Finite Group Databasebeta

← #14570899

Subgroups — #14570899

Order 2432.

484 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 121 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#11926480C211yesmaximal, characteristic, complemented
2#11926473C212yesmaximal, complemented
3#11926462C212yesmaximal, complemented
4#11926453C211yesmaximal, characteristic
5#11926444C212yesmaximal, complemented
6#11926436C212yesmaximal, complemented
7#11926426C212yesmaximal, complemented
8#11926423C212yesmaximal, complemented
9C19×#381C211yesmaximal, characteristic, complemented
10C23×C4×C19C2211yescharacteristic
11C22×C22⋊D19C2212yes—
12C22×D76C2211yescharacteristic
13C2×C22⋊C4×C19C2211yescharacteristic
14C2×C22⋊C4×C19C2211yescharacteristic
15C2×C22⋊Dic19C2212yes—
16C2×(C2×D19)⋊C4C2212yes—
17C2×(C2×D19)⋊C4C2212yes—
18C2×(C2×D19)⋊C4C2212yes—
19C2×(C2×D19)⋊C4C2212yes—
20C2×(C2×D19)⋊C4C2212yes—
21C2×C4⋊Dic19C2211yescharacteristic
22C2×Dic19⋊C4C2212yes—
23C2×Dic19⋊C4C2212yes—
24C2×C4×Dic19C2212yes—
25C19×#95C2212yes—
26C19×#95C2212yes—
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2211yescharacteristic
30C19⋊#95C2211yescharacteristic
31C24×C19C2311yescharacteristic
32C23×D19C2312yes—
33C22×C4×C19—22no—
34C22×C4×C19—41no—
35C22×C4×C19—41no—
36C22×C4×C19C2311yescharacteristic
37C22×C4×C19C2311yescharacteristic
38C22×C4×C19C2312yes—
39C22×C4×C19C2312yes—
40C2×C22⋊D19—24no—
41C2×C22⋊D19—24no—
42C2×C22⋊D19—42no—
43C22×Dic19C2312yes—
44C22×Dic19C2312yes—
45C22×Dic19C2312yes—
46C2×D76—42no—
47C2×D76—41no—
48C22⋊C4×C19—41no—
49C22⋊C4×C19—41no—
50C22⋊Dic19—42no—
51(C2×D19)⋊C4—24no—
52(C2×D19)⋊C4—42no—
53(C2×D19)⋊C4—42no—
54(C2×D19)⋊C4—42no—
55(C2×D19)⋊C4—42no—
56C4⋊Dic19—41no—
57Dic19⋊C4—24no—
58Dic19⋊C4—42no—
59C4×Dic19—42no—
60C23×C19—22no—
61C23×C19—22no—
62C23×C19—21no—
63C23×C19—21no—
64C23×C19#4112yes—
65C23×C19C2411yescharacteristic
66C22×D19—22no—
67C22×D19—22no—
68C22×D19—22no—
69C22×D19—22no—
70C22×D19—22no—
71C22×D19—22no—
72C22×D19—22no—
73C2×C4×C19—22no—
74C2×C4×C19—22no—
75C2×C4×C19—22no—
76C2×C4×C19—22no—
77C2×C4×C19—22no—
78C2×C4×C19—21no—
79C2×C4×C19—22no—
80C2×C4×C19—22no—
81C2×C4×C19—22no—
82C2×C4×C19—21no—
83C2×C4×C19—44no—
84C22⋊D19—48no—
85C2×Dic19—22no—
86C2×Dic19—22no—
87C2×Dic19—22no—
88C2×Dic19—22no—
89C2×Dic19—22no—
90C2×Dic19—22no—
91C2×Dic19—22no—
92C2×Dic19—22no—
93C2×Dic19#4114yes—
94D76—44no—
95#2752—191nomaximal, Sylow
96C22×C19—22no—
97C22×C19—24no—
98C22×C19—42no—
99C22×C19—41no—
100C22×C19—41no—
101C22×C19C2×#4111yescharacteristic
102C22×C19C2×#4112yes—
103C22×C19H(5,𝔽2)11yescharacteristic
104C22×C19H(5,𝔽2)11yescharacteristic
105C22×C19H(5,𝔽2)12yes—
106C2×D19—42no—
107C2×D19—42no—
108C2×D19—42no—
109C2×D19—42no—
110C2×D19—42no—
111C2×D19—42no—
112C2×D19—42no—
113C4×C19—42no—
114C4×C19—42no—
115C4×C19—41no—
116C4×C19—41no—
117Dic19—24no—
118Dic19—42no—
119Dic19—42no—
120#399—191no—
121#397—192no—
122#394—192no—
123#392—191no—
