Finite Group Databasebeta

← #16797510

Subgroups — #16797510

Order 3328.

1170 conjugacy classes of subgroups; only the 312 normal subgroups are shown.

normal subgroups only

This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 312 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
1C2×#11719127C212yesmaximal
2#13130577C218yesmaximal, complemented
3#13130566C214yesmaximal, complemented
4#13117216C211yesmaximal, characteristic
5C23×C4×D13C2211yescharacteristic
6C22×#6118C2214yes—
7C2×#88131C2212yes—
8C2×C22⋊#1057C2214yes—
9#11719127C4116yescomplemented
10C2×#88111C2214yes—
11C2×#88110C2214yescomplemented
12C2×C4×#1057C2214yescomplemented
13C13×#381C411yescharacteristic
14#11718872C411yescharacteristic
15#11718616C412yes—
16#11718328C414yes—
17#11718327C2214yes—
18#11718290C2218yescomplemented
19C24×D13C2×C411yescharacteristic
20C23×C4×C13C2×C411yescharacteristic
21C23×Dic13C2311yescharacteristic
22C22×C4×D13—44no—
23C22×C4×D13C2×C412yes—
24C22×C4×D13C2×C418yes—
25C22×C4×D13C2312yes—
26C22×#1057C2318yes—
27C2×#6118—48no—
28C2×#6118C2×C4116yes—
29C2×C13×C22⋊C4C2×C412yes—
30C2×C22⋊Dic13C2×C412yes—
31C2×#6103C2×C418yes—
32C2×#6101C2×C414yes—
33C2×C4×Dic13C2314yes—
34#88131—44no—
35C22⋊#1057C2×C4116yes—
36#88111C2×C4116yes—
37#88110—44no—
38C4×#1057—44no—
39C13×#95C2×C414yes—
40#88071C2×C414yes—
41#20529—131nomaximal, Sylow
42C24×C13C22×C411yescharacteristic
43C23×D13—42no—
44C23×D13—44no—
45C23×D13C4214yes—
46C23×D13C22×C412yes—
47C22×C4×C13—42no—
48C22×C4×C13C4214yes—
49C22×C4×C13C22×C414yes—
50C22×C4×C13C22×C412yes—
51C22×Dic13—24no—
52C22×Dic13C22×C414yes—
53C22×Dic13C22×C411yescharacteristic
54C22×Dic13C22×C414yes—
55C22×Dic13C2411yescharacteristic
56C2×C4×D13—28no—
57C2×C4×D13—416no—
58C2×C4×D13—44no—
59C2×C4×D13C4218yes—
60C2×C4×D13C22×C414yes—
61C2×C4×D13C22×C414yes—
62C2×#1057—28no—
63C2×#1057—28no—
64C2×#1057C22×C4116yes—
65#6118—416no—
66C13×C22⋊C4—42no—
67C22⋊Dic13—42no—
68#6103—48no—
69#6101—44no—
70C4×Dic13—24no—
71C4×Dic13—24no—
72C2×#407—132no—
73#2280—131no—
74#1753—138no—
75#1750—134no—
76C23×C13—22no—
77C23×C13—24no—
78C23×C13C2×C4212yes—
79C23×C13C23×C411yescharacteristic
80C22×D13—24no—
81C22×D13—24no—
82C22×D13—24no—
83C22×D13—44no—
84C22×D13—48no—
85C22×D13—416no—
86C22×D13C2×C4214yes—
87C2×C4×C13—24no—
88C2×C4×C13—24no—
89C2×C4×C13—28no—
90C2×C4×C13—44no—
91C2×C4×C13C2×C4214yes—
92C2×Dic13—22no—
93C2×Dic13—28no—
94C2×Dic13—24no—
95C2×Dic13—28no—
96C2×Dic13C2×C4212yes—
97C2×Dic13C23×C412yes—
98C2×Dic13H(5,𝔽2)14yes—
99C4×D13—28no—
100C4×D13—28no—
101C4×D13—48no—
102#1057—216no—
103C24×C4—131no—
104C22×M16—134no—
105C2×#117—132no—
106#407—1316no—
107C2×C22⋊C8—134no—
108C2×C22⋊C8—134no—
109C2×#97—134no—
110C2×C4×C8—134no—
111#381—131no—
112#381#26111yescharacteristic
113#380—134no—
