Finite Group Databasebeta

← #14565619

Subgroups — #14565619

Order 2432.

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

normal subgroups only

This group has 354 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#11926730C212yesmaximal, complemented
2#11926711C211yesmaximal, characteristic, complemented
3#11926337C211yesmaximal, characteristic, complemented
4#11926331C212yesmaximal, complemented
5D42×C19C211yesmaximal, characteristic, complemented
6C22×D4×C19—22no—
7#10597430C2211yescharacteristic, complemented
8C19×#127C2211yescharacteristic
9C19×#121—22no—
10C19×#120—21no—
11C19×#120C2212yes—
12C4×D4×C19—21no—
13#10597399—22no—
14#10597378—21no—
15#10597291C2212yescomplemented
16#10597290C2211yescharacteristic, complemented
17#10597263—22no—
18#10597262—21no—
19C24×C19—21no—
20C24×C19D412yescomplemented
21C2×D4×C19—21no—
22C2×D4×C19—22no—
23C2×D4×C19—22no—
24C2×D4×C19—22no—
25C2×D4×C19—48no—
26C2×D4×C19D411yescharacteristic, complemented
27C2×D4×C19C2311yescharacteristic
28C22×C4×C19—22no—
29C2×C22⋊D19—22no—
30C2×C22⋊D19—42no—
31#64543—41no—
32D4×D19—41no—
33#64541—21no—
34C4⋊C4×C19—21no—
35C22⋊C4×C19—21no—
36C22⋊C4×C19—22no—
37C22⋊C4×C19D412yescomplemented
38C42×C19D411yescharacteristic, complemented
39C22⋊Dic19—22no—
40C22⋊Dic19—42no—
41#64526—41no—
42#64525—41no—
43#64520—21no—
44C23×C19—22no—
45C23×C19—21no—
46C23×C19—42no—
47C23×C19—44no—
48C23×C19—44no—
49C23×C19—81no—
50C23×C19C2×D412yes—
51C22×D19—22no—
52D4×C19—24no—
53D4×C19—41no—
54D4×C19—41no—
55D4×C19—44no—
56D4×C19—44no—
57D4×C19—44no—
58C2×C4×C19—21no—
59C2×C4×C19—22no—
60C2×C4×C19—44no—
61C2×C4×C19C2×D411yescharacteristic
62C22⋊D19—42no—
63C22⋊D19—41no—
64C22⋊D19—84no—
65C2×Dic19—22no—
66C2×Dic19—42no—
67D76—21no—
68C4×D19—41no—
69Dic38—21no—
70C19⋊C8—41no—
71#2196—191nomaximal, Sylow
72C22×C19—24no—
73C22×C19—22no—
74C22×C19—42no—
75C22×C19—42no—
76C22×C19—42no—
77C22×C19—44no—
78C22×C19—42no—
79C22×C19—41no—
80C22×C19—82no—
81C22×C19—84no—
82C22×C19#12011yescharacteristic
83C2×D19—41no—
84C2×D19—82no—
85C4×C19—22no—
86C4×C19—21no—
87C4×C19—42no—
88Dic19—41no—
89Dic19—82no—
90D42D1911yescharacteristic, complemented
91B(4,𝔽2)—192no—
92#453—191no—
93#353—191no—
94AΣL(1,𝔽16)—192no—
95C2×C19—21no—
96C2×C19—42no—
97C2×C19—44no—
98C2×C19—81no—
99C2×C19B(4,𝔽2)11yescharacteristic
100D19—81no—
101H(5,𝔽2)—191no—
102C22×D4—22no—
103AGL(1,ℤ/8)—381no—
104#127C2×D1911yescharacteristic
105#121—22no—
106#120—21no—
107#120—382no—
108#120C2×D1912yes—
109C4×D4—21no—
110#104—381no—
111#100—191no—
112#99—192no—
113#99—382no—
114C19#219611yescharacteristic, complemented, Sylow
115C24—21no—
116C24C22⋊D1912yescomplemented
117#41—381no—
118#41—761no—
119C2×D4—21no—
120C2×D4—22no—
121C2×D4—22no—
122C2×D4—22no—
123C2×D4—48no—
124C2×D4—382no—
125C2×D4—761no—
126C2×D4—762no—
127C2×D4C22⋊D1911yescharacteristic, complemented
128C2×D4C22×D1911yescharacteristic
129C22×C4—22no—
130SD16—761no—
131D8—761no—
132M16—381no—
133C4⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—22no—
136C22⋊C4—382no—
137C22⋊C4—762no—
138C22⋊C4C22⋊D1912yescomplemented
139C42C22⋊D1911yescharacteristic, complemented
140C23—22no—
141C23—21no—
142C23—42no—
143C23—44no—
144C23—44no—
145C23—81no—
146C23—382no—
147C23C2×C22⋊D1912yes—
148Q8—381no—
149D4—24no—
150D4—41no—
151D4—41no—
152D4—44no—
153D4—44no—
154D4—44no—
155D4—381no—
156D4—762no—
157D4—761no—
158D4—1524no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—44no—
162C2×C4—382no—
163C2×C4—761no—
164C2×C4—762no—
165C2×C4C2×C22⋊D1911yescharacteristic
166C8—761no—
167C22—24no—
168C22—22no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—44no—
173C22—42no—
174C22—41no—
175C22—82no—
176C22—84no—
177C22—761no—
178C22—1522no—
179C22#1059739911yescharacteristic
180C4—22no—
181C4—21no—
182C4—42no—
183C4—761no—
184C4—1522no—
185C2—21no—
186C2—42no—
187C2—44no—
188C2—81no—
189C2—1521no—
190C2#1192673111yescharacteristic
subgroupG/H
centerC2#11926731
commutator, cosocleC2×D4×C19C23
FrattiniC2×D4C22×D19
FittingD42×C19C2
socleC2×C19B(4,𝔽2)
hypercenterD42D19
hypocenterC19#2196
LCSG ▷ C2×D4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #11926730C2semidirect
2. #11926711C2semidirect
3. #11926337C2semidirect
4. #11926331C2semidirect
5. D42×C19C2semidirect
7. #10597430C22semidirect
15. #10597291C22semidirect
16. #10597290C22semidirect
20. C24×C19D4semidirect
26. C2×D4×C19D4semidirect
37. C22⋊C4×C19D4semidirect
38. C42×C19D4semidirect
90. D42D19semidirect
114. C19#2196semidirect
116. C24C22⋊D19semidirect
127. C2×D4C22⋊D19semidirect
138. C22⋊C4C22⋊D19semidirect
139. C42C22⋊D19semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#119267302
#119267112
#119263372
#119263312
D42×C192
#219619