Finite Group Databasebeta

← C22×#10597383 #14576850

Subgroups — C22×#10597383 #14576850

Order 2432.

4544 conjugacy classes of subgroups; only the 725 normal subgroups are shown.

normal subgroups only

This group has 4544 conjugacy classes of subgroups — too many to draw. Only its 725 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
1C25×D19C211yesmaximal, characteristic, complemented
2C23×C22⋊D19C212yesmaximal, complemented
3C2×#10597383C2124yesmaximal, direct product factor
4C22×C22⋊Dic19C211yesmaximal, characteristic, complemented
5C22×(C2×D19)⋊C4C212yesmaximal, complemented
6C23×D4×C19C211yesmaximal, characteristic, complemented
7C25×C19C2211yescharacteristic
8C25×C19C2211yescharacteristic, complemented
9C24×D19—28no—
10C24×D19—216no—
11C24×D19C2212yes—
12C24×D19C22112yescomplemented
13C22×D4×C19—28no—
14C22×D4×C19C22112yescomplemented
15C23×C4×C19C2211yescharacteristic, complemented
16C22×C22⋊D19—216no—
17C22×C22⋊D19C22124yescomplemented
18C23×Dic19C2212yescomplemented
19C2×C22⋊Dic19C22112yescomplemented
20#10597383C22164yesdirect product factor
21C2×(C2×D19)⋊C4C22124yescomplemented
22C24×C19—28no—
23C24×C19—28no—
24C24×C19—24no—
25C24×C19D418yescomplemented
26C24×C19C2316yes—
27C24×C19C2311yescharacteristic
28C24×C19C2316yescomplemented
29C23×D19—2128no—
30C23×D19—28no—
31C23×D19—28no—
32C23×D19—248no—
33C23×D19—296no—
34C23×D19D4116yescomplemented
35C23×D19C23112yes—
36C23×D19C23116yescomplemented
37C2×D4×C19—248no—
38C2×D4×C19C23116yescomplemented
39C22×C4×C19—24no—
40C22×C4×C19C2316yescomplemented
41C2×C22⋊D19—296no—
42C2×C22⋊D19C23132yescomplemented
43C22×Dic19—28no—
44C22×Dic19C23112yescomplemented
45C22⋊Dic19C23116yescomplemented
46(C2×D19)⋊C4C23132yescomplemented
47C23×C19—232no—
48C23×C19—224no—
49C23×C19—224no—
50C23×C19—212no—
51C23×C19—416no—
52C23×C19C2×D418yes—
53C23×C19C2×D414yes—
54C23×C19C2×D4124yescomplemented
55C23×C19C2414yes—
56C23×C19C2413yes—
57C23×C19C2414yescomplemented
58C22×D19—2384no—
59C22×D19—264no—
60C22×D19—224no—
61C22×D19—224no—
62C22×D19—232no—
63C22×D19—264no—
64C22×D19C2×D4148yescomplemented
65C22×D19C2418yes—
66D4×C19—232no—
67C2×C4×C19—212no—
68C2×C4×C19C2414yescomplemented
69C22⋊D19—264no—
70C2×Dic19—224no—
71C2×Dic19C2418yescomplemented
72C22×#120—191nomaximal, Sylow
73C22×C19—248no—
74C22×C19—28no—
75C22×C19—28no—
76C22×C19—24no—
77C22×C19—424no—
78C22×C19#120116yescomplemented
79C22×C19C22×D4112yes—
80C22×C19C22×D416yes—
81C22×C19C22×D418yescomplemented
82C22×C19C2511yescharacteristic
83C2×D19—2128no—
84C2×D19—296no—
85C2×D19—28no—
86C2×D19—28no—
87C2×D19C22×D4116yescomplemented
88C4×C19—24no—
89Dic19—28no—
90C26—191no—
91C23×D4—192no—
92C23×D4D1911yescharacteristic, complemented
93C2×#120—1924no—
94C22×C22⋊C4—191no—
95C22×C22⋊C4—192no—
96C2×C19—28no—
97C2×C19—44no—
98C2×C19C2×#120112yescomplemented
99C2×C19C23×D412yes—
100C2×C19C23×D411yescharacteristic
101D19—216no—
102C25—192no—
103C25—1912no—
104C25—3816no—
105C25—388no—
106C25C2×D1911yescharacteristic
107C25C2×D1911yescharacteristic, complemented
108C22×D4—28no—
109C22×D4—1924no—
110C22×D4—3816no—
111C22×D4C2×D19112yescomplemented
112C23×C4—192no—
113C23×C4C2×D1911yescharacteristic, complemented
114#120—1964no—
115C2×C22⋊C4—1912no—
