Finite Group Databasebeta

← #14572869

Subgroups — #14572869

Order 2432.

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

normal subgroups only

This group has 738 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×#10597388C212yesmaximal, complemented
2#11927055C211yesmaximal, characteristic
3#11926700C214yesmaximal, complemented
4#11926683C214yesmaximal, complemented
5#11926553C212yesmaximal, complemented
6#11926508C211yesmaximal, characteristic, complemented
7C23×Q8×C19C211yesmaximal, characteristic, complemented
8C22×Q8×C19—28no—
9C22×Q8×C19—22no—
10C22×Q8×C19—21no—
11C22×Q8×C19C2214yes—
12C22×Q8×C19C2212yes—
13C23×C4×C19—21no—
14C23×C4×C19C2211yescharacteristic
15C2×#64541C2211yescharacteristic
16#10597399—21no—
17C2×#64528C2214yescomplemented
18#10597388—28no—
19C2×#64527C2214yescomplemented
20#10597376C2212yes—
21#10597375—21no—
22C4×C22⋊D19—22no—
23#10597372C2211yescharacteristic
24#10597370C2212yes—
25C2×#64520C2212yes—
26#10597292C2218yescomplemented
27C22⋊(C19⋊C8)C2214yes—
28C24×C19D411yescharacteristic
29C2×Q8×C19—216no—
30C2×Q8×C19—28no—
31C2×Q8×C19—216no—
32C2×Q8×C19—24no—
33C2×Q8×C19—24no—
34C2×Q8×C19—22no—
35C2×Q8×C19D418yescomplemented
36C2×Q8×C19C2314yes—
37C22×C4×C19—28no—
38C22×C4×C19—24no—
39C22×C4×C19—22no—
40C22×C4×C19—24no—
41C22×C4×C19D412yes—
42C22×C4×C19D411yescharacteristic
43C22×C4×C19C2312yes—
44C22×C4×C19C2311yescharacteristic
45C2×C22⋊D19—22no—
46C2×C22⋊D19—21no—
47#64541—24no—
48C2×D76C2311yescharacteristic
49C2×C4×D19—21no—
50C2×Dic38C2311yescharacteristic
51C22⋊Dic19—22no—
52C22⋊Dic19—21no—
53#64528—28no—
54#64527—28no—
55(C2×D19)⋊C4—22no—
56C4⋊Dic19C2312yes—
57Dic19⋊C4—22no—
58C4×Dic19—21no—
59#64520—24no—
60C2×C19⋊C8C2314yes—
61C23×C19—22no—
62C23×C19—24no—
63C23×C19C2×D411yescharacteristic
64C23×C19C2×D412yes—
65C22×D19—21no—
66Q8×C19—216no—
67Q8×C19—28no—
68Q8×C19—24no—
69Q8×C19C2×D418yes—
70C2×C4×C19—216no—
71C2×C4×C19—28no—
72C2×C4×C19—22no—
73C2×C4×C19—24no—
74C2×C4×C19—24no—
75C2×C4×C19—24no—
76C2×C4×C19C2×D412yes—
77C2×C4×C19C2×D411yescharacteristic
78C2×C4×C19C2×D414yes—
79C2×C4×C19C2411yescharacteristic
80C22⋊D19—42no—
81C22⋊D19—44no—
82C2×Dic19—22no—
83C2×Dic19—21no—
84D76—22no—
85C4×D19—42no—
86Dic38—22no—
87C19⋊C8—24no—
88#3004—191nomaximal, Sylow
89C22×C19—28no—
90C22×C19—22no—
91C22×C19—22no—
92C22×C19—22no—
93C22×C19#12012yes—
94C22×C19#13714yescomplemented
95C22×C19C22×D411yescharacteristic
96C2×D19—41no—
97C2×D19—42no—
98C4×C19—28no—
99C4×C19—22no—
100C4×C19#12012yes—
101C4×C19C22×D412yes—
102Dic19—41no—
103Dic19—42no—
104C23×Q8D1911yescharacteristic, complemented
105C2×#137—192no—
106#525—191no—
107#451—194no—
108#448—194no—
109#419—192no—
110#407—191no—
111C2×C19—22no—
112C2×C19—24no—
