Finite Group Databasebeta

← C22×#10597384 #14576854

Subgroups — C22×#10597384 #14576854

Order 2432.

2528 conjugacy classes of subgroups; only the 685 normal subgroups are shown.

normal subgroups only

This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 685 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
1C23×C22⋊D19C212yesmaximal, complemented
2C23×C4×D19C211yesmaximal, characteristic, complemented
3C2×#10597384C2124yesmaximal, direct product factor
4C22×C4⋊Dic19C211yesmaximal, characteristic, complemented
5C22×C22⋊Dic19C212yesmaximal, complemented
6C23×D4×C19C211yesmaximal, characteristic, complemented
7C25×C19C2212yes—
8C24×D19C2211yescharacteristic
9C22×D4×C19—28no—
10C22×D4×C19C22112yescomplemented
11C23×C4×C19C2211yescharacteristic
12C22×C22⋊D19—216no—
13C22×C22⋊D19C22124yescomplemented
14C23×Dic19C2211yescharacteristic
15C23×Dic19C2212yes—
16C22×C4×D19—28no—
17C22×C4×D19C22112yescomplemented
18C2×C22⋊Dic19C22124yescomplemented
19#10597384C22164yesdirect product factor
20C2×C4⋊Dic19C22112yescomplemented
21C24×C19—28no—
22C24×C19—28no—
23C24×C19—28no—
24C24×C19C23112yes—
25C24×C19C2311yescharacteristic
26C23×D19—24no—
27C23×D19—24no—
28C23×D19D418yescomplemented
29C23×D19C2316yes—
30C2×D4×C19—248no—
31C2×D4×C19C23116yescomplemented
32C22×C4×C19D418yescomplemented
33C22×C4×C19C2316yes—
34C2×C22⋊D19—296no—
35C2×C22⋊D19C23132yescomplemented
36C22×Dic19—24no—
37C22×Dic19—28no—
38C22×Dic19C2316yes—
39C22×Dic19C23112yes—
40C2×C4×D19—248no—
41C2×C4×D19C23116yescomplemented
42C22⋊Dic19C23132yescomplemented
43C4⋊Dic19C23116yescomplemented
44C23×C19—224no—
45C23×C19—224no—
46C23×C19—224no—
47C23×C19—432no—
48C23×C19C2×D414yes—
49C23×C19C2×D414yes—
50C23×C19#4114yes—
51C23×C19C2418yes—
52C23×C19C2413yes—
53C22×D19—232no—
54C22×D19—212no—
55C22×D19—212no—
56C22×D19C2×D4124yescomplemented
57C22×D19C2414yes—
58D4×C19—232no—
59C2×C4×C19C2×D4124yescomplemented
60C2×C4×C19C2414yes—
61C22⋊D19—264no—
62C2×Dic19—212no—
63C2×Dic19—224no—
64C2×Dic19C2418yes—
65C2×Dic19C2414yes—
66C4×D19—232no—
67C22×#121—191nomaximal, Sylow
68C22×C19—28no—
69C22×C19—28no—
70C22×C19—28no—
71C22×C19—448no—
72C22×C19#121116yescomplemented
73C22×C19C22×D416yes—
74C22×C19C22×D416yes—
75C22×C19C2×#4116yes—
76C22×C19C2511yescharacteristic
77C2×D19—248no—
78C2×D19—24no—
79C2×D19—24no—
80C2×D19C22×D418yescomplemented
81C4×C19C22×D418yescomplemented
82Dic19—24no—
83Dic19—28no—
84C23×D4—192no—
85C23×D4D1911yescharacteristic, complemented
86C24×C4—191no—
87C2×#121—1924no—
88C22×C4⋊C4—191no—
89C22×C22⋊C4—192no—
90C2×C19—48no—
91C2×C19C2×#121112yescomplemented
92C2×C19C23×D411yescharacteristic
93C2×C19C23×D411yescharacteristic
94C2×C19C22×#4111yescharacteristic
95D19—28no—
96C25—191no—
97C25C2×D1912yes—
98C22×D4—28no—
99C22×D4—1924no—
100C22×D4—3816no—
101C22×D4C2×D19112yescomplemented
