Finite Group Databasebeta

← #14563523

Subgroups — #14563523

Order 2432.

280 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C2×#10597265C212yesmaximal
2C2×C8×Dic19C211yesmaximal, characteristic
3C4⋊C4×Dic19C212yesmaximal
4#11926307C211yesmaximal, characteristic
5C19×#340C211yesmaximal, characteristic
6C22×C8×C19C2211yescharacteristic
7C2×C4⋊C4×C19C2212yes—
8C2×C4⋊Dic19C2212yes—
9C2×C4×Dic19—22no—
10C2×C4×Dic19C2211yescharacteristic
11C22×C19⋊C8C2211yescharacteristic
12C19⋊#95—22no—
13C8×Dic19C414yescomplemented
14#10597265C418yescomplemented
15C22×C4×C19—22no—
16C22×C4×C19C2311yescharacteristic
17C22×Dic19—22no—
18C22×Dic19D411yescharacteristic
19C22×Dic19D411yescharacteristic
20C2×C8×C19—22no—
21C2×C8×C19C2×C412yes—
22C4⋊C4×C19—22no—
23C4⋊C4×C19C2×C414yes—
24C4⋊Dic19—22no—
25C4⋊Dic19C2×C414yes—
26C4×Dic19—44no—
27C4×Dic19C2×C412yes—
28C4×Dic19Q812yes—
29C2×C19⋊C8C2×C414yes—
30C2×C19⋊C8C2×C412yes—
31C23×C19C2×D411yescharacteristic
32C2×C4×C19—24no—
33C2×C4×C19—42no—
34C2×C4×C19—42no—
35C2×C4×C19C22×C411yescharacteristic
36C2×C4×C19C22×C412yes—
37C2×C4×C19C2×Q811yescharacteristic
38C2×C4×C19#4112yes—
39C2×Dic19—21no—
40C2×Dic19—21no—
41C2×Dic19—24no—
42C2×Dic19—42no—
43C2×Dic19—42no—
44C2×Dic19C4⋊C412yes—
45C2×Dic19C4⋊C412yes—
46C2×Dic19SD1614yes—
47C8×C19—22no—
48C19⋊C8C4214yescomplemented
49C4×#106—191nomaximal, Sylow
50C22×C19C2×C4⋊C411yescharacteristic
51C22×C19C4×D412yes—
52C22×C19C2×SD1612yes—
53C22×C19#13511yescharacteristic
54C22×C19#13511yescharacteristic
55C4×C19—44no—
56C4×C19C2×C4211yescharacteristic
57C4×C19#11711yescharacteristic
58C4×C19C4×Q812yes—
59Dic19—22no—
60Dic19—44no—
61Dic19#10614yescomplemented
62C2×#106—192no—
63C2×C4×C8—191no—
64C4×C4⋊C4—192no—
65#340—191no—
66#340D1911yescharacteristic
67C2×C19C4×C4⋊C411yescharacteristic
68C2×C19C2×#10611yescharacteristic
69C2×C19#42711yescharacteristic
70C2×C19C4×SD1612yes—
71C2×C19C4×SD1612yes—
72C22×C8—191no—
73C22×C8C2×D1911yescharacteristic
74C2×C4⋊C4—192no—
75C2×C4⋊C4C2×D1912yes—
76C2×C42—191no—
77C2×C42—382no—
78#106—198no—
79C4×C8—194no—
80#95—382no—
81C19C4×#10611yescharacteristic, complemented, Sylow
82C22×C4—22no—
83C22×C4—191no—
84C22×C4—191no—
85C22×C4—382no—
86C22×C4C22×D1911yescharacteristic
87C2×C8—22no—
88C2×C8—192no—
89C2×C8—194no—
90C2×C8C4×D1912yes—
91C4⋊C4—22no—
92C4⋊C4—194no—
93C4⋊C4—382no—
94C4⋊C4C4×D1914yes—
95C42—192no—
96C42—192no—
97C42—764no—
98C23D4×D1911yescharacteristic
99C2×C4—24no—
100C2×C4—42no—
101C2×C4—42no—
102C2×C4—192no—
103C2×C4—194no—
104C2×C4—192no—
105C2×C4—381no—
106C2×C4—381no—
107C2×C4—384no—
108C2×C4—762no—
109C2×C4—762no—
110C2×C4C2×C4×D1911yescharacteristic
111C2×C4C2×C4×D1912yes—
112C2×C4#6454312yes—
113C2×C4Q8×D1911yescharacteristic
114C8—22no—
115C8—194no—
116C22(C22⋊D19)⋊C412yes—
117C22C4⋊C4×D1911yescharacteristic
118C22#1059735811yescharacteristic
119C22SD16×D1912yes—
120C22#1059736511yescharacteristic
121C4—44no—
122C4—194no—
123C4—382no—
124C4—764no—
125C4C42×D1911yescharacteristic
126C4#1059732311yescharacteristic
127C4#1059733312yes—
128C2#1192639511yescharacteristic
129C2#106×D1911yescharacteristic
130C2#1192658111yescharacteristic
131C2#1192662912yes—
132C2#1192663512yes—
subgroupG/H
centerC23D4×D19
commutatorC4×C19C2×C42
FrattiniC22×C4C22×D19
FittingC19×#340C2
socle, prime radicalC23×C19C2×D4
cosocleC22×C4×C19C23
hypercenter#340D19
hypocenterC19C4×#106
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
13. C8×Dic19C4semidirect
14. #10597265C4semidirect
48. C19⋊C8C42semidirect
61. Dic19#106semidirect
81. C19C4×#106semidirect

Maximal subgroups

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

subgroupindex
C2×#105972652
C2×C8×Dic192
C4⋊C4×Dic192
#119263072
C19×#3402
C4×#10619