Finite Group Databasebeta

← #14571928

Subgroups — #14571928

Order 2432.

1102 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1102 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×C4×D19C211yesmaximal, characteristic, complemented
2C2×#10597332C211yesmaximal, characteristic, complemented
3C2×#10597375C211yesmaximal, characteristic, complemented
4C2×#10597328C211yesmaximal, characteristic
5#11926422C214yesmaximal, complemented
6#11926418C214yesmaximal, complemented
7#11926405C211yesmaximal, characteristic, complemented
8#11926399C211yesmaximal, characteristic, complemented
9C19×#381C211yesmaximal, characteristic, complemented
10C24×D19C2211yescharacteristic
11C23×C4×C19C2211yescharacteristic
12C22×C22⋊D19C2211yescharacteristic
13C23×Dic19C2211yescharacteristic
14C22×D76C2212yes—
15C22×C4×D19—24no—
16C22×C4×D19—24no—
17C22×C4×D19—24no—
18C22×C4×D19C2214yes—
19C2×C22⋊C4×C19C2211yescharacteristic
20C2×C22⋊C4×C19C2211yescharacteristic
21C2×C22⋊Dic19C2211yescharacteristic
22#10597375—24no—
23C2×(C2×D19)⋊C4C2214yes—
24C2×(C2×D19)⋊C4C2212yes—
25C2×(C2×D19)⋊C4C2212yescomplemented
26C2×(C2×D19)⋊C4C2212yescomplemented
27C2×C4⋊Dic19C2212yescomplemented
28C2×Dic19⋊C4C2212yescomplemented
29#10597332—24no—
30#10597328—24no—
31C19×#95C2214yescomplemented
32C19⋊#95C2214yescomplemented
33C24×C19C2311yescharacteristic
34C23×D19—22no—
35C23×D19—22no—
36C23×D19—28no—
37C23×D19D414yes—
38C23×D19C2311yescharacteristic
39C23×D19C2312yes—
40C22×C4×C19—22no—
41C22×C4×C19—22no—
42C22×C4×C19D414yescomplemented
43C22×C4×C19C2312yes—
44C22×C4×C19C2312yes—
45C22×C4×C19C2312yes—
46C2×C22⋊D19—22no—
47C2×C22⋊D19—22no—
48C2×C22⋊D19—22no—
49C22×Dic19—22no—
50C22×Dic19—22no—
51C22×Dic19D414yescomplemented
52C22×Dic19C2312yes—
53C22×Dic19C2311yescharacteristic
54C22×Dic19C2312yes—
55C2×D76—24no—
56C2×D76—28no—
57C2×C4×D19—232no—
58C2×C4×D19—28no—
59C2×C4×D19—28no—
60C2×C4×D19—28no—
61C22⋊C4×C19—22no—
62C22⋊C4×C19—22no—
63C22⋊Dic19—22no—
64(C2×D19)⋊C4—24no—
65(C2×D19)⋊C4—28no—
66(C2×D19)⋊C4—24no—
67(C2×D19)⋊C4—24no—
68C4⋊Dic19—24no—
69Dic19⋊C4—24no—
70C23×C19—24no—
71C23×C19C2×D412yes—
72C23×C19C2×D412yes—
73C23×C19C2×D412yes—
74C23×C19C2411yescharacteristic
75C22×D19—216no—
76C22×D19—216no—
77C22×D19—28no—
78C22×D19—22no—
79C22×D19—22no—
80C22×D19—24no—
81C22×D19—216no—
82C22×D19—21no—
83C22×D19—21no—
84C22×D19—21no—
85C22×D19—24no—
86C22×D19C2×D414yes—
87C22×D19#4118yes—
88C2×C4×C19—28no—
89C2×C4×C19—22no—
90C2×C4×C19—22no—
91C2×C4×C19—22no—
92C2×C4×C19—22no—
93C2×C4×C19—24no—
94C2×C4×C19—24no—
95C2×C4×C19C2×D414yes—
96C22⋊D19—44no—
97C2×Dic19—28no—
98C2×Dic19—22no—
99C2×Dic19—22no—
100C2×Dic19—21no—
101C2×Dic19—22no—
102C2×Dic19—21no—
103C2×Dic19—21no—
104C2×Dic19—24no—
105C2×Dic19C2×D414yes—
106D76—48no—
107C4×D19—232no—
108#2849—191nomaximal, Sylow
109C22×C19—24no—
110C22×C19—24no—
111C22×C19—24no—
112C22×C19#12014yes—
113C22×C19C22×D411yescharacteristic
114C22×C19C22×D411yescharacteristic
115C22×C19C22×D411yescharacteristic
116C22×C19C2×#4114yes—
117C2×D19—232no—
118C2×D19—24no—
119C2×D19—24no—
120C2×D19—28no—
121C2×D19—28no—
122C2×D19—41no—
123C2×D19—42no—
124C2×D19—42no—
125C2×D19—42no—
126C2×D19#12318yescomplemented
127C4×C19—24no—
128C4×C19—42no—
129C4×C19—42no—
130Dic19—24no—
131Dic19—41no—
132Dic19—42no—
133C24×C4—191no—
134C2×#123—191no—
135C2×#123—191no—
136C2×#120—191no—
137#386—194no—
138#385—194no—
139#381—191no—
140#381D1911yescharacteristic, complemented
