Finite Group Databasebeta

← C23×C22⋊#1057 #16808030

Subgroups — C23×C22⋊#1057 #16808030

Order 3328.

7646 conjugacy classes of subgroups; only the 2232 normal subgroups are shown.

normal subgroups only

This group has 7646 conjugacy classes of subgroups — too many to draw. Only its 2232 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
1C24×#1057C212yesmaximal, complemented
2C22×C22⋊#1057C2128yesmaximal, direct product factor
3C25×Dic13C211yesmaximal, characteristic
4C26×C13C411yescharacteristic
5C24×Dic13—216no—
6C24×Dic13C4114yes—
7C24×Dic13C411yescharacteristic
8C24×Dic13C22114yes—
9C24×Dic13C2211yescharacteristic
10C23×#1057—216no—
11C23×#1057C22128yescomplemented
12C2×C22⋊#1057C221112yesdirect product factor
13C25×C13—28no—
14C25×C13—28no—
15C25×C13C8116yescomplemented
16C25×C13C2×C4114yes—
17C25×C13C2×C411yescharacteristic
18C23×Dic13—28no—
19C23×Dic13—2112no—
20C23×Dic13—2112no—
21C23×Dic13C2×C4114yes—
22C23×Dic13C2×C4184yes—
23C23×Dic13C2×C417yes—
24C23×Dic13D4116yes—
25C23×Dic13C23128yes—
26C23×Dic13C2317yes—
27C22×#1057—2112no—
28C22×#1057C23156yescomplemented
29C22⋊#1057C23164yesdirect product factor
30C23×C22⋊C8—131nomaximal, Sylow
31C24×C13—2128no—
32C24×C13—256no—
33C24×C13—256no—
34C24×C13C22⋊C418yes—
35C24×C13C2×C818yes—
36C24×C13C2×C81112yescomplemented
37C24×C13M1618yes—
38C24×C13C22×C4128yes—
39C24×C13C22×C417yes—
40C22×Dic13—256no—
41C22×Dic13—2336no—
42C22×Dic13—2112no—
43C22×Dic13C22⋊C4156yes—
44C22×Dic13C22×C4128yes—
45C22×Dic13C22×C4156yes—
46C22×Dic13C22×C4121yes—
47C22×Dic13C2×D4156yes—
48C22×Dic13C2418yes—
49C22×Dic13C2417yes—
50C2×#1057—2112no—
51C2×#1057C24116yescomplemented
52C25×C4—131no—
53C24×C8—132no—
54C22×C22⋊C8—1328no—
55C23×C13—256no—
56C23×C13—256no—
57C23×C13—2448no—
58C23×C13C22⋊C8164yescomplemented
59C23×C13C2×C22⋊C4128yes—
60C23×C13C22×C8128yes—
61C23×C13C22×C81112yescomplemented
62C23×C13C2×M16128yes—
63C23×C13C23×C418yes—
64C23×C13C23×C417yes—
65C2×Dic13—256no—
66C2×Dic13—2112no—
67C2×Dic13—216no—
68C2×Dic13C2×C22⋊C4184yes—
69C2×Dic13C23×C418yes—
70C2×Dic13C23×C417yes—
71C2×Dic13C22×D4128yes—
72C2×Dic13C2511yescharacteristic
73#1057—216no—
74C26#26111yescharacteristic
75C24×C4—131no—
76C24×C4—1314no—
77C24×C4—1314no—
78C24×C4—131no—
79C24×C4—2616no—
80C23×C8—1328no—
81C23×C8—2616no—
82C2×C22⋊C8—13112no—
83C22×C13—2224no—
84C22×C13—28no—
85C22×C13—28no—
86C22×C13C2×C22⋊C81112yescomplemented
87C22×C13C22×C22⋊C4114yes—
88C22×C13C23×C8114yes—
89C22×C13C23×C8116yescomplemented
90C22×C13C22×M16114yes—
91C22×C13C24×C411yescharacteristic
92Dic13—28no—
93Dic13C22×C22⋊C4114yes—
94Dic13C23×D412yes—
95C25—28no—
96C25—28no—
97C25#1057116yescomplemented
98C25C2×#261114yes—
99C25C2×#26111yescharacteristic
100C23×C4—1316no—
101C23×C4—137no—
