Finite Group Databasebeta

← #14565623

Subgroups — #14565623

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#11926734C211yesmaximal, characteristic, complemented
3#11926722C211yesmaximal, characteristic, complemented
4#11926338C211yesmaximal, characteristic, complemented
5#11926333C211yesmaximal, characteristic, complemented
6#11926331C211yesmaximal, characteristic, complemented
7C19×B(4,𝔽2)C211yesmaximal, characteristic
8C19×H(5,𝔽2)C2211yescharacteristic
9C19×#120—21no—
10C19×#120C2211yescharacteristic
11C2×C22⋊Dic19—21no—
12#10597397—21no—
13#10597382C2211yescharacteristic
14#10597381—21no—
15#10597381—21no—
16#10597381C2211yescharacteristic
17D4×Dic19—21no—
18#10597325—21no—
19#10597324—21no—
20#10597323—21no—
21C19×#99—21no—
22C19×#99C2211yescharacteristic
23#10597294—21no—
24#10597291—21no—
25#10597291C2211yescharacteristic
26#10597290C2211yescharacteristic
27C24×C19D411yescharacteristic
28#41×C19—21no—
29#41×C19—41no—
30C2×D4×C19—21no—
31C2×D4×C19—21no—
32C2×D4×C19—21no—
33C2×D4×C19—41no—
34C2×D4×C19—41no—
35C2×D4×C19C2311yescharacteristic
36C22×Dic19—21no—
37C22×Dic19—21no—
38C22×Dic19D411yescharacteristic, complemented
39C2×Dic38D411yescharacteristic, complemented
40C22⋊C4×C19—21no—
41C22⋊C4×C19—21no—
42C22⋊C4×C19—41no—
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#64528—41no—
53#64526—41no—
54C4⋊Dic19—21no—
55Dic19⋊C4—21no—
56Dic19⋊C4—21no—
57Dic19⋊C4—21no—
58Dic19⋊C4—41no—
59C4×Dic19—21no—
60C4×Dic19D411yescharacteristic, complemented
61#64520—21no—
62C23×C19—21no—
63C23×C19—21no—
64C23×C19—21no—
65C23×C19—41no—
66C23×C19—42no—
67C23×C19C2×D411yescharacteristic
68C23×C19C2×D411yescharacteristic
69Q8×C19—21no—
70D4×C19—21no—
71D4×C19—41no—
72D4×C19—42no—
73D4×C19—41no—
74D4×C19—41no—
75D4×C19—41no—
76D4×C19—82no—
77C2×C4×C19—21no—
78C2×C4×C19—21no—
79C2×C4×C19—21no—
80C2×C4×C19—41no—
81C2×C4×C19—41no—
82C2×C4×C19C2×D411yescharacteristic
83C2×Dic19—21no—
84C2×Dic19—21no—
85C2×Dic19—21no—
86C2×Dic19—21no—
87C2×Dic19—42no—
88C2×Dic19—41no—
89C2×Dic19—41no—
90C2×Dic19—81no—
91Dic38—41no—
92C19⋊C8—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—41no—
103C22×C19—81no—
104C22×C19—81no—
105C22×C19—81no—
106C22×C19#12011yescharacteristic
107C4×C19—21no—
108C4×C19—41no—
109C4×C19—41no—
110C4×C19—81no—
111Dic19—41no—
112Dic19—41no—
113Dic19—41no—
114Dic19—41no—
115Dic19—81no—
116#551—191no—
117#458—191no—
118B(4,𝔽2)D1911yescharacteristic
119#455—191no—
120#354—191no—
121#352—191no—
122AΣL(1,𝔽16)—191no—
123C2×C19—21no—
124C2×C19—41no—
125C2×C19—41no—
126C2×C19—42no—
127C2×C19—81no—
128C2×C19B(4,𝔽2)11yescharacteristic
129H(5,𝔽2)C2×D1911yescharacteristic
130#137—381no—
131#126—381no—
132#124—191no—
133#123—191no—
134#123—381no—
135#123—381no—
136C22⋊Q8—381no—
137#120—21no—
138#120C2×D1911yescharacteristic
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
149C24C22⋊D1911yescharacteristic
150#41—21no—
151#41—41no—
152C2×Q8—191no—
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—21no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4C22×D1911yescharacteristic
159C22×C4—191no—
160C22×C4—381no—
161C22×C4—381no—
162Q16—761no—
163SD16—761no—
164M16—381no—
165C4⋊C4—381no—
166C4⋊C4—381no—
167C4⋊C4—381no—
168C4⋊C4—381no—
169C4⋊C4—761no—
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
182C42—191no—
183C42—381no—
184C23—21no—
185C23—21no—
186C23—21no—
187C23—41no—
188C23—42no—
189C23D4×D1911yescharacteristic
190C23C2×C22⋊D1911yescharacteristic
191Q8—21no—
192Q8—761no—
193D4—21no—
194D4—41no—
195D4—41no—
196D4—41no—
197D4—42no—
198D4—41no—
199D4—82no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—381no—
206C2×C4—381no—
207C2×C4—381no—
208C2×C4—381no—
209C2×C4—762no—
210C2×C4—761no—
211C2×C4—761no—
212C2×C4—1521no—
213C2×C4D4×D1911yescharacteristic
214C8—761no—
215C22—22no—
216C22—21no—
217C22—21no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—42no—
222C22—41no—
223C22—41no—
224C22—81no—
225C22—81no—
226C22—81no—
227C22#1059738311yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—81no—
232C4—761no—
233C4—761no—
234C4—761no—
235C4—761no—
236C4—1521no—
237C2—21no—
238C2—41no—
239C2—41no—
240C2—42no—
241C2—81no—
242C2#1192673011yescharacteristic
subgroupG/H
centerC2#11926730
commutator, cosocleC2×D4×C19C23
FrattiniC2×D4C22×D19
Fitting, prime radicalC19×B(4,𝔽2)C2
socleC2×C19B(4,𝔽2)
hypercenterB(4,𝔽2)D19
hypocenterC19#2197
LCSG ▷ C2×D4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ B(4,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #11927225C2semidirect
2. #11926734C2semidirect
3. #11926722C2semidirect
4. #11926338C2semidirect
5. #11926333C2semidirect
6. #11926331C2semidirect
38. C22×Dic19D4semidirect
39. C2×Dic38D4semidirect
51. C22⋊Dic19D4semidirect
60. C4×Dic19D4semidirect
148. C19#2197semidirect

Maximal subgroups

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

subgroupindex
#119272252
#119267342
#119267222
#119263382
#119263332
#119263312
C19×B(4,𝔽2)2
#219719