Finite Group Databasebeta

← #16782125

Subgroups — #16782125

Order 3328.

786 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 112 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×#11718604C211yesmaximal, characteristic
4C24×Dic13C2211yescharacteristic
5C22×C13×C22⋊C4C411yescharacteristic
6C22×C22⋊Dic13C411yescharacteristic
7C2×C22⋊#1057—22no—
8C2×C22⋊#1057—22no—
9C2×C22⋊#1057C2214yes—
10C2×#88071C412yes—
11C2×#88071C2212yes—
12#11718604—22no—
13#11718604—22no—
14C25×C13C2×C411yescharacteristic
15C23×C4×C13C2×C412yes—
16C23×Dic13—24no—
17C23×Dic13—42no—
18C23×Dic13—42no—
19C23×Dic13C2×C412yes—
20C23×Dic13C2×C411yescharacteristic
21C23×Dic13D412yes—
22C23×Dic13D412yes—
23C23×Dic13C2311yescharacteristic
24C22×#1057—24no—
25C2×C13×C22⋊C4—21no—
26C2×C13×C22⋊C4—21no—
27C2×C13×C22⋊C4—42no—
28C2×C22⋊Dic13—21no—
29C2×C22⋊Dic13—21no—
30C2×C22⋊Dic13—42no—
31C22⋊#1057—28no—
32C22⋊#1057—44no—
33C22⋊#1057—44no—
34#88071—24no—
35#88071—24no—
36#8702—131nomaximal, Sylow
37C24×C13—22no—
38C24×C13—22no—
39C24×C13—22no—
40C24×C13—24no—
41C24×C13—42no—
42C24×C13C22⋊C411yescharacteristic
43C24×C13C22⋊C411yescharacteristic
44C24×C13C22×C411yescharacteristic
45C22×C4×C13—22no—
46C22×C4×C13—24no—
47C22×C4×C13—42no—
48C22×C4×C13—42no—
49C22×Dic13—24no—
50C22×Dic13—24no—
51C22×Dic13—22no—
52C22×Dic13—24no—
53C22×Dic13—24no—
54C22×Dic13—22no—
55C22×Dic13—24no—
56C22×Dic13—41no—
57C22×Dic13—41no—
58C22×Dic13—42no—
59C22×Dic13—42no—
60C22×Dic13—41no—
61C22×Dic13—41no—
62C22×Dic13—416no—
63C22×Dic13—42no—
64C22×Dic13—42no—
65C22×Dic13C22⋊C412yes—
66C22×Dic13C2×D412yes—
67C22×Dic13#4114yes—
68C2×#1057—44no—
69C2×#1057—44no—
70C2×#1057—44no—
71C13×C22⋊C4—42no—
72C13×C22⋊C4—42no—
73C22⋊Dic13—42no—
74C22⋊Dic13—42no—
75C2×#381—131no—
76#1779—132no—
77#1280—134no—
78C23×C13—21no—
79C23×C13—21no—
80C23×C13—22no—
81C23×C13—28no—
82C23×C13—21no—
83C23×C13—21no—
84C23×C13—22no—
85C23×C13—22no—
86C23×C13—21no—
87C23×C13—21no—
88C23×C13—22no—
89C23×C13—22no—
90C23×C13—48no—
91C23×C13—48no—
92C23×C13—44no—
93C23×C13—44no—
94C23×C13#9912yes—
95C23×C13#9912yes—
96C23×C13C2×C22⋊C411yescharacteristic
97C23×C13#11712yes—
98C23×C13#13114yes—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—84no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13—44no—
109C2×Dic13—48no—
110C2×Dic13—48no—
111C2×Dic13—44no—
112C2×Dic13—42no—
113C2×Dic13—42no—
114C2×Dic13—42no—
115C2×Dic13—84no—
116C2×Dic13#12314yes—
117#1057—84no—
118C24×C4—131no—
119C22×C22⋊C4—131no—
120C22×C22⋊C4#26111yescharacteristic
121C2×C22⋊C8—134no—
122C2×C22⋊C8—262no—
123C2×C22⋊C8—262no—
124#381—262no—
125#381—262no—
126C2×#95—132no—
127C2×#95—132no—
128C22×C13—22no—
129C22×C13—22no—
130C22×C13—24no—
131C22×C13—24no—
132C22×C13—22no—
133C22×C13—22no—
134C22×C13—24no—
135C22×C13—24no—
136C22×C13—416no—
137C22×C13—41no—
138C22×C13—41no—
139C22×C13—41no—
140C22×C13—41no—
141C22×C13—42no—
142C22×C13—42no—
143C22×C13#38111yescharacteristic
144C22×C13#40812yes—
145C22×C13C2×#9911yescharacteristic
146C22×C13C2×#9911yescharacteristic
147C22×C13#41312yes—
148C22×C13#43314yes—
