Finite Group Databasebeta

← #15760609

Subgroups — #15760609

Order 3328.

498 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 111 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#13123865C211yesmaximal, characteristic
2#13113553C212yesmaximal, complemented
3#13113177C211yesmaximal, characteristic
4#13112692C212yesmaximal, complemented
5C13×#2563C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C13×#393—21no—
9C13×#393—21no—
10C13×#390C412yes—
11C13×#382C412yes—
12C13×#380—21no—
13C13×#380—21no—
14C4×C13×C4⋊C4C2211yescharacteristic
15#11718868—21no—
16C2×C22⋊#1055—21no—
17#11718672—24no—
18#11718587C2212yes—
19#11718587C2212yes—
20#11718139—24no—
21#11718117—21no—
22#11718117—21no—
23C22×Q8×C13—21no—
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C13×C4⋊Q8—22no—
28C13×C4⋊Q8—22no—
29C4×D4×C13—22no—
30C4×D4×C13—22no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C412yes—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4D411yescharacteristic
38C2×C13×C22⋊C4D411yescharacteristic
39C2×C42×C13C2×C412yes—
40C2×C42×C13C2311yescharacteristic
41C2×#6099—22no—
42C22×#1055—22no—
43C13×#95—22no—
44C13×#95—22no—
45C13×#95—21no—
46C22⋊#1055—22no—
47C22⋊#1055—22no—
48C22⋊#1055—22no—
49C22⋊#1055—22no—
50C4⋊#1055—22no—
51C4⋊#1055D414yes—
52#88043—22no—
53#88043—22no—
54#9453—131nomaximal, Sylow
55C24×C13C22⋊C411yescharacteristic
56C24×C13C22⋊C411yescharacteristic
57C2×Q8×C13—42no—
58C2×Q8×C13—82no—
59C2×D4×C13—22no—
60C2×D4×C13—22no—
61C2×D4×C13—41no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C13×C4⋊C4—22no—
76C13×C4⋊C4—24no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C22⋊C4—22no—
81C13×C22⋊C4—22no—
82C13×C22⋊C4—82no—
83C13×C22⋊C4—82no—
84C42×C13—42no—
85C42×C13C2×D412yes—
86C42×C13#4112yes—
87#6099—82no—
88C2×#1055—24no—
89C2×#1055—42no—
90C2×#1055—82no—
91#2973—131no—
92#2563D1311yescharacteristic
93#1556—132no—
94#1466—131no—
95#1285—132no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13#10112yes—
106C23×C13C2×C22⋊C411yescharacteristic
107Q8×C13—84no—
108D4×C13—44no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—22no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—41no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—81no—
126C2×C4×C13—81no—
127C2×C4×C13C4×D412yes—
128C2×C4×C13#12011yescharacteristic
129C2×C4×C13#12112yes—
130C2×C4×C13#12311yescharacteristic
131#1055—44no—
132#1055—82no—
133C2×C4⋊Q8C2×D1311yescharacteristic
134C2×C4×D4C2×D1311yescharacteristic
135#435—264no—
136#432—132no—
137#432—132no—
138#407—261no—
139C2×C22⋊C8—261no—
140#393—21no—
141#393—21no—
142#390Dic1312yes—
143#382Dic1312yes—
144#380—21no—
145#380—21no—
146C4×C4⋊C4C2×D1311yescharacteristic
147#332—264no—
148#323—261no—
149#323—261no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13—22no—
153C22×C13—42no—
154C22×C13—42no—
155C22×C13—41no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—81no—
161C22×C13—81no—
162C22×C13#38611yescharacteristic
163C22×C13C2×#10111yescharacteristic
164C22×C13#41311yescharacteristic
165C4×C13—21no—
166C4×C13—22no—
167C4×C13—22no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—82no—
171C4×C13—82no—
172C4×C13#45512yes—
173C22×Q8—21no—
174C22×D4C2×Dic1311yescharacteristic
175C23×C4C22⋊D1311yescharacteristic
176C23×C4C22⋊D1311yescharacteristic
177C2×M16—262no—
178C22×C8—262no—
179C4⋊Q8—22no—
180C4⋊Q8—22no—
181C4×D4—22no—
182C4×D4—22no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4C2×Dic1312yes—
186C2×C4⋊C4C2×Dic1311yescharacteristic
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4C22⋊D1311yescharacteristic
190C2×C22⋊C4C22⋊D1311yescharacteristic
191C2×C42C2×Dic1312yes—
192C2×C42C22×D1311yescharacteristic
193C4⋊C8—134no—
194C4⋊C8—262no—
195C22⋊C8—262no—
196C22⋊C8—262no—
197C22⋊C8—262no—
198C22⋊C8—262no—
199#97—262no—
200#97—262no—
201#95—22no—
202#95—22no—
203#95—21no—
204C2×C13—21no—
205C2×C13—21no—
206C2×C13—42no—
207C2×C13—81no—
208C2×C13#188511yescharacteristic
209C2×C13#190111yescharacteristic
210C2×C13#191011yescharacteristic
211C24C22⋊Dic1311yescharacteristic
212C24C22⋊Dic1311yescharacteristic
213C2×Q8—42no—
214C2×Q8—82no—
215C2×D4—22no—
216C2×D4—22no—
217C2×D4—41no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4C22⋊Dic1311yescharacteristic
227C22×C4C22⋊Dic1311yescharacteristic
228C22×C4C22×Dic1311yescharacteristic
229C22×C4C2×C22⋊D1311yescharacteristic
230C22×C4C2×C22⋊D1311yescharacteristic
231M16—1042no—
232C2×C8—264no—
233C2×C8—522no—
234C2×C8—1042no—
235C4⋊C4—22no—
236C4⋊C4—24no—
237C4⋊C4—42no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C22⋊C4—22no—
241C22⋊C4—22no—
242C22⋊C4—82no—
243C22⋊C4—82no—
244C42—42no—
245C42D4×D1312yes—
246C42#612912yes—
247C13#945311yescharacteristic, complemented, Sylow
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23#8807612yes—
258C23C2×C22⋊Dic1311yescharacteristic
259Q8—84no—
260D4—44no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4D4×Dic1312yes—
280C2×C4#8818911yescharacteristic
281C2×C4#8819111yescharacteristic
282C2×C4#8819312yes—
283C8—524no—
284C8—1042no—
285C22—21no—
286C22—21no—
287C22—22no—
288C22—42no—
289C22—42no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—81no—
297C22#1171888111yescharacteristic
298C22C2×#8807611yescharacteristic
299C22#1171889811yescharacteristic
300C4—21no—
301C4—22no—
302C4—22no—
303C4—41no—
304C4—41no—
305C4—82no—
306C4—82no—
307C4#1171872212yes—
308C2—21no—
309C2—21no—
310C2—42no—
311C2—81no—
312C2#1311522511yescharacteristic
313C2#1311530511yescharacteristic
314C2#1311536411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2563C2
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenter#2563D13
hypocenterC13#9453
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2563

Complements

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

NH ≅ G/Ntype
2. #13113553C2semidirect
4. #13112692C2semidirect
247. C13#9453semidirect

Maximal subgroups

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

subgroupindex
#131238652
#131135532
#131131772
#131126922
C13×#25632
#945313