Finite Group Databasebeta

← #19133906

Subgroups — #19133906

Order 5504.

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

normal subgroups only

This group has 196 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#14583309C212yesmaximal, complemented
2#14583294C211yesmaximal, characteristic
3#14582641C212yesmaximal, complemented
4#14582639C211yesmaximal, characteristic
5C43×#563C211yesmaximal, characteristic
6C2×#10621885—21no—
7C2×#10621883—21no—
8#13063325C2211yescharacteristic
9#13063258—22no—
10#13063256—22no—
11#13063236C2212yes—
12#13063236C2211yescharacteristic
13C4⋊Q8×C43—21no—
14#126×C43—22no—
15#125×C43C2212yes—
16#124×C43C2211yescharacteristic
17#123×C43—21no—
18C22⋊Q8×C43—22no—
19C2×Q8×C43—21no—
20C2×Q8×C43D411yescharacteristic
21C2×D4×C43D411yescharacteristic
22C22×C4×C43—21no—
23C2×Dic86—21no—
24C4⋊C4×C43—22no—
25C4⋊C4×C43—22no—
26C4⋊C4×C43—22no—
27C4⋊C4×C43D412yes—
28C4⋊C4×C43D412yes—
29C22⋊C4×C43—22no—
30C22⋊C4×C43—21no—
31C22⋊C4×C43—22no—
32C42×C43—21no—
33C42×C43C2311yescharacteristic
34#10621885—42no—
35#10621883—42no—
36C4⋊Dic43—22no—
37C2×C43⋊C8—22no—
38C2×C43⋊C8—21no—
39C23×C43—21no—
40Q8×C43—41no—
41Q8×C43—81no—
42D4×C43—41no—
43C2×C4×C43—22no—
44C2×C4×C43—21no—
45C2×C4×C43—22no—
46C2×C4×C43—81no—
47C2×C4×C43C2×D412yes—
48C2×C4×C43C2×D411yescharacteristic
49C2×Dic43—41no—
50Dic86—41no—
51Dic86—41no—
52C43⋊C8—24no—
53C43⋊C8—22no—
54C22×C43—41no—
55C22×C43—42no—
56C22×C43#12011yescharacteristic
57C4×C43—21no—
58C4×C43—22no—
59C4×C43—42no—
60C4×C43—41no—
61C4×C43—42no—
62Dic43—81no—
63#1660—431nomaximal, Sylow
64C2×C43—81no—
65C2×C43#45311yescharacteristic
66C2×C43#45612yes—
67#563D4311yescharacteristic
68#501—432no—
69#497—431no—
70#330—432no—
71#329—431no—
72C43#166011yescharacteristic, complemented, Sylow
73C2×Q16—861no—
74C2×SD16—861no—
75C4⋊Q8—21no—
76C4⋊Q8—431no—
77#126—22no—
78#125C2×D4312yes—
79#124C2×D4311yescharacteristic
80#123—21no—
81C22⋊Q8—22no—
82#107—862no—
83#106—862no—
84#97—432no—
85#97—431no—
86C2×Q8—21no—
87C2×Q8—861no—
88C2×Q8C22⋊D4311yescharacteristic
89C2×D4C22⋊D4311yescharacteristic
90C22×C4—21no—
91Q16—1722no—
92SD16—1722no—
93C2×C8—862no—
94C2×C8—861no—
95C4⋊C4—22no—
96C4⋊C4—22no—
97C4⋊C4—22no—
98C4⋊C4—862no—
99C4⋊C4C22⋊D4312yes—
100C4⋊C4C22⋊D4312yes—
101C22⋊C4—22no—
102C22⋊C4—21no—
103C22⋊C4—22no—
104C42—21no—
105C42C22×D4311yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—81no—
109Q8—1721no—
110Q8—1721no—
111D4—41no—
112C2×C4—22no—
113C2×C4—21no—
114C2×C4—22no—
115C2×C4—81no—
116C2×C4—1721no—
117C2×C4C2×C22⋊D4312yes—
118C2×C4C2×C22⋊D4311yescharacteristic
119C8—862no—
120C8—864no—
121C22—41no—
122C22—42no—
123C22#1306329411yescharacteristic
124C4—21no—
125C4—22no—
126C4—42no—
127C4—41no—
128C4—42no—
129C4—3441no—
130C2—81no—
131C2#1458306711yescharacteristic
132C2#1458308212yes—
subgroupG/H
centerC22#13063294
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#563C2
socleC22×C43#120
hypercenter#563D43
hypocenterC43#1660
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #14583309C2semidirect
3. #14582641C2semidirect
72. C43#1660semidirect