Finite Group Databasebeta

← #14565631

Subgroups — #14565631

Order 2432.

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

normal subgroups only

This group has 246 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#11926733C212yesmaximal, complemented
2#11926711C211yesmaximal, characteristic
3#11926337C211yesmaximal, characteristic, complemented
4#11926334C212yesmaximal, complemented
5C19×#559C211yesmaximal, characteristic, complemented
6#10597430C2211yescharacteristic
7C19×#127C2211yescharacteristic
8C19×#124—22no—
9C19×#123—21no—
10C19×#123C2212yes—
11C4×Q8×C19—21no—
12C4×D4×C19—22no—
13#10597378—21no—
14#10597375—22no—
15#10597291C2212yes—
16#10597290C2211yescharacteristic
17#10597263—22no—
18#10597262—21no—
19C2×Q8×C19—21no—
20C2×D4×C19—22no—
21C2×D4×C19D411yescharacteristic
22C2×D4×C19C2311yescharacteristic
23C22×C4×C19—21no—
24C22×C4×C19D412yes—
25C2×C22⋊D19—22no—
26#64543—41no—
27D4×D19—41no—
28#64541—21no—
29C4⋊C4×C19—21no—
30C4⋊C4×C19—22no—
31C22⋊C4×C19—22no—
32C22⋊C4×C19—21no—
33C22⋊C4×C19—22no—
34C22⋊C4×C19D412yes—
35C42×C19—22no—
36C42×C19D411yescharacteristic
37C22⋊Dic19—22no—
38#64526—41no—
39#64525—41no—
40(C2×D19)⋊C4—42no—
41Dic19⋊C4—42no—
42#64520—21no—
43C23×C19—21no—
44C23×C19C2×D412yes—
45C22×D19—22no—
46Q8×C19—42no—
47D4×C19—41no—
48D4×C19—41no—
49D4×C19—44no—
50C2×C4×C19—21no—
51C2×C4×C19—22no—
52C2×C4×C19—22no—
53C2×C4×C19—42no—
54C2×C4×C19—81no—
55C2×C4×C19C2×D411yescharacteristic
56C22⋊D19—42no—
57C22⋊D19—41no—
58C2×Dic19—22no—
59C2×Dic19—42no—
60D76—21no—
61C4×D19—41no—
62Dic38—21no—
63C19⋊C8—41no—
64#2198—191nomaximal, Sylow
65C22×C19—22no—
66C22×C19—42no—
67C22×C19—42no—
68C22×C19—41no—
69C22×C19#12011yescharacteristic
70C2×D19—41no—
71C2×D19—82no—
72C4×C19—22no—
73C4×C19—21no—
74C4×C19—42no—
75C4×C19—42no—
76Dic19—41no—
77Dic19—82no—
78#559D1911yescharacteristic, complemented
79#458—192no—
80#453—191no—
81#353—191no—
82#352—192no—
83C2×C19—21no—
84C2×C19—42no—
85C2×C19—81no—
86C2×C19B(4,𝔽2)11yescharacteristic
87D19—81no—
88H(5,𝔽2)—191no—
89AGL(1,ℤ/8)—381no—
90#127C2×D1911yescharacteristic
91#124—22no—
92#123—21no—
93#123—382no—
94#123C2×D1912yes—
95C4×Q8—21no—
96C4×D4—22no—
97#104—381no—
98#100—191no—
99#99—192no—
100#99—382no—
101C19#219811yescharacteristic, complemented, Sylow
102#41—381no—
103#41—761no—
104C2×Q8—21no—
105C2×D4—22no—
106C2×D4—382no—
107C2×D4—761no—
108C2×D4C22⋊D1911yescharacteristic
109C2×D4C22×D1911yescharacteristic
110C22×C4—21no—
111C22×C4C22⋊D1912yes—
112SD16—761no—
113D8—761no—
114M16—381no—
115C4⋊C4—21no—
116C4⋊C4—22no—
117C4⋊C4—762no—
118C22⋊C4—22no—
119C22⋊C4—21no—
120C22⋊C4—22no—
121C22⋊C4—382no—
122C22⋊C4—762no—
123C22⋊C4C22⋊D1912yes—
124C42—22no—
125C42C22⋊D1911yescharacteristic
126C23—21no—
127C23—382no—
128C23C2×C22⋊D1912yes—
129Q8—42no—
130Q8—381no—
131D4—41no—
132D4—41no—
133D4—44no—
134D4—381no—
135D4—762no—
136D4—761no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—42no—
141C2×C4—81no—
142C2×C4—382no—
143C2×C4—761no—
144C2×C4—762no—
145C2×C4C2×C22⋊D1911yescharacteristic
146C8—761no—
147C22—22no—
148C22—42no—
149C22—42no—
150C22—41no—
151C22—761no—
152C22—1522no—
153C22#1059739911yescharacteristic
154C4—22no—
155C4—21no—
156C4—42no—
157C4—42no—
158C4—761no—
159C4—1522no—
160C2—21no—
161C2—42no—
162C2—81no—
163C2—1521no—
164C2#1192673111yescharacteristic
subgroupG/H
centerC2#11926731
commutator, cosocleC2×D4×C19C23
FrattiniC2×D4C22×D19
FittingC19×#559C2
socleC2×C19B(4,𝔽2)
prime radical#11926711C2
hypercenter#559D19
hypocenterC19#2198
LCSG ▷ C2×D4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #11926733C2semidirect
3. #11926337C2semidirect
4. #11926334C2semidirect
5. C19×#559C2semidirect
78. #559D19semidirect
101. C19#2198semidirect

Maximal subgroups

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

subgroupindex
#119267332
#119267112
#119263372
#119263342
C19×#5592
#219819