Finite Group Databasebeta

← #14564081

Subgroups — #14564081

Order 2432.

358 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 89 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#11927055C211yesmaximal, characteristic
2C2×#10597372C211yesmaximal, characteristic, complemented
3C2×#10597282C212yesmaximal, complemented
4#11926305C212yesmaximal, complemented
5C19×#407C211yesmaximal, characteristic, complemented
6C23×C4×C19C2211yescharacteristic
7C2×#64541C2211yescharacteristic
8C2×M16×C19C2212yes—
9#10597399—21no—
10C2×C22⋊Dic19—21no—
11#10597376C412yescomplemented
12#10597375—21no—
13C4×C22⋊D19—22no—
14#10597372—24no—
15#10597372C2211yescharacteristic
16C2×C4⋊Dic19—21no—
17#10597370C412yescomplemented
18C2×C4×Dic19C2212yes—
19C19×C22⋊C8—22no—
20#10597282—24no—
21C24×C19D411yescharacteristic
22C22×C4×C19—22no—
23C22×C4×C19—22no—
24C22×C4×C19C2×C412yes—
25C22×C4×C19D411yescharacteristic
26C22×C4×C19D412yes—
27C22×C4×C19C2311yescharacteristic
28C2×C22⋊D19—22no—
29C2×C22⋊D19—21no—
30C22×Dic19—22no—
31#64541—22no—
32#64541—22no—
33C2×D76C2×C411yescharacteristic
34C2×C4×D19—21no—
35C2×Dic38C2×C411yescharacteristic
36M16×C19—22no—
37M16×C19—22no—
38C2×C8×C19—22no—
39C22⋊Dic19—24no—
40C22⋊Dic19—22no—
41C22⋊Dic19—21no—
42(C2×D19)⋊C4—22no—
43C4⋊Dic19—24no—
44C4⋊Dic19C2×C412yes—
45Dic19⋊C4—22no—
46C4×Dic19—22no—
47C4×Dic19—21no—
48C4×Dic19D414yescomplemented
49C23×C19—21no—
50C23×C19—21no—
51C23×C19—42no—
52C23×C19C22⋊C412yes—
53C23×C19C2×D411yescharacteristic
54C22×D19—21no—
55C2×C4×C19—21no—
56C2×C4×C19—21no—
57C2×C4×C19—24no—
58C2×C4×C19—24no—
59C2×C4×C19C22⋊C412yes—
60C2×C4×C19C22×C411yescharacteristic
61C2×C4×C19C2×D412yes—
62C2×C4×C19C2×D411yescharacteristic
63C2×C4×C19#4112yes—
64C22⋊D19—44no—
65C22⋊D19—41no—
66C22⋊D19—41no—
67C2×Dic19—22no—
68C2×Dic19—21no—
69C2×Dic19—24no—
70C2×Dic19—44no—
71D76—22no—
72C4×D19—42no—
73Dic38—22no—
74C8×C19—42no—
75#1897—191nomaximal, Sylow
76C22×C19—22no—
77C22×C19—22no—
78C22×C19—22no—
79C22×C19—22no—
80C22×C19—42no—
81C22×C19—42no—
82C22×C19C2×C22⋊C411yescharacteristic
83C22×C19#12011yescharacteristic
84C22×C19#12311yescharacteristic
85C2×D19—41no—
86C2×D19—42no—
87C4×C19—22no—
88C4×C19C4×D412yes—
89C4×C19#12112yes—
90Dic19—44no—
91Dic19—41no—
92Dic19—42no—
93#525—191no—
94C2×#117—191no—
95C2×#104—192no—
96#407D1911yescharacteristic, complemented
97#339—192no—
98C2×C19—21no—
99C2×C19—21no—
100C2×C19—42no—
101C2×C19#38611yescharacteristic
102C2×C19#42112yes—
103D19—81no—
104C2×#41—191no—
105C23×C4C2×D1911yescharacteristic
106C2×M16C2×D1912yes—
107#123—381no—
108C22⋊Q8—192no—
109#121—192no—
110#120—381no—
111C4×D4—382no—
112#117—191no—
113#117—384no—
114C2×C4⋊C4—381no—
115C2×C22⋊C4—381no—
116C2×C42—192no—
117#104—384no—
118C22⋊C8—22no—
119C19#189711yescharacteristic, complemented, Sylow
120C24D7611yescharacteristic
121#41—382no—
122#41—382no—
123C2×Q8—191no—
124C2×D4—191no—
125C2×D4—382no—
126C2×D4—381no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—382no—
130C22×C4—381no—
131C22×C4C4×D1912yes—
132C22×C4D7611yescharacteristic
133C22×C4C22⋊D1912yes—
134C22×C4C22×D1911yescharacteristic
135M16—22no—
136M16—22no—
137C2×C8—22no—
138C4⋊C4—192no—
139C4⋊C4—384no—
140C4⋊C4—382no—
141C22⋊C4—384no—
142C22⋊C4—382no—
143C22⋊C4—381no—
144C22⋊C4—382no—
145C42—194no—
146C42—382no—
147C42—381no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—381no—
152C23(C2×D19)⋊C412yes—
153C23C2×D7611yescharacteristic
154Q8—382no—
155D4—382no—
156D4—764no—
157D4—761no—
158D4—761no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—384no—
164C2×C4—382no—
165C2×C4—381no—
166C2×C4—764no—
167C2×C4—762no—
168C2×C4(C2×D19)⋊C412yes—
169C2×C4C2×C4×D1911yescharacteristic
170C2×C4D4×D1912yes—
171C2×C4#6454312yes—
172C2×C4C2×C22⋊D1911yescharacteristic
173C8—42no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—762no—
181C22—761no—
182C22#1059732811yescharacteristic
183C22#1059733211yescharacteristic
184C22C2×(C2×D19)⋊C411yescharacteristic
185C4—22no—
186C4—764no—
187C4—762no—
188C4—761no—
189C4(C22⋊D19)⋊C412yes—
190C4#1059738512yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—1521no—
195C2#1192642111yescharacteristic
196C2#1192656012yes—
subgroupG/H
centerC2×C4C2×C22⋊D19
commutatorC2×C4×C19C22×C4
FrattiniC22×C4C22×D19
FittingC19×#407C2
socleC22×C19C2×C22⋊C4
prime radical#11927055C2
cosocleC22×C4×C19C23
hypercenter#407D19
hypocenterC19#1897
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#10597372C2semidirect
3. C2×#10597282C2semidirect
4. #11926305C2semidirect
5. C19×#407C2semidirect
11. #10597376C4semidirect
17. #10597370C4semidirect
48. C4×Dic19D4semidirect
96. #407D19semidirect
119. C19#1897semidirect

Maximal subgroups

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

subgroupindex
#119270552
C2×#105973722
C2×#105972822
#119263052
C19×#4072
#189719