Finite Group Databasebeta

← #14564051

Subgroups — #14564051

Order 2432.

342 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 85 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#11927311C211yesmaximal, characteristic, complemented
2#11927051C211yesmaximal, characteristic
3#11926507C212yesmaximal, complemented
4#11926316C212yesmaximal, complemented
5C19×#413C211yesmaximal, characteristic, complemented
6C2×#41×C19C2211yescharacteristic
7C22×C4×D19C2211yescharacteristic
8C2×M16×C19C2212yes—
9#10597394—24no—
10#10597392—21no—
11#10597384—21no—
12#10597383C412yes—
13#10597381C412yes—
14C4×C22⋊D19—22no—
15#10597372C2211yescharacteristic
16C2×#64520—22no—
17C2×#64520C2212yes—
18C19×#101—21no—
19C19×#100—21no—
20(C2×D19)⋊C8—24no—
21C23×D19C2×C411yescharacteristic
22#41×C19—22no—
23#41×C19—22no—
24C2×Q8×C19D411yescharacteristic
25C2×D4×C19C2×C412yes—
26C2×D4×C19D411yescharacteristic
27C22×C4×C19D412yes—
28C22×C4×C19C2311yescharacteristic
29C2×C22⋊D19—22no—
30C22×Dic19C2×C411yescharacteristic
31C2×C4×D19—21no—
32C2×C4×D19—22no—
33C2×C4×D19—21no—
34C2×C4×D19—22no—
35M16×C19—22no—
36M16×C19—22no—
37C2×C8×C19—22no—
38C22⋊Dic19—22no—
39C22⋊Dic19C2×C412yes—
40(C2×D19)⋊C4—22no—
41C4⋊Dic19—21no—
42Dic19⋊C4—22no—
43C4×Dic19—21no—
44#64520—24no—
45#64520—22no—
46#64520—22no—
47C2×C19⋊C8—24no—
48C2×C19⋊C8D414yescomplemented
49C23×C19C22⋊C412yes—
50C23×C19C22×C411yescharacteristic
51C22×D19—21no—
52C22×D19—22no—
53C22×D19—42no—
54Q8×C19—22no—
55D4×C19—24no—
56D4×C19—22no—
57C2×C4×C19—22no—
58C2×C4×C19—22no—
59C2×C4×C19C22⋊C412yes—
60C2×C4×C19C2×D411yescharacteristic
61C2×C4×C19C2×D412yes—
62C2×C4×C19C2×D411yescharacteristic
63C2×C4×C19#4112yes—
64C22⋊D19—44no—
65C2×Dic19—22no—
66C2×Dic19—21no—
67C2×Dic19—22no—
68C4×D19—41no—
69C4×D19—42no—
70C4×D19—41no—
71C8×C19—42no—
72C19⋊C8—24no—
73#1891—191nomaximal, Sylow
74C22×C19—22no—
75C22×C19—41no—
76C22×C19—42no—
77C22×C19C2×C22⋊C411yescharacteristic
78C22×C19C4×D412yes—
79C2×D19—22no—
80C2×D19—24no—
81C2×D19—41no—
82C2×D19—42no—
83C2×D19—41no—
84C4×C19—22no—
85C4×C19#12011yescharacteristic
86C4×C19#12112yes—
87C4×C19#12311yescharacteristic
88Dic19—42no—
89Dic19—41no—
90#568—191no—
91#525—191no—
92#413D1911yescharacteristic, complemented
93#407—192no—
94#344—192no—
95C2×C19—21no—
96C2×C19—22no—
97C2×C19—42no—
98C2×C19#38611yescharacteristic
99D19—42no—
100C2×#41C2×D1911yescharacteristic
101C23×C4—191no—
102#131—384no—
103C2×M16—192no—
104C2×M16—382no—
105C2×M16C2×D1912yes—
106#123—192no—
107C22⋊Q8—381no—
108#121—381no—
109#120—192no—
110C4×D4—382no—
111#117—191no—
112#101—21no—
113#100—21no—
114C22⋊C8—384no—
115C19#189111yescharacteristic, complemented, Sylow
116C24—191no—
117#41—22no—
118#41—22no—
119C2×Q8C22⋊D1911yescharacteristic
120C2×D4—382no—
121C2×D4C4×D1912yes—
122C2×D4C22⋊D1911yescharacteristic
123C22×C4—191no—
124C22×C4—381no—
125C22×C4—382no—
126C22×C4—382no—
127C22×C4—381no—
128C22×C4D7612yes—
129C22×C4C22×D1911yescharacteristic
130M16—22no—
131M16—22no—
132M16—384no—
133M16—382no—
134M16—382no—
135C2×C8—22no—
136C2×C8—194no—
137C2×C8—384no—
138C4⋊C4—382no—
139C4⋊C4—381no—
140C22⋊C4—192no—
141C22⋊C4—382no—
142C22⋊C4—382no—
143C42—381no—
144C23—382no—
145C23—381no—
146C23—762no—
147C23(C2×D19)⋊C412yes—
148C23C2×C4×D1911yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—764no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—382no—
156C2×C4—382no—
157C2×C4—381no—
158C2×C4—762no—
159C2×C4—761no—
160C2×C4—761no—
161C2×C4(C2×D19)⋊C412yes—
162C2×C4C2×D7611yescharacteristic
163C2×C4D4×D1912yes—
164C2×C4#6454312yes—
165C2×C4C2×C22⋊D1911yescharacteristic
166C8—42no—
167C8—384no—
168C22—22no—
169C22—41no—
170C22—42no—
171C22—382no—
172C22—384no—
173C22—761no—
174C22—762no—
175C22—761no—
176C22(C22⋊D19)⋊C412yes—
177C22C2×(C2×D19)⋊C411yescharacteristic
178C4—22no—
179C4—762no—
180C4—761no—
181C4#1059732811yescharacteristic
182C4#1059733211yescharacteristic
183C4#1059738512yes—
184C2—21no—
185C2—22no—
186C2—42no—
187C2—762no—
188C2#1192642111yescharacteristic
subgroupG/H
centerC4#10597328
commutatorC23×C19C22×C4
FrattiniC22×C4C22×D19
FittingC19×#413C2
socleC2×C19#386
prime radical#11927051C2
cosocleC22×C4×C19C23
hypercenter#413D19
hypocenterC19#1891
LCSG ▷ C23×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #11927311C2semidirect
3. #11926507C2semidirect
4. #11926316C2semidirect
5. C19×#413C2semidirect
48. C2×C19⋊C8D4semidirect
92. #413D19semidirect
115. C19#1891semidirect

Maximal subgroups

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

subgroupindex
#119273112
#119270512
#119265072
#119263162
C19×#4132
#189119