Finite Group Databasebeta

← #14565622

Subgroups — #14565622

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#11927222C211yesmaximal, characteristic, complemented
2#11926731C211yesmaximal, characteristic
3#11926722C211yesmaximal, characteristic, complemented
4#11926338C211yesmaximal, characteristic, complemented
5#11926334C211yesmaximal, characteristic, complemented
6#11926330C211yesmaximal, characteristic, complemented
7C19×#458C211yesmaximal, characteristic, complemented
8C19×H(5,𝔽2)C2211yescharacteristic
9C19×#123—21no—
10C19×#123C2211yescharacteristic
11#10597397—21no—
12#10597383—21no—
13#10597383C2211yescharacteristic
14#10597382C2211yescharacteristic
15C4×C22⋊D19—21no—
16#10597342—21no—
17#10597338—21no—
18#10597329—21no—
19C22⋊C4×D19—21no—
20#10597325—21no—
21C19×#99—21no—
22C19×#99C2211yescharacteristic
23#10597294—21no—
24#10597291—21no—
25#10597291C2211yescharacteristic
26#10597290C2211yescharacteristic
27C23×D19D411yescharacteristic
28#41×C19—21no—
29#41×C19—41no—
30C2×D4×C19—21no—
31C2×D4×C19—21no—
32C2×D4×C19—41no—
33C2×D4×C19C2311yescharacteristic
34C22×C4×C19D411yescharacteristic, complemented
35C2×C22⋊D19—21no—
36C2×C22⋊D19—41no—
37C2×C4×D19—21no—
38C2×C4×D19—21no—
39C2×Dic38D411yescharacteristic, complemented
40C4⋊C4×C19—21no—
41C4⋊C4×C19—41no—
42C22⋊C4×C19—21no—
43C22⋊C4×C19—21no—
44C22⋊C4×C19—41no—
45C22⋊C4×C19D411yescharacteristic, complemented
46C22⋊Dic19—21no—
47C22⋊Dic19—21no—
48C22⋊Dic19—21no—
49C22⋊Dic19D411yescharacteristic
50#64528—41no—
51#64526—41no—
52(C2×D19)⋊C4—21no—
53(C2×D19)⋊C4—21no—
54(C2×D19)⋊C4—21no—
55(C2×D19)⋊C4—41no—
56C4⋊Dic19—21no—
57Dic19⋊C4—21no—
58Dic19⋊C4—21no—
59C4×Dic19—21no—
60C4×Dic19D411yescharacteristic, complemented
61#64520—21no—
62C23×C19—21no—
63C23×C19—21no—
64C23×C19C2×D411yescharacteristic
65C23×C19C2×D411yescharacteristic
66C22×D19—21no—
67C22×D19—42no—
68C22×D19—41no—
69Q8×C19—21no—
70D4×C19—21no—
71D4×C19—41no—
72D4×C19—41no—
73D4×C19—41no—
74D4×C19—41no—
75C2×C4×C19—21no—
76C2×C4×C19—21no—
77C2×C4×C19—21no—
78C2×C4×C19—21no—
79C2×C4×C19—41no—
80C2×C4×C19—41no—
81C2×C4×C19—41no—
82C2×C4×C19C2×D411yescharacteristic
83C22⋊D19—42no—
84C22⋊D19—82no—
85C2×Dic19—21no—
86C2×Dic19—21no—
87C2×Dic19—21no—
88C2×Dic19—41no—
89C4×D19—42no—
90C4×D19—81no—
91Dic38—41no—
92C19⋊C8—41no—
93#2197—191nomaximal, Sylow
94C22×C19—21no—
95C22×C19—21no—
96C22×C19—41no—
97C22×C19—41no—
98C22×C19—41no—
99C22×C19—81no—
100C22×C19—81no—
101C22×C19#12011yescharacteristic
102C2×D19—22no—
103C2×D19—41no—
104C2×D19—41no—
105C2×D19—42no—
106C2×D19—81no—
107C4×C19—21no—
108C4×C19—41no—
109C4×C19—41no—
110C4×C19—41no—
111C4×C19—81no—
112Dic19—41no—
113Dic19—41no—
114Dic19—41no—
115Dic19—81no—
116#551—191no—
117#458D1911yescharacteristic, complemented
118B(4,𝔽2)—191no—
119#455—191no—
120#354—191no—
121#352—191no—
122AΣL(1,𝔽16)—191no—