102C23×C4—137no—
103C23×C4—1328no—
104C23×C4—1384no—
105C23×C4—1314no—
106C23×C4—26112no—
107C23×C4—26112no—
108C23×C4—268no—
109C22×C8—1356no—
110C22×C8—26112no—
111C22⋊C8—1364no—
112C2×C13—216no—
113C2×C13C22×C22⋊C8128yescomplemented
114C2×C13C23×C22⋊C411yescharacteristic
115C2×C13C24×C811yescharacteristic
116C2×C13C23×M1611yescharacteristic
117C24—2128no—
118C24—256no—
119C24—256no—
120C24C2×#105718yes—
121C24C2×#10571112yescomplemented
122C24#612218yes—
123C24C22⋊#26118yes—
124C24C22×#261128yes—
125C24C22×#26117yes—
126C22×C4—1356no—
127C22×C4—1356no—
128C22×C4—137no—
129C22×C4—1321no—
130C22×C4—138no—
131C22×C4—1356no—
132C22×C4—1328no—
133C22×C4—26112no—
134C22×C4—26336no—
135C22×C4—2656no—
136C2×C8—1316no—
137C2×C8—26112no—
138C13C23×C22⋊C811yescharacteristic, complemented, Sylow
139C23—2448no—
140C23—256no—
141C23—256no—
142C23C22⋊#1057164yesdirect product factor
143C23C22×#1057128yes—
144C23C22×#10571112yescomplemented
145C23C2×#6122128yes—
146C23C2×C22⋊#261128yes—
147C23C23×#26118yes—
148C23C23×#26117yes—
149C2×C4—1328no—
150C2×C4—1384no—
151C2×C4—131no—
152C2×C4—137no—
153C2×C4—138no—
154C2×C4—26112no—
155C2×C4—2616no—
156C2×C4—2656no—
157C8—2616no—
158C22—28no—
159C22—28no—
160C22—2224no—
161C22C2×C22⋊#10571112yesdirect product factor
162C22C23×#1057114yes—
163C22C23×#1057116yescomplemented
164C22C22×#6122114yes—
165C22C22×C22⋊#261114yes—
166C22C24×#26111yescharacteristic
167C4—1314no—
168C4—132no—
169C4—268no—
170C2—216no—
171C2C22×C22⋊#1057128yesdirect product factor
172C2C23×C22⋊#26111yescharacteristic
173C2C24×#105711yescharacteristic
174C2C23×#612211yescharacteristic
subgroupG/H
centerC25C2×#261
commutatorC2×C13C24×C8
FrattiniC22C24×#261
Fitting, prime radicalC26×C13C4
socleC25×C13C2×C4
cosocleC2×Dic13C25
hypercenterC26#261
hypocenterC13C23×C22⋊C8
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C25 ◁ C26

Complements

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

NH ≅ G/Ntype
1. C24×#1057C2semidirect
2. C22×C22⋊#1057C2direct (N × H)
11. C23×#1057C22semidirect
12. C2×C22⋊#1057C22direct (N × H)
15. C25×C13C8semidirect
28. C22×#1057C23semidirect
29. C22⋊#1057C23direct (N × H)
36. C24×C13C2×C8semidirect
51. C2×#1057C24semidirect
58. C23×C13C22⋊C8semidirect
61. C23×C13C22×C8semidirect
86. C22×C13C2×C22⋊C8semidirect
89. C22×C13C23×C8semidirect
97. C25#1057semidirect
113. C2×C13C22×C22⋊C8semidirect
121. C24C2×#1057semidirect
138. C13C23×C22⋊C8semidirect
142. C23C22⋊#1057direct (N × H)
144. C23C22×#1057semidirect
161. C22C2×C22⋊#1057direct (N × H)
163. C22C23×#1057semidirect
171. C2C22×C22⋊#1057direct (N × H)

Maximal subgroups

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

subgroupindex
C24×#10572
C22×C22⋊#10572
C25×Dic132
C23×C22⋊C813