Finite Group Databasebeta

← #14567273

Subgroups — #14567273

Order 2432.

1348 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 197 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×D76C211yesmaximal, characteristic, complemented
2C2×#10597386C212yesmaximal, complemented
3C2×#10597383C214yesmaximal, complemented
4#11926453C214yesmaximal, complemented
5#11926445C212yesmaximal, complemented
6C4×C22⋊Dic19C211yesmaximal, characteristic, complemented
7C2×C19×#121C211yesmaximal, characteristic, complemented
8C24×D19C2212yes—
9C22×D4×C19C2212yes—
10C22×D4×C19C2211yescharacteristic, complemented
11C23×C4×C19C2211yescharacteristic
12C22×C22⋊D19C2218yescomplemented
13C22×D76—24no—
14C22×D76—28no—
15C22×D76C2212yes—
16C22×D76C2212yes—
17C19×#121—24no—
18C2×C4⋊C4×C19C2211yescharacteristic, complemented
19C2×C22⋊C4×C19C2212yescomplemented
20C2×C22⋊Dic19C2212yes—
21#10597386—28no—
22#10597383—216no—
23C2×(C2×D19)⋊C4C2218yescomplemented
24C2×C4×Dic19C2212yescomplemented
25C19⋊#95C2212yescomplemented
26C24×C19C2312yes—
27C24×C19C2311yescharacteristic
28C23×D19—24no—
29C23×D19—28no—
30C23×D19—28no—
31C23×D19—44no—
32C23×D19C2314yes—
33C2×D4×C19—28no—
34C2×D4×C19—24no—
35C2×D4×C19—24no—
36C2×D4×C19—22no—
37C22×C4×C19—24no—
38C22×C4×C19D414yescomplemented
39C22×C4×C19C2312yes—
40C22×C4×C19C2311yescharacteristic
41C22×C4×C19C2311yescharacteristic
42C2×C22⋊D19—216no—
43C2×C22⋊D19—216no—
44C2×C22⋊D19—48no—
45C22×Dic19C2314yes—
46C2×D76—232no—
47C2×D76—28no—
48C2×D76—24no—
49C2×D76—24no—
50C2×D76—24no—
51C2×D76D418yescomplemented
52C4⋊C4×C19—22no—
53C22⋊C4×C19—24no—
54C22⋊Dic19D418yescomplemented
55(C2×D19)⋊C4—216no—
56C4×Dic19—24no—
57C23×C19—22no—
58C23×C19—22no—
59C23×C19—22no—
60C23×C19—24no—
61C23×C19—24no—
62C23×C19—24no—
63C23×C19C2×D414yes—
64C23×C19C2×D412yes—
65C23×C19C2411yescharacteristic
66C22×D19—216no—
67C22×D19—28no—
68C22×D19—24no—
69C22×D19—24no—
70C22×D19—28no—
71C22×D19—432no—
72C22×D19—48no—
73C22×D19—48no—
74C22×D19C2×D418yes—
75D4×C19—48no—
76D4×C19—44no—
77C2×C4×C19—22no—
78C2×C4×C19—28no—
79C2×C4×C19—24no—
80C2×C4×C19—22no—
81C2×C4×C19C2×D414yes—
82C2×C4×C19C2×D412yes—
83C2×C4×C19C2×D412yes—
84C22⋊D19—432no—
85C2×Dic19—24no—
86C2×Dic19—24no—
87C2×Dic19C2×D418yescomplemented
88D76—216no—
89D76—216no—
90#2433—191nomaximal, Sylow
91C22×C19—22no—
92C22×C19—22no—
93C22×C19—28no—
94C22×C19—42no—
95C22×C19—42no—
96C22×C19—42no—
97C22×C19—48no—
98C22×C19#12714yescomplemented
99C22×C19C22×D412yes—
100C22×C19C22×D412yes—
101C22×C19C22×D411yescharacteristic
102C22×C19H(5,𝔽2)12yes—
103C2×D19—28no—
104C2×D19—216no—
105C2×D19—432no—
106C2×D19—44no—
107C2×D19—44no—
108C2×D19—48no—
109C4×C19—22no—
110C4×C19—42no—
111C4×C19#12014yescomplemented
112Dic19—28no—
113C23×D4—191no—
114C2×#127—192no—
115C2×#121D1911yescharacteristic, complemented
116C2×#120—194no—
117#392—194no—
118#390—192no—
119C4×C22⋊C4—191no—
120C2×C19—24no—
121C2×C19—82no—
122C2×C19C2×#12011yescharacteristic
123C2×C19C2×#12711yescharacteristic
124C2×C19#53511yescharacteristic
125C2×C19D4214yes—
126D19—48no—
127C25—192no—
128C22×D4—198no—
129C22×D4—192no—
130C22×D4—192no—
131C22×D4—388no—
