Finite Group Databasebeta

← #16786984

Subgroups — #16786984

Order 3328.

662 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 80 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#13130087C212yesmaximal, complemented
2#13129762C212yesmaximal, complemented
3#13129760C212yesmaximal
4#13117219C211yesmaximal, characteristic
5C24×C4×C13C411yescharacteristic
6C2×#88180C411yescharacteristic
7C2×#88180C2211yescharacteristic
8#11719128—22no—
9#11718908C411yescharacteristic
10#11718908C2211yescharacteristic
11#11718873—22no—
12#11718872C411yescharacteristic
13#11718872C2211yescharacteristic
14C4×C22⋊Dic13—22no—
15#11718305C2214yes—
16#11718285—22no—
17C25×C13C2×C411yescharacteristic
18C23×C4×C13—22no—
19C23×C4×C13—21no—
20C23×C4×C13—21no—
21C23×C4×C13—22no—
22C23×C4×C13—42no—
23C23×C4×C13—42no—
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C2×C22⋊Dic13—22no—
27C2×C22⋊Dic13—22no—
28C2×C22⋊Dic13C2×C411yescharacteristic
29C2×C22⋊Dic13C2×C411yescharacteristic
30C2×C22⋊Dic13C2×C411yescharacteristic
31C2×C22⋊Dic13C2311yescharacteristic
32#88180—42no—
33#88180—42no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13D412yes—
36C2×C4×Dic13—21no—
37C2×C4×Dic13D412yes—
38C22⋊#1057—24no—
39#88112—42no—
40#88110—42no—
41#88071—22no—
42#88071—22no—
43#11501—131nomaximal, Sylow
44C24×C13—21no—
45C24×C13—21no—
46C24×C13—41no—
47C24×C13—41no—
48C24×C13—44no—
49C24×C13M1612yes—
50C24×C13C22×C411yescharacteristic
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13—24no—
56C22×C4×C13—24no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—48no—
60C22×C4×C13—48no—
61C22×C4×C13—42no—
62C22×C4×C13—42no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13—41no—
66C22×C4×C13—41no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13M1612yes—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13C22⋊C412yes—
73C22×Dic13C2×D412yes—
74C2×#1057—44no—
75C22⋊Dic13—41no—
76C22⋊Dic13—41no—
77C22⋊Dic13—44no—
78C22⋊Dic13—44no—
79C22⋊Dic13—41no—
80C22⋊Dic13—41no—
81C4⋊Dic13—42no—
82C4⋊Dic13—42no—
83C4×Dic13—22no—
84C4×Dic13—22no—
85C4×Dic13—42no—
86#2280—131no—
87#1464—132no—
88#1317—132no—
89#1316—132no—
90C23×C13—24no—
91C23×C13—22no—
92C23×C13—21no—
93C23×C13—21no—
94C23×C13—42no—
95C23×C13—42no—
96C23×C13—44no—
97C23×C13—42no—
98C23×C13—44no—
99C23×C13—42no—
100C23×C13—48no—
101C23×C13—44no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13—44no—
105C23×C13C2×C22⋊C411yescharacteristic
106C23×C13C2×M1611yescharacteristic
107C23×C13C2×M1611yescharacteristic
108C2×C4×C13—24no—
109C2×C4×C13—24no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—22no—
115C2×C4×C13—48no—
116C2×C4×C13—48no—
117C2×C4×C13—42no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—42no—
121C2×C4×C13#9912yes—
122C2×C4×C13#10012yes—
123C2×Dic13—22no—
124C2×Dic13—22no—
125C2×Dic13—42no—
126C2×Dic13—42no—
127C2×Dic13—42no—
128C2×Dic13—42no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131#1057—84no—
132C24×C4#26111yescharacteristic
133C2×#117—131no—
134C2×#117—131no—
135#432—262no—
136#381—131no—
137#381—131no—
138#380—262no—
139#379—131no—
140#379—131no—
141C4×C22⋊C4—262no—
142#324—262no—
143#323—134no—
144C22×C13—22no—
145C22×C13—24no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13—41no—
149C22×C13—41no—
150C22×C13—44no—
