Finite Group Databasebeta

← #19133901

Subgroups — #19133901

Order 5504.

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

normal subgroups only

This group has 228 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#14583294C211yesmaximal, characteristic, complemented
2#14583258C212yesmaximal, complemented
3#14582639C212yesmaximal, complemented
4#14582639C211yesmaximal, characteristic, complemented
5C43×H(3,𝔽4)C211yesmaximal, characteristic
6C2×#10621885—21no—
7C2×#10621883—21no—
8#13063325C2211yescharacteristic, complemented
9#13063249—22no—
10#13063246—22no—
11#13063236C2212yescomplemented
12#13063236C2211yescharacteristic, complemented
13#124×C43—22no—
14#124×C43—21no—
15#124×C43C2212yes—
16#124×C43C2211yescharacteristic
17#120×C43—22no—
18#120×C43—21no—
19C24×C43—21no—
20C2×Q8×C43D412yes—
21C2×Q8×C43D411yescharacteristic
22C2×D4×C43—22no—
23C2×D4×C43—21no—
24C2×D4×C43D412yes—
25C2×D4×C43D411yescharacteristic
26C2×Dic86—21no—
27C22⋊C4×C43—21no—
28C22⋊C4×C43—22no—
29C22⋊C4×C43—22no—
30C22⋊C4×C43—22no—
31C22⋊C4×C43—22no—
32C42×C43—21no—
33C42×C43C2311yescharacteristic
34#10621885—42no—
35#10621883—42no—
36C4⋊Dic43—22no—
37C2×C43⋊C8—21no—
38C2×C43⋊C8—22no—
39C23×C43—21no—
40C23×C43—22no—
41C23×C43—81no—
42C23×C43—82no—
43Q8×C43—41no—
44Q8×C43—42no—
45D4×C43—41no—
46D4×C43—42no—
47D4×C43—81no—
48D4×C43—82no—
49C2×C4×C43—21no—
50C2×C4×C43—22no—
51C2×C4×C43C2×D412yes—
52C2×C4×C43C2×D411yescharacteristic
53C2×Dic43—41no—
54Dic86—41no—
55Dic86—41no—
56C43⋊C8—22no—
57C43⋊C8—42no—
58C22×C43—41no—
59C22×C43—42no—
60C22×C43—42no—
61C22×C43—42no—
62C22×C43—42no—
63C22×C43—84no—
64C22×C43#12011yescharacteristic
65C4×C43—21no—
66C4×C43—22no—
67C4×C43—41no—
68C4×C43—42no—
69Dic43—81no—
70#1659—431nomaximal, Sylow
71C2×C43—81no—
72C2×C43—82no—
73C2×C43#45311yescharacteristic
74C2×C43#45512yes—
75H(3,𝔽4)D4311yescharacteristic
76#497—431no—
77#489—432no—
78#329—431no—
79#329—432no—
80C43#165911yescharacteristic, complemented, Sylow
81C2×Q16—861no—
82C2×SD16—861no—
83C4⋊Q8—431no—
84#124—22no—
85#124—21no—
86#124C2×D4312yes—
87#124C2×D4311yescharacteristic
88#120—22no—
89#120—21no—
90#103—862no—
91#102—862no—
92#97—432no—
93#97—431no—
94C24—21no—
95C2×Q8—861no—
96C2×Q8C22⋊D4312yes—
97C2×Q8C22⋊D4311yescharacteristic
98C2×D4—21no—
99C2×D4—22no—
100C2×D4C22⋊D4312yes—
101C2×D4C22⋊D4311yescharacteristic
102Q16—1722no—
103SD16—1722no—
104C2×C8—861no—
105C2×C8—862no—
106C4⋊C4—862no—
107C22⋊C4—22no—
108C22⋊C4—21no—
109C22⋊C4—22no—
110C22⋊C4—22no—
111C22⋊C4—22no—
112C42—21no—
113C42C22×D4311yescharacteristic
114C23—21no—
115C23—22no—
116C23—81no—
117C23—82no—
118Q8—41no—
119Q8—42no—
120Q8—1721no—
121Q8—1721no—
122D4—41no—
123D4—42no—
124D4—81no—
125D4—82no—
126C2×C4—21no—
127C2×C4—22no—
128C2×C4—1721no—
129C2×C4C2×C22⋊D4312yes—
130C2×C4C2×C22⋊D4311yescharacteristic
131C8—862no—
132C8—1722no—
133C22—41no—
134C22—42no—
135C22—42no—
136C22—42no—
137C22—42no—
138C22—84no—
139C22#1306329411yescharacteristic
140C4—21no—
141C4—22no—
142C4—41no—
143C4—42no—
144C4—3441no—
145C2—81no—
146C2—82no—
147C2#1458306711yescharacteristic
148C2#1458307712yes—
subgroupG/H
centerC22#13063294
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×H(3,𝔽4)C2
socleC22×C43#120
hypercenterH(3,𝔽4)D43
hypocenterC43#1659
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #14583294C2semidirect
2. #14583258C2semidirect
3. #14582639C2semidirect
4. #14582639C2semidirect
8. #13063325C22semidirect
11. #13063236C22semidirect
12. #13063236C22semidirect
80. C43#1659semidirect