Finite Group Databasebeta

← #14564076

Subgroups — #14564076

Order 2432.

442 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 97 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
2C22×C4×Dic19C211yesmaximal, characteristic, complemented
3C2×#10597282C212yesmaximal, complemented
4#11926305C212yesmaximal, complemented
5C19×#407C211yesmaximal, characteristic, complemented
6C23×C4×C19C2211yescharacteristic
7C23×Dic19—21no—
8C2×#64541C2211yescharacteristic
9C2×M16×C19C2212yes—
10#10597399—21no—
11#10597376C412yescomplemented
12#10597375—21no—
13C4×C22⋊D19—22no—
14#10597372C2211yescharacteristic
15#10597370C412yescomplemented
16C2×C4×Dic19—21no—
17C2×C4×Dic19—24no—
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—28no—
31C22×Dic19—24no—
32C22×Dic19—22no—
33#64541—22no—
34#64541—22no—
35C2×D76C2×C411yescharacteristic, complemented
36C2×C4×D19—21no—
37C2×Dic38C2×C411yescharacteristic, complemented
38M16×C19—22no—
39M16×C19—22no—
40C2×C8×C19—22no—
41C22⋊Dic19—22no—
42C22⋊Dic19—21no—
43(C2×D19)⋊C4—22no—
44C4⋊Dic19C2×C412yescomplemented
45Dic19⋊C4—22no—
46C4×Dic19—24no—
47C4×Dic19—22no—
48C4×Dic19—21no—
49C4×Dic19D414yescomplemented
50C23×C19—24no—
51C23×C19—21no—
52C23×C19—21no—
53C23×C19C22⋊C412yes—
54C23×C19C2×D411yescharacteristic
55C22×D19—21no—
56C2×C4×C19—21no—
57C2×C4×C19—21no—
58C2×C4×C19—24no—
59C2×C4×C19—24no—
60C2×C4×C19C22⋊C412yes—
61C2×C4×C19C22×C411yescharacteristic
62C2×C4×C19C2×D412yes—
63C2×C4×C19C2×D411yescharacteristic
64C2×C4×C19#4112yes—
65C22⋊D19—44no—
66C22⋊D19—41no—
67C22⋊D19—41no—
68C2×Dic19—216no—
69C2×Dic19—28no—
70C2×Dic19—24no—
71C2×Dic19—22no—
72C2×Dic19—21no—
73D76—22no—
74C4×D19—42no—
75Dic38—22no—
76C8×C19—42no—
77#1896—191nomaximal, Sylow
78C22×C19—24no—
79C22×C19—24no—
80C22×C19—22no—
81C22×C19—22no—
82C22×C19—22no—
83C22×C19#10414yescomplemented
84C22×C19C2×C22⋊C411yescharacteristic
85C22×C19#12011yescharacteristic
86C22×C19#12311yescharacteristic
87C2×D19—41no—
88C2×D19—42no—
89C4×C19—22no—
90C4×C19C4×D412yes—
91C4×C19#12112yes—
92Dic19—28no—
93Dic19—41no—
94Dic19—42no—
95#525—191no—
96C22×C42—191no—
97C2×#104—192no—
98#407D1911yescharacteristic, complemented
99#339—192no—
100C2×C19—21no—
101C2×C19—24no—
102C2×C19—21no—
103C2×C19#38611yescharacteristic
104C2×C19C2×#10412yes—
105D19—81no—
106C2×#41—191no—
107C23×C4—381no—
108C23×C4C2×D1911yescharacteristic
109C2×M16C2×D1912yes—
110#123—381no—
111C22⋊Q8—192no—
112#121—192no—
113#120—381no—
114C4×D4—382no—
115#117—191no—
116C2×C42—192no—
117C2×C42—384no—
118C2×C42—381no—
119#104—384no—
120C22⋊C8—22no—
121C19#189611yescharacteristic, complemented, Sylow
122C24D7611yescharacteristic
123#41—382no—
124#41—382no—
125C2×Q8—191no—
126C2×D4—191no—
127C2×D4—382no—
128C2×D4—381no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—384no—
132C22×C4—388no—
133C22×C4—382no—
134C22×C4—381no—
135C22×C4C4×D1912yes—
136C22×C4D7611yescharacteristic
137C22×C4C22⋊D1912yes—
138C22×C4C22×D1911yescharacteristic
139M16—22no—
140M16—22no—
141C2×C8—22no—
142C4⋊C4—192no—
143C4⋊C4—382no—
144C22⋊C4—382no—
145C22⋊C4—381no—
146C22⋊C4—382no—
147C42—194no—
148C42—384no—
149C42—382no—
150C42—381no—
151C23—24no—
152C23—21no—
153C23—21no—
154C23—381no—
155C23(C2×D19)⋊C412yes—
156C23C2×D7611yescharacteristic
157Q8—382no—
158D4—382no—
159D4—764no—
160D4—761no—
161D4—761no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—24no—
165C2×C4—24no—
166C2×C4—3816no—
167C2×C4—388no—
168C2×C4—384no—
169C2×C4—382no—
170C2×C4—381no—
171C2×C4—762no—
172C2×C4(C2×D19)⋊C412yes—
173C2×C4C2×C4×D1911yescharacteristic
174C2×C4D4×D1912yes—
175C2×C4#6454312yes—
176C2×C4C2×C22⋊D1911yescharacteristic
177C8—42no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—762no—
184C22—761no—
185C22#1059728214yescomplemented
186C22#1059732811yescharacteristic
187C22#1059733211yescharacteristic
188C22C2×(C2×D19)⋊C411yescharacteristic
189C4—22no—
190C4—388no—
191C4—762no—
192C4—761no—
193C4(C22⋊D19)⋊C412yes—
194C4#1059738512yes—
195C2—21no—
196C2—24no—
197C2—21no—
198C2—1521no—
199C2#1192642111yescharacteristic
200C2C2×#1059728212yes—
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#1896
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. C22×C4×Dic19C2semidirect
3. C2×#10597282C2semidirect
4. #11926305C2semidirect
5. C19×#407C2semidirect
11. #10597376C4semidirect
15. #10597370C4semidirect
35. C2×D76C2×C4semidirect
37. C2×Dic38C2×C4semidirect
44. C4⋊Dic19C2×C4semidirect
49. C4×Dic19D4semidirect
83. C22×C19#104semidirect
98. #407D19semidirect
121. C19#1896semidirect
185. C22#10597282semidirect

Maximal subgroups

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

subgroupindex
#119270552
C22×C4×Dic192
C2×#105972822
#119263052
C19×#4072
#189619