Finite Group Databasebeta

← #14565646

Subgroups — #14565646

Order 2432.

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

normal subgroups only

This group has 226 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#11927297C211yesmaximal, characteristic, complemented
2#11926734C211yesmaximal, characteristic
3#11926722C211yesmaximal, characteristic
4#11926338C211yesmaximal, characteristic, complemented
5#11926334C211yesmaximal, characteristic, complemented
6#11926333C211yesmaximal, characteristic, complemented
7C19×#458C211yesmaximal, characteristic
8C19×H(5,𝔽2)C2211yescharacteristic
9C19×#123—21no—
10C19×#123C2211yescharacteristic
11#10597397—21no—
12#10597382C2211yescharacteristic
13#10597381—21no—
14#10597381C2211yescharacteristic
15#10597370—21no—
16#10597335—21no—
17#10597334—21no—
18#10597325—21no—
19#10597325—21no—
20#10597324—21no—
21C19×#99—21no—
22C19×#99C2211yescharacteristic
23#10597294—21no—
24#10597291—21no—
25#10597291C2211yescharacteristic
26#10597290C2211yescharacteristic
27#41×C19—21no—
28#41×C19—41no—
29C2×D4×C19—21no—
30C2×D4×C19—21no—
31C2×D4×C19—41no—
32C2×D4×C19C2311yescharacteristic
33C22×C4×C19D411yescharacteristic
34C22×Dic19D411yescharacteristic
35C2×Dic38—21no—
36C2×Dic38D411yescharacteristic
37C4⋊C4×C19—21no—
38C4⋊C4×C19—41no—
39C22⋊C4×C19—21no—
40C22⋊C4×C19—21no—
41C22⋊C4×C19—41no—
42C22⋊C4×C19D411yescharacteristic
43C22⋊Dic19—21no—
44C22⋊Dic19—21no—
45C22⋊Dic19—21no—
46C22⋊Dic19—21no—
47C22⋊Dic19—41no—
48C22⋊Dic19D411yescharacteristic
49#64528—41no—
50#64526—41no—
51C4⋊Dic19—21no—
52C4⋊Dic19—21no—
53Dic19⋊C4—21no—
54Dic19⋊C4—21no—
55Dic19⋊C4—21no—
56Dic19⋊C4—21no—
57Dic19⋊C4—21no—
58Dic19⋊C4—41no—
59C4×Dic19—21no—
60C4×Dic19D411yescharacteristic
61#64520—21no—
62C23×C19—21no—
63C23×C19—21no—
64C23×C19C2×D411yescharacteristic
65C23×C19C2×D411yescharacteristic
66Q8×C19—21no—
67D4×C19—21no—
68D4×C19—41no—
69D4×C19—41no—
70D4×C19—41no—
71D4×C19—41no—
72C2×C4×C19—21no—
73C2×C4×C19—21no—
74C2×C4×C19—21no—
75C2×C4×C19—21no—
76C2×C4×C19—41no—
77C2×C4×C19—41no—
78C2×C4×C19—41no—
79C2×C4×C19C2×D411yescharacteristic
80C2×Dic19—21no—
81C2×Dic19—21no—
82C2×Dic19—21no—
83C2×Dic19—21no—
84C2×Dic19—41no—
85C2×Dic19—41no—
86Dic38—41no—
87Dic38—81no—
88C19⋊C8—41no—
89#2201—191nomaximal, Sylow
90C22×C19—21no—
91C22×C19—21no—
92C22×C19—41no—
93C22×C19—41no—
94C22×C19—41no—
95C22×C19—81no—
96C22×C19—81no—
97C22×C19#12011yescharacteristic
98C4×C19—21no—
99C4×C19—41no—
100C4×C19—41no—
101C4×C19—41no—
102C4×C19—81no—
103Dic19—41no—
104Dic19—41no—
105Dic19—41no—
106Dic19—41no—
107Dic19—81no—
108#563—191no—
109#458—191no—
110#458D1911yescharacteristic
111#455—191no—
112#354—191no—
113#352—191no—
114#352—191no—
115C2×C19—21no—
116C2×C19—41no—
117C2×C19—41no—
118C2×C19—81no—
119C2×C19B(4,𝔽2)11yescharacteristic
120H(5,𝔽2)C2×D1911yescharacteristic
121#137—381no—
122C4⋊Q8—381no—
123#126—381no—
124#126—381no—
125#125—381no—
126#124—191no—
127#123—21no—
128#123—191no—
129#123—381no—
130#123C2×D1911yescharacteristic
131C22⋊Q8—381no—
132C22⋊Q8—381no—
133#104—381no—
134#100—191no—
135#99—21no—
136#99—191no—
137#99—381no—
138#99C2×D1911yescharacteristic
139C19#220111yescharacteristic, complemented, Sylow
140#41—21no—
141#41—41no—
142C2×Q8—191no—
143C2×Q8—381no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—41no—
147C2×D4C22×D1911yescharacteristic
148C22×C4—191no—
149C22×C4C22⋊D1911yescharacteristic
150Q16—761no—
151SD16—761no—
152M16—381no—
153C4⋊C4—21no—
154C4⋊C4—41no—
155C4⋊C4—381no—
156C4⋊C4—381no—
157C4⋊C4—381no—
158C4⋊C4—381no—
159C4⋊C4—381no—
160C4⋊C4—381no—
161C4⋊C4—381no—
162C4⋊C4—761no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—41no—
166C22⋊C4—191no—
167C22⋊C4—381no—
168C22⋊C4—381no—
169C22⋊C4—381no—
170C22⋊C4—381no—
171C22⋊C4—761no—
172C22⋊C4C22⋊D1911yescharacteristic
173C42—191no—
174C42—381no—
175C23—21no—
176C23—21no—
177C23D4×D1911yescharacteristic
178C23C2×C22⋊D1911yescharacteristic
179Q8—21no—
180Q8—761no—
181Q8—1521no—
182D4—21no—
183D4—41no—
184D4—41no—
185D4—41no—
186D4—41no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—381no—
195C2×C4—381no—
196C2×C4—381no—
197C2×C4—381no—
198C2×C4—761no—
199C2×C4—761no—
200C2×C4D4×D1911yescharacteristic
201C8—761no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—81no—
208C22—81no—
209C22#1059738311yescharacteristic
210C4—21no—
211C4—41no—
212C4—41no—
213C4—41no—
214C4—81no—
215C4—761no—
216C4—761no—
217C4—761no—
218C4—761no—
219C4—1521no—
220C2—21no—
221C2—41no—
222C2—41no—
223C2—81no—
224C2#1192673011yescharacteristic
subgroupG/H
centerC2#11926730
commutator, cosocleC2×D4×C19C23
FrattiniC2×D4C22×D19
FittingC19×#458C2
socleC2×C19B(4,𝔽2)
prime radicalC19×H(5,𝔽2)C22
hypercenter#458D19
hypocenterC19#2201
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. #11927297C2semidirect
4. #11926338C2semidirect
5. #11926334C2semidirect
6. #11926333C2semidirect
139. C19#2201semidirect

Maximal subgroups

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

subgroupindex
#119272972
#119267342
#119267222
#119263382
#119263342
#119263332
C19×#4582
#220119