Finite Group Databasebeta

← #14572861

Subgroups — #14572861

Order 2432.

994 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 157 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×#10597395C212yesmaximal, complemented
3#11926694C214yesmaximal, complemented
4#11926677C214yesmaximal, complemented
5#11926548C212yesmaximal, complemented
6#11926508C211yesmaximal, characteristic, complemented
7C19×#525C211yesmaximal, characteristic, complemented
8C24×D19—21no—
9C2×#41×C19C2211yescharacteristic, complemented
10C23×C4×C19C2211yescharacteristic
11C22×D76—22no—
12C22×D76—21no—
13C22×D76—28no—
14C22×D76C2214yes—
15C22×D76C2212yes—
16C19×#123—21no—
17C19×C22⋊Q8C2212yescomplemented
18C19×#121C2212yescomplemented
19C19×#120—21no—
20C4×D4×C19—22no—
21C19×#117C2211yescharacteristic, complemented
22#10597395—28no—
23C2×#64527C2214yescomplemented
24C2×#64525C2214yescomplemented
25C2×#64520C2212yescomplemented
26C22⋊(C19⋊C8)C2214yescomplemented
27#10597266C2218yescomplemented
28C24×C19D411yescharacteristic
29C23×D19—28no—
30C23×D19—24no—
31C23×D19—22no—
32C23×D19—48no—
33#41×C19—24no—
34C2×Q8×C19C2311yescharacteristic, complemented
35C2×D4×C19—22no—
36C2×D4×C19—21no—
37C2×D4×C19C2311yescharacteristic, complemented
38C22×C4×C19—24no—
39C22×C4×C19—21no—
40C22×C4×C19D412yes—
41C22×C4×C19D411yescharacteristic
42C22×C4×C19C2312yes—
43C22×C4×C19C2311yescharacteristic
44C2×D76—28no—
45C2×D76—216no—
46C2×D76—24no—
47C2×D76—24no—
48C2×D76—22no—
49C2×D76—216no—
50C2×D76D418yescomplemented
51C2×D76C2314yes—
52C4⋊C4×C19—22no—
53C4⋊C4×C19C2312yescomplemented
54C22⋊C4×C19—21no—
55C22⋊C4×C19—22no—
56C22⋊C4×C19—22no—
57C42×C19—21no—
58#64527—28no—
59#64525—28no—
60#64520—24no—
61C2×C19⋊C8C2314yescomplemented
62C23×C19—22no—
63C23×C19—24no—
64C23×C19—21no—
65C23×C19C2×D411yescharacteristic
66C23×C19C2×D412yes—
67C22×D19—216no—
68C22×D19—28no—
69C22×D19—24no—
70C22×D19—432no—
71C22×D19—48no—
72C22×D19—48no—
73C22×D19—48no—
74Q8×C19—22no—
75D4×C19—22no—
76D4×C19—42no—
77D4×C19—44no—
78C2×C4×C19—22no—
79C2×C4×C19—24no—
80C2×C4×C19—24no—
81C2×C4×C19—22no—
82C2×C4×C19—21no—
83C2×C4×C19—42no—
84C2×C4×C19C2×D414yes—
85C2×C4×C19C2×D412yes—
86C2×C4×C19C2×D411yescharacteristic
87C2×C4×C19C2411yescharacteristic
88D76—216no—
89D76—28no—
90D76—24no—
91D76C2×D418yes—
92C19⋊C8—24no—
93#3003—191nomaximal, Sylow
94C22×C19—28no—
95C22×C19—22no—
96C22×C19—22no—
97C22×C19—22no—
98C22×C19—41no—
99C22×C19—42no—
100C22×C19#12012yes—
101C22×C19AGL(1,ℤ/8)14yescomplemented
102C22×C19C22×D411yescharacteristic
103C2×D19—28no—
104C2×D19—416no—
105C2×D19—432no—
106C2×D19—48no—
107C4×C19—22no—
108C4×C19—41no—
109C4×C19—42no—
110C4×C19#12012yes—
111C4×C19C22×D412yes—
112C23×D4—191no—
113C2×AGL(1,ℤ/8)—192no—
114#525D1911yescharacteristic, complemented
115#450—194no—
116#447—194no—
117#418—192no—
118#407—191no—
119C2×C19—22no—
120C2×C19—24no—
121C2×C19—81no—
122C2×C19C2×#12011yescharacteristic
123C2×C19C2×AGL(1,ℤ/8)12yes—
124D19—48no—
125C25—381no—
126C2×#41C2×D1911yescharacteristic, complemented
127C22×D4—192no—
128C22×D4—194no—
129C22×D4—388no—
130C22×D4—382no—
131C22×D4—381no—
132C23×C4C2×D1911yescharacteristic
133AGL(1,ℤ/8)—388no—