124#390—192no—
125#388—192no—
126#387—192no—
127#386—192no—
128#381D1911yescharacteristic, complemented
129C2×C19—42no—
130C2×C19#53811yescharacteristic
131C2×C19#54012yes—
132C2×C19#55112yes—
133C2×C19#55911yescharacteristic
134C2×C19#56011yescharacteristic
135D19—82no—
136C22×D4—192no—
137C22×D4—191no—
138C23×C4C2×D1911yescharacteristic
139C2×C4⋊C4—192no—
140C2×C4⋊C4—192no—
141C2×C4⋊C4—191no—
142C2×C22⋊C4—192no—
143C2×C22⋊C4—192no—
144C2×C22⋊C4—192no—
145C2×C22⋊C4—192no—
146C2×C22⋊C4—192no—
147C2×C22⋊C4—192no—
148C2×C22⋊C4C2×D1911yescharacteristic
149C2×C22⋊C4C2×D1911yescharacteristic
150C2×C42—192no—
151#95—192no—
152#95—192no—
153#95—191no—
154#95—191no—
155#95C2×D1912yes—
156#95C2×D1912yes—
157C19#275211yescharacteristic, complemented, Sylow
158C24—192no—
159C24C22×D1911yescharacteristic
160C2×D4—384no—
161C2×D4—384no—
162C2×D4—761no—
163C2×D4—762no—
164C2×D4—762no—
165C22×C4—22no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—192no—
169C22×C4—192no—
170C22×C4—192no—
171C22×C4C22×D1912yes—
172C22×C4C22×D1911yescharacteristic
173C22×C4C22×D1911yescharacteristic
174C22×C4C22×D1912yes—
175C4⋊C4—384no—
176C4⋊C4—762no—
177C4⋊C4—761no—
178C22⋊C4—41no—
179C22⋊C4—41no—
180C22⋊C4—384no—
181C22⋊C4—762no—
182C22⋊C4—762no—
183C22⋊C4—762no—
184C22⋊C4—762no—
185C22⋊C4—762no—
186C42—762no—
187C23—21no—
188C23—21no—
189C23—22no—
190C23—22no—
191C23—382no—
192C23—382no—
193C23—382no—
194C23—382no—
195C23—382no—
196C23—382no—
197C23—382no—
198C23#6454112yes—
199C23C23×D1911yescharacteristic
200D4—764no—
201D4—768no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—44no—
213C2×C4—194no—
214C2×C4—382no—
215C2×C4—382no—
216C2×C4—382no—
217C2×C4—382no—
218C2×C4—382no—
219C2×C4—382no—
220C2×C4—382no—
221C2×C4—382no—
222C22—22no—
223C22—24no—
224C22—42no—
225C22—41no—
226C22—41no—
227C22—762no—
228C22—762no—
229C22—762no—
230C22—762no—
231C22—762no—
232C22—762no—
233C22—762no—
234C22C2×#6454111yescharacteristic
235C22#1059743011yescharacteristic
236C22#1059743011yescharacteristic
237C22#41×D1912yes—
238C22#1059743512yes—
239C4—42no—
240C4—42no—
241C4—41no—
242C4—41no—
243C4—384no—
244C4—762no—
245C4—762no—
246C2—42no—
247C2—1522no—
248C2#1192713211yescharacteristic
249C2#1192714612yes—
250C2#1192721812yes—
251C2#1192727811yescharacteristic
252C2#1192728411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#381C2
prime radical#11926453C2
hypercenter#381D19
hypocenterC19#2752
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. #11926480C2semidirect
2. #11926473C2semidirect
3. #11926462C2semidirect
5. #11926444C2semidirect
6. #11926436C2semidirect
7. #11926426C2semidirect
8. #11926423C2semidirect
9. C19×#381C2semidirect
128. #381D19semidirect
157. C19#2752semidirect

Maximal subgroups

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

subgroupindex
#119264802
#119264732
#119264622
#119264532
#119264442
#119264362
#119264262
#119264232
C19×#3812
#275219