Finite Group Databasebeta

← #14571607

Subgroups — #14571607

Order 2432.

408 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 137 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
1#11926486C212yesmaximal, complemented
2#11926480C211yesmaximal, characteristic
3#11926480C211yesmaximal, characteristic
4#11926477C212yesmaximal, complemented
5#11926441C212yesmaximal, complemented
6#11926440C212yesmaximal, complemented
7#11926437C212yesmaximal
8#11926417C212yesmaximal
9C19×#385C211yesmaximal, characteristic
10C23×C4×C19C2211yescharacteristic
11C2×C4⋊C4×C19C2212yes—
12C2×C22⋊C4×C19C2211yescharacteristic
13C2×C22⋊C4×C19C2211yescharacteristic
14C2×C22⋊Dic19C2212yes—
15C2×C22⋊Dic19C2212yes—
16C2×C4⋊Dic19C2212yes—
17C2×C4⋊Dic19C2211yescharacteristic
18C2×C4⋊Dic19C2211yescharacteristic
19C2×Dic19⋊C4C2212yes—
20C2×Dic19⋊C4C2212yes—
21C2×Dic19⋊C4C2212yes—
22C2×Dic19⋊C4C2212yes—
23C2×C4×Dic19C2212yes—
24C19×#95C2212yes—
25C19⋊#95C2212yes—
26C19⋊#95C2212yes—
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2211yescharacteristic
30C19⋊#95C2211yescharacteristic
31C24×C19C2311yescharacteristic
32C22×C4×C19—41no—
33C22×C4×C19—42no—
34C22×C4×C19C2311yescharacteristic
35C22×C4×C19C2311yescharacteristic
36C22×C4×C19C2312yes—
37C22×C4×C19C2312yes—
38C22×Dic19C2312yes—
39C22×Dic19C2312yes—
40C22×Dic19C2312yes—
41C22×Dic19C2312yes—
42C4⋊C4×C19—42no—
43C22⋊C4×C19—41no—
44C22⋊C4×C19Q814yes—
45C22⋊Dic19—24no—
46C22⋊Dic19—42no—
47C4⋊Dic19—24no—
48C4⋊Dic19—41no—
49C4⋊Dic19—41no—
50Dic19⋊C4—24no—
51Dic19⋊C4—42no—
52Dic19⋊C4—42no—
53Dic19⋊C4—42no—
54C4×Dic19—42no—
55C23×C19—22no—
56C23×C19—22no—
57C23×C19—21no—
58C23×C19—21no—
59C23×C19C2×Q812yes—
60C23×C19C2411yescharacteristic
61C2×C4×C19—22no—
62C2×C4×C19—22no—
63C2×C4×C19—22no—
64C2×C4×C19—22no—
65C2×C4×C19—22no—
66C2×C4×C19—22no—
67C2×C4×C19—21no—
68C2×C4×C19—21no—
69C2×C4×C19—22no—
70C2×C4×C19—44no—
71C2×C4×C19C2×Q814yes—
72C2×Dic19—22no—
73C2×Dic19—22no—
74C2×Dic19—22no—
75C2×Dic19—22no—
76C2×Dic19—22no—
77C2×Dic19—22no—
78C2×Dic19—22no—
79C2×Dic19—22no—
80C2×Dic19—22no—
81C2×Dic19—22no—
82C2×Dic19—22no—
83C2×Dic19#4114yes—
84#2807—191nomaximal, Sylow
85C22×C19—22no—
86C22×C19—24no—
87C22×C19—42no—
88C22×C19—41no—
89C22×C19—41no—
90C22×C19C22×Q811yescharacteristic
91C22×C19C2×#4112yes—
92C22×C19H(5,𝔽2)12yes—
93C22×C19H(5,𝔽2)11yescharacteristic
94C22×C192−1+411yescharacteristic
95C4×C19—24no—
96C4×C19—41no—
97C4×C19—41no—
98C4×C19—42no—
99Dic19—24no—
100Dic19—42no—
101Dic19—42no—
102Dic19—42no—
103#400—192no—
104#399—191no—
105#399—191no—
106#398—192no—
107#389—192no—
108#389—192no—
109#388—192no—
110#385—192no—
111#385D1911yescharacteristic
112C2×C19—42no—
113C2×C19#53912yes—
114C2×C19#54411yescharacteristic
115C2×C19#55412yes—
116C2×C19#55911yescharacteristic
117C2×C19#56011yescharacteristic
118C23×C4C2×D1911yescharacteristic
119C2×C4⋊C4—192no—
120C2×C4⋊C4—192no—
121C2×C4⋊C4—192no—
122C2×C4⋊C4—192no—
123C2×C4⋊C4—191no—
124C2×C4⋊C4—192no—
125C2×C4⋊C4—191no—
126C2×C4⋊C4C2×D1912yes—
127C2×C22⋊C4—192no—
128C2×C22⋊C4—192no—
129C2×C22⋊C4C2×D1911yescharacteristic
130C2×C22⋊C4C2×D1911yescharacteristic
131C2×C42—192no—
132#95—192no—
133#95—192no—
134#95—192no—
135#95—192no—
136#95—191no—
137#95—191no—
138#95C2×D1912yes—
139C19#280711yescharacteristic, complemented, Sylow
140C24C22×D1911yescharacteristic
141C22×C4—42no—
142C22×C4—41no—
143C22×C4—192no—
144C22×C4—192no—
145C22×C4—192no—
146C22×C4—192no—
147C22×C4C22×D1912yes—
148C22×C4C22×D1911yescharacteristic
149C22×C4C22×D1911yescharacteristic
150C22×C4C22×D1912yes—
151C4⋊C4—42no—
152C4⋊C4—384no—
153C4⋊C4—384no—
154C4⋊C4—762no—
155C4⋊C4—762no—
156C4⋊C4—762no—
157C4⋊C4—761no—
158C4⋊C4—761no—
159C22⋊C4—41no—
160C22⋊C4—384no—
161C22⋊C4—762no—
162C22⋊C4Dic3814yes—
163C42—762no—
164C23—21no—
165C23—22no—
166C23—21no—
167C23—22no—
168C23C2×Dic3812yes—
169C23C23×D1911yescharacteristic
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—44no—
180C2×C4—194no—
181C2×C4—382no—
182C2×C4—382no—
183C2×C4—382no—
184C2×C4—382no—
185C2×C4—382no—
186C2×C4—382no—
187C2×C4—382no—
188C2×C4—382no—
189C2×C4—382no—
190C2×C4—382no—
191C2×C4—382no—
192C2×C4C2×Dic3814yes—
193C22—22no—
194C22—24no—
195C22—42no—
196C22—41no—
197C22—41no—
198C22C22×Dic3811yescharacteristic
199C22#1059743012yes—
200C22#1059743011yescharacteristic
201C22#1059743311yescharacteristic
202C22#41×D1912yes—
203C4—24no—
204C4—41no—
205C4—42no—
206C4—41no—
207C4—384no—
208C4—762no—
209C4—762no—
210C4—762no—
211C2—42no—
212C2#1192714012yes—
213C2#1192717511yescharacteristic
214C2#1192725312yes—
215C2#1192727811yescharacteristic
216C2#1192728311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#385C2
prime radicalC24×C19C23
hypercenter#385D19
hypocenterC19#2807
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #11926486C2semidirect
4. #11926477C2semidirect
5. #11926441C2semidirect
6. #11926440C2semidirect
139. C19#2807semidirect

Maximal subgroups

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

subgroupindex
#119264862
#119264802
#119264772
#119264412
#119264402
#119264372
#119264172
C19×#3852
#280719