151C22×C13—42no—
152C22×C13—42no—
153C22×C13—44no—
154C22×C13—48no—
155C22×C13—44no—
156C22×C13—44no—
157C22×C13—42no—
158C22×C13—42no—
159C22×C13#40711yescharacteristic
160C22×C13C2×#9911yescharacteristic
161C22×C13C2×#10011yescharacteristic
162C4×C13—22no—
163C4×C13—22no—
164C4×C13—42no—
165Dic13—42no—
166Dic13—42no—
167Dic13—81no—
168Dic13—81no—
169C25C2×#26111yescharacteristic
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—42no—
175C23×C4—42no—
176C23×C4C2×#26111yescharacteristic
177C23×C4C2×#26111yescharacteristic
178#117—522no—
179#117—522no—
180C2×C4⋊C4—132no—
181C2×C4⋊C4—261no—
182C2×C22⋊C4—131no—
183C2×C22⋊C4—131no—
184C2×C22⋊C4—131no—
185C2×C22⋊C4—131no—
186C2×C22⋊C4—262no—
187C2×C22⋊C4—262no—
188C2×C42—132no—
189C2×C42—261no—
190C4⋊C8—522no—
191C22⋊C8—264no—
192#97—522no—
193#95—262no—
194#95—262no—
195C2×C13—21no—
196C2×C13—21no—
197C2×C13—44no—
198C2×C13—41no—
199C2×C13—41no—
200C2×C13#146211yescharacteristic
201C2×C13#212012yes—
202C24—21no—
203C24—21no—
204C24—41no—
205C24—41no—
206C24—44no—
207C24#612212yes—
208C24C22×#26111yescharacteristic
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—24no—
214C22×C4—24no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—48no—
218C22×C4—48no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—132no—
226C22×C4—132no—
227C22×C4—261no—
228C22×C4—261no—
229C22×C4#612212yes—
230C22×C4C22⋊#26111yescharacteristic
231C22×C4C22⋊#26111yescharacteristic
232C2×C8—524no—
233C4⋊C4—522no—
234C4⋊C4—522no—
235C22⋊C4—521no—
236C22⋊C4—521no—
237C22⋊C4—524no—
238C22⋊C4—524no—
239C22⋊C4—521no—
240C22⋊C4—521no—
241C42—262no—
242C42—262no—
243C42—522no—
244C13#1150111yescharacteristic, complemented, Sylow
245C23—24no—
246C23—22no—
247C23—21no—
248C23—21no—
249C23—42no—
250C23—44no—
251C23—42no—
252C23—42no—
253C23—42no—
254C23—44no—
255C23—44no—
256C23—48no—
257C23—44no—
258C23—41no—
259C23—41no—
260C23C2×#612211yescharacteristic
261C23C2×#612211yescharacteristic
262C23C2×C22⋊#26111yescharacteristic
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—48no—
271C2×C4—48no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—262no—
277C2×C4—262no—
278C2×C4—522no—
279C2×C4—522no—
280C2×C4—522no—
281C2×C4—522no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4#8811912yes—
285C2×C4#8812112yes—
286C8—1044no—
287C22—22no—
288C22—24no—
289C22—21no—
290C22—21no—
291C22—41no—
292C22—41no—
293C22—44no—
294C22—42no—
295C22—42no—
296C22—44no—
297C22—44no—
298C22—48no—
299C22—44no—
300C22—42no—
301C22—42no—
302C22C2×#8811911yescharacteristic
303C22#1171916911yescharacteristic
304C22C2×#8812111yescharacteristic
305C4—22no—
306C4—22no—
307C4—42no—
308C4—522no—
309C4—522no—
310C4—1041no—
311C4—1041no—
312C2—21no—
313C2—21no—
314C2—44no—
315C2—41no—
316C2—41no—
317C2#1313008111yescharacteristic
318C2#1313108712yes—
subgroupG/H
centerC22C2×#88119
commutatorC24×C13C22×C4
FrattiniC24C22×#261
FittingC24×C4×C13C4
socleC22×C13C2×#99
prime radicalC25×C13C2×C4
cosocleC2×C22⋊Dic13C23
hypercenterC24×C4#261
hypocenterC13#11501
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
1. #13130087C2semidirect
2. #13129762C2semidirect
244. C13#11501semidirect

Maximal subgroups

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

subgroupindex
#131300872
#131297622
#131297602
#131172192
#1150113