Finite Group Databasebeta

← #14565618

Subgroups — #14565618

Order 2432.

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#11927179C211yesmaximal, characteristic, complemented
2#11926731C212yesmaximal, complemented
3#11926337C211yesmaximal, characteristic, complemented
4#11926332C212yesmaximal, complemented
5C19×#453C211yesmaximal, characteristic, complemented
6C19×H(5,𝔽2)C2211yescharacteristic, complemented
7C2×D4×D19—22no—
8C19×AGL(1,ℤ/8)—21no—
9C19×#127C2211yescharacteristic
10#10597384—22no—
11#10597383—21no—
12#10597383—22no—
13#10597383C2212yes—
14C4×D76—21no—
15C19×#104—21no—
16C19×#100C2211yescharacteristic, complemented
17#10597291—22no—
18#10597291C2212yescomplemented
19C23×D19—21no—
20C23×D19D412yescomplemented
21#41×C19—21no—
22#41×C19—41no—
23C2×D4×C19—22no—
24C2×D4×C19—22no—
25C2×D4×C19—41no—
26C2×D4×C19D411yescharacteristic, complemented
27C2×D4×C19C2311yescharacteristic
28C2×C22⋊D19—22no—
29C2×C22⋊D19—22no—
30C2×C22⋊D19—42no—
31D4×D19—48no—
32C2×D76—21no—
33C2×C4×D19—22no—
34SD16×C19—41no—
35D8×C19—41no—
36M16×C19—21no—
37C42×C19D411yescharacteristic, complemented
38C22⋊Dic19—21no—
39C22⋊Dic19—22no—
40C22⋊Dic19D412yescomplemented
41(C2×D19)⋊C4—22no—
42(C2×D19)⋊C4—42no—
43C4⋊Dic19—21no—
44C23×C19—22no—
45C23×C19—21no—
46C23×C19C2×D412yes—
47C22×D19—22no—
48C22×D19—44no—
49C22×D19—44no—
50C22×D19—42no—
51C22×D19—81no—
52Q8×C19—21no—
53D4×C19—21no—
54D4×C19—41no—
55D4×C19—41no—
56D4×C19—44no—
57D4×C19—42no—
58D4×C19—41no—
59C2×C4×C19—21no—
60C2×C4×C19—22no—
61C2×C4×C19—41no—
62C2×C4×C19C2×D411yescharacteristic
63C22⋊D19—44no—
64C22⋊D19—44no—
65C22⋊D19—84no—
66C2×Dic19—22no—
67C2×Dic19—42no—
68D76—24no—
69C4×D19—44no—
70C8×C19—41no—
71#2196—191nomaximal, Sylow
72C22×C19—22no—
73C22×C19—42no—
74C22×C19—42no—
75C22×C19—41no—
76C22×C19—41no—
77C22×C19—82no—
78C22×C19#12011yescharacteristic
79C2×D19—24no—
80C2×D19—42no—
81C2×D19—42no—
82C2×D19—44no—
83C2×D19—82no—
84C2×D19—84no—
85C4×C19—22no—
86C4×C19—21no—
87C4×C19—41no—
88Dic19—42no—
89Dic19—82no—
90D42—191no—
91B(4,𝔽2)—192no—
92#453D1911yescharacteristic, complemented
93#353—191no—
94AΣL(1,𝔽16)—192no—
95C2×C19—21no—
96C2×C19—42no—
97C2×C19—81no—
98C2×C19—81no—
99C2×C19B(4,𝔽2)11yescharacteristic
100D19—44no—
101H(5,𝔽2)C2×D1911yescharacteristic, complemented
102C22×D4—382no—
103AGL(1,ℤ/8)—21no—
104#127C2×D1911yescharacteristic
105#121—382no—
106#120—192no—
107#120—381no—
108#120—382no—
109C4×D4—381no—
110#104—21no—
111#100C2×D1911yescharacteristic, complemented
112#99—192no—
113#99—382no—
114C19#219611yescharacteristic, complemented, Sylow
115C24—192no—
116C24—381no—
117#41—21no—
118#41—41no—
119C2×D4—22no—
120C2×D4—22no—
121C2×D4—41no—
122C2×D4—381no—
123C2×D4—382no—
124C2×D4—382no—
125C2×D4—768no—
126C2×D4—762no—
127C2×D4C22⋊D1911yescharacteristic, complemented
128C2×D4C22×D1911yescharacteristic
129C22×C4—382no—
130SD16—41no—
131D8—41no—
132M16—21no—
133C4⋊C4—381no—
134C22⋊C4—192no—
135C22⋊C4—381no—
136C22⋊C4—382no—
137C22⋊C4—382no—
138C22⋊C4—762no—
139C42C22⋊D1911yescharacteristic, complemented
140C23—22no—
141C23—21no—
142C23—382no—
143C23—762no—
144C23—764no—
145C23—764no—
146C23—1521no—
147C23D4×D1912yes—
148Q8—21no—
149D4—21no—
150D4—41no—
151D4—41no—
152D4—44no—
153D4—42no—
154D4—41no—
155D4—384no—
156D4—764no—
157D4—764no—
158D4—1524no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—41no—
162C2×C4—382no—
163C2×C4—764no—
164C2×C4—762no—
165C2×C4C2×C22⋊D1911yescharacteristic
166C8—41no—
167C22—22no—
168C22—42no—
169C22—42no—
170C22—41no—
171C22—41no—
172C22—82no—
173C22—384no—
174C22—762no—
175C22—764no—
176C22—762no—
177C22—1522no—
178C22—1524no—
179C22#1059738311yescharacteristic
180C4—22no—
181C4—21no—
182C4—41no—
183C4—762no—
184C4—1522no—
185C2—21no—
186C2—42no—
187C2—81no—
188C2—81no—
189C2—764no—
190C2#1192673011yescharacteristic
subgroupG/H
centerC2#11926730
commutator, cosocleC2×D4×C19C23
FrattiniC2×D4C22×D19
FittingC19×#453C2
socleC2×C19B(4,𝔽2)
hypercenter#453D19
hypocenterC19#2196
LCSG ▷ C2×D4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #11927179C2semidirect
2. #11926731C2semidirect
3. #11926337C2semidirect
4. #11926332C2semidirect
5. C19×#453C2semidirect
6. C19×H(5,𝔽2)C22semidirect
16. C19×#100C22semidirect
18. #10597291C22semidirect
20. C23×D19D4semidirect
26. C2×D4×C19D4semidirect
37. C42×C19D4semidirect
40. C22⋊Dic19D4semidirect
92. #453D19semidirect
101. H(5,𝔽2)C2×D19semidirect
111. #100C2×D19semidirect
114. C19#2196semidirect
127. C2×D4C22⋊D19semidirect
139. C42C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
#119271792
#119267312
#119263372
#119263322
C19×#4532
#219619