Finite Group Databasebeta

← #14565627

Subgroups — #14565627

Order 2432.

258 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 41 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#11927225C211yesmaximal, characteristic, complemented
2#11926735C211yesmaximal, characteristic, complemented
3#11926730C211yesmaximal, characteristic
4#11926724C211yesmaximal, characteristic, complemented
5#11926338C211yesmaximal, characteristic, complemented
6#11926335C211yesmaximal, characteristic, complemented
7C19×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
8#10597430C2211yescharacteristic
9C19×#120C2211yescharacteristic
10#10597399—21no—
11C2×C22⋊Dic19—21no—
12#10597382C2211yescharacteristic
13#10597381—21no—
14#10597381C2211yescharacteristic
15D4×Dic19—21no—
16#10597355—21no—
17#10597332—21no—
18#10597325—21no—
19#10597324—21no—
20#10597323—21no—
21C19×#100C2211yescharacteristic
22C19×#99C2211yescharacteristic
23#10597291C2211yescharacteristic
24#10597282—21no—
25#10597263—21no—
26#10597263—21no—
27C24×C19D411yescharacteristic
28C2×D4×C19—21no—
29C2×D4×C19C2311yescharacteristic
30C2×C22⋊D19—21no—
31C2×C22⋊D19—21no—
32C2×C22⋊D19—41no—
33C22×Dic19—21no—
34C22×Dic19—21no—
35C22×Dic19D411yescharacteristic, complemented
36#64543—41no—
37D4×D19—41no—
38#64541—21no—
39C2×Dic38D411yescharacteristic, complemented
40M16×C19—21no—
41C22⋊C4×C19—21no—
42C22⋊C4×C19—21no—
43C22⋊C4×C19D411yescharacteristic
44C22⋊Dic19—21no—
45C22⋊Dic19—21no—
46C22⋊Dic19—21no—
47C22⋊Dic19—21no—
48C22⋊Dic19—21no—
49C22⋊Dic19—21no—
50C22⋊Dic19—41no—
51C22⋊Dic19D411yescharacteristic, complemented
52(C2×D19)⋊C4—41no—
53C4⋊Dic19—21no—
54C4⋊Dic19—41no—
55Dic19⋊C4—21no—
56Dic19⋊C4—21no—
57Dic19⋊C4—21no—
58C4×Dic19—21no—
59C4×Dic19D411yescharacteristic, complemented
60Dic76—41no—
61#64516—41no—
62C23×C19—21no—
63C23×C19—41no—
64C23×C19—42no—
65C23×C19C2×D411yescharacteristic
66C23×C19C2×D411yescharacteristic
67C22×D19—21no—
68C22×D19—21no—
69D4×C19—41no—
70D4×C19—42no—
71C2×C4×C19—21no—
72C2×C4×C19—41no—
73C2×C4×C19C2×D411yescharacteristic
74C22⋊D19—41no—
75C22⋊D19—41no—
76C22⋊D19—41no—
77C22⋊D19—82no—
78C2×Dic19—21no—
79C2×Dic19—21no—
80C2×Dic19—21no—
81C2×Dic19—21no—
82C2×Dic19—21no—
83C2×Dic19—21no—
84C2×Dic19—42no—
85C2×Dic19—41no—
86C2×Dic19—41no—
87C2×Dic19—81no—
88D76—21no—
89C4×D19—41no—
90Dic38—21no—
91Dic38—41no—
92C8×C19—41no—
93#2197—191nomaximal, Sylow
94C22×C19—22no—
95C22×C19—21no—
96C22×C19—21no—
97C22×C19—41no—
98C22×C19—41no—
99C22×C19—41no—
100C22×C19—42no—
101C22×C19—41no—
102C22×C19—81no—
103C22×C19#12011yescharacteristic
104C2×D19—41no—
105C2×D19—81no—
106C2×D19—81no—
107C4×C19—21no—
108C4×C19—41no—
109C4×C19—81no—
110Dic19—41no—
111Dic19—41no—
112Dic19—41no—
113Dic19—41no—
114Dic19—41no—
115Dic19—81no—
116#551—191no—
117#458—191no—
118B(4,𝔽2)—191no—
119#455—191no—
120#354—191no—
121#352—191no—
