Finite Group Databasebeta

← #14567905

Subgroups — #14567905

Order 2432.

672 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×(C2×D19)⋊C4C211yesmaximal, characteristic
2#11926479C212yesmaximal, complemented
3#11926470C212yesmaximal, complemented
4#11926435C214yesmaximal, complemented
5#11926416C212yesmaximal, complemented
6#11926407C211yesmaximal, characteristic, complemented
7#11926399C212yesmaximal
8C2×C19×#117C211yesmaximal, characteristic, complemented
9C24×D19C2211yescharacteristic
10C23×C4×C19C2211yescharacteristic
11C23×Dic19C2211yescharacteristic
12C19×#117—24no—
13C2×C4⋊C4×C19C2211yescharacteristic, complemented
14C2×C4⋊C4×C19C2211yescharacteristic, complemented
15C2×C22⋊C4×C19C2212yes—
16C2×C42×C19C2212yescomplemented
17C2×C22⋊Dic19C2212yes—
18C2×(C2×D19)⋊C4—24no—
19C2×(C2×D19)⋊C4C2214yes—
20C2×(C2×D19)⋊C4C2212yes—
21C2×(C2×D19)⋊C4C2212yes—
22C2×(C2×D19)⋊C4C2214yes—
23C2×Dic19⋊C4C2214yescomplemented
24C19⋊#95C2212yescomplemented
25C19⋊#95C2212yescomplemented
26C19⋊#95C2214yescomplemented
27C24×C19C2311yescharacteristic
28C23×D19—22no—
29C23×D19—24no—
30C23×D19—24no—
31C23×D19—42no—
32C23×D19C2312yes—
33C22×C4×C19—24no—
34C22×C4×C19D414yes—
35C22×C4×C19C2312yes—
36C22×C4×C19C2312yes—
37C22×C4×C19C2311yescharacteristic
38C22×C4×C19C2311yescharacteristic
39C22×Dic19—22no—
40C22×Dic19—42no—
41C22×Dic19C2314yes—
42C22×Dic19C2312yes—
43C4⋊C4×C19—22no—
44C4⋊C4×C19—22no—
45C22⋊C4×C19—24no—
46C42×C19—24no—
47C22⋊Dic19—24no—
48(C2×D19)⋊C4—28no—
49(C2×D19)⋊C4—24no—
50(C2×D19)⋊C4—24no—
51(C2×D19)⋊C4—44no—
52Dic19⋊C4—44no—
53C23×C19—22no—
54C23×C19—22no—
55C23×C19C2×D412yes—
56C23×C19#4114yes—
57C23×C19C2411yescharacteristic
58C22×D19—28no—
59C22×D19—22no—
60C22×D19—24no—
61C22×D19—22no—
62C22×D19—24no—
63C22×D19—416no—
64C22×D19—44no—
65C22×D19—44no—
66C22×D19#4114yes—
67C2×C4×C19—28no—
68C2×C4×C19—22no—
69C2×C4×C19—22no—
70C2×C4×C19—22no—
71C2×C4×C19—22no—
72C2×C4×C19—24no—
73C2×C4×C19—24no—
74C2×C4×C19C2×D412yes—
75C2×C4×C19C2×D412yes—
76C2×Dic19—22no—
77C2×Dic19—24no—
78C2×Dic19—24no—
79C2×Dic19—24no—
80C2×Dic19—24no—
81C2×Dic19—44no—
82#2482—191nomaximal, Sylow
83C22×C19—22no—
84C22×C19—22no—
85C22×C19—28no—
86C22×C19#12314yes—
87C22×C19C22×D411yescharacteristic
88C22×C19C2×#4112yes—
89C22×C19C2×#4112yes—
90C22×C19H(5,𝔽2)12yes—
91C2×D19—24no—
92C2×D19—28no—
93C2×D19—416no—
94C2×D19—42no—
95C2×D19—42no—
96C2×D19—44no—
97C4×C19—22no—
98C4×C19—22no—
99C4×C19—42no—
100C4×C19—42no—
101Dic19—42no—
102Dic19—44no—
103C2×#117D1911yescharacteristic, complemented
104C22×C22⋊C4—191no—
105#399—192no—
106#397—192no—
107#388—194no—
108#385—192no—
109#381—191no—
110#379—192no—
111C2×C19—24no—
112C2×C19C2×#12311yescharacteristic
113C2×C19#52511yescharacteristic
114C2×C19#53511yescharacteristic
115C2×C19#55114yes—
116D19—44no—
