Finite Group Databasebeta

← #14561981

Subgroups — #14561981

Order 2432.

280 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 73 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×#10597375C211yesmaximal, characteristic
2#11926508C211yesmaximal, characteristic, complemented
3#11926269C212yesmaximal, complemented
4#11926267C212yesmaximal, complemented
5C2×C19×C22⋊C8C211yesmaximal, characteristic, complemented
6C23×C4×C19C2211yescharacteristic
7C22×C22⋊D19C411yescharacteristic
8C22×C8×C19—21no—
9C2×C22⋊Dic19C411yescharacteristic
10#10597375—21no—
11#10597375—21no—
12#10597375—21no—
13#10597375—21no—
14C2×(C2×D19)⋊C4C411yescharacteristic
15C2×(C2×D19)⋊C4C2211yescharacteristic
16C2×Dic19⋊C4C411yescharacteristic
17C2×Dic19⋊C4C2211yescharacteristic
18C2×#64520—21no—
19C19×C22⋊C8—21no—
20C19×C22⋊C8C2212yes—
21C22⋊(C19⋊C8)—21no—
22C22⋊(C19⋊C8)C2212yes—
23C24×C19C2×C411yescharacteristic
24C23×D19C2×C411yescharacteristic
25C22×C4×C19—42no—
26C22×C4×C19C2×C411yescharacteristic
27C22×C4×C19D411yescharacteristic
28C22×C4×C19D411yescharacteristic
29C22×C4×C19D411yescharacteristic
30C22×C4×C19D411yescharacteristic
31C22×C4×C19C2311yescharacteristic
32C2×C22⋊D19—21no—
33C2×C22⋊D19—21no—
34C2×C22⋊D19—42no—
35C22×Dic19C2×C411yescharacteristic
36C22×Dic19C2×C411yescharacteristic
37C22×Dic19C2×C411yescharacteristic
38C2×C8×C19—22no—
39C2×C8×C19—42no—
40C22⋊Dic19—21no—
41C22⋊Dic19—21no—
42(C2×D19)⋊C4—21no—
43(C2×D19)⋊C4—21no—
44(C2×D19)⋊C4—21no—
45(C2×D19)⋊C4—21no—
46Dic19⋊C4—21no—
47Dic19⋊C4—21no—
48Dic19⋊C4—21no—
49Dic19⋊C4—21no—
50#64520—42no—
51C2×C19⋊C8—22no—
52C23×C19—22no—
53C23×C19—22no—
54C23×C19—41no—
55C23×C19C22⋊C411yescharacteristic
56C23×C19C22⋊C411yescharacteristic
57C23×C19C22×C411yescharacteristic
58C22×D19—21no—
59C22×D19—22no—
60C22×D19—41no—
61C22×D19—41no—
62C2×C4×C19—22no—
63C2×C4×C19—22no—
64C2×C4×C19—41no—
65C2×C4×C19—41no—
66C2×C4×C19—41no—
67C2×C4×C19—41no—
68C2×C4×C19C22⋊C411yescharacteristic
69C2×C4×C19C22⋊C411yescharacteristic
70C2×C4×C19C2×D411yescharacteristic
71C2×C4×C19C2×D411yescharacteristic
72C22⋊D19—42no—
73C22⋊D19—42no—
74C2×Dic19—21no—
75C2×Dic19—21no—
76C2×Dic19—21no—
77C2×Dic19—22no—
78C2×Dic19—41no—
79C2×Dic19—41no—
80C8×C19—42no—
81C19⋊C8—42no—
82#1468—191nomaximal, Sylow
83C22×C19—21no—
84C22×C19—21no—
85C22×C19—21no—
86C22×C19—21no—
87C22×C19—21no—
88C22×C19—21no—
89C22×C19—21no—
90C22×C19—44no—
91C22×C19#9912yes—
92C22×C19C2×C22⋊C411yescharacteristic
93C22×C19#13112yes—
94C2×D19—41no—
95C2×D19—41no—
96C2×D19—41no—
97C2×D19—82no—
98C4×C19—21no—
99C4×C19—21no—
100C4×C19—21no—
101C4×C19—21no—
102Dic19—41no—
103Dic19—41no—
104Dic19—41no—
105C2×#123—191no—
106#407—191no—
107C2×C22⋊C8D1911yescharacteristic, complemented
