Finite Group Databasebeta

← #19133899

Subgroups — #19133899

Order 5504.

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

normal subgroups only

This group has 228 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#14583641C211yesmaximal, characteristic
2#14583261C212yesmaximal, complemented
3#14582639C211yesmaximal, characteristic, complemented
4#14582638C212yesmaximal, complemented
5C43×#497C211yesmaximal, characteristic, complemented
6#13063314—21no—
7#13063313C2212yes—
8#13063311—22no—
9#13063295—22no—
10#13063293—21no—
11#13063248—22no—
12#13063245—22no—
13#13063236C2212yescomplemented
14C2×Q16×C43—21no—
15C2×SD16×C43—21no—
16C4⋊Q8×C43C2211yescharacteristic, complemented
17#124×C43C2211yescharacteristic
18#97×C43C2211yescharacteristic, complemented
19C23×D43—21no—
20C2×Q8×C43—21no—
21C2×Q8×C43D411yescharacteristic
22C2×D4×C43D411yescharacteristic
23C2×C22⋊D43—22no—
24C2×D172—21no—
25C2×D172D412yes—
26C2×Dic86D412yes—
27Q16×C43—42no—
28SD16×C43—42no—
29C2×C8×C43—21no—
30C4⋊C4×C43—22no—
31C22⋊C4×C43—22no—
32C42×C43C2311yescharacteristic
33C22⋊Dic43—21no—
34(C2×D43)⋊C4—22no—
35(C2×D43)⋊C4—22no—
36(C2×D43)⋊C4—22no—
37C4×Dic43—21no—
38C2×C43⋊C8—22no—
39C23×C43—21no—
40C22×D43—22no—
41C22×D43—81no—
42C22×D43—82no—
43Q8×C43—41no—
44Q8×C43—41no—
45Q8×C43—41no—
46D4×C43—41no—
47C2×C4×C43—21no—
48C2×C4×C43—41no—
49C2×C4×C43C2×D412yes—
50C2×C4×C43C2×D411yescharacteristic
51C22⋊D43—82no—
52C2×Dic43—22no—
53D172—42no—
54D172—81no—
55Dic86—42no—
56C8×C43—22no—
57C43⋊C8—42no—
58C22×C43—41no—
59C22×C43—42no—
60C22×C43#12011yescharacteristic
61C2×D43—42no—
62C2×D43—42no—
63C2×D43—42no—
64C2×D43—84no—
65C4×C43—21no—
66C4×C43—22no—
67C4×C43—41no—
68C4×C43—81no—
69Dic43—42no—
70#1659—431nomaximal, Sylow
71C2×C43—81no—
72C2×C43#45311yescharacteristic
73C2×C43#45512yes—
74D43—82no—
75H(3,𝔽4)—431no—
76#497D4311yescharacteristic, complemented
77#489—432no—
78#329—431no—
79#329—432no—
80C43#165911yescharacteristic, complemented, Sylow
81C2×Q16—21no—
82C2×SD16—21no—
83C4⋊Q8C2×D4311yescharacteristic, complemented
84#124—432no—
85#124—862no—
86#124—861no—
87#124C2×D4311yescharacteristic
88#120—862no—
89#120—861no—
90#103—862no—
91#102—862no—
92#97—432no—
93#97C2×D4311yescharacteristic, complemented
94C24—861no—
95C2×Q8—21no—
96C2×Q8—432no—
97C2×Q8C22⋊D4311yescharacteristic
98C2×D4—432no—
99C2×D4—861no—
100C2×D4—862no—
101C2×D4C22⋊D4311yescharacteristic
102Q16—42no—
103SD16—42no—
104C2×C8—21no—
105C2×C8—862no—
106C4⋊C4—22no—
107C22⋊C4—22no—
108C22⋊C4—862no—
109C22⋊C4—861no—
110C22⋊C4—862no—
111C22⋊C4—862no—
112C42—861no—
113C42C22×D4311yescharacteristic
114C23—21no—
115C23—862no—
116C23—3441no—
117C23—3442no—
118Q8—41no—
119Q8—41no—
120Q8—41no—
121Q8—1722no—
122D4—41no—
123D4—3441no—
124D4—3442no—
125D4—1722no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—862no—
129C2×C4D4×D4312yes—
130C2×C4C2×C22⋊D4311yescharacteristic
131C8—22no—
132C8—1722no—
133C22—41no—
134C22—42no—
135C22—3444no—
136C22—1722no—
137C22—1722no—
138C22—1722no—
139C22#1306329311yescharacteristic
140C4—21no—
141C4—22no—
142C4—41no—
143C4—81no—
144C4—1722no—
145C2—81no—
146C2—3442no—
147C2#1458306611yescharacteristic
148C2#1458307512yes—
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#497C2
socleC22×C43#120
hypercenter#497D43
hypocenterC43#1659
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. #14583261C2semidirect
3. #14582639C2semidirect
4. #14582638C2semidirect
5. C43×#497C2semidirect
13. #13063236C22semidirect
16. C4⋊Q8×C43C22semidirect
18. #97×C43C22semidirect
76. #497D43semidirect
80. C43#1659semidirect
83. C4⋊Q8C2×D43semidirect
93. #97C2×D43semidirect