Finite Group Databasebeta

← #14571898

Subgroups — #14571898

Order 2432.

548 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 125 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#11926481C211yesmaximal, characteristic, complemented
2#11926479C213yesmaximal, complemented
3#11926468C211yesmaximal, characteristic, complemented
4#11926467C213yesmaximal, complemented
5#11926466C213yesmaximal, complemented
6#11926399C213yesmaximal
7C19×#396C211yesmaximal, characteristic, complemented
8C24×D19C2211yescharacteristic
9C2×C4⋊C4×C19C2213yescomplemented
10C2×C22⋊C4×C19C2213yes—
11C2×C22⋊Dic19C2213yes—
12C2×(C2×D19)⋊C4C2213yes—
13C2×(C2×D19)⋊C4C2213yes—
14C2×(C2×D19)⋊C4C2213yes—
15C2×(C2×D19)⋊C4C2213yes—
16C2×C4⋊Dic19C2213yescomplemented
17C2×Dic19⋊C4C2213yescomplemented
18C2×Dic19⋊C4C2213yescomplemented
19C19×#95C2211yescharacteristic, complemented
20C19⋊#95C2213yescomplemented
21C24×C19C2311yescharacteristic
22C23×D19—43no—
23C23×D19—43no—
24C23×D19Q814yes—
25C23×D19C2311yescharacteristic
26C23×D19C2311yescharacteristic
27C22×C4×C19C2313yes—
28C22×C4×C19C2313yes—
29C22×Dic19C2313yes—
30C22×Dic19C2313yes—
31C4⋊C4×C19—43no—
32C22⋊C4×C19—43no—
33C22⋊Dic19—43no—
34(C2×D19)⋊C4—43no—
35(C2×D19)⋊C4—43no—
36(C2×D19)⋊C4—43no—
37(C2×D19)⋊C4—43no—
38C4⋊Dic19—43no—
39Dic19⋊C4—43no—
40Dic19⋊C4—43no—
41C23×C19—23no—
42C23×C19—23no—
43C23×C19C2×Q812yes—
44C23×C19C2411yescharacteristic
45C22×D19—23no—
46C22×D19—23no—
47C22×D19—23no—
48C22×D19—23no—
49C22×D19—412no—
50C22×D19—412no—
51C22×D19—44no—
52C22×D19C2×Q812yes—
53C22×D19C2×Q812yes—
54C2×C4×C19—23no—
55C2×C4×C19—23no—
56C2×C4×C19—23no—
57C2×C4×C19—23no—
58C2×C4×C19—23no—
59C2×C4×C19—23no—
60C2×Dic19—23no—
61C2×Dic19—23no—
62C2×Dic19—23no—
63C2×Dic19—23no—
64C2×Dic19—23no—
65C2×Dic19—23no—
66#2842—191nomaximal, Sylow
67C22×C19—26no—
68C22×C19—43no—
69C22×C19—41no—
70C22×C19C22×Q811yescharacteristic
71C22×C19H(5,𝔽2)13yes—
72C22×C19H(5,𝔽2)13yes—
73C2×D19—26no—
74C2×D19—26no—
75C2×D19—416no—
76C2×D19—43no—
77C2×D19—43no—
78C2×D19—41no—
79C2×D19—41no—
80C4×C19—43no—
81C4×C19—43no—
82Dic19—43no—
83Dic19—43no—
84#399—193no—
85#399—191no—
86#396—193no—
87#396—193no—
88#396—191no—
89#396D1911yescharacteristic, complemented
90#379—193no—
91C2×C19—42no—
92C2×C19#54313yes—
93C2×C19#56013yes—
94C2×C19#56011yescharacteristic
95D19—42no—
96D19—42no—
97C25—191no—
98C2×C4⋊C4—193no—
99C2×C4⋊C4—193no—
100C2×C4⋊C4—193no—
101C2×C4⋊C4C2×D1913yescomplemented
102C2×C22⋊C4—193no—
103C2×C22⋊C4—193no—
104C2×C22⋊C4—193no—
105C2×C22⋊C4—193no—
106C2×C22⋊C4—193no—
107C2×C22⋊C4C2×D1913yes—
108#95—193no—
109#95C2×D1911yescharacteristic, complemented
110C19#284211yescharacteristic, complemented, Sylow
111C24—191no—
112C24—191no—
113C24—194no—
114C24—763no—
115C24—763no—
116C24C22×D1911yescharacteristic
117C22×C4—193no—
118C22×C4—193no—
119C22×C4C22×D1913yes—
120C22×C4C22×D1913yes—
121C4⋊C4—43no—
122C4⋊C4—763no—
123C4⋊C4—763no—
124C4⋊C4—763no—
125C22⋊C4—43no—
126C22⋊C4—763no—
127C22⋊C4—763no—
128C22⋊C4—763no—
129C22⋊C4—763no—
130C22⋊C4—763no—
131C23—23no—
132C23—23no—
133C23—192no—
134C23—192no—
135C23—383no—
136C23—383no—
137C23—383no—
138C23—383no—
139C23—7612no—
140C23—7612no—
141C23—764no—
142C23Q8×D1912yes—
143C23C23×D1911yescharacteristic
144C2×C4—23no—
145C2×C4—23no—
146C2×C4—23no—
147C2×C4—23no—
148C2×C4—23no—
149C2×C4—23no—
150C2×C4—383no—
151C2×C4—383no—
152C2×C4—383no—
153C2×C4—383no—
154C2×C4—383no—
155C2×C4—383no—
156C22—26no—
157C22—43no—
158C22—41no—
159C22—386no—
160C22—386no—
161C22—7616no—
162C22—763no—
163C22—763no—
164C22—761no—
165C22—761no—
166C22#1059743013yes—
167C22C2×Q8×D1911yescharacteristic
168C22#1059743513yes—
169C4—43no—
170C4—43no—
171C4—763no—
172C4—763no—
173C2—42no—
174C2—762no—
175C2—762no—
176C2#1192716913yes—
177C2#1192728213yes—
178C2#1192728511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#396C2
prime radicalC24×D19C22
hypercenter#396D19
hypocenterC19#2842
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. #11926481C2semidirect
2. #11926479C2semidirect
3. #11926468C2semidirect
4. #11926467C2semidirect
5. #11926466C2semidirect
7. C19×#396C2semidirect
9. C2×C4⋊C4×C19C22semidirect
16. C2×C4⋊Dic19C22semidirect
17. C2×Dic19⋊C4C22semidirect
18. C2×Dic19⋊C4C22semidirect
19. C19×#95C22semidirect
20. C19⋊#95C22semidirect
89. #396D19semidirect
101. C2×C4⋊C4C2×D19semidirect
109. #95C2×D19semidirect
110. C19#2842semidirect

Maximal subgroups

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

subgroupindex
#119264812
#119264792
#119264682
#119264672
#119264662
#119263992
C19×#3962
#284219