Finite Group Databasebeta

← #14572095

Subgroups — #14572095

Order 2432.

800 conjugacy classes of subgroups; only the 249 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 249 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×#10597430C211yesmaximal, characteristic
2#11927019C211yesmaximal, characteristic, complemented
3#11926517C214yesmaximal, complemented
4C2×#10597263C218yesmaximal, complemented
5C19×#518C211yesmaximal, characteristic, complemented
6C22×D4×C19C2211yescharacteristic
7C22×C22⋊D19C2214yes—
8#10597430—24no—
9#10597430—24no—
10C2×#64543C414yescomplemented
11C2×D4×D19C414yescomplemented
12C2×#64541C2212yes—
13C4×D4×C19—24no—
14C19×#117C2212yescomplemented
15C2×C22⋊C4×C19C2214yescomplemented
16C2×C22⋊Dic19C2214yescomplemented
17D4×Dic19—24no—
18#10597372C2212yescomplemented
19#10597263C22116yescomplemented
20C24×C19C2312yes—
21C23×D19C2×C414yescomplemented
22C2×D4×C19C2×C414yes—
23C2×D4×C19D414yes—
24C2×D4×C19D414yes—
25C22×C4×C19—24no—
26C22×C4×C19C2311yescharacteristic
27C2×C22⋊D19—28no—
28C2×C22⋊D19—28no—
29C2×C22⋊D19C2×C418yescomplemented
30C2×C22⋊D19C2314yes—
31C22×Dic19—24no—
32C22×Dic19C2×C414yescomplemented
33#64543—216no—
34D4×D19—216no—
35#64541—24no—
36#64541—24no—
37C2×D76C2×C412yescomplemented
38C2×C4×D19C2×C414yescomplemented
39C2×Dic38C2×C412yescomplemented
40C4⋊C4×C19—22no—
41C22⋊C4×C19—24no—
42C22⋊C4×C19C2314yes—
43C42×C19—22no—
44C22⋊Dic19—24no—
45C22⋊Dic19C2314yes—
46C4⋊Dic19—22no—
47C4×Dic19—22no—
48C23×C19—82no—
49C23×C19C22×C414yes—
50C23×C19C2×D414yes—
51C23×C19C2×D414yes—
52C23×C19C2411yescharacteristic
53C22×D19—28no—
54C22×D19—84no—
55C22×D19C22×C414yes—
56D4×C19C22⋊C4116yes—
57C2×C4×C19—24no—
58C2×C4×C19—84no—
59C2×C4×C19C22×C412yes—
60C2×C4×C19C2×D412yes—
61C2×C4×C19C2×D412yes—
62C22⋊D19—216no—
63C22⋊D19—24no—
64C22⋊D19—24no—
65C2×Dic19—28no—
66C2×Dic19—24no—
67C2×Dic19—84no—
68C2×Dic19C22×C414yes—
69D76—24no—
70C4×D19—28no—
71Dic38—24no—
72#2883—191nomaximal, Sylow
73C22×C19—44no—
74C22×C19—44no—
75C22×C19—44no—
76C22×C19—41no—
77C22×C19C2×C22⋊C418yes—
78C22×C19C23×C411yescharacteristic
79C22×C19C22×D411yescharacteristic
80C22×C19C22×D411yescharacteristic
81C2×D19—24no—
82C2×D19—44no—
83C2×D19—88no—
84C4×C19—44no—
85C4×C19C2×C22⋊C414yes—
86Dic19—24no—
87Dic19—44no—
88C2×H(5,𝔽2)—191no—
89#518—191no—
90#518D1911yescharacteristic, complemented
91#410—194no—
92C2×#99—198no—
93C2×C19—21no—
94C2×C19—21no—
95C2×C19—21no—
96C2×C19—28no—
97C2×C19C22×C22⋊C411yescharacteristic
98D19—44no—
99H(5,𝔽2)—384no—
100H(5,𝔽2)—384no—
101C2×#41—194no—
102C2×#41—192no—
103C22×D4—194no—
104C22×D4—194no—