117C25—191no—
118C23×C4—191no—
119C23×C4C2×D1911yescharacteristic
120#117—24no—
121C2×C4⋊C4—194no—
122C2×C4⋊C4C2×D1911yescharacteristic, complemented
123C2×C4⋊C4C2×D1911yescharacteristic, complemented
124C2×C22⋊C4—192no—
125C2×C22⋊C4—192no—
126C2×C22⋊C4—192no—
127C2×C22⋊C4—194no—
128C2×C22⋊C4—194no—
129C2×C22⋊C4—384no—
130C2×C22⋊C4C2×D1912yes—
131C2×C42C2×D1912yescomplemented
132#95—192no—
133#95—192no—
134#95—194no—
135C19#248211yescharacteristic, complemented, Sylow
136C24—192no—
137C24—384no—
138C24—382no—
139C24—384no—
140C24—762no—
141C24C22×D1911yescharacteristic
142C22×C4—24no—
143C22×C4—194no—
144C22×C4—192no—
145C22×C4—382no—
146C22×C4—762no—
147C22×C4C22⋊D1914yes—
148C22×C4C22×D1912yes—
149C22×C4C22×D1912yes—
150C22×C4C22×D1911yescharacteristic
151C22×C4C22×D1911yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—764no—
155C22⋊C4—24no—
156C22⋊C4—388no—
157C22⋊C4—384no—
158C22⋊C4—384no—
159C22⋊C4—384no—
160C22⋊C4—764no—
161C42—24no—
162C23—22no—
163C23—22no—
164C23—194no—
165C23—388no—
166C23—384no—
167C23—382no—
168C23—384no—
169C23—382no—
170C23—7616no—
171C23—764no—
172C23—764no—
173C23#6454114yes—
174C23C2×C22⋊D1912yes—
175C23C23×D1911yescharacteristic
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—28no—
179C2×C4—24no—
180C2×C4—24no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—384no—
184C2×C4—384no—
185C2×C4—384no—
186C2×C4—384no—
187C2×C4—382no—
188C2×C4—764no—
189C2×C4C2×C22⋊D1912yes—
190C2×C4C2×C22⋊D1912yes—
191C22—22no—
192C22—22no—
193C22—28no—
194C22—384no—
195C22—388no—
196C22—7616no—
197C22—762no—
198C22—762no—
199C22—764no—
200C22#1059737514yes—
201C22C2×#6454112yes—
202C22#41×D1912yes—
203C22#1059743512yes—
204C22C22×C22⋊D1911yescharacteristic
205C4—22no—
206C4—22no—
207C4—42no—
208C4—42no—
209C4—762no—
210C4—764no—
211C2—24no—
212C2—764no—
213C2C2×#1059737511yescharacteristic
214C2#1192705111yescharacteristic
215C2#1192710811yescharacteristic
216C2#1192721814yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#117C2
prime radicalC24×D19C22
hypercenterC2×#117D19
hypocenterC19#2482
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #11926479C2semidirect
3. #11926470C2semidirect
4. #11926435C2semidirect
5. #11926416C2semidirect
6. #11926407C2semidirect
8. C2×C19×#117C2semidirect
13. C2×C4⋊C4×C19C22semidirect
14. C2×C4⋊C4×C19C22semidirect
16. C2×C42×C19C22semidirect
23. C2×Dic19⋊C4C22semidirect
24. C19⋊#95C22semidirect
25. C19⋊#95C22semidirect
26. C19⋊#95C22semidirect
103. C2×#117D19semidirect
122. C2×C4⋊C4C2×D19semidirect
123. C2×C4⋊C4C2×D19semidirect
131. C2×C42C2×D19semidirect
135. C19#2482semidirect

Maximal subgroups

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

subgroupindex
C22×(C2×D19)⋊C42
#119264792
#119264702
#119264352
#119264162
#119264072
#119263992
C2×C19×#1172
#248219