Finite Group Databasebeta

← #16797508

Subgroups — #16797508

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×#11719169C212yesmaximal
2#13130578C218yesmaximal, complemented
3#13130566C214yesmaximal, complemented
4#13117214C211yesmaximal, characteristic
5C24×Dic13C2211yescharacteristic
6C22×#6122C2214yes—
7C2×#88131C2212yes—
8#11719169C4116yescomplemented
9C2×C22⋊#1057C2214yes—
10C2×C22⋊#1057C2214yes—
11C2×#88110C2214yescomplemented
12C2×C4×#1057C2214yescomplemented
13C13×#379C411yescharacteristic
14#11718908C411yescharacteristic
15#11718604C412yes—
16#11718603C414yes—
17C22⋊C4×Dic13C2214yes—
18#11718290C2218yescomplemented
19C25×C13C2×C411yescharacteristic
20C23×Dic13—44no—
21C23×Dic13C2×C412yes—
22C23×Dic13C2×C411yescharacteristic
23C23×Dic13C2×C418yes—
24C23×Dic13C2311yescharacteristic
25C23×Dic13C2312yes—
26C2×#6122—48no—
27C2×#6122C2×C4116yes—
28C22×#1057C2318yes—
29C2×C13×C22⋊C4C2×C412yes—
30C2×C13×C22⋊C4C2×C414yes—
31C2×C22⋊Dic13C2×C412yes—
32C2×C22⋊Dic13C2×C414yes—
33C2×#6101C2×C414yes—
34C2×C4×Dic13C2314yes—
35#88131—44no—
36C22⋊#1057C2×C4116yes—
37C22⋊#1057C2×C4116yes—
38#88110—44no—
39C4×#1057—44no—
40#88071C2×C418yes—
41#20529—131nomaximal, Sylow
42C24×C13—42no—
43C24×C13—44no—
44C24×C13C4214yes—
45C24×C13C22×C411yescharacteristic
46C24×C13C22×C412yes—
47C22×C4×C13C22×C414yes—
48C22×Dic13—24no—
49C22×Dic13—28no—
50C22×Dic13—416no—
51C22×Dic13—44no—
52C22×Dic13—42no—
53C22×Dic13C4218yes—
54C22×Dic13C4214yes—
55C22×Dic13C22×C414yes—
56C22×Dic13C22×C412yes—
57C22×Dic13C22×C411yescharacteristic
58C22×Dic13C22×C414yes—
59C22×Dic13C22×C414yes—
60C22×Dic13C22×C414yes—
61C22×Dic13C2411yescharacteristic
62#6122—416no—
63C2×#1057—28no—
64C2×#1057—28no—
65C2×#1057C22×C4116yes—
66C13×C22⋊C4—42no—
67C13×C22⋊C4—44no—
68C22⋊Dic13—42no—
69C22⋊Dic13—44no—
70#6101—44no—
71C4×Dic13—24no—
72C4×Dic13—24no—
73C2×#407—132no—
74#2280—131no—
75#1753—138no—
76#1750—134no—
77C23×C13—22no—
78C23×C13—24no—
79C23×C13—24no—
80C23×C13—24no—
81C23×C13—24no—
82C23×C13—44no—
83C23×C13—48no—
84C23×C13—416no—
85C23×C13C2×C4212yes—
86C23×C13C2×C4214yes—
87C23×C13C23×C411yescharacteristic
88C2×C4×C13—24no—
89C2×C4×C13—28no—
90C2×Dic13—22no—
91C2×Dic13—24no—
92C2×Dic13—28no—
93C2×Dic13—28no—
94C2×Dic13—28no—
95C2×Dic13—24no—
96C2×Dic13—28no—
97C2×Dic13—48no—
98C2×Dic13—44no—
99C2×Dic13C2×C4214yes—
100C2×Dic13C2×C4212yes—
101C2×Dic13C23×C412yes—
102C2×Dic13H(5,𝔽2)14yes—
103#1057—216no—
104C24×C4—131no—
105C22×M16—134no—
106C2×#117—132no—
107#407—1316no—
108C2×C22⋊C8—134no—
109C2×C22⋊C8—134no—
110C2×#97—134no—
111C2×C4×C8—134no—
112#381—132no—
113#380—134no—
114#379—131no—
115#379#26111yescharacteristic
116C4×C22⋊C4—134no—
117#336—138no—
118C22×C13—24no—
119C22×C13—24no—