116C2×C22⋊C4—1924no—
117C19C22×#12011yescharacteristic, complemented, Sylow
118C24—28no—
119C24—28no—
120C24—24no—
121C24—1916no—
122C24—1912no—
123C24—1916no—
124C24—3896no—
125C24—38128no—
126C24—388no—
127C24—388no—
128C24—3848no—
129C24C22⋊D1918yescomplemented
130C24C22×D1916yes—
131C24C22×D1911yescharacteristic
132C24C22×D1916yescomplemented
133C2×D4—248no—
134C2×D4—1932no—
135C2×D4—3896no—
136C2×D4C22×D19116yescomplemented
137C22×C4—24no—
138C22×C4—1912no—
139C22×C4—388no—
140C22×C4C22×D1916yescomplemented
141C22⋊C4—1916no—
142C22⋊C4—1932no—
143C23—232no—
144C23—224no—
145C23—224no—
146C23—212no—
147C23—416no—
148C23—1948no—
149C23—198no—
150C23—3864no—
151C23—38384no—
152C23—3864no—
153C23—3824no—
154C23—3824no—
155C23—3832no—
156C23D4×D1918yes—
157C23C2×C22⋊D1914yes—
158C23C2×C22⋊D19124yescomplemented
159C23C23×D1914yes—
160C23C23×D1913yes—
161C23C23×D1914yescomplemented
162D4—232no—
163D4—3864no—
164C2×C4—212no—
165C2×C4—198no—
166C2×C4—3824no—
167C2×C4C23×D1914yescomplemented
168C22—28no—
169C22—248no—
170C22—28no—
171C22—24no—
172C22—424no—
173C22—1916no—
174C22—38128no—
175C22—388no—
176C22—388no—
177C22—3896no—
178C22#10597383116yesdirect product factor
179C22C2×D4×D19112yes—
180C22C22×C22⋊D1916yes—
181C22C22×C22⋊D1918yescomplemented
182C22C24×D1911yescharacteristic
183C4—24no—
184C4—388no—
185C2—28no—
186C2—44no—
187C2—3816no—
188C2C2×#10597383112yesdirect product factor
189C2C22×D4×D1912yes—
190C2C23×C22⋊D1911yescharacteristic
subgroupG/H
centerC24C22×D19
commutator, cosocleC22×C19C25
FrattiniC22C24×D19
FittingC23×D4×C19C2
socleC24×C19C23
hypercenterC23×D4D19
hypocenterC19C22×#120
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C25×D19C2semidirect
2. C23×C22⋊D19C2semidirect
3. C2×#10597383C2direct (N × H)
4. C22×C22⋊Dic19C2semidirect
5. C22×(C2×D19)⋊C4C2semidirect
6. C23×D4×C19C2semidirect
8. C25×C19C22semidirect
12. C24×D19C22semidirect
14. C22×D4×C19C22semidirect
15. C23×C4×C19C22semidirect
17. C22×C22⋊D19C22semidirect
18. C23×Dic19C22semidirect
19. C2×C22⋊Dic19C22semidirect
20. #10597383C22direct (N × H)
21. C2×(C2×D19)⋊C4C22semidirect
25. C24×C19D4semidirect
28. C24×C19C23semidirect
34. C23×D19D4semidirect
36. C23×D19C23semidirect
38. C2×D4×C19C23semidirect
40. C22×C4×C19C23semidirect
42. C2×C22⋊D19C23semidirect
44. C22×Dic19C23semidirect
45. C22⋊Dic19C23semidirect
46. (C2×D19)⋊C4C23semidirect
54. C23×C19C2×D4semidirect
57. C23×C19C24semidirect
64. C22×D19C2×D4semidirect
68. C2×C4×C19C24semidirect
71. C2×Dic19C24semidirect
78. C22×C19#120semidirect
81. C22×C19C22×D4semidirect
87. C2×D19C22×D4semidirect
92. C23×D4D19semidirect
98. C2×C19C2×#120semidirect
107. C25C2×D19semidirect
111. C22×D4C2×D19semidirect
113. C23×C4C2×D19semidirect
117. C19C22×#120semidirect
129. C24C22⋊D19semidirect
132. C24C22×D19semidirect
136. C2×D4C22×D19semidirect
140. C22×C4C22×D19semidirect
158. C23C2×C22⋊D19semidirect
161. C23C23×D19semidirect
167. C2×C4C23×D19semidirect
178. C22#10597383direct (N × H)
181. C22C22×C22⋊D19semidirect
188. C2C2×#10597383direct (N × H)

Maximal subgroups

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

subgroupindex
C25×D192
C23×C22⋊D192
C2×#105973832
C22×C22⋊Dic192
C22×(C2×D19)⋊C42
C23×D4×C192
C22×#12019