Finite Group Databasebeta

← #19133916

Subgroups — #19133916

Order 5504.

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

normal subgroups only

This group has 196 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
2#14583261C212yesmaximal, complemented
3#14582641C211yesmaximal, characteristic, complemented
4#14582638C212yesmaximal, complemented
5C43×#491C211yesmaximal, characteristic, complemented
6#13063313C2212yes—
7#13063310—22no—
8#13063303—22no—
9#13063300—22no—
10#13063248—22no—
11#13063245—22no—
12#13063236C2212yes—
13C4⋊Q8×C43C2211yescharacteristic
14#125×C43C2211yescharacteristic
15#103×C43—22no—
16#97×C43C2211yescharacteristic
17C2×Q8×C43—21no—
18C2×D172—22no—
19C2×D172D412yes—
20C2×C4×D43—22no—
21C2×Dic86D412yes—
22C2×C8×C43—21no—
23C4⋊C4×C43—22no—
24C4⋊C4×C43—22no—
25C4⋊C4×C43D412yes—
26C42×C43C2311yescharacteristic
27(C2×D43)⋊C4—22no—
28(C2×D43)⋊C4—22no—
29(C2×D43)⋊C4—22no—
30Dic43⋊C4—22no—
31C2×C43⋊C8—22no—
32C22×D43—22no—
33Q8×C43—42no—
34C2×C4×C43—22no—
35C2×C4×C43—41no—
36C2×C4×C43C2×D412yes—
37C2×C4×C43C2×D411yescharacteristic
38C2×Dic43—22no—
39D172—42no—
40D172—82no—
41C4×D43—82no—
42Dic86—42no—
43C8×C43—41no—
44C43⋊C8—42no—
45C22×C43#12011yescharacteristic
46C2×D43—42no—
47C2×D43—42no—
48C2×D43—42no—
49C4×C43—21no—
50C4×C43—22no—
51C4×C43—42no—
52C4×C43—81no—
53Dic43—42no—
54#1662—431nomaximal, Sylow
55C2×C43#45411yescharacteristic
56C2×C43#45512yes—
57D43—82no—
58#562—431no—
59#491D4311yescharacteristic, complemented
60#489—432no—
61#330—431no—
62#329—432no—
63C43#166211yescharacteristic, complemented, Sylow
64C4⋊Q8C2×D4311yescharacteristic
65#125C2×D4311yescharacteristic
66#124—432no—
67#123—862no—
68C22⋊Q8—862no—
69#121—862no—
70#103—22no—
71#103—862no—
72#102—862no—
73#97—432no—
74#97C2×D4311yescharacteristic
75C2×Q8—21no—
76C2×Q8—432no—
77C2×D4—432no—
78C2×D4—862no—
79C22×C4—862no—
80C2×C8—21no—
81C2×C8—862no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—862no—
85C4⋊C4C22⋊D4312yes—
86C22⋊C4—862no—
87C22⋊C4—862no—
88C22⋊C4—862no—
89C42C22×D4311yescharacteristic
90C23—862no—
91Q8—42no—
92Q8—1722no—
93D4—3442no—
94D4—1722no—
95C2×C4—22no—
96C2×C4—41no—
97C2×C4—862no—
98C2×C4—3442no—
99C2×C4D4×D4312yes—
100C2×C4C2×C22⋊D4311yescharacteristic
101C8—41no—
102C8—1722no—
103C22—1722no—
104C22—1722no—
105C22—1722no—
106C22#1306329311yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—81no—
111C4—1722no—
112C2—3442no—
113C2#1458307111yescharacteristic
114C2#1458307512yes—
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#491C2
socleC22×C43#120
hypercenter#491D43
hypocenterC43#1662
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #14583261C2semidirect
3. #14582641C2semidirect
4. #14582638C2semidirect
5. C43×#491C2semidirect
59. #491D43semidirect
63. C43#1662semidirect