Finite Group Databasebeta

← C22×#10597376 #14576857

Subgroups — C22×#10597376 #14576857

Order 2432.

2528 conjugacy classes of subgroups; only the 725 normal subgroups are shown.

normal subgroups only

This group has 2528 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
1C23×D76C211yesmaximal, characteristic, complemented
2C23×C22⋊D19C212yesmaximal, complemented
3C2×#10597376C2124yesmaximal, direct product factor
4C22×C4⋊Dic19C211yesmaximal, characteristic, complemented
5C22×(C2×D19)⋊C4C212yesmaximal, complemented
6C24×C4×C19C211yesmaximal, characteristic, complemented
7C25×C19C2211yescharacteristic
8C24×D19C2212yes—
9C23×C4×C19—28no—
10C23×C4×C19C2211yescharacteristic
11C23×C4×C19C2211yescharacteristic
12C23×C4×C19C22112yescomplemented
13C22×C22⋊D19—216no—
14C22×C22⋊D19C22124yescomplemented
15C23×Dic19C2212yes—
16C22×D76—28no—
17C22×D76C22112yescomplemented
18#10597376C22164yesdirect product factor
19C2×(C2×D19)⋊C4C22124yescomplemented
20C2×C4⋊Dic19C22112yescomplemented
21C24×C19—24no—
22C24×C19—24no—
23C24×C19D418yescomplemented
24C24×C19C2316yes—
25C24×C19C2311yescharacteristic
26C23×D19—28no—
27C23×D19—28no—
28C23×D19—28no—
29C23×D19C23112yes—
30C22×C4×C19—24no—
31C22×C4×C19—248no—
32C22×C4×C19D418yescomplemented
33C22×C4×C19C2316yes—
34C22×C4×C19C2316yes—
35C22×C4×C19C23116yescomplemented
36C2×C22⋊D19—296no—
37C2×C22⋊D19C23132yescomplemented
38C22×Dic19—28no—
39C22×Dic19C23112yes—
40C2×D76—248no—
41C2×D76C23116yescomplemented
42(C2×D19)⋊C4C23132yescomplemented
43C4⋊Dic19C23116yescomplemented
44C23×C19—232no—
45C23×C19—212no—
46C23×C19—212no—
47C23×C19C2×D414yes—
48C23×C19C2×D414yes—
49C23×C19C2×D4124yescomplemented
50C23×C19#4114yes—
51C23×C19C2414yes—
52C23×C19C2413yes—
53C22×D19—224no—
54C22×D19—224no—
55C22×D19—224no—
56C22×D19—432no—
57C22×D19C2418yes—
58C2×C4×C19—212no—
59C2×C4×C19—232no—
60C2×C4×C19C2×D4124yescomplemented
61C2×C4×C19C2414yes—
62C2×C4×C19C2414yes—
63C22⋊D19—264no—
64C2×Dic19—224no—
65C2×Dic19C2418yes—
66D76—232no—
67C22×#121—191nomaximal, Sylow
68C22×C19—248no—
69C22×C19—24no—
70C22×C19—24no—
71C22×C19#121116yescomplemented
72C22×C19C22×D416yes—
73C22×C19C22×D416yes—
74C22×C19C22×D418yescomplemented
75C22×C19C2×#4116yes—
76C22×C19C2511yescharacteristic
77C2×D19—28no—
78C2×D19—28no—
79C2×D19—28no—
80C2×D19—448no—
81C4×C19—24no—
82C4×C19C22×D418yescomplemented
83Dic19—28no—
84C23×D4—192no—
85C23×D4—191no—
86C24×C4D1911yescharacteristic, complemented
87C2×#121—1924no—
88C22×C4⋊C4—191no—
89C22×C22⋊C4—192no—
90C2×C19—28no—
91C2×C19C2×#121112yescomplemented
92C2×C19C23×D411yescharacteristic
93C2×C19C23×D411yescharacteristic
94C2×C19C22×#4111yescharacteristic
95D19—48no—
96C25—192no—
97C25C2×D1911yescharacteristic
98C22×D4—1924no—
99C22×D4—1912no—
100C22×D4—3816no—
101C22×D4—388no—
102C23×C4—28no—
103C23×C4—192no—
104C23×C4C2×D1911yescharacteristic
105C23×C4C2×D1911yescharacteristic
106C23×C4C2×D19112yescomplemented
