Finite Group Databasebeta

← #14565636

Subgroups — #14565636

Order 2432.

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

normal subgroups only

This group has 270 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#11926721C211yesmaximal, characteristic, complemented
3#11926339C211yesmaximal, characteristic, complemented
4#11926331C212yesmaximal, complemented
5C19×H(3,𝔽4)C211yesmaximal, characteristic, complemented
6#10597430C2211yescharacteristic
7C19×#124—21no—
8C19×#124—22no—
9C19×#124—21no—
10C19×#124C2211yescharacteristic
11C19×#120—22no—
12C19×#120C2212yes—
13#10597399—22no—
14#10597388—21no—
15#10597291C2212yes—
16#10597290C2211yescharacteristic
17#10597263—22no—
18#10597262—21no—
19C24×C19D412yescomplemented
20C2×Q8×C19—21no—
21C2×Q8×C19D411yescharacteristic, complemented
22C2×D4×C19—21no—
23C2×D4×C19—21no—
24C2×D4×C19—22no—
25C2×D4×C19C2311yescharacteristic
26C2×C22⋊D19—22no—
27C2×C22⋊D19—42no—
28#64543—41no—
29D4×D19—41no—
30#64541—21no—
31C22⋊C4×C19—22no—
32C22⋊C4×C19—22no—
33C22⋊C4×C19—22no—
34C22⋊C4×C19—22no—
35C22⋊C4×C19D412yescomplemented
36C42×C19—21no—
37C42×C19D411yescharacteristic, complemented
38C22⋊Dic19—22no—
39C22⋊Dic19—42no—
40#64528—41no—
41#64527—41no—
42#64520—21no—
43C23×C19—22no—
44C23×C19—42no—
45C23×C19—82no—
46C23×C19C2×D412yes—
47C22×D19—22no—
48Q8×C19—41no—
49Q8×C19—81no—
50D4×C19—41no—
51D4×C19—82no—
52D4×C19—81no—
53D4×C19—81no—
54C2×C4×C19—21no—
55C2×C4×C19—22no—
56C2×C4×C19—21no—
57C2×C4×C19C2×D411yescharacteristic
58C22⋊D19—42no—
59C22⋊D19—41no—
60C22⋊D19—84no—
61C2×Dic19—22no—
62C2×Dic19—42no—
63D76—21no—
64C4×D19—41no—
65Dic38—21no—
66C19⋊C8—41no—
67#2199—191nomaximal, Sylow
68C22×C19—22no—
69C22×C19—42no—
70C22×C19—42no—
71C22×C19—42no—
72C22×C19—44no—
73C22×C19—42no—
74C22×C19—82no—
75C22×C19#12011yescharacteristic
76C2×D19—41no—
77C2×D19—82no—
78C4×C19—21no—
79C4×C19—42no—
80C4×C19—41no—
81C4×C19—41no—
82Dic19—41no—
83Dic19—82no—
84H(3,𝔽4)D1911yescharacteristic, complemented
85B(4,𝔽2)—192no—
86#455—191no—
87#354—191no—
88AΣL(1,𝔽16)—192no—
89C2×C19—21no—
90C2×C19—42no—
91C2×C19—82no—
92C2×C19B(4,𝔽2)11yescharacteristic
93D19—81no—
94H(5,𝔽2)—191no—
95#137—381no—
96#124—21no—
97#124—22no—
98#124—21no—
99#124C2×D1911yescharacteristic
100#120—22no—
101#120—382no—
102#120C2×D1912yes—
103#104—381no—
104#100—191no—
105#99—192no—
106#99—382no—
107C19#219911yescharacteristic, complemented, Sylow
108C24C22⋊D1912yescomplemented
109#41—381no—
110#41—761no—
111C2×Q8—21no—
112C2×Q8C22⋊D1911yescharacteristic, complemented
113C2×D4—21no—
114C2×D4—21no—
115C2×D4—22no—
116C2×D4—382no—
117C2×D4—761no—
118C2×D4—762no—
119C2×D4C22×D1911yescharacteristic
120Q16—761no—
121SD16—761no—
122M16—381no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—22no—
127C22⋊C4—382no—
128C22⋊C4—762no—
129C22⋊C4C22⋊D1912yescomplemented
130C42—21no—
131C42C22⋊D1911yescharacteristic, complemented
132C23—22no—
133C23—42no—
134C23—82no—
135C23—382no—
136C23C2×C22⋊D1912yes—
137Q8—41no—
138Q8—81no—
139Q8—381no—
140D4—41no—
141D4—82no—
142D4—81no—
143D4—81no—
144D4—381no—
145D4—762no—
146D4—761no—
147D4—1524no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—382no—
152C2×C4—761no—
153C2×C4—762no—
154C2×C4C2×C22⋊D1911yescharacteristic
155C8—761no—
156C22—22no—
157C22—42no—
158C22—42no—
159C22—42no—
160C22—44no—
161C22—42no—
162C22—82no—
163C22—761no—
164C22—1522no—
165C22#1059739911yescharacteristic
166C4—21no—
167C4—42no—
168C4—41no—
169C4—41no—
170C4—761no—
171C4—1522no—
172C2—21no—
173C2—42no—
174C2—82no—
175C2—1521no—
176C2#1192673111yescharacteristic
subgroupG/H
centerC2#11926731
commutator, cosocleC2×D4×C19C23
FrattiniC2×D4C22×D19
FittingC19×H(3,𝔽4)C2
socleC2×C19B(4,𝔽2)
hypercenterH(3,𝔽4)D19
hypocenterC19#2199
LCSG ▷ C2×D4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #11926730C2semidirect
2. #11926721C2semidirect
3. #11926339C2semidirect
4. #11926331C2semidirect
5. C19×H(3,𝔽4)C2semidirect
19. C24×C19D4semidirect
21. C2×Q8×C19D4semidirect
35. C22⋊C4×C19D4semidirect
37. C42×C19D4semidirect
84. H(3,𝔽4)D19semidirect
107. C19#2199semidirect
108. C24C22⋊D19semidirect
112. C2×Q8C22⋊D19semidirect
129. C22⋊C4C22⋊D19semidirect
131. C42C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
#119267302
#119267212
#119263392
#119263312
C19×H(3,𝔽4)2
#219919