Finite Group Databasebeta

← #14566962

Subgroups — #14566962

Order 2432.

1116 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C23×C22⋊D19C211yesmaximal, characteristic
2C2×#10597375C212yesmaximal, complemented
3#11926459C214yesmaximal, complemented
4#11926423C212yesmaximal, complemented
5#11926416C212yesmaximal, complemented
6#11926400C211yesmaximal, characteristic, complemented
7#11926399C212yesmaximal, complemented
8C22×C22⋊C4×C19C211yesmaximal, characteristic, complemented
9C25×C19C2211yescharacteristic
10C24×D19C2211yescharacteristic
11C23×C4×C19C2211yescharacteristic, complemented
12C23×C4×C19C2211yescharacteristic, complemented
13C22×C22⋊D19—24no—
14C22×C22⋊D19—28no—
15C22×C22⋊D19C2212yes—
16C22×C22⋊D19C2212yes—
17C23×Dic19C2211yescharacteristic
18C2×C22⋊C4×C19—24no—
19C2×C22⋊C4×C19C2212yes—
20C2×C22⋊C4×C19C2212yescomplemented
21C2×C22⋊Dic19C2212yes—
22C2×C22⋊Dic19C2212yescomplemented
23C2×C22⋊Dic19C2212yescomplemented
24#10597375—28no—
25C2×(C2×D19)⋊C4C2214yescomplemented
26C2×(C2×D19)⋊C4C2214yescomplemented
27C2×Dic19⋊C4C2214yescomplemented
28C19⋊#95C2214yescomplemented
29C24×C19—24no—
30C24×C19—24no—
31C24×C19—42no—
32C24×C19D414yes—
33C24×C19C2311yescharacteristic
34C24×C19C2311yescharacteristic
35C24×C19C2311yescharacteristic
36C23×D19—22no—
37C23×D19—24no—
38C23×D19—24no—
39C23×D19—42no—
40C23×D19C2312yes—
41C22×C4×C19—22no—
42C22×C4×C19—22no—
43C22×C4×C19—24no—
44C22×C4×C19—42no—
45C22×C4×C19C2312yes—
46C22×C4×C19C2312yes—
47C2×C22⋊D19—232no—
48C2×C22⋊D19—24no—
49C2×C22⋊D19—24no—
50C2×C22⋊D19—24no—
51C2×C22⋊D19—24no—
52C2×C22⋊D19—24no—
53C2×C22⋊D19D418yes—
54C22×Dic19—22no—
55C22×Dic19—24no—
56C22×Dic19C2314yes—
57C22×Dic19C2312yes—
58C22⋊C4×C19—24no—
59C22⋊C4×C19—24no—
60C22⋊Dic19—24no—
61C22⋊Dic19—24no—
62C22⋊Dic19—42no—
63(C2×D19)⋊C4—28no—
64(C2×D19)⋊C4—44no—
65Dic19⋊C4—28no—
66C23×C19—22no—
67C23×C19—22no—
68C23×C19—22no—
69C23×C19—22no—
70C23×C19—28no—
71C23×C19—28no—
72C23×C19—22no—
73C23×C19—22no—
74C23×C19—22no—
75C23×C19—44no—
76C23×C19—416no—
77C23×C19C2×D414yes—
78C23×C19C2×D412yes—
79C23×C19C2×D412yes—
80C23×C19C2×D412yes—
81C23×C19#4114yes—
82C23×C19C2411yescharacteristic
83C22×D19—28no—
84C22×D19—22no—
85C22×D19—22no—
86C22×D19—24no—
87C22×D19—24no—
88C22×D19—416no—
89C22×D19—44no—
90C22×D19—44no—
91C22×D19C2×D414yes—
92C2×C4×C19—24no—
93C2×C4×C19—22no—
94C2×C4×C19—22no—
95C2×C4×C19—24no—
96C2×C4×C19—44no—
97C2×C4×C19—44no—
98C22⋊D19—216no—
99C22⋊D19—216no—
100C2×Dic19—28no—
101C2×Dic19—22no—
102C2×Dic19—22no—
103C2×Dic19—24no—
104C2×Dic19—24no—
105C2×Dic19—24no—
106C2×Dic19C2×D414yes—
107#2405—191nomaximal, Sylow
108C22×C19—22no—
109C22×C19—22no—
110C22×C19—22no—
111C22×C19—22no—
112C22×C19—28no—
113C22×C19—28no—
114C22×C19—22no—
115C22×C19—22no—
116C22×C19—22no—
117C22×C19—416no—
118C22×C19—44no—
119C22×C19#12014yes—
120C22×C19#12314yescomplemented
121C22×C19C22×D412yes—
122C22×C19C22×D411yescharacteristic
123C22×C19C2×#4112yes—
124C22×C19H(5,𝔽2)12yes—
125C2×D19—24no—
126C2×D19—28no—
127C2×D19—416no—
128C2×D19—42no—
129C2×D19—42no—
130C2×D19—44no—
131C4×C19—42no—
132C4×C19—42no—
133Dic19—24no—
134Dic19—44no—
135C23×D4—191no—
136C2×#123—192no—
137C22×C22⋊C4D1911yescharacteristic, complemented
138#394—194no—
139#386—192no—
140#385—192no—
141#379—191no—
142#379—192no—
143C2×C19—24no—
144C2×C19—24no—
145C2×C19—42no—
146C2×C19C2×#12011yescharacteristic
147C2×C19C2×#12311yescharacteristic
148C2×C19#53411yescharacteristic
149C2×C19#54614yes—
