Finite Group Databasebeta

← D19×#392 #14566829

Subgroups — D19×#392 #14566829

Order 2432.

1812 conjugacy classes of subgroups; only the 223 normal subgroups are shown.

normal subgroups only

This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 223 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×D4×D19C213yesmaximal, complemented
2C2×C22⋊C4×D19C213yesmaximal, complemented
3#11926454C211yesmaximal, characteristic, complemented
4#11926453C213yesmaximal, complemented
5#11926452C213yesmaximal, complemented
6#95×D19C211yesmaximal, characteristic, complemented
7C19×#392C211yesmaximal, characteristic, complemented
8C24×D19C2213yes—
9C22×D4×C19C2213yescomplemented
10C22×C22⋊D19C2216yescomplemented
11C2×D4×D19—224no—
12C2×D4×D19—212no—
13C22×D76C2213yescomplemented
14C22×C4×D19C2211yescharacteristic
15C22×C4×D19C2213yes—
16C2×C22⋊C4×C19C2213yescomplemented
17C2×C22⋊Dic19C2213yescomplemented
18C2×(C2×D19)⋊C4C2213yescomplemented
19C2×(C2×D19)⋊C4C2213yescomplemented
20C22⋊C4×D19—212no—
21C19×#95C2211yescharacteristic, complemented
22C19⋊#95C2213yescomplemented
23C24×C19C2313yes—
24C23×D19—212no—
25C23×D19—212no—
26C23×D19—26no—
27C23×D19—26no—
28C23×D19D4112yescomplemented
29C23×D19C2313yes—
30C23×D19C2311yescharacteristic
31C2×D4×C19—212no—
32C2×D4×C19—26no—
33C22×C4×C19C2311yescharacteristic
34C22×C4×C19C2313yes—
35C2×C22⋊D19—212no—
36C2×C22⋊D19—212no—
37C2×C22⋊D19—212no—
38C22×Dic19C2311yescharacteristic
39C22×Dic19C2313yes—
40D4×D19—296no—
41C2×D76—212no—
42C2×D76—26no—
43C2×C4×D19—212no—
44C2×C4×D19—26no—
45C2×C4×D19D4112yescomplemented
46C22⋊C4×C19—26no—
47C22⋊Dic19—26no—
48(C2×D19)⋊C4—26no—
49(C2×D19)⋊C4—26no—
50C23×C19—23no—
51C23×C19—26no—
52C23×C19—26no—
53C23×C19—23no—
54C23×C19C2×D416yescomplemented
55C23×C19C2411yescharacteristic
56C22×D19—23no—
57C22×D19—26no—
58C22×D19—26no—
59C22×D19—23no—
60C22×D19—248no—
61C22×D19—224no—
62C22×D19—412no—
63C22×D19—424no—
64C22×D19—412no—
65C22×D19C2×D416yes—
66C22×D19C2×D416yes—
67C22×D19C2×D416yescomplemented
68C22×D19#4112yes—
69D4×C19—224no—
70C2×C4×C19—26no—
71C2×C4×C19—23no—
72C2×C4×C19C2×D416yescomplemented
73C22⋊D19—248no—
74C2×Dic19—26no—
75C2×Dic19—23no—
76C2×Dic19C2×D416yescomplemented
77D76—224no—
78C4×D19—224no—
79C4×D19—44no—
80C2×#392—191nomaximal, Sylow
81C22×C19—212no—
82C22×C19—26no—
83C22×C19—43no—
84C22×C19—46no—
85C22×C19—43no—
86C22×C19C22×D413yes—
87C22×C19C22×D413yes—
88C22×C19C2×#4111yescharacteristic
89C2×D19—212no—
90C2×D19—26no—
91C2×D19—43no—
92C2×D19—46no—
93C2×D19—43no—
94C2×D19—448no—
95C2×D19#120112yes—
96C2×D19#121112yes—
97C2×D19#12714yes—
98C4×C19—26no—
99C4×C19—41no—
100Dic19—26no—
101Dic19—41no—
102C23×D4—193no—
103C22×C22⋊C4—193no—
104#392—193no—
105#392—193no—
106#392—191no—
107#392D1911yescharacteristic, direct product factor
108C2×#95—191no—
109C2×C19—46no—
110C2×C19C2×#12013yes—
111C2×C19C2×#12113yes—
112C2×C19C2×#12711yescharacteristic
