Finite Group Databasebeta

← C2×#11927106 #14576938

Subgroups — C2×#11927106 #14576938

Order 2432.

1984 conjugacy classes of subgroups; only the 565 normal subgroups are shown.

normal subgroups only

This group has 1984 conjugacy classes of subgroups — too many to draw. Only its 565 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
2#11927106C2116yesmaximal, direct product factor
3C2×#10597332C214yesmaximal, complemented
4C2×#10597376C214yesmaximal, complemented
5C2×#10597328C214yesmaximal, complemented
6C22×C22⋊C4×C19C211yesmaximal, characteristic, complemented
7C25×C19C2211yescharacteristic
8C24×D19C2212yescomplemented
9C23×C4×C19C2212yescomplemented
10C22×C22⋊D19—216no—
11C22×C22⋊D19C2214yes—
12C22×C22⋊D19C2214yescomplemented
13C22×C22⋊D19C22116yescomplemented
14C23×Dic19C2212yescomplemented
15C22×D76C2214yescomplemented
16C2×C22⋊C4×C19C2214yescomplemented
17C2×C22⋊C4×C19C2218yescomplemented
18#10597376C22132yescomplemented
19C2×(C2×D19)⋊C4C2218yescomplemented
20C2×C4⋊Dic19C2214yescomplemented
21#10597332C22132yescomplemented
22#10597328C22132yescomplemented
23C24×C19—44no—
24C24×C19D418yescomplemented
25C24×C19C2312yes—
26C24×C19C2311yescharacteristic
27C24×C19C2314yes—
28C23×D19—28no—
29C23×D19—48no—
30C23×D19C2314yes—
31C23×D19C2318yescomplemented
32C22×C4×C19—44no—
33C22×C4×C19C2314yes—
34C22×C4×C19C2318yescomplemented
35C2×C22⋊D19—216no—
36C2×C22⋊D19—216no—
37C2×C22⋊D19—264no—
38C2×C22⋊D19C23116yes—
39C2×C22⋊D19C23116yescomplemented
40C22×Dic19—28no—
41C22×Dic19C2314yes—
42C22×Dic19C2318yescomplemented
43C2×D76—48no—
44C2×D76C23116yescomplemented
45C22⋊C4×C19C23116yescomplemented
46(C2×D19)⋊C4C23132yescomplemented
47C4⋊Dic19C23116yescomplemented
48C23×C19—24no—
49C23×C19—28no—
50C23×C19—416no—
51C23×C19—48no—
52C23×C19C2×D418yes—
53C23×C19C2×D414yes—
54C23×C19C2×D4116yescomplemented
55C23×C19C2414yes—
56C23×C19C2412yes—
57C23×C19C2411yescharacteristic
58C22×D19—28no—
59C22×D19—216no—
60C22×D19—216no—
61C22×D19—416no—
62C22×D19—432no—
63C22×D19C2418yes—
64C2×C4×C19—28no—
65C2×C4×C19—48no—
66C2×C4×C19C2418yes—
67C22⋊D19—232no—
68C22⋊D19—232no—
69C2×Dic19—28no—
70C2×Dic19—216no—
71C2×Dic19C2418yes—
72D76—416no—
73C2×#534—191nomaximal, Sylow
74C22×C19—216no—
75C22×C19—28no—
76C22×C19—24no—
77C22×C19—28no—
78C22×C19—416no—
79C22×C19C22×D418yes—
80C22×C19C22×D414yes—
81C22×C19C22×D412yes—
82C22×C19H(5,𝔽2)14yes—
83C22×C19C2511yescharacteristic
84C2×D19—28no—
85C2×D19—216no—
86C2×D19—432no—
87C2×D19—416no—
88C4×C19—28no—
89Dic19—28no—
90C23×D4—192no—
91#534—1916no—
92C2×#123—194no—
93C2×#121—194no—
94C2×#120—194no—
95C22×C22⋊C4D1911yescharacteristic, complemented
96C2×C19—28no—
97C2×C19—24no—
98C2×C19#53414yescomplemented
99C2×C19C23×D411yescharacteristic
100C2×C19C2×H(5,𝔽2)12yes—
101D19—48no—
102C25—192no—
103C25C2×D1911yescharacteristic
104C22×D4—194no—
105C22×D4—194no—
106C22×D4—1916no—
107C22×D4—194no—
108C22×D4—3816no—
109C23×C4—192no—
110C23×C4C2×D1912yescomplemented
111#123—1932no—