150D19—44no—
151C25—191no—
152C25C2×D1911yescharacteristic
153C22×D4—192no—
154C22×D4—192no—
155C22×D4—388no—
156C22×D4—384no—
157C23×C4—191no—
158C23×C4C2×D1911yescharacteristic, complemented
159C23×C4C2×D1911yescharacteristic, complemented
160#123—388no—
161C2×C4⋊C4—194no—
162C2×C22⋊C4—24no—
163C2×C22⋊C4—192no—
164C2×C22⋊C4—192no—
165C2×C22⋊C4—194no—
166C2×C22⋊C4—192no—
167C2×C22⋊C4—194no—
168C2×C22⋊C4C2×D1912yes—
169C2×C22⋊C4C2×D1912yescomplemented
170#95—194no—
171C19#240511yescharacteristic, complemented, Sylow
172C24—24no—
173C24—24no—
174C24—42no—
175C24—192no—
176C24—384no—
177C24—382no—
178C24—384no—
179C24—762no—
180C24C22⋊D1914yes—
181C24C22×D1911yescharacteristic
182C24C22×D1911yescharacteristic
183C24C22×D1911yescharacteristic
184C2×D4—198no—
185C2×D4—384no—
186C2×D4—384no—
187C2×D4—3832no—
188C2×D4—384no—
189C2×D4—384no—
190C2×D4—384no—
191C22×C4—24no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—42no—
195C22×C4—192no—
196C22×C4—194no—
197C22×C4—384no—
198C22×C4—382no—
199C22×C4C22×D1912yes—
200C22×C4C22×D1912yes—
201C4⋊C4—388no—
202C22⋊C4—24no—
203C22⋊C4—24no—
204C22⋊C4—388no—
205C22⋊C4—384no—
206C22⋊C4—384no—
207C22⋊C4—764no—
208C22⋊C4—762no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—28no—
214C23—22no—
215C23—22no—
216C23—22no—
217C23—28no—
218C23—44no—
219C23—416no—
220C23—194no—
221C23—388no—
222C23—384no—
223C23—382no—
224C23—384no—
225C23—382no—
226C23—7616no—
227C23—764no—
228C23—764no—
229C23#6454114yes—
230C23D4×D1914yes—
231C23C2×C22⋊D1912yes—
232C23C2×C22⋊D1912yes—
233C23C2×C22⋊D1912yes—
234C23C23×D1911yescharacteristic
235D4—3816no—
236D4—3816no—
237C2×C4—24no—
238C2×C4—24no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—44no—
242C2×C4—44no—
243C2×C4—194no—
244C2×C4—388no—
245C2×C4—382no—
246C2×C4—382no—
247C2×C4—384no—
248C2×C4—384no—
249C2×C4—384no—
250C22—22no—
251C22—22no—
252C22—22no—
253C22—28no—
254C22—28no—
255C22—22no—
256C22—22no—
257C22—22no—
258C22—22no—
259C22—416no—
260C22—44no—
261C22—388no—
262C22—384no—
263C22—7616no—
264C22—762no—
265C22—762no—
266C22—764no—
267C22#1059737514yescomplemented
268C22#1059738314yes—
269C22C2×#6454112yes—
270C22C2×D4×D1912yes—
271C22#1059743012yes—
272C22C22×C22⋊D1911yescharacteristic
273C4—42no—
274C4—42no—
275C4—384no—
276C4—764no—
277C2—24no—
278C2—24no—
279C2—42no—
280C2—764no—
281C2C2×#1059738311yescharacteristic
282C2C2×#1059737511yescharacteristic
283C2#1192710311yescharacteristic
284C2#1192718414yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC22×C22⋊C4×C19C2
prime radicalC23×C22⋊D19C2
hypercenterC22×C22⋊C4D19
hypocenterC19#2405
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10597375C2semidirect
3. #11926459C2semidirect
4. #11926423C2semidirect
5. #11926416C2semidirect
6. #11926400C2semidirect
7. #11926399C2semidirect
8. C22×C22⋊C4×C19C2semidirect
11. C23×C4×C19C22semidirect
12. C23×C4×C19C22semidirect
20. C2×C22⋊C4×C19C22semidirect
22. C2×C22⋊Dic19C22semidirect
23. C2×C22⋊Dic19C22semidirect
25. C2×(C2×D19)⋊C4C22semidirect
26. C2×(C2×D19)⋊C4C22semidirect
27. C2×Dic19⋊C4C22semidirect
28. C19⋊#95C22semidirect
120. C22×C19#123semidirect
137. C22×C22⋊C4D19semidirect
158. C23×C4C2×D19semidirect
159. C23×C4C2×D19semidirect
169. C2×C22⋊C4C2×D19semidirect
171. C19#2405semidirect
267. C22#10597375semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊D192
C2×#105973752
#119264592
#119264232
#119264162
#119264002
#119263992
C22×C22⋊C4×C192
#240519