Finite Group Databasebeta

← #14562655

Subgroups — #14562655

Order 2432.

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

normal subgroups only

This group has 288 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#11926860C212yesmaximal, complemented
2#11926480C211yesmaximal, characteristic, complemented
3#11926278C212yesmaximal, complemented
4#11926268C211yesmaximal, characteristic, complemented
5C19×#534C211yesmaximal, characteristic
6C22×D4×C19—21no—
7C19×#123—22no—
8C19×#121—21no—
9C19×#121C2212yes—
10C19×#120—22no—
11C2×C22⋊C4×C19C2211yescharacteristic
12C2×C22⋊Dic19—21no—
13C2×C4⋊Dic19C2211yescharacteristic, complemented
14C2×Dic19⋊C4—21no—
15#10597289—22no—
16C19⋊#95C2211yescharacteristic, complemented
17C22⋊(C19⋊C8)C2212yescomplemented
18#10597265—22no—
19C24×C19—21no—
20C24×C19D411yescharacteristic
21C2×D4×C19—22no—
22C2×D4×C19—22no—
23C2×D4×C19—21no—
24C2×D4×C19—42no—
25C2×D4×C19—42no—
26C2×D4×C19D412yes—
27C22×C4×C19—21no—
28C22×C4×C19D411yescharacteristic
29C22×C4×C19C2311yescharacteristic
30C22×Dic19—21no—
31C22×Dic19—21no—
32C4⋊C4×C19—21no—
33C4⋊C4×C19D412yes—
34C22⋊C4×C19—22no—
35C22⋊C4×C19—22no—
36C22⋊C4×C19—22no—
37C22⋊Dic19—42no—
38C4⋊Dic19—22no—
39Dic19⋊C4—42no—
40C2×C19⋊C8—22no—
41C23×C19—21no—
42C23×C19—21no—
43C23×C19—22no—
44C23×C19—41no—
45C23×C19—41no—
46C23×C19—42no—
47C23×C19—81no—
48C23×C19—81no—
49C23×C19SD1612yes—
50C23×C19C2×D411yescharacteristic
51D4×C19—42no—
52D4×C19—44no—
53D4×C19—42no—
54D4×C19—42no—
55D4×C19—81no—
56C2×C4×C19—21no—
57C2×C4×C19—22no—
58C2×C4×C19—41no—
59C2×C4×C19—42no—
60C2×C4×C19—41no—
61C2×C4×C19C2×D412yes—
62C2×Dic19—22no—
63C2×Dic19—41no—
64C2×Dic19—41no—
65C2×Dic19—41no—
66C2×Dic19—41no—
67C2×Dic19—41no—
68C19⋊C8—42no—
69#1613—191nomaximal, Sylow
70C22×C19—21no—
71C22×C19—21no—
72C22×C19—22no—
73C22×C19—42no—
74C22×C19—41no—
75C22×C19—41no—
76C22×C19—42no—
77C22×C19—42no—
78C22×C19—42no—
79C22×C19—81no—
80C22×C19—84no—
81C22×C19#12011yescharacteristic
82C22×C19C2×SD1611yescharacteristic
83C22×C19AGL(1,ℤ/8)11yescharacteristic
84C4×C19—22no—
85C4×C19—42no—
86C4×C19—41no—
87Dic19—42no—
88Dic19—81no—
89#534D1911yescharacteristic
90#481—192no—
91#399—191no—
92#327—192no—
93#323—191no—
94C2×C19—21no—
95C2×C19—21no—
96C2×C19—42no—
97C2×C19—82no—
98C2×C19#45011yescharacteristic
99C2×C19#45311yescharacteristic
100C2×C19#45811yescharacteristic
101C22×D4—21no—
102#123—22no—
103#121—21no—
104#121C2×D1912yes—
105#120—22no—
106C2×C4⋊C4—191no—
107C2×C4⋊C4—381no—
108C2×C22⋊C4—381no—
109C2×C22⋊C4C2×D1911yescharacteristic
110#106—382no—
111#102—382no—
112C22⋊C8—192no—
113#95—191no—
114C19#161311yescharacteristic, complemented, Sylow
115C24—21no—
116C24C22⋊D1911yescharacteristic
117C2×D4—22no—
118C2×D4—22no—
119C2×D4—21no—
120C2×D4—42no—
121C2×D4—42no—
122C2×D4C22⋊D1912yes—
123C22×C4—21no—
124C22×C4—381no—
125C22×C4—381no—
126C22×C4C22⋊D1911yescharacteristic
127C22×C4C22×D1911yescharacteristic
128C2×C8—382no—
129C4⋊C4—21no—
130C4⋊C4—382no—
131C4⋊C4—762no—
132C4⋊C4C22⋊D1912yes—
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—762no—
137C23—21no—
138C23—21no—
139C23—22no—
140C23—41no—
141C23—41no—
142C23—42no—
143C23—81no—
144C23—81no—
145C23#6452612yes—
146C23C2×C22⋊D1911yescharacteristic
147D4—42no—
148D4—44no—
149D4—42no—
150D4—42no—
151D4—81no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—42no—
156C2×C4—41no—
157C2×C4—382no—
158C2×C4—761no—
159C2×C4—761no—
160C2×C4—761no—
161C2×C4—761no—
162C2×C4—761no—
163C2×C4C2×C22⋊D1912yes—
164C8—762no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—42no—
172C22—42no—
173C22—42no—
174C22—81no—
175C22—84no—
176C22#1059737811yescharacteristic
177C22C2×#6452611yescharacteristic
178C22#1059739911yescharacteristic
179C4—22no—
180C4—42no—
181C4—41no—
182C4—762no—
183C4—1521no—
184C2—21no—
185C2—21no—
186C2—42no—
187C2—82no—
188C2#1192669511yescharacteristic
189C2#1192671211yescharacteristic
190C2#1192673411yescharacteristic
subgroupG/H
centerC22#10597399
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
Fitting, prime radicalC19×#534C2
socleC22×C19#120
hypercenter#534D19
hypocenterC19#1613
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #11926860C2semidirect
2. #11926480C2semidirect
3. #11926278C2semidirect
4. #11926268C2semidirect
13. C2×C4⋊Dic19C22semidirect
16. C19⋊#95C22semidirect
17. C22⋊(C19⋊C8)C22semidirect
114. C19#1613semidirect

Maximal subgroups

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

subgroupindex
#119268602
#119264802
#119262782
#119262682
C19×#5342
#161319