Finite Group Databasebeta

← C22×#10597341 #14576858

Subgroups — C22×#10597341 #14576858

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×D76C212yesmaximal, complemented
2C23×D76C211yesmaximal, characteristic, complemented
3C23×C4×D19C211yesmaximal, characteristic, complemented
4C2×#10597341C2124yesmaximal, direct product factor
5C22×(C2×D19)⋊C4C212yesmaximal, complemented
6C22×C4⋊C4×C19C211yesmaximal, characteristic, complemented
7C24×D19C2212yes—
8C24×D19C2211yescharacteristic
9C23×C4×C19C2212yes—
10C23×C4×C19C2211yescharacteristic
11C23×Dic19C2211yescharacteristic
12C22×D76—216no—
13C22×D76—28no—
14C22×D76C22124yescomplemented
15C22×D76C22112yescomplemented
16C22×C4×D19—28no—
17C22×C4×D19C22112yescomplemented
18C2×C4⋊C4×C19C22112yescomplemented
19C2×(C2×D19)⋊C4C22124yescomplemented
20#10597341C22164yesdirect product factor
21C24×C19C2311yescharacteristic
22C23×D19—24no—
23C23×D19—24no—
24C23×D19—28no—
25C23×D19—28no—
26C23×D19—28no—
27C23×D19D418yescomplemented
28C23×D19C23112yes—
29C23×D19C2316yes—
30C22×C4×C19—28no—
31C22×C4×C19D418yescomplemented
32C22×C4×C19C23112yes—
33C22×C4×C19C2316yes—
34C22×Dic19—24no—
35C22×Dic19C2316yes—
36C2×D76—296no—
37C2×D76—248no—
38C2×D76C23132yescomplemented
39C2×D76C23116yescomplemented
40C2×C4×D19—248no—
41C2×C4×D19C23116yescomplemented
42C4⋊C4×C19C23116yescomplemented
43(C2×D19)⋊C4C23132yescomplemented
44C23×C19C2×D414yes—
45C23×C19C2×D414yes—
46C23×C19#4114yes—
47C23×C19C2413yes—
48C22×D19—232no—
49C22×D19—212no—
50C22×D19—212no—
51C22×D19—224no—
52C22×D19—224no—
53C22×D19—224no—
54C22×D19—432no—
55C22×D19C2×D4124yescomplemented
56C22×D19C2418yes—
57C22×D19C2414yes—
58C2×C4×C19—224no—
59C2×C4×C19C2×D4124yescomplemented
60C2×C4×C19C2418yes—
61C2×C4×C19C2414yes—
62C2×Dic19—212no—
63C2×Dic19C2414yes—
64D76—264no—
65D76—232no—
66C4×D19—232no—
67C22×#121—191nomaximal, Sylow
68C22×C19#121116yescomplemented
69C22×C19C22×D416yes—
70C22×C19C22×D416yes—
71C22×C19C2×#4116yes—
72C22×C19C2511yescharacteristic
73C2×D19—248no—
74C2×D19—24no—
75C2×D19—24no—
76C2×D19—28no—
77C2×D19—28no—
78C2×D19—28no—
79C2×D19—448no—
80C2×D19C22×D418yescomplemented
81C4×C19—28no—
82C4×C19C22×D418yescomplemented
83Dic19—24no—
84C23×D4—192no—
85C23×D4—191no—
86C24×C4—191no—
87C2×#121—1924no—
88C22×C4⋊C4D1911yescharacteristic, complemented
89C22×C22⋊C4—192no—
90C2×C19C2×#121112yescomplemented
91C2×C19C23×D411yescharacteristic
92C2×C19C23×D411yescharacteristic
93C2×C19C22×#4111yescharacteristic
94D19—28no—
95D19—48no—
96C25—191no—
97C25—192no—
98C22×D4—1924no—
99C22×D4—1912no—
100C22×D4—3816no—
101C22×D4—388no—
102C23×C4—191no—
103C23×C4—1912no—
104C23×C4—388no—
105C23×C4C2×D1912yes—
106C23×C4C2×D1911yescharacteristic