123C2×C19—21no—
124C2×C19—41no—
125C2×C19—41no—
126C2×C19—81no—
127C2×C19B(4,𝔽2)11yescharacteristic
128D19—42no—
129H(5,𝔽2)C2×D1911yescharacteristic
130#137—381no—
131#126—381no—
132#124—191no—
133#123—21no—
134#123—381no—
135#123C2×D1911yescharacteristic
136C22⋊Q8—381no—
137#120—191no—
138#120—381no—
139C4×D4—381no—
140#117—381no—
141C2×C22⋊C4—381no—
142#104—381no—
143#100—191no—
144#99—21no—
145#99—191no—
146#99—381no—
147#99C2×D1911yescharacteristic
148C19#219711yescharacteristic, complemented, Sylow
149C24—191no—
150#41—21no—
151#41—41no—
152C2×Q8—191no—
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—41no—
156C2×D4—381no—
157C2×D4—761no—
158C2×D4C22×D1911yescharacteristic
159C22×C4—381no—
160C22×C4—381no—
161C22×C4C22⋊D1911yescharacteristic, complemented
162Q16—761no—
163SD16—761no—
164M16—381no—
165C4⋊C4—21no—
166C4⋊C4—41no—
167C4⋊C4—381no—
168C4⋊C4—381no—
169C4⋊C4—381no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—41no—
173C22⋊C4—191no—
174C22⋊C4—381no—
175C22⋊C4—381no—
176C22⋊C4—381no—
177C22⋊C4—381no—
178C22⋊C4—381no—
179C22⋊C4—381no—
180C22⋊C4—761no—
181C22⋊C4C22⋊D1911yescharacteristic, complemented
182C42—191no—
183C42—381no—
184C23—21no—
185C23—21no—
186C23—381no—
187C23—761no—
188C23—762no—
189C23D4×D1911yescharacteristic
190C23C2×C22⋊D1911yescharacteristic
191Q8—21no—
192Q8—761no—
193D4—21no—
194D4—41no—
195D4—41no—
196D4—41no—
197D4—41no—
198D4—762no—
199D4—1522no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—381no—
208C2×C4—381no—
209C2×C4—381no—
210C2×C4—762no—
211C2×C4—761no—
212C2×C4—1521no—
213C2×C4D4×D1911yescharacteristic
214C8—761no—
215C22—21no—
216C22—21no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—81no—
221C22—81no—
222C22—382no—
223C22—761no—
224C22—762no—
225C22—761no—
226C22—1521no—
227C22#1059738311yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—41no—
232C4—81no—
233C4—761no—
234C4—761no—
235C4—761no—
236C4—1521no—
237C2—21no—
238C2—41no—
239C2—41no—
240C2—81no—
241C2—762no—
242C2#1192673011yescharacteristic
subgroupG/H
centerC2#11926730
commutator, cosocleC2×D4×C19C23
FrattiniC2×D4C22×D19
FittingC19×#458C2
socleC2×C19B(4,𝔽2)
prime radical#11926731C2
hypercenter#458D19
hypocenterC19#2197
LCSG ▷ C2×D4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #458

Complements

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

NH ≅ G/Ntype
1. #11927222C2semidirect
3. #11926722C2semidirect
4. #11926338C2semidirect
5. #11926334C2semidirect
6. #11926330C2semidirect
7. C19×#458C2semidirect
34. C22×C4×C19D4semidirect
39. C2×Dic38D4semidirect
45. C22⋊C4×C19D4semidirect
60. C4×Dic19D4semidirect
117. #458D19semidirect
148. C19#2197semidirect
161. C22×C4C22⋊D19semidirect
181. C22⋊C4C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
#119272222
#119267312
#119267222
#119263382
#119263342
#119263302
C19×#4582
#219719