Finite Group Databasebeta

← #19136578

Subgroups — #19136578

Order 5504.

354 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 41 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#14583534C211yesmaximal, characteristic, complemented
2#14583086C212yesmaximal, complemented
3#14582692C211yesmaximal, characteristic, complemented
4#14582687C212yesmaximal, complemented
5C43×#453C211yesmaximal, characteristic, complemented
6C2×D4×D43—22no—
7#13063296—22no—
8#13063293—21no—
9#13063293—22no—
10#13063293C2212yes—
11C4×D172—21no—
12#13063240—22no—
13#13063240C2212yescomplemented
14H(5,𝔽2)×C43C2211yescharacteristic, complemented
15AGL(1,ℤ/8)×C43—21no—
16#127×C43C2211yescharacteristic
17#104×C43—21no—
18#100×C43C2211yescharacteristic, complemented
19C23×D43—21no—
20C23×D43D412yescomplemented
21#41×C43—21no—
22#41×C43—41no—
23C2×D4×C43—22no—
24C2×D4×C43—22no—
25C2×D4×C43—41no—
26C2×D4×C43D411yescharacteristic, complemented
27C2×D4×C43C2311yescharacteristic
28C2×C22⋊D43—22no—
29C2×C22⋊D43—22no—
30C2×C22⋊D43—42no—
31D4×D43—48no—
32C2×D172—21no—
33C2×C4×D43—22no—
34SD16×C43—41no—
35D8×C43—41no—
36M16×C43—21no—
37C42×C43D411yescharacteristic, complemented
38C22⋊Dic43—21no—
39C22⋊Dic43—22no—
40C22⋊Dic43D412yescomplemented
41(C2×D43)⋊C4—22no—
42(C2×D43)⋊C4—42no—
43C4⋊Dic43—21no—
44C23×C43—22no—
45C23×C43—21no—
46C23×C43C2×D412yes—
47C22×D43—22no—
48C22×D43—44no—
49C22×D43—44no—
50C22×D43—42no—
51C22×D43—81no—
52Q8×C43—21no—
53D4×C43—21no—
54D4×C43—41no—
55D4×C43—41no—
56D4×C43—44no—
57D4×C43—42no—
58D4×C43—41no—
59C2×C4×C43—21no—
60C2×C4×C43—22no—
61C2×C4×C43—41no—
62C2×C4×C43C2×D411yescharacteristic
63C22⋊D43—44no—
64C22⋊D43—44no—
65C22⋊D43—84no—
66C2×Dic43—22no—
67C2×Dic43—42no—
68D172—24no—
69C4×D43—44no—
70C8×C43—41no—
71C22×C43—22no—
72C22×C43—42no—
73C22×C43—42no—
74C22×C43—41no—
75C22×C43—41no—
76C22×C43—82no—
77C22×C43#12011yescharacteristic
78C2×D43—24no—
79C2×D43—42no—
80C2×D43—42no—
81C2×D43—44no—
82C2×D43—82no—
83C2×D43—84no—
84C4×C43—22no—
85C4×C43—21no—
86C4×C43—41no—
87Dic43—42no—
88Dic43—82no—
89#2196—431nomaximal, Sylow
90C2×C43—21no—
91C2×C43—42no—
92C2×C43—81no—
93C2×C43—81no—
94C2×C43B(4,𝔽2)11yescharacteristic
95D43—44no—
96D42—431no—
97B(4,𝔽2)—432no—
98#453D4311yescharacteristic, complemented
99#353—431no—
100AΣL(1,𝔽16)—432no—
101C43#219611yescharacteristic, complemented, Sylow
102H(5,𝔽2)C2×D4311yescharacteristic, complemented
103C22×D4—862no—
104AGL(1,ℤ/8)—21no—
105#127C2×D4311yescharacteristic
106#121—862no—
107#120—432no—
108#120—861no—
109#120—862no—
110C4×D4—861no—
111#104—21no—
112#100C2×D4311yescharacteristic, complemented
113#99—432no—
114#99—862no—
115C24—432no—
116C24—861no—
117#41—21no—
118#41—41no—
119C2×D4—22no—
120C2×D4—22no—
121C2×D4—41no—
122C2×D4—861no—
123C2×D4—862no—
124C2×D4—862no—
125C2×D4—1728no—
126C2×D4—1722no—
127C2×D4C22⋊D4311yescharacteristic, complemented
128C2×D4C22×D4311yescharacteristic
129C22×C4—862no—
130SD16—41no—
131D8—41no—
132M16—21no—
133C4⋊C4—861no—
134C22⋊C4—432no—
135C22⋊C4—861no—
136C22⋊C4—862no—
137C22⋊C4—862no—
138C22⋊C4—1722no—
139C42C22⋊D4311yescharacteristic, complemented
140C23—22no—
141C23—21no—
142C23—862no—
143C23—3441no—
144C23—1722no—
145C23—1724no—
146C23—1724no—
147C23D4×D4312yes—
148Q8—21no—
149D4—21no—
150D4—41no—
151D4—41no—
152D4—44no—
153D4—42no—
154D4—41no—
155D4—864no—
156D4—3444no—
157D4—1724no—
158D4—1724no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—41no—
162C2×C4—862no—
163C2×C4—1724no—
164C2×C4—1722no—
165C2×C4C2×C22⋊D4311yescharacteristic
166C8—41no—
167C22—22no—
168C22—42no—
169C22—42no—
170C22—41no—
171C22—41no—
172C22—82no—
173C22—864no—
174C22—3442no—
175C22—3444no—
176C22—1722no—
177C22—1724no—
178C22—1722no—
179C22#1306329311yescharacteristic
180C4—22no—
181C4—21no—
182C4—41no—
183C4—3442no—
184C4—1722no—
185C2—21no—
186C2—42no—
187C2—81no—
188C2—81no—
189C2—1724no—
190C2#1458308511yescharacteristic
subgroupG/H
centerC2#14583085
commutatorC2×D4×C43C23
FrattiniC2×D4C22×D43
FittingC43×#453C2
socleC2×C43B(4,𝔽2)
hypercenter#453D43
hypocenterC43#2196
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #14583534C2semidirect
2. #14583086C2semidirect
3. #14582692C2semidirect
4. #14582687C2semidirect
5. C43×#453C2semidirect
13. #13063240C22semidirect
14. H(5,𝔽2)×C43C22semidirect
18. #100×C43C22semidirect
20. C23×D43D4semidirect
26. C2×D4×C43D4semidirect
37. C42×C43D4semidirect
40. C22⋊Dic43D4semidirect
98. #453D43semidirect
101. C43#2196semidirect
102. H(5,𝔽2)C2×D43semidirect
112. #100C2×D43semidirect
127. C2×D4C22⋊D43semidirect
139. C42C22⋊D43semidirect