Finite Group Databasebeta

← #16782121

Subgroups — #16782121

Order 3328.

898 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 898 conjugacy classes of subgroups — too many to draw. Only its 140 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
1#13130658C212yesmaximal
2#13129674C214yesmaximal, complemented
3C2×C22⋊C4×Dic13C211yesmaximal, characteristic
4C24×Dic13C2211yescharacteristic
5C22×C13×C22⋊C4C411yescharacteristic
6C22×C22⋊Dic13C411yescharacteristic
7C22×C4×Dic13C412yes—
8C2×C22⋊#1057—24no—
9C2×C22⋊#1057C2214yes—
10C2×#88071C2212yes—
11C22⋊C4×Dic13—24no—
12C25×C13C2×C411yescharacteristic
13C23×C4×C13C2×C412yes—
14C23×Dic13—24no—
15C23×Dic13—44no—
16C23×Dic13C2×C411yescharacteristic
17C23×Dic13C2×C412yes—
18C23×Dic13D414yes—
19C23×Dic13C2311yescharacteristic
20C22×#1057—24no—
21C2×C13×C22⋊C4—22no—
22C2×C13×C22⋊C4—24no—
23C2×C22⋊Dic13—22no—
24C2×C22⋊Dic13—22no—
25C2×C22⋊Dic13C814yescomplemented
26C2×C4×Dic13—22no—
27C2×C4×Dic13—22no—
28C2×C4×Dic13—44no—
29C22⋊#1057—28no—
30C22⋊#1057—48no—
31#88071—24no—
32#8700—131nomaximal, Sylow
33C24×C13—22no—
34C24×C13—22no—
35C24×C13—42no—
36C24×C13—42no—
37C24×C13C22⋊C412yes—
38C24×C13C2×C812yes—
39C24×C13M1612yes—
40C24×C13C22×C411yescharacteristic
41C22×C4×C13—22no—
42C22×C4×C13—22no—
43C22×C4×C13—42no—
44C22×C4×C13—42no—
45C22×C4×C13M1614yes—
46C22×Dic13—22no—
47C22×Dic13—24no—
48C22×Dic13—22no—
49C22×Dic13—22no—
50C22×Dic13—28no—
51C22×Dic13—28no—
52C22×Dic13—44no—
53C22×Dic13—42no—
54C22×Dic13—416no—
55C22×Dic13—42no—
56C22×Dic13—42no—
57C22×Dic13C22⋊C412yes—
58C22×Dic13C2×C814yes—
59C22×Dic13C2×D412yes—
60C22×Dic13#4114yes—
61C2×#1057—48no—
62C2×#1057—44no—
63C13×C22⋊C4—28no—
64C22⋊Dic13—28no—
65C4×Dic13—44no—
66C4×Dic13—44no—
67C2×C4×C22⋊C4—131no—
68#1779—132no—
69#1280—134no—
70C23×C13—22no—
71C23×C13—22no—
72C23×C13—22no—
73C23×C13—22no—
74C23×C13—24no—
75C23×C13—24no—
76C23×C13—24no—
77C23×C13—24no—
78C23×C13—44no—
79C23×C13—44no—
80C23×C13—44no—
81C23×C13—44no—
82C23×C13—44no—
83C23×C13—44no—
84C23×C13C22⋊C814yes—
85C23×C13C2×C22⋊C411yescharacteristic
86C23×C13#11712yes—
87C23×C13C22×C811yescharacteristic
88C23×C13C2×M1611yescharacteristic
89C23×C13C2×M1612yes—
90C2×C4×C13—24no—
91C2×C4×C13—44no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—44no—
95C2×Dic13—28no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—24no—
99C2×Dic13—24no—
100C2×Dic13—44no—
101C2×Dic13—416no—
102C2×Dic13—44no—
103C2×Dic13—42no—
104C2×Dic13—42no—
105C2×Dic13—44no—
106C2×Dic13#9914yes—
107C2×Dic13#12314yes—
108#1057—84no—
109C24×C4—131no—
110C22×C22⋊C4—131no—
111C22×C22⋊C4#26111yescharacteristic
112C22×C42—132no—
113C2×C22⋊C8—134no—
114C2×C22⋊C8—264no—
115C4×C22⋊C4—264no—
116C2×#95—132no—
117C22×C13—22no—
118C22×C13—22no—
119C22×C13—22no—
120C22×C13—22no—
121C22×C13—22no—
122C22×C13—22no—
123C22×C13—24no—
124C22×C13—28no—
125C22×C13—48no—
126C22×C13—48no—
127C22×C13—42no—
128C22×C13—42no—
129C22×C13—44no—
130C22×C13#38111yescharacteristic
131C22×C13C2×C22⋊C811yescharacteristic
132C22×C13#40711yescharacteristic
133C22×C13C2×#9912yes—