141#379—191no—
142C2×C19—24no—
143C2×C19C2×#12011yescharacteristic
144C2×C19C2×#12312yes—
145C2×C19#52512yes—
146C2×C19#52512yes—
147D19—28no—
148D19—81no—
149C25—191no—
150C22×D4—191no—
151C22×D4—192no—
152C23×C4—191no—
153C23×C4—194no—
154C23×C4—384no—
155C23×C4—384no—
156C23×C4—384no—
157C23×C4C2×D1911yescharacteristic
158#123—384no—
159#123—384no—
160#120—384no—
161C2×C4⋊C4—192no—
162C2×C4⋊C4—192no—
163C2×C22⋊C4—191no—
164C2×C22⋊C4—192no—
165C2×C22⋊C4—192no—
166C2×C22⋊C4—192no—
167C2×C22⋊C4—194no—
168C2×C22⋊C4C2×D1911yescharacteristic
169C2×C22⋊C4C2×D1911yescharacteristic
170#95—194no—
171#95C2×D1914yescomplemented
172C19#284911yescharacteristic, complemented, Sylow
173C24—192no—
174C24—194no—
175C24—191no—
176C24—388no—
177C24—382no—
178C24—382no—
179C24C22×D1911yescharacteristic
180C2×D4—384no—
181C2×D4—388no—
182C2×D4—382no—
183C2×D4—382no—
184C2×D4—382no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—194no—
188C22×C4—192no—
189C22×C4—192no—
190C22×C4—191no—
191C22×C4—388no—
192C22×C4—388no—
193C22×C4—3832no—
194C22×C4—382no—
195C22×C4—382no—
196C22×C4—388no—
197C22×C4D7614yescomplemented
198C22×C4C22×D1912yes—
199C22×C4C22×D1912yes—
200C22×C4C22×D1912yes—
201C4⋊C4—384no—
202C4⋊C4—384no—
203C22⋊C4—22no—
204C22⋊C4—22no—
205C22⋊C4—384no—
206C22⋊C4—388no—
207C22⋊C4—384no—
208C22⋊C4—382no—
209C22⋊C4—384no—
210C23—24no—
211C23—194no—
212C23—198no—
213C23—3816no—
214C23—3816no—
215C23—3816no—
216C23—382no—
217C23—382no—
218C23—384no—
219C23—388no—
220C23—381no—
221C23—381no—
222C23—381no—
223C23—384no—
224C23C2×D7612yes—
225C23D4×D1912yes—
226C23D4×D1912yes—
227C23C23×D1911yescharacteristic
228D4—768no—
229D4—764no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—28no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—24no—
236C2×C4—24no—
237C2×C4—194no—
238C2×C4—3832no—
239C2×C4—382no—
240C2×C4—382no—
241C2×C4—388no—
242C2×C4—382no—
243C2×C4—381no—
244C2×C4—381no—
245C2×C4—381no—
246C2×C4—384no—
247C2×C4C2×D7614yes—
248C22—24no—
249C22—24no—
250C22—24no—
251C22—198no—
252C22—3832no—
253C22—384no—
254C22—388no—
255C22—388no—
256C22—384no—
257C22—762no—
258C22—762no—
259C22—762no—
260C22—761no—
261C22#1059732814yes—
262C22C22×D7611yescharacteristic
263C22C2×D4×D1911yescharacteristic
264C22C2×D4×D1911yescharacteristic
265C22#41×D1914yes—
266C4—24no—
267C4—42no—
268C4—42no—
269C4—384no—
270C4—762no—
271C4—761no—
272C2—24no—
273C2—388no—
274C2—1521no—
275C2C2×#1059732811yescharacteristic
276C2#123×D1912yes—
277C2#1192705212yes—
278C2#1192705612yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#381C2
prime radicalC2×#10597328C2
hypercenter#381D19
hypocenterC19#2849
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C23×C4×D19C2semidirect
2. C2×#10597332C2semidirect
3. C2×#10597375C2semidirect
5. #11926422C2semidirect
6. #11926418C2semidirect
7. #11926405C2semidirect
8. #11926399C2semidirect
9. C19×#381C2semidirect
25. C2×(C2×D19)⋊C4C22semidirect
26. C2×(C2×D19)⋊C4C22semidirect
27. C2×C4⋊Dic19C22semidirect
28. C2×Dic19⋊C4C22semidirect
31. C19×#95C22semidirect
32. C19⋊#95C22semidirect
42. C22×C4×C19D4semidirect
51. C22×Dic19D4semidirect
126. C2×D19#123semidirect
140. #381D19semidirect
171. #95C2×D19semidirect
172. C19#2849semidirect
197. C22×C4D76semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D192
C2×#105973322
C2×#105973752
C2×#105973282
#119264222
#119264182
#119264052
#119263992
C19×#3812
#284919