Finite Group Databasebeta

← #15760235

Subgroups — #15760235

Order 3328.

570 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123860C211yesmaximal, characteristic
2#13114824C211yesmaximal, characteristic
3#13113408C212yesmaximal, complemented
4#13112715C212yesmaximal, complemented
5C13×#2564C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C2211yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C13×#400C411yescharacteristic, complemented
9C13×#399C411yescharacteristic, complemented
10C13×#395C411yescharacteristic, complemented
11C13×#393C411yescharacteristic, complemented
12C13×#387—21no—
13C13×#386—21no—
14C13×#385—21no—
15C13×#380—21no—
16C2×C13×#95C2211yescharacteristic
17C2×#88074—21no—
18#11718873C2212yes—
19C2×C22⋊#1055—21no—
20C2×C22⋊#1055C2212yes—
21D4×#1055—24no—
22#11718586—21no—
23#11718130—24no—
24#11718118—21no—
25C22×Q8×C13C2×C411yescharacteristic
26C22×D4×C13D411yescharacteristic
27C23×C4×C13—21no—
28C23×C4×C13D411yescharacteristic
29C23×C4×C13C2311yescharacteristic
30C13×C22⋊Q8—22no—
31C13×C22⋊Q8—22no—
32C4×D4×C13—22no—
33C4×D4×C13—22no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4C2×C411yescharacteristic
43C2×C13×C22⋊C4D411yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C22⋊Dic13—22no—
46C2×C4⋊Dic13—22no—
47C22×#1055—22no—
48C22×#1055—22no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95C2×C411yescharacteristic
55C13×#95C2×C411yescharacteristic
56#88074—42no—
57#88071—22no—
58C22⋊#1055—22no—
59C22⋊#1055—22no—
60C22⋊#1055D414yes—
61C4⋊#1055—22no—
62C4×#1055—22no—
63#9383—131nomaximal, Sylow
64C24×C13C22⋊C411yescharacteristic
65C24×C13C2×D411yescharacteristic
66C2×Q8×C13—22no—
67C2×Q8×C13—81no—
68C2×D4×C13—22no—
69C2×D4×C13—22no—
70C2×D4×C13SD1612yes—
71C2×D4×C13Q1612yes—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—42no—
79C22×C4×C13—42no—
80C22×C4×C13—81no—
81C22×C4×C13—81no—
82C22×C4×C13—81no—
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13C22⋊C411yescharacteristic
85C22×C4×C13C22⋊C411yescharacteristic
86C22×C4×C13C22×C411yescharacteristic
87C22×C4×C13C2×D412yes—
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13#4112yes—
90C22×Dic13—42no—
91C13×C4⋊C4—22no—
92C13×C4⋊C4—22no—
93C13×C4⋊C4—42no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—81no—
97C13×C22⋊C4—22no—
98C13×C22⋊C4—22no—
99C13×C22⋊C4—42no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—81no—
102C42×C13—21no—
103C42×C13—21no—
104C22⋊Dic13—42no—
105C22⋊Dic13—42no—
106C4⋊Dic13—82no—
107C2×#1055—24no—
108C2×#1055—82no—
109C2×#1055—82no—
110#2972—131no—
111#2564D1311yescharacteristic
112#1799—131no—
113#1520—132no—
114#1294—132no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13#10312yes—
122C23×C13C2×C22⋊C411yescharacteristic
123C23×C13#12112yes—
124C23×C13C2×SD1611yescharacteristic
125C23×C13C2×Q1611yescharacteristic
126C23×C13#13512yes—
127Q8×C13—82no—
128D4×C13—24no—
129D4×C13—24no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—22no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—42no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—81no—
154C2×C4×C13—84no—
155C2×C4×C13#10312yes—
156C2×C4×C13C4×D412yes—
157C2×C4×C13#12011yescharacteristic
158C2×C4×C13#12311yescharacteristic
159C2×Dic13—82no—
160C2×Dic13—82no—
161C2×Dic13—82no—
162#1055—44no—
163C2×C22⋊Q8C2×D1311yescharacteristic
164C2×C4×D4C2×D1311yescharacteristic
165C8×D4—264no—
166#431—261no—
167C2×#99—261no—
168C2×C22⋊C8—132no—
169C2×C22⋊C8—261no—
170#400Dic1311yescharacteristic, complemented
171#399Dic1311yescharacteristic, complemented
172#395Dic1311yescharacteristic, complemented
173#393Dic1311yescharacteristic, complemented
174#387—21no—
175#386—21no—
176#385—21no—
177#380—21no—
178#380—132no—
179C2×#95C2×D1311yescharacteristic
180#342—261no—
181#328—264no—
182C22×C13—22no—
183C22×C13—21no—
184C22×C13—22no—
185C22×C13—21no—
186C22×C13—22no—
187C22×C13—42no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—42no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—81no—
194C22×C13#38611yescharacteristic
