Finite Group Databasebeta

← #19133799

Subgroups — #19133799

Order 5504.

208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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#14583610C211yesmaximal, characteristic
2#14583181C211yesmaximal, characteristic, complemented
3#14583101C211yesmaximal, characteristic
4#14582648C211yesmaximal, characteristic, complemented
5#14582631C211yesmaximal, characteristic, complemented
6#14582628C211yesmaximal, characteristic
7C43×#487C211yesmaximal, characteristic, complemented
8C2×#10621884—21no—
9#13063316—21no—
10#13063305—21no—
11#13063301—22no—
12C4×Dic86C2211yescharacteristic
13C4×D172C2211yescharacteristic
14#13063287—21no—
15C4⋊C4×D43—21no—
16#13063256—21no—
17C4⋊(C43⋊C8)C2211yescharacteristic
18C4⋊(C43⋊C8)C2211yescharacteristic
19#13063249—21no—
20#13063248—21no—
21C4⋊Q8×C43C2211yescharacteristic
22C4⋊Q8×C43C2211yescharacteristic
23#103×C43—22no—
24C4×C8×C43C2211yescharacteristic
25C2×Q8×C43—21no—
26C2×Q8×C43D412yes—
27C2×D172D411yescharacteristic
28C2×C4×D43—21no—
29C2×C4×D43—22no—
30C2×Dic86D411yescharacteristic
31C2×C8×C43—21no—
32C4⋊C4×C43—21no—
33C4⋊C4×C43—21no—
34C4⋊C4×C43—21no—
35C4⋊C4×C43—21no—
36C42×C43C2311yescharacteristic
37#10621884—42no—
38(C2×D43)⋊C4—22no—
39(C2×D43)⋊C4—21no—
40C4⋊Dic43—22no—
41C4⋊Dic43D411yescharacteristic
42C4⋊Dic43D411yescharacteristic
43Dic43⋊C4—22no—
44Dic43⋊C4—21no—
45C4×Dic43—21no—
46C2×C43⋊C8—21no—
47C2×C43⋊C8—21no—
48C22×D43—21no—
49Q8×C43—42no—
50Q8×C43—41no—
51Q8×C43—41no—
52C2×C4×C43—22no—
53C2×C4×C43—41no—
54C2×C4×C43C2×D411yescharacteristic
55C2×C4×C43C2×D411yescharacteristic
56C2×C4×C43C2×D411yescharacteristic
57C2×Dic43—21no—
58C2×Dic43—21no—
59C2×Dic43—21no—
60D172—21no—
61D172SD1612yes—
62C4×D43—41no—
63C4×D43—41no—
64C4×D43—82no—
65Dic86—21no—
66Dic86—21no—
67C8×C43—41no—
68C43⋊C8—41no—
69C43⋊C8—41no—
70C22×C43#12011yescharacteristic
71C2×D43—22no—
72C2×D43—41no—
73C2×D43—41no—
74C4×C43—21no—
75C4×C43—42no—
76C4×C43—81no—
77C4×C43C2×SD1611yescharacteristic
78C4×C43#13511yescharacteristic
79C4×C43#13711yescharacteristic
80C4×C43#13711yescharacteristic
81Dic43—41no—
82Dic43—41no—
83Dic43—41no—
84#1643—431nomaximal, Sylow
85C2×C43#44811yescharacteristic
86C2×C43#45211yescharacteristic
87C2×C43#45511yescharacteristic
88D43—42no—
89#554—431no—
90#487D4311yescharacteristic, complemented
91#475—431no—
92#461—431no—
93#333—431no—
94Q8⋊C8—431no—
95D4⋊C8—431no—
96C43#164311yescharacteristic, complemented, Sylow
97C2×SD16—861no—
98C4⋊Q8C2×D4311yescharacteristic
99C4⋊Q8C2×D4311yescharacteristic
100#125—861no—
101C22⋊Q8—861no—
102C22⋊Q8—862no—
103C4×Q8—431no—
104C4×D4—431no—
105C4×D4—861no—
106C2×C4⋊C4—861no—
107#106—861no—
108C4⋊C8—431no—
109C4⋊C8—431no—
110#103—22no—
111#103—861no—
112#103—861no—
113C4×C8C2×D4311yescharacteristic
114C2×Q8—21no—
115C2×Q8—431no—
116C2×Q8C22⋊D4312yes—
117C2×D4—431no—
118C22×C4—862no—
119C22×C4—861no—
120SD16—1722no—
121C2×C8—21no—
122C2×C8—861no—
123C2×C8—861no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—431no—
129C4⋊C4—431no—
130C4⋊C4—862no—
131C4⋊C4—862no—
132C4⋊C4—861no—
133C22⋊C4—862no—
134C22⋊C4—861no—
135C42—861no—
136C42C22×D4311yescharacteristic
137C23—861no—
138Q8—42no—
139Q8—41no—
140Q8—41no—
141Q8—861no—
142Q8—861no—
143D4—432no—
144D4—861no—
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—861no—
148C2×C4—861no—
149C2×C4—861no—
150C2×C4—3442no—
151C2×C4—1721no—
152C2×C4—1721no—
153C2×C4D4×D4311yescharacteristic
154C2×C4D4×D4311yescharacteristic
155C2×C4C2×C22⋊D4311yescharacteristic
156C8—41no—
157C8—1721no—
158C8—1721no—
159C22—862no—
160C22—1721no—
161C22—1721no—
162C22#1306329311yescharacteristic
163C4—21no—
164C4—42no—
165C4—81no—
166C4—1721no—
167C4—1721no—
168C4—1721no—
169C4SD16×D4311yescharacteristic
170C4#1306334811yescharacteristic
171C4#1306335411yescharacteristic
172C4#1306335711yescharacteristic
173C2—1722no—
174C2#1458303611yescharacteristic
175C2#1458306011yescharacteristic
176C2#1458307611yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#487C2
socleC22×C43#120
hypercenter#487D43
hypocenterC43#1643
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #14583181C2semidirect
4. #14582648C2semidirect
5. #14582631C2semidirect
7. C43×#487C2semidirect
90. #487D43semidirect
96. C43#1643semidirect