107#121—1964no—
108C2×C4⋊C4C2×D19112yescomplemented
109C2×C22⋊C4—1924no—
110C19C22×#12111yescharacteristic, complemented, Sylow
111C24—198no—
112C24—196no—
113C24—1912no—
114C24—384no—
115C24—384no—
116C24—388no—
117C24—388no—
118C24—388no—
119C24C22×D1911yescharacteristic
120C2×D4—1932no—
121C2×D4—1916no—
122C2×D4—3896no—
123C2×D4—3848no—
124C22×C4—28no—
125C22×C4—196no—
126C22×C4—1916no—
127C22×C4—384no—
128C22×C4—3848no—
129C22×C4D7618yescomplemented
130C22×C4C22×D19112yes—
131C22×C4C22×D1916yes—
132C4⋊C4C22×D19116yescomplemented
133C22⋊C4—1932no—
134C23—1924no—
135C23—194no—
136C23—198no—
137C23—3812no—
138C23—3812no—
139C23—3832no—
140C23—3824no—
141C23—3824no—
142C23—3824no—
143C23—7632no—
144C23C2×D7614yes—
145C23D4×D1914yes—
146C23#6454514yes—
147C23C23×D1913yes—
148D4—3864no—
149D4—3832no—
150C2×C4—224no—
151C2×C4—194no—
152C2×C4—3812no—
153C2×C4—3832no—
154C2×C4C2×D76124yescomplemented
155C2×C4C23×D1918yes—
156C2×C4C23×D1914yes—
157C22—198no—
158C22—384no—
159C22—384no—
160C22—3848no—
161C22—388no—
162C22—388no—
163C22—388no—
164C22—7648no—
165C22#10597341116yesdirect product factor
166C22C22×D7616yes—
167C22C2×D4×D1916yes—
168C22C2×#6454516yes—
169C22C24×D1911yescharacteristic
170C4—28no—
171C4—384no—
172C4C22×D7618yescomplemented
173C2—388no—
174C2—768no—
175C2C2×#10597341112yesdirect product factor
176C2C22×D4×D1911yescharacteristic
177C2C23×D7611yescharacteristic
178C2C22×#6454511yescharacteristic
subgroupG/H
centerC24C22×D19
commutator, cosocleC22×C19C25
FrattiniC22C24×D19
FittingC22×C4⋊C4×C19C2
socleC24×C19C23
hypercenterC22×C4⋊C4D19
hypocenterC19C22×#121
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×D76C2semidirect
2. C23×D76C2semidirect
3. C23×C4×D19C2semidirect
4. C2×#10597341C2direct (N × H)
5. C22×(C2×D19)⋊C4C2semidirect
6. C22×C4⋊C4×C19C2semidirect
14. C22×D76C22semidirect
15. C22×D76C22semidirect
17. C22×C4×D19C22semidirect
18. C2×C4⋊C4×C19C22semidirect
19. C2×(C2×D19)⋊C4C22semidirect
20. #10597341C22direct (N × H)
27. C23×D19D4semidirect
31. C22×C4×C19D4semidirect
38. C2×D76C23semidirect
39. C2×D76C23semidirect
41. C2×C4×D19C23semidirect
42. C4⋊C4×C19C23semidirect
43. (C2×D19)⋊C4C23semidirect
55. C22×D19C2×D4semidirect
59. C2×C4×C19C2×D4semidirect
68. C22×C19#121semidirect
80. C2×D19C22×D4semidirect
82. C4×C19C22×D4semidirect
88. C22×C4⋊C4D19semidirect
90. C2×C19C2×#121semidirect
108. C2×C4⋊C4C2×D19semidirect
110. C19C22×#121semidirect
129. C22×C4D76semidirect
132. C4⋊C4C22×D19semidirect
154. C2×C4C2×D76semidirect
165. C22#10597341direct (N × H)
172. C4C22×D76semidirect
175. C2C2×#10597341direct (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×C4×D192
C2×#105973412
C22×(C2×D19)⋊C42
C22×C4⋊C4×C192
C22×#12119