149C4×C13—82no—
150Dic13—24no—
151Dic13—42no—
152Dic13—82no—
153C25C2×#26111yescharacteristic
154C23×C4—131no—
155C23×C4—132no—
156C23×C4—132no—
157C23×C4—131no—
158C23×C4—132no—
159C23×C4—264no—
160C23×C4—522no—
161C23×C4—522no—
162C23×C4C2×#26112yes—
163C22×C8—264no—
164C2×C22⋊C4—21no—
165C2×C22⋊C4—21no—
166C2×C22⋊C4—42no—
167C2×C22⋊C4—261no—
168C2×C22⋊C4—261no—
169C2×C22⋊C4—522no—
170C22⋊C8—268no—
171C22⋊C8—524no—
172C22⋊C8—524no—
173#95—264no—
174#95—264no—
175C2×C13—24no—
176C2×C13—42no—
177C2×C13—42no—
178C2×C13#146812yes—
179C2×C13#146812yes—
180C2×C13#181811yescharacteristic
181C2×C13#181911yescharacteristic
182C2×C13#182211yescharacteristic
183C24—22no—
184C24—22no—
185C24—22no—
186C24—24no—
187C24—42no—
188C24C22⋊#26111yescharacteristic
189C24C22⋊#26111yescharacteristic
190C24C22×#26111yescharacteristic
191C22×C4—22no—
192C22×C4—24no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4—132no—
196C22×C4—134no—
197C22×C4—132no—
198C22×C4—264no—
199C22×C4—264no—
200C22×C4—264no—
201C22×C4—264no—
202C22×C4—262no—
203C22×C4—262no—
204C22×C4—264no—
205C22×C4—521no—
206C22×C4—522no—
207C22×C4—521no—
208C22×C4—522no—
209C22×C4—521no—
210C22×C4—521no—
211C22×C4—5216no—
212C22×C4—522no—
213C22×C4—522no—
214C2×C8—524no—
215C2×C8—524no—
216C2×C8—524no—
217C22⋊C4—42no—
218C22⋊C4—42no—
219C22⋊C4—522no—
220C22⋊C4—522no—
221C13#870211yescharacteristic, complemented, Sylow
222C23—21no—
223C23—22no—
224C23—21no—
225C23—28no—
226C23—21no—
227C23—21no—
228C23—21no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—21no—
234C23—48no—
235C23—48no—
236C23—44no—
237C23—44no—
238C23#8810712yes—
239C23#8811912yes—
240C23#8823712yes—
241C23#8823814yes—
242C23C2×C22⋊#26111yescharacteristic
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—84no—
247C2×C4—134no—
248C2×C4—262no—
249C2×C4—262no—
250C2×C4—262no—
251C2×C4—262no—
252C2×C4—262no—
253C2×C4—524no—
254C2×C4—528no—
255C2×C4—528no—
256C2×C4—524no—
257C2×C4—522no—
258C2×C4—522no—
259C2×C4—522no—
260C2×C4—1044no—
261C8—1044no—
262C22—24no—
263C22—24no—
264C22—22no—
265C22—22no—
266C22—24no—
267C22—24no—
268C22—22no—
269C22—22no—
270C22—416no—
271C22—42no—
272C22—42no—
273C22—41no—
274C22—41no—
275C22—41no—
276C22—41no—
277C22#1171906814yes—
278C22C2×#8810711yescharacteristic
279C22#1171913511yescharacteristic
280C22#1171914612yes—
281C22#1171914812yes—
282C22C2×#8811911yescharacteristic
283C4—82no—
284C4—264no—
285C4—522no—
286C4—1042no—
287C2—24no—
288C2—42no—
289C2—42no—
290C2#1313010112yes—
291C2#1313010312yes—
292C2#1313072911yescharacteristic
293C2#1313073111yescharacteristic
294C2#1313073811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC24×C13C22×C4
FrattiniC24C22×#261
FittingC22×C13×C22⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC25×C13C2×C4
cosocleC23×Dic13C23
hypercenterC22×C22⋊C4#261
hypocenterC13#8702
LCSG ▷ C24×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
221. C13#8702semidirect

Maximal subgroups

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

subgroupindex
#131306582
#131296742
C2×#117186042
#870213