Finite Group Databasebeta

← #14572862

Subgroups — #14572862

Order 2432.

994 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C2×#10597378C212yesmaximal, complemented
2#11927055C211yesmaximal, characteristic, complemented
3#11926695C214yesmaximal, complemented
4#11926678C214yesmaximal, complemented
5#11926549C212yesmaximal, complemented
6#11926508C211yesmaximal, characteristic, complemented
7C23×D4×C19C211yesmaximal, characteristic, complemented
8C25×C19—21no—
9C22×D4×C19—28no—
10C22×D4×C19—22no—
11C22×D4×C19—21no—
12C22×D4×C19C2214yes—
13C22×D4×C19C2212yes—
14C23×C4×C19C2211yescharacteristic
15C2×#64541C2211yescharacteristic, complemented
16#10597399—21no—
17C2×#64526C2214yescomplemented
18#10597378—28no—
19C2×#64525C2214yescomplemented
20#10597376C2212yescomplemented
21#10597375—21no—
22C4×C22⋊D19—22no—
23#10597372C2211yescharacteristic, complemented
24#10597370C2212yescomplemented
25C2×#64520C2212yescomplemented
26#10597289C2218yescomplemented
27C22⋊(C19⋊C8)C2214yescomplemented
28C24×C19—28no—
29C24×C19—24no—
30C24×C19—22no—
31C24×C19—48no—
32C24×C19D411yescharacteristic
33C2×D4×C19—28no—
34C2×D4×C19—216no—
35C2×D4×C19—216no—
36C2×D4×C19—24no—
37C2×D4×C19—22no—
38C2×D4×C19—24no—
39C2×D4×C19D418yescomplemented
40C2×D4×C19C2314yes—
41C22×C4×C19—24no—
42C22×C4×C19D412yes—
43C22×C4×C19D411yescharacteristic
44C22×C4×C19C2312yes—
45C22×C4×C19C2311yescharacteristic
46C2×C22⋊D19—22no—
47C2×C22⋊D19—21no—
48#64541—24no—
49C2×D76C2311yescharacteristic, complemented
50C2×C4×D19—21no—
51C2×Dic38C2311yescharacteristic, complemented
52C22⋊Dic19—22no—
53C22⋊Dic19—21no—
54#64526—28no—
55#64525—28no—
56(C2×D19)⋊C4—22no—
57C4⋊Dic19C2312yescomplemented
58Dic19⋊C4—22no—
59C4×Dic19—21no—
60#64520—24no—
61C2×C19⋊C8C2314yescomplemented
62C23×C19—22no—
63C23×C19—24no—
64C23×C19—216no—
65C23×C19—28no—
66C23×C19—24no—
67C23×C19—432no—
68C23×C19—48no—
69C23×C19—48no—
70C23×C19—48no—
71C23×C19C2×D411yescharacteristic
72C23×C19C2×D412yes—
73C22×D19—21no—
74D4×C19—216no—
75D4×C19—28no—
76D4×C19—24no—
77D4×C19C2×D418yes—
78C2×C4×C19—22no—
79C2×C4×C19—24no—
80C2×C4×C19—24no—
81C2×C4×C19C2×D412yes—
82C2×C4×C19C2×D411yescharacteristic
83C2×C4×C19C2×D414yes—
84C2×C4×C19C2411yescharacteristic
85C22⋊D19—42no—
86C22⋊D19—44no—
87C2×Dic19—22no—
88C2×Dic19—21no—
89D76—22no—
90C4×D19—42no—
91Dic38—22no—
92C19⋊C8—24no—
93#3003—191nomaximal, Sylow
94C22×C19—28no—
95C22×C19—22no—
96C22×C19—22no—
97C22×C19—22no—
98C22×C19—28no—
99C22×C19—416no—
100C22×C19—432no—
101C22×C19—48no—
102C22×C19#12012yes—
103C22×C19AGL(1,ℤ/8)14yescomplemented
104C22×C19C22×D411yescharacteristic
105C2×D19—41no—
106C2×D19—42no—
107C4×C19—22no—
108C4×C19#12012yes—
109C4×C19C22×D412yes—
110Dic19—41no—
111Dic19—42no—
112C23×D4D1911yescharacteristic, complemented
113C2×AGL(1,ℤ/8)—192no—
114#525—191no—
115#450—194no—
116#447—194no—
117#418—192no—
118#407—191no—
119C2×C19—22no—
120C2×C19—24no—
121C2×C19—48no—
122C2×C19C2×#12011yescharacteristic
123C2×C19C2×AGL(1,ℤ/8)12yes—
124D19—81no—
125C25—21no—
126C2×#41—191no—