114#379—132no—
115C4×C22⋊C4—134no—
116#336—138no—
117C22×C13—24no—
118C22×C13—22no—
119C22×C13—44no—
120C22×C13C22×C4211yescharacteristic
121C22×C13#51812yes—
122C22×C13#56814yes—
123C2×D13—24no—
124C2×D13—24no—
125C2×D13—24no—
126C2×D13—416no—
127C2×D13—48no—
128C4×C13—24no—
129C4×C13—44no—
130Dic13—22no—
131Dic13—44no—
132Dic13#51814yes—
133C25—131no—
134C23×C4—131no—
135C23×C4—132no—
136C23×C4—138no—
137C23×C4—132no—
138C23×C4—524no—
139C23×C4C2×#26111yescharacteristic
140C2×M16—1316no—
141C2×M16—528no—
142C22×C8—138no—
143#117—524no—
144C2×C4⋊C4—134no—
145C2×C22⋊C4—132no—
146C2×C22⋊C4—138no—
147C2×C22⋊C4C2×#26112yes—
148C2×C42—134no—
149C22⋊C8—1316no—
150C22⋊C8—1316no—
151#97—524no—
152C4×C8—524no—
153#95—134no—
154#95C2×#26114yes—
155C2×C13—42no—
156C2×C13#227311yescharacteristic
157C2×C13#287312yes—
158C2×C13#297814yes—
159D13—44no—
160C24—132no—
161C24—134no—
162C24—522no—
163C24—524no—
164C24C22×#26111yescharacteristic
165C22×C4—42no—
166C22×C4—131no—
167C22×C4—134no—
168C22×C4—131no—
169C22×C4—134no—
170C22×C4—134no—
171C22×C4—138no—
172C22×C4—134no—
173C22×C4—268no—
174C22×C4—264no—
175C22×C4—524no—
176C22×C4—5216no—
177C22×C4C4×#26114yes—
178C22×C4C22×#26114yes—
179C22×C4C22×#26112yes—
180M16—5216no—
181C2×C8—1316no—
182C2×C8—268no—
183C2×C8—268no—
184C4⋊C4—524no—
185C22⋊C4—42no—
186C22⋊C4—528no—
187C22⋊C4—522no—
188C42—264no—
189C42—264no—
190C13#2052911yescharacteristic, complemented, Sylow
191C23—22no—
192C23—24no—
193C23—134no—
194C23—264no—
195C23—264no—
196C23—264no—
197C23—524no—
198C23—528no—
199C23—5216no—
200C23C2×C4×#26112yes—
201C23C23×#26111yescharacteristic
202C2×C4—24no—
203C2×C4—24no—
204C2×C4—28no—
205C2×C4—44no—
206C2×C4—132no—
207C2×C4—134no—
208C2×C4—132no—
209C2×C4—268no—
210C2×C4—268no—
211C2×C4—268no—
212C2×C4—262no—
213C2×C4—264no—
214C2×C4—268no—
215C2×C4—528no—
216C2×C4C2×C4×#26114yes—
217C8—2616no—
218C22—22no—
219C22—24no—
220C22—44no—
221C22—264no—
222C22—264no—
223C22—264no—
224C22—5216no—
225C22—528no—
226C22C22×C4×#26111yescharacteristic
227C22#1171962312yes—
228C22#1171962914yes—
229C4—24no—
230C4—44no—
231C4—134no—
232C4—262no—
233C4—524no—
234C2—42no—
235C2—524no—
236C2#1313127211yescharacteristic
237C2#1313140112yes—
238C2#1313171414yes—
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC13×#381C4
socleC23×C13C23×C4
prime radicalC24×D13C2×C4
cosocleC22×Dic13C24
hypercenter#381#261
hypocenterC13#20529
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. #13130577C2semidirect
3. #13130566C2semidirect
9. #11719127C4semidirect
11. C2×#88110C22semidirect
12. C2×C4×#1057C22semidirect
18. #11718290C22semidirect
190. C13#20529semidirect

Maximal subgroups

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

subgroupindex
C2×#117191272
#131305772
#131305662
#131172162
#2052913