108#324—192no—
109#323—192no—
110C2×C19—22no—
111C2×C19—22no—
112C2×C19—41no—
113C2×C19#40811yescharacteristic
114C2×C19C2×#9911yescharacteristic
115C2×C19#41311yescharacteristic
116D19—81no—
117C22×D4—191no—
118C23×C4C2×D1911yescharacteristic
119C2×M16—381no—
120C22×C8—21no—
121#123—381no—
122#123—381no—
123#123—381no—
124#123—381no—
125C2×C4⋊C4—191no—
126C2×C4⋊C4—191no—
127C2×C22⋊C4—191no—
128C2×C22⋊C4—191no—
129C2×C22⋊C4—191no—
130C22⋊C8—21no—
131C22⋊C8—192no—
132C22⋊C8—381no—
133C22⋊C8C2×D1912yes—
134C19#146811yescharacteristic, complemented, Sylow
135C24—191no—
136C24C4×D1911yescharacteristic
137C2×D4—381no—
138C2×D4—381no—
139C2×D4—762no—
140C22×C4—42no—
141C22×C4—191no—
142C22×C4—191no—
143C22×C4—191no—
144C22×C4C4×D1911yescharacteristic
145C22×C4D7611yescharacteristic
146C22×C4D7611yescharacteristic
147C22×C4C22⋊D1911yescharacteristic
148C22×C4C22⋊D1911yescharacteristic
149C22×C4C22×D1911yescharacteristic
150M16—762no—
151C2×C8—22no—
152C2×C8—42no—
153C2×C8—382no—
154C4⋊C4—381no—
155C4⋊C4—381no—
156C4⋊C4—381no—
157C4⋊C4—381no—
158C22⋊C4—381no—
159C22⋊C4—381no—
160C22⋊C4—381no—
161C22⋊C4—381no—
162C22⋊C4—381no—
163C22⋊C4—381no—
164C23—22no—
165C23—22no—
166C23—41no—
167C23—381no—
168C23—382no—
169C23—761no—
170C23—761no—
171C23(C2×D19)⋊C411yescharacteristic
172C23(C2×D19)⋊C411yescharacteristic
173C23C2×C4×D1911yescharacteristic
174D4—762no—
175D4—762no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—382no—
183C2×C4—381no—
184C2×C4—381no—
185C2×C4—381no—
186C2×C4—761no—
187C2×C4—761no—
188C2×C4(C2×D19)⋊C411yescharacteristic
189C2×C4(C2×D19)⋊C411yescharacteristic
190C2×C4C2×D7611yescharacteristic
191C2×C4C2×C22⋊D1911yescharacteristic
192C8—42no—
193C8—762no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—761no—
203C22—761no—
204C22—761no—
205C22—1522no—
206C22#1059726312yes—
207C22#1059734712yes—
208C22C2×(C2×D19)⋊C411yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—761no—
214C4—761no—
215C4—761no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—1521no—
220C2#1192651011yescharacteristic
221C2C2×#1059726311yescharacteristic
222C2#1192652611yescharacteristic
subgroupG/H
centerC22C2×(C2×D19)⋊C4
commutatorC23×C19C22×C4
FrattiniC22×C4C22×D19
FittingC2×C19×C22⋊C8C2
socleC22×C19C2×C22⋊C4
prime radicalC22×C22⋊D19C4
cosocleC22×C4×C19C23
hypercenterC2×C22⋊C8D19
hypocenterC19#1468
LCSG ▷ C23×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #11926508C2semidirect
3. #11926269C2semidirect
4. #11926267C2semidirect
5. C2×C19×C22⋊C8C2semidirect
107. C2×C22⋊C8D19semidirect
134. C19#1468semidirect

Maximal subgroups

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

subgroupindex
C2×#105973752
#119265082
#119262692
#119262672
C2×C19×C22⋊C82
#146819