127C22×D4—28no—
128C22×D4—22no—
129C22×D4—21no—
130C22×D4C2×D1914yes—
131C22×D4C2×D1912yes—
132C23×C4C2×D1911yescharacteristic
133AGL(1,ℤ/8)—388no—
134C2×SD16—194no—
135C2×D8—194no—
136C2×M16—192no—
137#123—381no—
138C22⋊Q8—192no—
139#121—192no—
140#120—381no—
141C4×D4—382no—
142#117—191no—
143#102—198no—
144C22⋊C8—194no—
145C19#300311yescharacteristic, complemented, Sylow
146C24—28no—
147C24—24no—
148C24—22no—
149C24—48no—
150C24C22⋊D1911yescharacteristic
151#41—384no—
152C2×Q8—191no—
153C2×D4—28no—
154C2×D4—216no—
155C2×D4—216no—
156C2×D4—24no—
157C2×D4—22no—
158C2×D4—24no—
159C2×D4—191no—
160C2×D4—382no—
161C2×D4—381no—
162C2×D4C22⋊D1918yescomplemented
163C2×D4C22×D1914yes—
164C22×C4—24no—
165C22×C4—381no—
166C22×C4C22⋊D1912yes—
167C22×C4C22⋊D1911yescharacteristic
168C22×C4C22×D1912yes—
169C22×C4C22×D1911yescharacteristic
170SD16—388no—
171D8—388no—
172M16—384no—
173C2×C8—194no—
174C4⋊C4—192no—
175C4⋊C4—382no—
176C22⋊C4—381no—
177C22⋊C4—382no—
178C22⋊C4—382no—
179C42—381no—
180C23—24no—
181C23—22no—
182C23—216no—
183C23—28no—
184C23—24no—
185C23—432no—
186C23—48no—
187C23—48no—
188C23—48no—
189C23—381no—
190C23C2×C22⋊D1912yes—
191C23C2×C22⋊D1911yescharacteristic
192Q8—382no—
193D4—216no—
194D4—28no—
195D4—24no—
196D4—382no—
197D4—764no—
198D4—762no—
199D4C2×C22⋊D1918yes—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—24no—
203C2×C4—382no—
204C2×C4—381no—
205C2×C4—762no—
206C2×C4C2×C22⋊D1912yes—
207C2×C4C2×C22⋊D1911yescharacteristic
208C2×C4C2×C22⋊D1914yes—
209C2×C4C23×D1911yescharacteristic
210C8—384no—
211C22—28no—
212C22—22no—
213C22—22no—
214C22—22no—
215C22—28no—
216C22—432no—
217C22—416no—
218C22—48no—
219C22—762no—
220C22—761no—
221C22#1059737814yescomplemented
222C22#1059739912yes—
223C22C22×C22⋊D1911yescharacteristic
224C4—22no—
225C4—762no—
226C4—761no—
227C4#1059739912yes—
228C4C22×C22⋊D1912yes—
229C2—24no—
230C2—22no—
231C2—48no—
232C2—1521no—
233C2C2×#1059739911yescharacteristic
234C2C2×#1059737812yes—
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC23×D4×C19C2
socleC22×C19C22×D4
hypercenterC23×D4D19
hypocenterC19#3003
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10597378C2semidirect
2. #11927055C2semidirect
3. #11926695C2semidirect
4. #11926678C2semidirect
5. #11926549C2semidirect
6. #11926508C2semidirect
7. C23×D4×C19C2semidirect
15. C2×#64541C22semidirect
17. C2×#64526C22semidirect
19. C2×#64525C22semidirect
20. #10597376C22semidirect
23. #10597372C22semidirect
24. #10597370C22semidirect
25. C2×#64520C22semidirect
26. #10597289C22semidirect
27. C22⋊(C19⋊C8)C22semidirect
39. C2×D4×C19D4semidirect
49. C2×D76C23semidirect
51. C2×Dic38C23semidirect
57. C4⋊Dic19C23semidirect
61. C2×C19⋊C8C23semidirect
103. C22×C19AGL(1,ℤ/8)semidirect
112. C23×D4D19semidirect
145. C19#3003semidirect
162. C2×D4C22⋊D19semidirect
221. C22#10597378semidirect

Maximal subgroups

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

subgroupindex
C2×#105973782
#119270552
#119266952
#119266782
#119265492
#119265082
C23×D4×C192
#300319