113D19—46no—
114D19#39218yesdirect product factor
115C25—193no—
116C22×D4—196no—
117C22×D4—193no—
118C22×D4—3812no—
119C22×D4—3824no—
120C22×D4C2×D1913yescomplemented
121C23×C4—193no—
122C23×C4—191no—
123C2×C22⋊C4—193no—
124C2×C22⋊C4—193no—
125C2×C22⋊C4—193no—
126C2×C22⋊C4—3812no—
127C2×C22⋊C4C2×D1913yescomplemented
128#95—193no—
129#95C2×D1911yescharacteristic, complemented
130C19C2×#39211yescharacteristic, complemented, Sylow
131C24—191no—
132C24—1912no—
133C24—193no—
134C24—386no—
135C24—3812no—
136C24—3812no—
137C24—386no—
138C24C22×D1913yes—
139C2×D4—212no—
140C2×D4—26no—
141C2×D4—3812no—
142C2×D4—3812no—
143C2×D4—3896no—
144C2×D4—3812no—
145C2×D4—3812no—
146C2×D4—386no—
147C22×C4—193no—
148C22×C4—1912no—
149C22×C4—191no—
150C22×C4—3812no—
151C22×C4—386no—
152C22×C4C22×D1911yescharacteristic
153C22×C4C22×D1913yes—
154C22⋊C4—26no—
155C22⋊C4—386no—
156C22⋊C4—386no—
157C22⋊C4—386no—
158C23—23no—
159C23—26no—
160C23—26no—
161C23—23no—
162C23—196no—
163C23—196no—
164C23—192no—
165C23—196no—
166C23—3848no—
167C23—3824no—
168C23—383no—
169C23—386no—
170C23—386no—
171C23—383no—
172C23—7612no—
173C23—7612no—
174C23—7624no—
175C23D4×D1916yescomplemented
176C23C23×D1911yescharacteristic
177D4—224no—
178D4—3824no—
179D4—3848no—
180C2×C4—26no—
181C2×C4—23no—
182C2×C4—196no—
183C2×C4—3824no—
184C2×C4—386no—
185C2×C4—383no—
186C2×C4—764no—
187C2×C4D4×D1916yescomplemented
188C22—212no—
189C22—26no—
190C22—43no—
191C22—43no—
192C22—46no—
193C22—194no—
194C22—1912no—
195C22—1912no—
196C22—3812no—
197C22—386no—
198C22—7648no—
199C22—763no—
200C22—763no—
201C22—766no—
202C22C2×D4×D1913yes—
203C22C2×D4×D1913yes—
204C22#41×D1911yescharacteristic
205C4—26no—
206C4—41no—
207C4—386no—
208C4—761no—
209C2—46no—
210C2—198no—
211C2—766no—
212C2#120×D1913yes—
213C2#121×D1913yes—
214C2#127×D1911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#392C2
hypercenter#392D19
hypocenterC19C2×#392
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D19C2semidirect
2. C2×C22⋊C4×D19C2semidirect
3. #11926454C2semidirect
4. #11926453C2semidirect
5. #11926452C2semidirect
6. #95×D19C2semidirect
7. C19×#392C2semidirect
9. C22×D4×C19C22semidirect
10. C22×C22⋊D19C22semidirect
13. C22×D76C22semidirect
16. C2×C22⋊C4×C19C22semidirect
17. C2×C22⋊Dic19C22semidirect
18. C2×(C2×D19)⋊C4C22semidirect
19. C2×(C2×D19)⋊C4C22semidirect
21. C19×#95C22semidirect
22. C19⋊#95C22semidirect
28. C23×D19D4semidirect
45. C2×C4×D19D4semidirect
54. C23×C19C2×D4semidirect
67. C22×D19C2×D4semidirect
72. C2×C4×C19C2×D4semidirect
76. C2×Dic19C2×D4semidirect
107. #392D19direct (N × H)
114. D19#392direct (N × H)
120. C22×D4C2×D19semidirect
127. C2×C22⋊C4C2×D19semidirect
129. #95C2×D19semidirect
130. C19C2×#392semidirect
175. C23D4×D19semidirect
187. C2×C4D4×D19semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D192
C2×C22⋊C4×D192
#119264542
#119264532
#119264522
#95×D192
C19×#3922
C2×#39219