195C22×C13C2×#10311yescharacteristic
196C22×C13#41611yescharacteristic
197C22×C13#46512yes—
198C22×C13#46712yes—
199C4×C13—22no—
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—22no—
203C4×C13—42no—
204C4×C13—41no—
205C4×C13—41no—
206C4×C13—81no—
207C4×C13—81no—
208C4×C13—81no—
209Dic13—162no—
210C22×Q8C2×Dic1311yescharacteristic
211C22×D4C22⋊D1311yescharacteristic
212C23×C4—21no—
213C23×C4C22⋊D1311yescharacteristic
214C23×C4C22×D1311yescharacteristic
215C22×C8—262no—
216C22×C8—262no—
217C22⋊Q8—22no—
218C22⋊Q8—22no—
219C4×D4—22no—
220C4×D4—22no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—262no—
225C2×C4⋊C4C2×Dic1311yescharacteristic
226C2×C4⋊C4C2×Dic1311yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—262no—
231C2×C22⋊C4C2×Dic1311yescharacteristic
232C2×C22⋊C4C22⋊D1311yescharacteristic
233C2×C42C22⋊D1311yescharacteristic
234C4⋊C8—262no—
235#99—522no—
236C22⋊C8—134no—
237C22⋊C8—262no—
238C22⋊C8—262no—
239C4×C8—262no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—262no—
246#95C2×Dic1311yescharacteristic
247#95C2×Dic1311yescharacteristic
248C2×C13—22no—
249C2×C13—21no—
250C2×C13—21no—
251C2×C13—22no—
252C2×C13—42no—
253C2×C13#188411yescharacteristic
254C2×C13#189211yescharacteristic
255C2×C13#191311yescharacteristic
256C24C22⋊Dic1311yescharacteristic
257C24C2×C22⋊D1311yescharacteristic
258C2×Q8—22no—
259C2×Q8—81no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4#610612yes—
263C2×D4#610712yes—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—81no—
273C22×C4—81no—
274C22×C4—81no—
275C22×C4—522no—
276C22×C4C22⋊Dic1311yescharacteristic
277C22×C4C22⋊Dic1311yescharacteristic
278C22×C4C22⋊Dic1311yescharacteristic
279C22×C4D4×D1312yes—
280C22×C4#612912yes—
281C22×C4C22×Dic1311yescharacteristic
282C22×C4C2×C22⋊D1311yescharacteristic
283C2×C8—264no—
284C2×C8—1042no—
285C2×C8—1042no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—42no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—81no—
292C4⋊C4—1042no—
293C22⋊C4—22no—
294C22⋊C4—22no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—81no—
298C22⋊C4—522no—
299C22⋊C4—522no—
300C42—21no—
301C42—21no—
302C13#938311yescharacteristic, complemented, Sylow
303C23—21no—
304C23—21no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23#8807512yes—
310C23#8819312yes—
311C23C2×#610611yescharacteristic
312C23C2×#610711yescharacteristic
313C23#8820412yes—
314C23C2×C22⋊Dic1311yescharacteristic
315Q8—82no—
316D4—24no—
317D4—24no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—81no—
342C2×C4—84no—
343C2×C4—1042no—
344C2×C4—1042no—
345C2×C4—1042no—
346C2×C4#8807512yes—
347C2×C4D4×Dic1312yes—
348C2×C4#8818911yescharacteristic
349C2×C4#8819111yescharacteristic
350C8—524no—
351C22—21no—
352C22—22no—
353C22—21no—
354C22—22no—
355C22—22no—
356C22—42no—
357C22—41no—
358C22—41no—
359C22—42no—
360C22—41no—
361C22—41no—
362C22—81no—
363C22#1171870912yes—
364C22#1171871212yes—
365C22#1171888111yescharacteristic
366C22C2×#8807511yescharacteristic
367C22#1171889411yescharacteristic
368C4—22no—
369C4—21no—
370C4—21no—
371C4—22no—
372C4—42no—
373C4—41no—
374C4—41no—
375C4—81no—
376C4—81no—
377C4—81no—
378C4—2082no—
379C2—21no—
380C2—22no—
381C2—21no—
382C2—22no—
383C2—42no—
384C2#1311522011yescharacteristic
385C2#1311526011yescharacteristic
386C2#1311537911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2564C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenter#2564D13
hypocenterC13#9383
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2564

Complements

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

NH ≅ G/Ntype
3. #13113408C2semidirect
4. #13112715C2semidirect
8. C13×#400C4semidirect
9. C13×#399C4semidirect
10. C13×#395C4semidirect
11. C13×#393C4semidirect
170. #400Dic13semidirect
171. #399Dic13semidirect
172. #395Dic13semidirect
173. #393Dic13semidirect
302. C13#9383semidirect

Maximal subgroups

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

subgroupindex
#131238602
#131148242
#131134082
#131127152
C13×#25642
#938313