⋊D4311yescharacteristic
110C2×C4C2×C22⋊D4312yes—
111C8—864no—
112C8—1721no—
113C22—42no—
114C22—42no—
115C22—42no—
116C22—3442no—
117C22—3441no—
118C22#1306329411yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C2—82no—
124C2—6881no—
125C2#1458306712yes—
126C2#1458307211yescharacteristic
subgroupG/H
centerC22#13063294
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#562C2
socleC22×C43#120
hypercenter#562D43
hypocenterC43#1656
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #14583289C2semidirect
2. #14583265C2semidirect
3. #14582641C2semidirect
4. #14582639C2semidirect
5. C43×#562C2semidirect
64. #562D43semidirect
69. C43#1656semidirect