132C22×D4—384no—
133C22×D4C2×D1912yes—
134C22×D4C2×D1911yescharacteristic, complemented
135C23×C4C2×D1911yescharacteristic
136#127—388no—
137#121—24no—
138#120—3816no—
139C2×C4⋊C4C2×D1911yescharacteristic, complemented
140C2×C22⋊C4—192no—
141C2×C22⋊C4—198no—
142C2×C22⋊C4C2×D1912yescomplemented
143C2×C42—192no—
144#95—192no—
145C19#243311yescharacteristic, complemented, Sylow
146C24—194no—
147C24—388no—
148C24—384no—
149C24—388no—
150C24—764no—
151C24C22×D1912yes—
152C24C22×D1911yescharacteristic
153C2×D4—28no—
154C2×D4—24no—
155C2×D4—24no—
156C2×D4—22no—
157C2×D4—198no—
158C2×D4—388no—
159C2×D4—3832no—
160C2×D4—3816no—
161C2×D4—3816no—
162C2×D4—384no—
163C2×D4—384no—
164C2×D4—384no—
165C2×D4—768no—
166C22×C4—24no—
167C22×C4—194no—
168C22×C4C22⋊D1914yescomplemented
169C22×C4C22×D1912yes—
170C22×C4C22×D1911yescharacteristic
171C22×C4C22×D1911yescharacteristic
172C4⋊C4—22no—
173C22⋊C4—24no—
174C22⋊C4—198no—
175C22⋊C4—3816no—
176C42—384no—
177C23—22no—
178C23—22no—
179C23—24no—
180C23—24no—
181C23—24no—
182C23—22no—
183C23—198no—
184C23—3816no—
185C23—388no—
186C23—384no—
187C23—388no—
188C23—384no—
189C23—7632no—
190C23—768no—
191C23—768no—
192C23D4×D1914yes—
193C23C2×C22⋊D1912yes—
194C23C23×D1911yescharacteristic
195D4—48no—
196D4—44no—
197D4—3816no—
198D4—3816no—
199D4—7632no—
200C2×C4—22no—
201C2×C4—28no—
202C2×C4—24no—
203C2×C4—22no—
204C2×C4—198no—
205C2×C4—384no—
206C2×C4—384no—
207C2×C4D4×D1914yes—
208C2×C4C2×C22⋊D1912yes—
209C2×C4C2×C22⋊D1912yes—
210C22—22no—
211C22—28no—
212C22—22no—
213C22—42no—
214C22—42no—
215C22—48no—
216C22—42no—
217C22—3816no—
218C22—388no—
219C22—7632no—
220C22—764no—
221C22—764no—
222C22—768no—
223C22#1059738614yescomplemented
224C22C2×D4×D1912yes—
225C22C2×D4×D1912yes—
226C22#1059743512yes—
227C22C22×C22⋊D1911yescharacteristic
228C4—22no—
229C4—42no—
230C4—388no—
231C4#1059738314yescomplemented
232C2—24no—
233C2—82no—
234C2—768no—
235C2C2×#1059738311yescharacteristic
236C2C2×#1059738611yescharacteristic
237C2#1192710811yescharacteristic
238C2#1192717814yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#121C2
hypercenterC2×#121D19
hypocenterC19#2433
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C23×D76C2semidirect
2. C2×#10597386C2semidirect
3. C2×#10597383C2semidirect
4. #11926453C2semidirect
5. #11926445C2semidirect
6. C4×C22⋊Dic19C2semidirect
7. C2×C19×#121C2semidirect
10. C22×D4×C19C22semidirect
12. C22×C22⋊D19C22semidirect
18. C2×C4⋊C4×C19C22semidirect
19. C2×C22⋊C4×C19C22semidirect
23. C2×(C2×D19)⋊C4C22semidirect
24. C2×C4×Dic19C22semidirect
25. C19⋊#95C22semidirect
38. C22×C4×C19D4semidirect
51. C2×D76D4semidirect
54. C22⋊Dic19D4semidirect
87. C2×Dic19C2×D4semidirect
98. C22×C19#127semidirect
111. C4×C19#120semidirect
115. C2×#121D19semidirect
134. C22×D4C2×D19semidirect
139. C2×C4⋊C4C2×D19semidirect
142. C2×C22⋊C4C2×D19semidirect
145. C19#2433semidirect
168. C22×C4C22⋊D19semidirect
223. C22#10597386semidirect
231. C4#10597383semidirect

Maximal subgroups

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

subgroupindex
C23×D762
C2×#105973862
C2×#105973832
#119264532
#119264452
C4×C22⋊Dic192
C2×C19×#1212
#243319