134C22×C13#41312yes—
135C22×C13#43112yes—
136C22×C13#43212yes—
137C4×C13—44no—
138Dic13—24no—
139Dic13—24no—
140Dic13—44no—
141C25C2×#26111yescharacteristic
142C23×C4—131no—
143C23×C4—131no—
144C23×C4—134no—
145C23×C4—132no—
146C23×C4—264no—
147C23×C4—524no—
148C23×C4C2×#26112yes—
149C22×C8—264no—
150C2×C22⋊C4—22no—
151C2×C22⋊C4—24no—
152C2×C22⋊C4—134no—
153C2×C22⋊C4—262no—
154C2×C22⋊C4—262no—
155C2×C42—262no—
156C2×C42—262no—
157C2×C42—524no—
158C22⋊C8—268no—
159C22⋊C8—528no—
160#95—264no—
161C2×C13—22no—
162C2×C13—22no—
163C2×C13—44no—
164C2×C13#145912yes—
165C2×C13#146512yes—
166C2×C13#181711yescharacteristic
167C2×C13#181911yescharacteristic
168C2×C13#182211yescharacteristic
169C24—22no—
170C24—22no—
171C24—42no—
172C24—42no—
173C24D13⋊C812yes—
174C24#611812yes—
175C24C22⋊#26112yes—
176C24C22×#26111yescharacteristic
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—42no—
180C22×C4—42no—
181C22×C4—132no—
182C22×C4—132no—
183C22×C4—134no—
184C22×C4—134no—
185C22×C4—264no—
186C22×C4—268no—
187C22×C4—268no—
188C22×C4—262no—
189C22×C4—262no—
190C22×C4—262no—
191C22×C4—524no—
192C22×C4—522no—
193C22×C4—5216no—
194C22×C4—522no—
195C22×C4—522no—
196C22×C4#612214yes—
197C2×C8—524no—
198C2×C8—528no—
199C22⋊C4—28no—
200C22⋊C4—268no—
201C42—524no—
202C42—524no—
203C13#870011yescharacteristic, complemented, Sylow
204C23—22no—
205C23—22no—
206C23—22no—
207C23—24no—
208C23—24no—
209C23—22no—
210C23—24no—
211C23—24no—
212C23—44no—
213C23—44no—
214C23—44no—
215C23—44no—
216C23—44no—
217C23—44no—
218C23#8811114yes—
219C23C2×D13⋊C811yescharacteristic
220C23C2×#611811yescharacteristic
221C23#8823712yes—
222C23C2×#612212yes—
223C23C2×C22⋊#26111yescharacteristic
224C2×C4—24no—
225C2×C4—44no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—44no—
229C2×C4—134no—
230C2×C4—134no—
231C2×C4—268no—
232C2×C4—262no—
233C2×C4—262no—
234C2×C4—264no—
235C2×C4—264no—
236C2×C4—524no—
237C2×C4—5216no—
238C2×C4—524no—
239C2×C4—522no—
240C2×C4—522no—
241C2×C4—524no—
242C8—1044no—
243C22—22no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—28no—
250C22—24no—
251C22—48no—
252C22—48no—
253C22—44no—
254C22—42no—
255C22—42no—
256C22C2×#8811111yescharacteristic
257C22#1171912512yes—
258C22#1171913012yes—
259C22#1171913511yescharacteristic
260C22D13⋊#9912yes—
261C22#1171914812yes—
262C22#1171916911yescharacteristic
263C4—44no—
264C4—264no—
265C4—264no—
266C4—524no—
267C2—22no—
268C2—22no—
269C2—44no—
270C2#1313007412yes—
271C2#1313009212yes—
272C2#1313072711yescharacteristic
273C2#1313073211yescharacteristic
274C2#1313073811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC23×C13C22×C8
FrattiniC24C22×#261
FittingC22×C13×C22⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC25×C13C2×C4
cosocleC23×Dic13C23
hypercenterC22×C22⋊C4#261
hypocenterC13#8700
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13129674C2semidirect
25. C2×C22⋊Dic13C8semidirect
203. C13#8700semidirect

Maximal subgroups

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

subgroupindex
#131306582
#131296742
C2×C22⋊C4×Dic132
#870013