112#121—1932no—
113#120—1932no—
114C2×C4⋊C4—194no—
115C2×C22⋊C4—198no—
116C2×C22⋊C4C2×D1914yescomplemented
117C2×C22⋊C4C2×D1918yescomplemented
118C19C2×#53411yescharacteristic, complemented, Sylow
119C24—44no—
120C24—194no—
121C24—198no—
122C24—388no—
123C24—768no—
124C24D7618yescomplemented
125C24C22×D1912yes—
126C24C22×D1911yescharacteristic
127C24C22×D1914yes—
128C2×D4—1916no—
129C2×D4—1916no—
130C2×D4—1916no—
131C2×D4—3816no—
132C2×D4—3816no—
133C2×D4—3864no—
134C2×D4—768no—
135C22×C4—44no—
136C22×C4—198no—
137C22×C4—194no—
138C22×C4—388no—
139C22×C4C22×D1914yes—
140C22×C4C22×D1918yescomplemented
141C4⋊C4—1916no—
142C22⋊C4—1932no—
143C22⋊C4C22×D19116yescomplemented
144C23—24no—
145C23—28no—
146C23—416no—
147C23—48no—
148C23—198no—
149C23—3816no—
150C23—388no—
151C23—3816no—
152C23—7616no—
153C23—7632no—
154C23C2×D7618yes—
155C23C2×D7614yes—
156C23C2×D76116yescomplemented
157C23C23×D1914yes—
158C23C23×D1912yes—
159C23C23×D1911yescharacteristic
160D4—3832no—
161D4—3832no—
162D4—7616no—
163C2×C4—28no—
164C2×C4—48no—
165C2×C4—198no—
166C2×C4—3816no—
167C2×C4—388no—
168C2×C4C23×D1918yes—
169C22—216no—
170C22—28no—
171C22—24no—
172C22—28no—
173C22—416no—
174C22—388no—
175C22—3816no—
176C22—7632no—
177C22—7616no—
178C22C22×D7618yes—
179C22C22×D7614yes—
180C22C22×D7612yes—
181C22#1059743014yes—
182C22C24×D1911yescharacteristic
183C4—28no—
184C4—388no—
185C2—28no—
186C2—24no—
187C2—768no—
188C2#1192710614yesdirect product factor
189C2C23×D7611yescharacteristic
190C2C2×#1059743012yes—
subgroupG/H
centerC23C23×D19
commutator, cosocleC22×C19C25
FrattiniC22C24×D19
FittingC22×C22⋊C4×C19C2
socleC23×C19C24
hypercenterC22×C22⋊C4D19
hypocenterC19C2×#534
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D19C2semidirect
2. #11927106C2direct (N × H)
3. C2×#10597332C2semidirect
4. C2×#10597376C2semidirect
5. C2×#10597328C2semidirect
6. C22×C22⋊C4×C19C2semidirect
8. C24×D19C22semidirect
9. C23×C4×C19C22semidirect
12. C22×C22⋊D19C22semidirect
13. C22×C22⋊D19C22semidirect
14. C23×Dic19C22semidirect
15. C22×D76C22semidirect
16. C2×C22⋊C4×C19C22semidirect
17. C2×C22⋊C4×C19C22semidirect
18. #10597376C22semidirect
19. C2×(C2×D19)⋊C4C22semidirect
20. C2×C4⋊Dic19C22semidirect
21. #10597332C22semidirect
22. #10597328C22semidirect
24. C24×C19D4semidirect
31. C23×D19C23semidirect
34. C22×C4×C19C23semidirect
39. C2×C22⋊D19C23semidirect
42. C22×Dic19C23semidirect
44. C2×D76C23semidirect
45. C22⋊C4×C19C23semidirect
46. (C2×D19)⋊C4C23semidirect
47. C4⋊Dic19C23semidirect
54. C23×C19C2×D4semidirect
95. C22×C22⋊C4D19semidirect
98. C2×C19#534semidirect
110. C23×C4C2×D19semidirect
116. C2×C22⋊C4C2×D19semidirect
117. C2×C22⋊C4C2×D19semidirect
118. C19C2×#534semidirect
124. C24D76semidirect
140. C22×C4C22×D19semidirect
143. C22⋊C4C22×D19semidirect
156. C23C2×D76semidirect
188. C2#11927106direct (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
#119271062
C2×#105973322
C2×#105973762
C2×#105973282
C22×C22⋊C4×C192
C2×#53419