Finite Group Databasebeta

← #19133918

Subgroups — #19133918

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#14583269C211yesmaximal, characteristic, complemented
2#14583258C212yesmaximal, complemented
3#14582641C211yesmaximal, characteristic, complemented
4#14582639C212yesmaximal, complemented
5C43×#562C211yesmaximal, characteristic
6#13063325C2211yescharacteristic
7#13063249—22no—
8#13063248—22no—
9#13063246—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×Dic86—21no—
22C4⋊C4×C43—22no—
23C4⋊C4×C43—22no—
24C4⋊C4×C43D412yes—
25C22⋊C4×C43—22no—
26C22⋊C4×C43—22no—
27C22⋊C4×C43—22no—
28C42×C43C2311yescharacteristic
29C4⋊Dic43—22no—
30C2×C43⋊C8—22no—
31C2×C43⋊C8—21no—
32C23×C43—22no—
33Q8×C43—42no—
34D4×C43—42no—
35D4×C43—82no—
36C2×C4×C43—22no—
37C2×C4×C43—22no—
38C2×C4×C43—82no—
39C2×C4×C43C2×D412yes—
40C2×C4×C43C2×D411yescharacteristic
41C2×Dic43—41no—
42Dic86—42no—
43C43⋊C8—41no—
44C43⋊C8—42no—
45C22×C43—42no—
46C22×C43—42no—
47C22×C43—42no—
48C22×C43#12011yescharacteristic
49C4×C43—21no—
50C4×C43—22no—
51C4×C43—42no—
52C4×C43—42no—
53Dic43—81no—
54#1662—431nomaximal, Sylow
55C2×C43—82no—
56C2×C43#45411yescharacteristic
57C2×C43#45512yes—
58#562D4311yescharacteristic
59#491—431no—
60#489—432no—
61#330—431no—
62#329—432no—
63C43#166211yescharacteristic, complemented, Sylow
64C4⋊Q8—431no—
65#125C2×D4311yescharacteristic
66#124C2×D4312yes—
67#123—22no—
68C22⋊Q8—22no—
69#121—22no—
70#103—862no—
71#103—862no—
72#102—862no—
73#97—431no—
74#97—432no—
75C2×Q8—861no—
76C2×Q8C22⋊D4312yes—
77C2×D4—22no—
78C2×D4C22⋊D4312yes—
79C22×C4—22no—
80C2×C8—862no—
81C2×C8—861no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—862no—
85C4⋊C4C22⋊D4312yes—
86C22⋊C4—22no—
87C22⋊C4—22no—
88C22⋊C4—22no—
89C42C22×D4311yescharacteristic
90C23—22no—
91Q8—42no—
92Q8—1722no—
93D4—42no—
94D4—82no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—82no—
98C2×C4—1721no—
99C2×C4C2×C22⋊D4311yescharacteristic
100C2×C4C2×C22⋊D4312yes—
101C8—1721no—
102C8—1722no—
103C22—42no—
104C22—42no—
105C22—42no—
106C22#1306329411yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—42no—
111C4—3441no—
112C2—82no—
113C2#1458307211yescharacteristic
114C2#1458307712yes—
subgroupG/H
centerC22#13063294
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#562C2
socleC22×C43#120
hypercenter#562D43
hypocenterC43#1662
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. #14583269C2semidirect
2. #14583258C2semidirect
3. #14582641C2semidirect
4. #14582639C2semidirect
63. C43#1662semidirect