122AΣL(1,𝔽16)D1911yescharacteristic, complemented
123C2×C19—21no—
124C2×C19—41no—
125C2×C19—41no—
126C2×C19—42no—
127C2×C19B(4,𝔽2)11yescharacteristic
128D19—81no—
129H(5,𝔽2)—191no—
130#137—381no—
131#126—381no—
132#124—191no—
133#123—191no—
134#123—381no—
135#123—381no—
136C22⋊Q8—381no—
137#120—381no—
138#120C2×D1911yescharacteristic
139C4×D4—381no—
140#117—381no—
141C2×C22⋊C4—381no—
142#104—381no—
143#100C2×D1911yescharacteristic
144#99—191no—
145#99—381no—
146#99—381no—
147#99C2×D1911yescharacteristic
148C19#219711yescharacteristic, complemented, Sylow
149C24D7611yescharacteristic
150#41—381no—
151#41—761no—
152C2×Q8—191no—
153C2×D4—21no—
154C2×D4—381no—
155C2×D4—381no—
156C2×D4—761no—
157C2×D4—761no—
158C2×D4C22×D1911yescharacteristic
159C22×C4—191no—
160C22×C4—381no—
161C22×C4—381no—
162Q16—761no—
163SD16—761no—
164M16—21no—
165C4⋊C4—381no—
166C4⋊C4—381no—
167C4⋊C4—381no—
168C4⋊C4—381no—
169C4⋊C4—761no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—191no—
173C22⋊C4—381no—
174C22⋊C4—381no—
175C22⋊C4—381no—
176C22⋊C4—381no—
177C22⋊C4—381no—
178C22⋊C4—381no—
179C22⋊C4—761no—
180C22⋊C4—761no—
181C22⋊C4D7611yescharacteristic
182C42—191no—
183C42—381no—
184C23—21no—
185C23—41no—
186C23—42no—
187C23—381no—
188C23—381no—
189C23C2×D7611yescharacteristic
190C23D4×D1911yescharacteristic
191Q8—381no—
192Q8—761no—
193D4—41no—
194D4—42no—
195D4—381no—
196D4—761no—
197D4—761no—
198D4—761no—
199D4—1522no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—381no—
203C2×C4—381no—
204C2×C4—381no—
205C2×C4—381no—
206C2×C4—381no—
207C2×C4—381no—
208C2×C4—761no—
209C2×C4—762no—
210C2×C4—761no—
211C2×C4—761no—
212C2×C4—1521no—
213C2×C4D4×D1911yescharacteristic
214C8—41no—
215C22—22no—
216C22—21no—
217C22—21no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—42no—
222C22—41no—
223C22—81no—
224C22—761no—
225C22—1521no—
226C22—1521no—
227C22#1059732811yescharacteristic
228C4—21no—
229C4—41no—
230C4—81no—
231C4—761no—
232C4—761no—
233C4—761no—
234C4—761no—
235C4—761no—
236C4—1521no—
237C2—21no—
238C2—41no—
239C2—41no—
240C2—42no—
241C2—1521no—
242C2#1192673211yescharacteristic
subgroupG/H
centerC2#11926732
commutator, cosocleC2×D4×C19C23
FrattiniC2×D4C22×D19
FittingC19×AΣL(1,𝔽16)C2
socleC2×C19B(4,𝔽2)
prime radical#11926730C2
hypercenterAΣL(1,𝔽16)D19
hypocenterC19#2197
LCSG ▷ C2×D4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
1. #11927225C2semidirect
2. #11926735C2semidirect
4. #11926724C2semidirect
5. #11926338C2semidirect
6. #11926335C2semidirect
7. C19×AΣL(1,𝔽16)C2semidirect
35. C22×Dic19D4semidirect
39. C2×Dic38D4semidirect
51. C22⋊Dic19D4semidirect
59. C4×Dic19D4semidirect
122. AΣL(1,𝔽16)D19semidirect
148. C19#2197semidirect

Maximal subgroups

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

subgroupindex
#119272252
#119267352
#119267302
#119267242
#119263382
#119263352
C19×AΣL(1,𝔽16)2
#219719