105C22×D4C2×D1911yescharacteristic
106C4×D4—24no—
107C4×D4—384no—
108#117—192no—
109#117C2×D1912yescomplemented
110C2×C22⋊C4—194no—
111C2×C22⋊C4C2×D1914yescomplemented
112#99—1916no—
113C19#288311yescharacteristic, complemented, Sylow
114C24—194no—
115C24C22×D1912yes—
116#41—3816no—
117#41—384no—
118#41—384no—
119C2×Q8—192no—
120C2×D4—198no—
121C2×D4—194no—
122C2×D4—192no—
123C2×D4—388no—
124C2×D4—388no—
125C2×D4—3816no—
126C2×D4C4×D1914yes—
127C2×D4D7614yes—
128C2×D4C22⋊D1914yes—
129C22×C4—24no—
130C22×C4—194no—
131C22×C4—194no—
132C22×C4—384no—
133C22×C4C22×D1911yescharacteristic
134C4⋊C4—22no—
135C4⋊C4—382no—
136C22⋊C4—24no—
137C22⋊C4—194no—
138C22⋊C4—384no—
139C22⋊C4C22×D1914yes—
140C42—22no—
141C42—382no—
142C23—82no—
143C23—194no—
144C23—388no—
145C23—1524no—
146C23C2×C4×D1914yes—
147C23C2×D7614yes—
148C23C2×C22⋊D1914yes—
149C23C23×D1911yescharacteristic
150Q8—384no—
151D4—384no—
152D4—384no—
153D4—3816no—
154D4—384no—
155D4(C2×D19)⋊C4116yes—
156C2×C4—24no—
157C2×C4—84no—
158C2×C4—194no—
159C2×C4—388no—
160C2×C4—388no—
161C2×C4—384no—
162C2×C4—1524no—
163C2×C4C2×C4×D1912yes—
164C2×C4C2×D7612yes—
165C2×C4C2×C22⋊D1912yes—
166C22—44no—
167C22—44no—
168C22—41no—
169C22—44no—
170C22—384no—
171C22—764no—
172C22—1528no—
173C22C2×(C2×D19)⋊C418yes—
174C22C22×C4×D1911yescharacteristic
175C22C22×D7611yescharacteristic
176C22C22×C22⋊D1911yescharacteristic
177C4—44no—
178C4—384no—
179C4—764no—
180C4C2×(C2×D19)⋊C414yes—
181C2—21no—
182C2—21no—
183C2—21no—
184C2—28no—
185C2—764no—
186C2C22×(C2×D19)⋊C411yescharacteristic
subgroupG/H
centerC2C22×(C2×D19)⋊C4
commutatorC22×C19C23×C4
FrattiniC23C23×D19
FittingC19×#518C2
socleC2×C19C22×C22⋊C4
prime radicalC2×#10597430C2
cosocleC23×C19C24
hypercenter#518D19
hypocenterC19#2883
LCSG ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22×D4 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #11927019C2semidirect
3. #11926517C2semidirect
4. C2×#10597263C2semidirect
5. C19×#518C2semidirect
10. C2×#64543C4semidirect
11. C2×D4×D19C4semidirect
14. C19×#117C22semidirect
15. C2×C22⋊C4×C19C22semidirect
16. C2×C22⋊Dic19C22semidirect
18. #10597372C22semidirect
19. #10597263C22semidirect
21. C23×D19C2×C4semidirect
29. C2×C22⋊D19C2×C4semidirect
32. C22×Dic19C2×C4semidirect
37. C2×D76C2×C4semidirect
38. C2×C4×D19C2×C4semidirect
39. C2×Dic38C2×C4semidirect
90. #518D19semidirect
109. #117C2×D19semidirect
111. C2×C22⋊C4C2×D19semidirect
113. C19#2883semidirect

Maximal subgroups

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

subgroupindex
C2×#105974302
#119270192
#119265172
C2×#105972632
C19×#5182
#288319