120C22×C13—24no—
121C22×C13—24no—
122C22×C13—22no—
123C22×C13—416no—
124C22×C13—44no—
125C22×C13—48no—
126C22×C13C22×C4211yescharacteristic
127C22×C13#51812yes—
128C22×C13#56814yes—
129C4×C13—44no—
130Dic13—22no—
131Dic13—24no—
132Dic13—44no—
133Dic13#51814yes—
134C25C2×#26111yescharacteristic
135C23×C4—131no—
136C23×C4—132no—
137C23×C4—138no—
138C23×C4—132no—
139C23×C4—131no—
140C23×C4—524no—
141C2×M16—1316no—
142C2×M16—528no—
143C22×C8—138no—
144#117—524no—
145C2×C4⋊C4—134no—
146C2×C22⋊C4—132no—
147C2×C22⋊C4—134no—
148C2×C22⋊C4C2×#26112yes—
149C2×C22⋊C4C2×#26114yes—
150C2×C42—134no—
151C22⋊C8—1316no—
152C22⋊C8—1316no—
153#97—524no—
154C4×C8—524no—
155#95—138no—
156C2×C13—44no—
157C2×C13—42no—
158C2×C13#227311yescharacteristic
159C2×C13#287312yes—
160C2×C13#297814yes—
161C24—42no—
162C24—44no—
163C24C4×#26114yes—
164C24C22×#26112yes—
165C24C22×#26111yescharacteristic
166C22×C4—131no—
167C22×C4—134no—
168C22×C4—134no—
169C22×C4—134no—
170C22×C4—132no—
171C22×C4—131no—
172C22×C4—138no—
173C22×C4—134no—
174C22×C4—134no—
175C22×C4—264no—
176C22×C4—268no—
177C22×C4—5216no—
178C22×C4—524no—
179C22×C4—522no—
180C22×C4C22×#26114yes—
181M16—5216no—
182C2×C8—1316no—
183C2×C8—268no—
184C2×C8—268no—
185C4⋊C4—524no—
186C22⋊C4—42no—
187C22⋊C4—44no—
188C22⋊C4—522no—
189C22⋊C4—524no—
190C42—264no—
191C42—264no—
192C13#2052911yescharacteristic, complemented, Sylow
193C23—24no—
194C23—24no—
195C23—24no—
196C23—22no—
197C23—24no—
198C23—44no—
199C23—48no—
200C23—416no—
201C23C2×C4×#26112yes—
202C23C2×C4×#26114yes—
203C23C23×#26111yescharacteristic
204C2×C4—28no—
205C2×C4—24no—
206C2×C4—132no—
207C2×C4—134no—
208C2×C4—132no—
209C2×C4—134no—
210C2×C4—268no—
211C2×C4—268no—
212C2×C4—268no—
213C2×C4—262no—
214C2×C4—264no—
215C2×C4—268no—
216C2×C4—264no—
217C2×C4—524no—
218C2×C4—528no—
219C8—2616no—
220C22—24no—
221C22—22no—
222C22—24no—
223C22—24no—
224C22—24no—
225C22—416no—
226C22—48no—
227C22—44no—
228C22C22×C4×#26111yescharacteristic
229C22#1171962114yes—
230C22#1171962312yes—
231C4—44no—
232C4—134no—
233C4—264no—
234C4—262no—
235C4—524no—
236C2—44no—
237C2—42no—
238C2#1313127211yescharacteristic
239C2#1313140012yes—
240C2#1313171214yes—
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC13×#379C4
socleC23×C13C23×C4
prime radicalC25×C13C2×C4
cosocleC22×Dic13C24
hypercenter#379#261
hypocenterC13#20529
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. #13130578C2semidirect
3. #13130566C2semidirect
8. #11719169C4semidirect
11. C2×#88110C22semidirect
12. C2×C4×#1057C22semidirect
18. #11718290C22semidirect
192. C13#20529semidirect

Maximal subgroups

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

subgroupindex
C2×#117191692
#131305782
#131305662
#131172142
#2052913