113C2×C19C2×#12011yescharacteristic
114C2×C19C2×#13712yes—
115D19—81no—
116C2×#41—191no—
117C22×Q8—28no—
118C22×Q8—22no—
119C22×Q8—21no—
120C22×Q8C2×D1914yes—
121C22×Q8C2×D1912yes—
122C23×C4—21no—
123C23×C4C2×D1911yescharacteristic
124#137—388no—
125C2×Q16—194no—
126C2×SD16—194no—
127C2×M16—192no—
128#123—381no—
129C22⋊Q8—192no—
130#121—192no—
131#120—381no—
132C4×D4—382no—
133#117—191no—
134#103—198no—
135C22⋊C8—194no—
136C19#300411yescharacteristic, complemented, Sylow
137C24C22⋊D1911yescharacteristic
138#41—384no—
139C2×Q8—216no—
140C2×Q8—28no—
141C2×Q8—216no—
142C2×Q8—24no—
143C2×Q8—24no—
144C2×Q8—22no—
145C2×Q8—191no—
146C2×Q8C22⋊D1918yescomplemented
147C2×Q8C22×D1914yes—
148C2×D4—191no—
149C2×D4—382no—
150C2×D4—381no—
151C22×C4—28no—
152C22×C4—24no—
153C22×C4—22no—
154C22×C4—24no—
155C22×C4—381no—
156C22×C4C22⋊D1912yes—
157C22×C4C22⋊D1911yescharacteristic
158C22×C4C22×D1912yes—
159C22×C4C22×D1911yescharacteristic
160Q16—388no—
161SD16—388no—
162M16—384no—
163C2×C8—194no—
164C4⋊C4—192no—
165C4⋊C4—382no—
166C22⋊C4—381no—
167C22⋊C4—382no—
168C22⋊C4—382no—
169C42—381no—
170C23—24no—
171C23—22no—
172C23—381no—
173C23C2×C22⋊D1912yes—
174C23C2×C22⋊D1911yescharacteristic
175Q8—216no—
176Q8—28no—
177Q8—24no—
178Q8—382no—
179Q8C2×C22⋊D1918yes—
180D4—382no—
181D4—764no—
182D4—762no—
183C2×C4—216no—
184C2×C4—28no—
185C2×C4—22no—
186C2×C4—24no—
187C2×C4—24no—
188C2×C4—24no—
189C2×C4—382no—
190C2×C4—381no—
191C2×C4—762no—
192C2×C4C2×C22⋊D1912yes—
193C2×C4C2×C22⋊D1911yescharacteristic
194C2×C4C2×C22⋊D1914yes—
195C2×C4C23×D1911yescharacteristic
196C8—384no—
197C22—28no—
198C22—22no—
199C22—22no—
200C22—22no—
201C22—762no—
202C22—761no—
203C22#1059738814yescomplemented
204C22#1059739912yes—
205C22C22×C22⋊D1911yescharacteristic
206C4—28no—
207C4—22no—
208C4—762no—
209C4—761no—
210C4#1059739912yes—
211C4C22×C22⋊D1912yes—
212C2—24no—
213C2—22no—
214C2—1521no—
215C2C2×#1059739911yescharacteristic
216C2C2×#1059738812yes—
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC23×Q8×C19C2
socleC22×C19C22×D4
prime radical#11927055C2
hypercenterC23×Q8D19
hypocenterC19#3004
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#10597388C2semidirect
3. #11926700C2semidirect
4. #11926683C2semidirect
5. #11926553C2semidirect
6. #11926508C2semidirect
7. C23×Q8×C19C2semidirect
17. C2×#64528C22semidirect
19. C2×#64527C22semidirect
26. #10597292C22semidirect
35. C2×Q8×C19D4semidirect
94. C22×C19#137semidirect
104. C23×Q8D19semidirect
136. C19#3004semidirect
146. C2×Q8C22⋊D19semidirect
203. C22#10597388semidirect

Maximal subgroups

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

subgroupindex
C2×#105973882
#119270552
#119267002
#119266832
#119265532
#119265082
C23×Q8×C192
#300419