134C2×SD16—194no—
135C2×D8—194no—
136C2×M16—192no—
137#123—21no—
138C22⋊Q8C2×D1912yescomplemented
139#121C2×D1912yescomplemented
140#120—21no—
141C4×D4—22no—
142#117C2×D1911yescharacteristic, complemented
143#102—198no—
144C22⋊C8—194no—
145C19#300311yescharacteristic, complemented, Sylow
146C24—388no—
147C24—384no—
148C24—382no—
149C24—768no—
150C24C22⋊D1911yescharacteristic
151#41—24no—
152C2×Q8C22×D1911yescharacteristic, complemented
153C2×D4—22no—
154C2×D4—21no—
155C2×D4—198no—
156C2×D4—194no—
157C2×D4—3816no—
158C2×D4—388no—
159C2×D4—3816no—
160C2×D4—384no—
161C2×D4—384no—
162C2×D4—382no—
163C2×D4C22×D1911yescharacteristic, complemented
164C22×C4—24no—
165C22×C4—21no—
166C22×C4C22⋊D1912yes—
167C22×C4C22⋊D1911yescharacteristic
168C22×C4C22×D1912yes—
169C22×C4C22×D1911yescharacteristic
170SD16—388no—
171D8—388no—
172M16—384no—
173C2×C8—194no—
174C4⋊C4—22no—
175C4⋊C4C22×D1912yescomplemented
176C22⋊C4—21no—
177C22⋊C4—22no—
178C22⋊C4—22no—
179C42—21no—
180C23—22no—
181C23—24no—
182C23—21no—
183C23—3816no—
184C23—388no—
185C23—384no—
186C23—7632no—
187C23—768no—
188C23—768no—
189C23—768no—
190C23C2×C22⋊D1911yescharacteristic
191C23C2×C22⋊D1912yes—
192Q8—22no—
193D4—22no—
194D4—42no—
195D4—44no—
196D4—198no—
197D4—3816no—
198D4—388no—
199D4—384no—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—24no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—42no—
206C2×C4D4×D1914yes—
207C2×C4C2×C22⋊D1912yes—
208C2×C4C2×C22⋊D1911yescharacteristic
209C2×C4C23×D1911yescharacteristic
210C8—384no—
211C22—28no—
212C22—22no—
213C22—22no—
214C22—22no—
215C22—42no—
216C22—41no—
217C22—388no—
218C22—7616no—
219C22—7632no—
220C22—768no—
221C22#1059738312yes—
222C22#1059739514yescomplemented
223C22C22×C22⋊D1911yescharacteristic
224C4—22no—
225C4—42no—
226C4—41no—
227C4#1059738312yes—
228C4C2×D4×D1912yes—
229C2—22no—
230C2—24no—
231C2—81no—
232C2—768no—
233C2C2×#1059738311yescharacteristic
234C2C2×#1059739512yes—
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#525C2
socleC22×C19C22×D4
hypercenter#525D19
hypocenterC19#3003
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C23×D76C2semidirect
2. C2×#10597395C2semidirect
3. #11926694C2semidirect
4. #11926677C2semidirect
5. #11926548C2semidirect
6. #11926508C2semidirect
7. C19×#525C2semidirect
9. C2×#41×C19C22semidirect
17. C19×C22⋊Q8C22semidirect
18. C19×#121C22semidirect
21. C19×#117C22semidirect
23. C2×#64527C22semidirect
24. C2×#64525C22semidirect
25. C2×#64520C22semidirect
26. C22⋊(C19⋊C8)C22semidirect
27. #10597266C22semidirect
34. C2×Q8×C19C23semidirect
37. C2×D4×C19C23semidirect
50. C2×D76D4semidirect
53. C4⋊C4×C19C23semidirect
61. C2×C19⋊C8C23semidirect
101. C22×C19AGL(1,ℤ/8)semidirect
114. #525D19semidirect
126. C2×#41C2×D19semidirect
138. C22⋊Q8C2×D19semidirect
139. #121C2×D19semidirect
142. #117C2×D19semidirect
145. C19#3003semidirect
152. C2×Q8C22×D19semidirect
163. C2×D4C22×D19semidirect
175. C4⋊C4C22×D19semidirect
222. C22#10597395semidirect

Maximal subgroups

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

subgroupindex
C23×D762
C2×#105973952
#119266942
#119266772
#119265482
#119265082
C19×#5252
#300319