102C23×C4—191no—
103C23×C4—192no—
104C23×C4—1912no—
105C23×C4—388no—
106C23×C4C2×D1911yescharacteristic
107#121—1964no—
108C2×C4⋊C4—1912no—
109C2×C22⋊C4—1924no—
110C19C22×#12111yescharacteristic, complemented, Sylow
111C24—28no—
112C24—28no—
113C24—28no—
114C24—198no—
115C24—196no—
116C24—384no—
117C24—384no—
118C24C22×D19112yes—
119C24C22×D1911yescharacteristic
120C2×D4—248no—
121C2×D4—1932no—
122C2×D4—3896no—
123C2×D4C22×D19116yescomplemented
124C22×C4—196no—
125C22×C4—1912no—
126C22×C4—1916no—
127C22×C4—388no—
128C22×C4—384no—
129C22×C4—3848no—
130C22×C4C22⋊D1918yescomplemented
131C22×C4C22×D1916yes—
132C4⋊C4—1916no—
133C22⋊C4—1932no—
134C23—224no—
135C23—224no—
136C23—224no—
137C23—432no—
138C23—1924no—
139C23—194no—
140C23—3832no—
141C23—3812no—
142C23—3812no—
143C23D4×D1914yes—
144C23#6454314yes—
145C23C2×C22⋊D1914yes—
146C23C23×D1918yes—
147C23C23×D1913yes—
148D4—232no—
149D4—3864no—
150C2×C4—194no—
151C2×C4—198no—
152C2×C4—3824no—
153C2×C4—3812no—
154C2×C4—3832no—
155C2×C4C2×C22⋊D19124yescomplemented
156C2×C4C23×D1914yes—
157C22—28no—
158C22—28no—
159C22—28no—
160C22—448no—
161C22—198no—
162C22—384no—
163C22—384no—
164C22—3848no—
165C22#10597384116yesdirect product factor
166C22C2×D4×D1916yes—
167C22C2×#6454316yes—
168C22C22×C22⋊D1916yes—
169C22C24×D1911yescharacteristic
170C4—388no—
171C4—384no—
172C4C22×C22⋊D1918yescomplemented
173C2—48no—
174C2—388no—
175C2C2×#10597384112yesdirect product factor
176C2C22×D4×D1911yescharacteristic
177C2C23×C22⋊D1911yescharacteristic
178C2C22×#6454311yescharacteristic
subgroupG/H
centerC24C22×D19
commutator, cosocleC22×C19C25
FrattiniC22C24×D19
FittingC23×D4×C19C2
socleC24×C19C23
hypercenterC23×D4D19
hypocenterC19C22×#121
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D19C2semidirect
2. C23×C4×D19C2semidirect
3. C2×#10597384C2direct (N × H)
4. C22×C4⋊Dic19C2semidirect
5. C22×C22⋊Dic19C2semidirect
6. C23×D4×C19C2semidirect
10. C22×D4×C19C22semidirect
13. C22×C22⋊D19C22semidirect
17. C22×C4×D19C22semidirect
18. C2×C22⋊Dic19C22semidirect
19. #10597384C22direct (N × H)
20. C2×C4⋊Dic19C22semidirect
28. C23×D19D4semidirect
31. C2×D4×C19C23semidirect
32. C22×C4×C19D4semidirect
35. C2×C22⋊D19C23semidirect
41. C2×C4×D19C23semidirect
42. C22⋊Dic19C23semidirect
43. C4⋊Dic19C23semidirect
56. C22×D19C2×D4semidirect
59. C2×C4×C19C2×D4semidirect
72. C22×C19#121semidirect
80. C2×D19C22×D4semidirect
81. C4×C19C22×D4semidirect
85. C23×D4D19semidirect
91. C2×C19C2×#121semidirect
101. C22×D4C2×D19semidirect
110. C19C22×#121semidirect
123. C2×D4C22×D19semidirect
130. C22×C4C22⋊D19semidirect
155. C2×C4C2×C22⋊D19semidirect
165. C22#10597384direct (N × H)
172. C4C22×C22⋊D19semidirect
175. C2C2×#10597384direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D192
C23×C4×D192
C2×#105973842
C22×C4⋊Dic192
C22×C22⋊Dic192
C23×D4×C192
C22×#12119