107#121—1964no—
108C2×C4⋊C4—1912no—
109C2×C22⋊C4—1924no—
110C19C22×#12111yescharacteristic, complemented, Sylow
111C24—24no—
112C24—24no—
113C24—1912no—
114C24—388no—
115C24—388no—
116C24—388no—
117C24D7618yescomplemented
118C24C22×D1916yes—
119C24C22×D1911yescharacteristic
120C2×D4—1932no—
121C2×D4—1916no—
122C2×D4—3896no—
123C2×D4—3848no—
124C22×C4—24no—
125C22×C4—248no—
126C22×C4—1912no—
127C22×C4—388no—
128C22×C4C22⋊D1918yescomplemented
129C22×C4C22×D1916yes—
130C22×C4C22×D1916yes—
131C22×C4C22×D19116yescomplemented
132C4⋊C4—1916no—
133C22⋊C4—1932no—
134C23—232no—
135C23—212no—
136C23—212no—
137C23—198no—
138C23—3824no—
139C23—3824no—
140C23—3824no—
141C23—7632no—
142C23C2×D7614yes—
143C23C2×D76124yescomplemented
144C23#6454114yes—
145C23C2×C22⋊D1914yes—
146C23C23×D1914yes—
147C23C23×D1913yes—
148D4—3864no—
149D4—3832no—
150C2×C4—212no—
151C2×C4—232no—
152C2×C4—198no—
153C2×C4—3824no—
154C2×C4C2×C22⋊D19124yescomplemented
155C2×C4C23×D1914yes—
156C2×C4C23×D1914yes—
157C22—24no—
158C22—24no—
159C22—248no—
160C22—388no—
161C22—388no—
162C22—388no—
163C22—7648no—
164C22#10597376116yesdirect product factor
165C22C22×D7616yes—
166C22C22×D7618yescomplemented
167C22C2×#6454116yes—
168C22C22×C22⋊D1916yes—
169C22C24×D1911yescharacteristic
170C4—24no—
171C4—388no—
172C4C22×C22⋊D1918yescomplemented
173C2—28no—
174C2—768no—
175C2C2×#10597376112yesdirect product factor
176C2C23×C22⋊D1911yescharacteristic
177C2C23×D7611yescharacteristic
178C2C22×#6454111yescharacteristic
subgroupG/H
centerC24C22×D19
commutator, cosocleC22×C19C25
FrattiniC22C24×D19
FittingC24×C4×C19C2
socleC24×C19C23
hypercenterC24×C4D19
hypocenterC19C22×#121
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C24 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
1. C23×D76C2semidirect
2. C23×C22⋊D19C2semidirect
3. C2×#10597376C2direct (N × H)
4. C22×C4⋊Dic19C2semidirect
5. C22×(C2×D19)⋊C4C2semidirect
6. C24×C4×C19C2semidirect
12. C23×C4×C19C22semidirect
14. C22×C22⋊D19C22semidirect
17. C22×D76C22semidirect
18. #10597376C22direct (N × H)
19. C2×(C2×D19)⋊C4C22semidirect
20. C2×C4⋊Dic19C22semidirect
23. C24×C19D4semidirect
32. C22×C4×C19D4semidirect
35. C22×C4×C19C23semidirect
37. C2×C22⋊D19C23semidirect
41. C2×D76C23semidirect
42. (C2×D19)⋊C4C23semidirect
43. C4⋊Dic19C23semidirect
49. C23×C19C2×D4semidirect
60. C2×C4×C19C2×D4semidirect
71. C22×C19#121semidirect
74. C22×C19C22×D4semidirect
82. C4×C19C22×D4semidirect
86. C24×C4D19semidirect
91. C2×C19C2×#121semidirect
106. C23×C4C2×D19semidirect
110. C19C22×#121semidirect
117. C24D76semidirect
128. C22×C4C22⋊D19semidirect
131. C22×C4C22×D19semidirect
143. C23C2×D76semidirect
154. C2×C4C2×C22⋊D19semidirect
164. C22#10597376direct (N × H)
166. C22C22×D76semidirect
172. C4C22×C22⋊D19semidirect
175. C2C2×#10597376direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D762
C23×C22⋊D192
C2×#105973762
C22×C4⋊Dic192
C22×(C2×D19)⋊C42
C24×C4×C192
C22×#12119