Finite Group Databasebeta

← #14562942

Subgroups — #14562942

Order 2432.

228 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 45 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#11927286C211yesmaximal, characteristic
2#11926939C211yesmaximal, characteristic, complemented
3#11926904C212yesmaximal, complemented
4#11926283C212yesmaximal, complemented
5C19×#329C211yesmaximal, characteristic, complemented
6C19×#124C2211yescharacteristic
7#10597393—21no—
8C2×#64528—21no—
9#10597383—21no—
10C2×#64526—21no—
11#10597331—22no—
12#10597328—22no—
13#10597321C2212yes—
14#10597315C2211yescharacteristic, complemented
15C19×#97C2212yescomplemented
16#10597278—22no—
17#10597273—22no—
18#10597260C2211yescharacteristic, complemented
19C23×D19—21no—
20C2×Q8×C19D411yescharacteristic
21C2×D4×C19D411yescharacteristic
22C2×C22⋊D19—22no—
23C2×D76—21no—
24C2×D76D412yes—
25C2×Dic38—21no—
26C2×Dic38D412yes—
27C2×C8×C19—22no—
28C22⋊C4×C19—22no—
29C42×C19C2311yescharacteristic
30C22⋊Dic19—21no—
31#64528—42no—
32#64526—42no—
33(C2×D19)⋊C4—22no—
34(C2×D19)⋊C4—22no—
35(C2×D19)⋊C4—22no—
36C4⋊Dic19—22no—
37C4×Dic19—21no—
38C2×C19⋊C8—21no—
39C23×C19—21no—
40C22×D19—22no—
41C22×D19—81no—
42C22×D19—82no—
43Q8×C19—41no—
44D4×C19—41no—
45C2×C4×C19—21no—
46C2×C4×C19C2×D411yescharacteristic
47C2×C4×C19C2×D412yes—
48C22⋊D19—82no—
49C2×Dic19—22no—
50C2×Dic19—41no—
51D76—42no—
52D76—81no—
53Dic38—42no—
54Dic38—41no—
55Dic38—41no—
56C8×C19—42no—
57C19⋊C8—22no—
58#1659—191nomaximal, Sylow
59C22×C19—41no—
60C22×C19—42no—
61C22×C19#12011yescharacteristic
62C2×D19—42no—
63C2×D19—42no—
64C2×D19—42no—
65C2×D19—84no—
66C4×C19—21no—
67C4×C19—22no—
68C4×C19—41no—
69Dic19—42no—
70Dic19—81no—
71H(3,𝔽4)—191no—
72#497—191no—
73#489—192no—
74#329—192no—
75#329D1911yescharacteristic, complemented
76C2×C19—81no—
77C2×C19#45311yescharacteristic
78C2×C19#45512yes—
79D19—82no—
80C2×Q16—381no—
81C2×SD16—381no—
82C4⋊Q8—191no—
83#124—192no—
84#124—382no—
85#124—381no—
86#124C2×D1911yescharacteristic
87#120—382no—
88#120—381no—
89#103—382no—
90#102—382no—
91#97—191no—
92#97C2×D1912yescomplemented
93C19#165911yescharacteristic, complemented, Sylow
94C24—381no—
95C2×Q8—192no—
96C2×Q8—381no—
97C2×Q8D7611yescharacteristic
98C2×D4—192no—
99C2×D4—381no—
100C2×D4—382no—
101C2×D4D7611yescharacteristic
102Q16—762no—
103SD16—762no—
104C2×C8—22no—
105C2×C8—381no—
106C4⋊C4—382no—
107C22⋊C4—22no—
108C22⋊C4—382no—
109C22⋊C4—381no—
110C22⋊C4—382no—
111C22⋊C4—382no—
112C42—381no—
113C42C22×D1911yescharacteristic
114C23—21no—
115C23—382no—
116C23—1521no—
117C23—1522no—
118Q8—41no—
119Q8—762no—
120Q8—761no—
121Q8—761no—
122D4—41no—
123D4—762no—
124D4—1521no—
125D4—1522no—
126C2×C4—21no—
127C2×C4—382no—
128C2×C4—761no—
129C2×C4C2×D7611yescharacteristic
130C2×C4D4×D1912yes—
131C8—42no—
132C8—382no—
133C22—41no—
134C22—42no—
135C22—762no—
136C22—762no—
137C22—762no—
138C22—1524no—
139C22#1059732811yescharacteristic
140C4—21no—
141C4—22no—
142C4—41no—
143C4—762no—
144C4—1521no—
145C2—81no—
146C2—1522no—
147C2#1192671411yescharacteristic
148C2#1192672312yes—
subgroupG/H
centerC22#10597328
commutator, cosocleC42×C19C23
FrattiniC42C22×D19
FittingC19×#329C2
socleC22×C19#120
prime radical#11927286C2
hypercenter#329D19
hypocenterC19#1659
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #11926939C2semidirect
3. #11926904C2semidirect
4. #11926283C2semidirect
5. C19×#329C2semidirect
14. #10597315C22semidirect
15. C19×#97C22semidirect
18. #10597260C22semidirect
75. #329D19semidirect
92. #97C2×D19semidirect
93. C19#1659semidirect

Maximal subgroups

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

subgroupindex
#119272862
#119269392
#119269042
#119262832
C19×#3292
#165919