Finite Group Databasebeta

← #19133891

Subgroups — #19133891

Order 5504.

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

normal subgroups only

This group has 206 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#14583649C211yesmaximal, characteristic, complemented
2#14583263C212yesmaximal, complemented
3#14582640C212yesmaximal, complemented
4#14582639C211yesmaximal, characteristic, complemented
5C43×#496C211yesmaximal, characteristic
6#13063323—21no—
7#13063318—22no—
8#13063317C2212yes—
9#13063306—21no—
10#13063302—22no—
11#13063246—22no—
12#13063246—22no—
13#13063236C2212yes—
14C2×SD16×C43—21no—
15C2×D8×C43—21no—
16#127×C43C2211yescharacteristic
17#124×C43C2211yescharacteristic
18#97×C43C2211yescharacteristic
19C2×Q8×C43D411yescharacteristic
20C2×D4×C43—21no—
21C2×D4×C43—22no—
22C2×D4×C43D411yescharacteristic
23C22×Dic43—21no—
24C2×Dic86—21no—
25SD16×C43—42no—
26D8×C43—42no—
27C2×C8×C43—21no—
28C22⋊C4×C43—22no—
29C42×C43C2311yescharacteristic
30C22⋊Dic43—22no—
31C22⋊Dic43—21no—
32C4⋊Dic43D412yes—
33C4⋊Dic43D412yes—
34Dic43⋊C4—22no—
35Dic43⋊C4—22no—
36Dic43⋊C4—22no—
37C4×Dic43—21no—
38C2×C43⋊C8—22no—
39C23×C43—21no—
40C23×C43—41no—
41Q8×C43—41no—
42D4×C43—41no—
43D4×C43—41no—
44D4×C43—41no—
45D4×C43—44no—
46C2×C4×C43—21no—
47C2×C4×C43C2×D412yes—
48C2×C4×C43C2×D411yescharacteristic
49C2×Dic43—22no—
50C2×Dic43—22no—
51C2×Dic43—81no—
52Dic86—81no—
53C8×C43—22no—
54C43⋊C8—42no—
55C22×C43—41no—
56C22×C43—42no—
57C22×C43—81no—
58C22×C43—82no—
59C22×C43#12011yescharacteristic
60C4×C43—21no—
61C4×C43—22no—
62C4×C43—41no—
63Dic43—42no—
64Dic43—42no—
65#1657—431nomaximal, Sylow
66C2×C43—81no—
67C2×C43—161no—
68C2×C43#45311yescharacteristic
69C2×C43#45412yes—
70#563—431no—
71#496D4311yescharacteristic
72#490—432no—
73#330—432no—
74#329—431no—
75C43#165711yescharacteristic, complemented, Sylow
76C2×SD16—21no—
77C2×D8—21no—
78C4⋊Q8—861no—
79#127C2×D4311yescharacteristic
80#126—862no—
81#125—432no—
82#124C2×D4311yescharacteristic
83#123—861no—
84C22⋊Q8—862no—
85#102—862no—
86#102—862no—
87#97—432no—
88#97C2×D4311yescharacteristic
89C2×Q8—861no—
90C2×Q8C22⋊D4311yescharacteristic
91C2×D4—22no—
92C2×D4—21no—
93C2×D4C22⋊D4311yescharacteristic
94C22×C4—861no—
95SD16—42no—
96D8—42no—
97C2×C8—21no—
98C2×C8—862no—
99C4⋊C4—432no—
100C4⋊C4—432no—
101C4⋊C4—862no—
102C4⋊C4—862no—
103C4⋊C4—862no—
104C22⋊C4—22no—
105C22⋊C4—862no—
106C22⋊C4—861no—
107C42—861no—
108C42C22×D4311yescharacteristic
109C23—21no—
110C23—41no—
111Q8—41no—
112Q8—3441no—
113D4—41no—
114D4—41no—
115D4—41no—
116D4—44no—
117C2×C4—21no—
118C2×C4—862no—
119C2×C4—862no—
120C2×C4—3441no—
121C2×C4D4×D4312yes—
122C2×C4C2×C22⋊D4311yescharacteristic
123C8—22no—
124C8—1722no—
125C22—41no—
126C22—42no—
127C22—81no—
128C22—82no—
129C22#1306329311yescharacteristic
130C4—21no—
131C4—22no—
132C4—41no—
133C4—1722no—
134C4—1722no—
135C2—81no—
136C2—161no—
137C2#1458306611yescharacteristic
138C2#1458307012yes—
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#496C2
socleC22×C43#120
hypercenter#496D43
hypocenterC43#1657
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #14583649C2semidirect
2. #14583263C2semidirect
3. #14582640C2semidirect
4. #14582639C2semidirect
75. C43#1657semidirect