Finite Group Databasebeta

← #14562575

Subgroups — #14562575

Order 2432.

266 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 57 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#11926694C212yesmaximal
2#11926461C211yesmaximal, characteristic
3#11926281C212yesmaximal, complemented
4#11926270C211yesmaximal, characteristic, complemented
5C19×#544C211yesmaximal, characteristic, complemented
6C22×D76C2211yescharacteristic
7C19×C4⋊Q8—22no—
8C19×#125—22no—
9C19×C22⋊Q8—21no—
10C19×C22⋊Q8C2212yes—
11C19×#117—21no—
12C2×C4⋊C4×C19C2211yescharacteristic
13C2×#64527—22no—
14C2×(C2×D19)⋊C4—21no—
15C2×(C2×D19)⋊C4—21no—
16C19⋊#95C2211yescharacteristic
17C22⋊(C19⋊C8)C2212yes—
18#10597266—22no—
19C23×D19—21no—
20C2×Q8×C19—21no—
21C2×Q8×C19D412yes—
22C22×C4×C19D411yescharacteristic
23C22×C4×C19D411yescharacteristic
24C22×C4×C19C2311yescharacteristic
25C22×Dic19—21no—
26C2×D76—22no—
27C2×D76—42no—
28C4⋊C4×C19—21no—
29C4⋊C4×C19—21no—
30C4⋊C4×C19—21no—
31C4⋊C4×C19—22no—
32C4⋊C4×C19—22no—
33C4⋊C4×C19—22no—
34C4⋊C4×C19D412yes—
35C22⋊C4×C19—22no—
36C42×C19—22no—
37#64527—44no—
38(C2×D19)⋊C4—42no—
39(C2×D19)⋊C4—42no—
40C2×C19⋊C8—22no—
41C23×C19C2×D411yescharacteristic
42C22×D19—22no—
43C22×D19—41no—
44C22×D19—41no—
45C22×D19—41no—
46C22×D19—41no—
47C22×D19—41no—
48C22×D19—41no—
49Q8×C19—42no—
50Q8×C19—81no—
51C2×C4×C19—21no—
52C2×C4×C19—21no—
53C2×C4×C19—22no—
54C2×C4×C19—22no—
55C2×C4×C19—21no—
56C2×C4×C19—41no—
57C2×C4×C19—41no—
58C2×C4×C19SD1612yescomplemented
59C2×C4×C19C2×D412yes—
60C2×Dic19—41no—
61C2×Dic19—41no—
62C2×Dic19—41no—
63D76—24no—
64D76—42no—
65C19⋊C8—42no—
66#1599—191nomaximal, Sylow
67C22×C19—21no—
68C22×C19—21no—
69C22×C19#12011yescharacteristic
70C22×C19C2×SD1611yescharacteristic
71C22×C19#13711yescharacteristic
72C2×D19—42no—
73C2×D19—42no—
74C2×D19—42no—
75C2×D19—81no—
76C2×D19—81no—
77C2×D19—81no—
78C2×D19—81no—
79C4×C19—22no—
80C4×C19—22no—
81C4×C19—42no—
82C4×C19—41no—
83C4×C19—42no—
84Dic19—81no—
85#544D1911yescharacteristic, complemented
86#450—192no—
87#394—191no—
88#328—192no—
89#324—191no—
90C2×C19—21no—
91C2×C19—21no—
92C2×C19#44811yescharacteristic
93C2×C19#45411yescharacteristic
94C2×C19B(4,𝔽2)11yescharacteristic
95D19—82no—
96C22×D4—191no—
97C2×SD16—382no—
98C4⋊Q8—22no—
99#125—22no—
100C22⋊Q8—21no—
101C22⋊Q8C2×D1912yes—
102#117—21no—
103C2×C4⋊C4C2×D1911yescharacteristic
104C2×C22⋊C4—381no—
105C2×C22⋊C4—381no—
106#102—382no—
107C22⋊C8—192no—
108#95—191no—
109C19#159911yescharacteristic, complemented, Sylow
110C24—381no—
111C2×Q8—21no—
112C2×Q8C22⋊D1912yes—
113C2×D4—382no—
114C2×D4—762no—
115C22×C4—381no—
116C22×C4C22⋊D1911yescharacteristic
117C22×C4C22⋊D1911yescharacteristic
118C22×C4C22×D1911yescharacteristic
119SD16—764no—
120C2×C8—382no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—22no—
125C4⋊C4—22no—
126C4⋊C4—22no—
127C4⋊C4C22⋊D1912yes—
128C22⋊C4—22no—
129C22⋊C4—762no—
130C22⋊C4—762no—
131C42—22no—
132C23—382no—
133C23—761no—
134C23—761no—
135C23—761no—
136C23—761no—
137C23—761no—
138C23—761no—
139C23C2×C22⋊D1911yescharacteristic
140Q8—42no—
141Q8—81no—
142D4—384no—
143D4—762no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—761no—
152C2×C4—761no—
153C2×C4—761no—
154C2×C4#6452712yescomplemented
155C2×C4C2×C22⋊D1912yes—
156C8—762no—
157C22—21no—
158C22—21no—
159C22—762no—
160C22—762no—
161C22—762no—
162C22—1521no—
163C22—1521no—
164C22—1521no—
165C22—1521no—
166C22C2×#6452711yescharacteristic
167C22#1059738811yescharacteristic
168C22#1059739911yescharacteristic
169C4—22no—
170C4—22no—
171C4—42no—
172C4—41no—
173C4—42no—
174C4—1521no—
175C2—21no—
176C2—21no—
177C2—1522no—
178C2#1192668311yescharacteristic
179C2#1192671711yescharacteristic
180C2#1192673111yescharacteristic
subgroupG/H
centerC22#10597399
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC19×#544C2
socleC22×C19#120
prime radicalC22×D76C22
hypercenter#544D19
hypocenterC19#1599
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
3. #11926281C2semidirect
4. #11926270C2semidirect
5. C19×#544C2semidirect
58. C2×C4×C19SD16semidirect
85. #544D19semidirect
109. C19#1599semidirect
154. C2×C4#64527semidirect

Maximal subgroups

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

subgroupindex
#119266942
#119264612
#119262812
#119262702
C19×#5442
#159919