Finite Group Databasebeta

← #15848180

Subgroups — #15848180

Order 3328.

628 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124931C211yesmaximal, characteristic
2#13124840C211yesmaximal, characteristic
3#13123859C211yesmaximal, characteristic
4#13114284C212yesmaximal, complemented
5#13114256C212yesmaximal, complemented
6#13114222C212yesmaximal, complemented
7#13114208C212yesmaximal, complemented
8#13113616C211yesmaximal, characteristic, complemented
9#13113546C211yesmaximal, characteristic, complemented
10#13113501C211yesmaximal, characteristic, complemented
11C13×#3231C211yesmaximal, characteristic, complemented
12C13×#533C2211yescharacteristic
13C13×#533C2211yescharacteristic
14C2×C4×D52C2211yescharacteristic
15C13×#500C2211yescharacteristic, complemented
16C13×#498C2211yescharacteristic, complemented
17C13×#487C2211yescharacteristic, complemented
18C13×#487C2211yescharacteristic, complemented
19C13×#485—22no—
20C13×#479—22no—
21C13×#431C2211yescharacteristic
22#11718748C2212yes—
23#11718745C2212yes—
24#11718744C2212yes—
25#11718744C2212yes—
26#11718707—21no—
27#11718707—21no—
28#11718705—21no—
29#11718704—21no—
30#11718687—22no—
31C4×#6106—22no—
32#11718587C2211yescharacteristic
33#11718586C2211yescharacteristic
34#11718586C2211yescharacteristic
35#11718495—22no—
36D13×C22⋊C8—22no—
37C8×D52C2212yes—
38C8×D52C2212yes—
39#11718139C2212yescomplemented
40#11718139C2212yescomplemented
41#11718139C2212yescomplemented
42#11718138C2212yescomplemented
43#11718050C2212yescomplemented
44#11718049C2212yescomplemented
45C22×D52D411yescharacteristic
46C22×C4×D13—21no—
47C13×C4⋊Q8C2311yescharacteristic
48C13×C4⋊Q8C2311yescharacteristic
49C13×C4⋊Q8C2311yescharacteristic
50C13×C4⋊Q8C2311yescharacteristic
51C13×#125—21no—
52C13×#125—21no—
53C13×C22⋊Q8—21no—
54C13×C22⋊Q8—21no—
55C13×C22⋊Q8—21no—
56C13×C22⋊Q8—21no—
57C4×Q8×C13—21no—
58C4×Q8×C13—21no—
59C4×Q8×C13—21no—
60C4×Q8×C13—21no—
61C13×#117—21no—
62C13×#117—21no—
63C2×C42×C13C2311yescharacteristic
64C2×#6106—22no—
65C2×#6106—22no—
66C2×#6103—21no—
67C2×C4⋊Dic13D411yescharacteristic
68C2×C8×D13—22no—
69C2×C8×D13—22no—
70C4×D52—21no—
71C4×D52—21no—
72C4×D52D412yes—
73C4×D52C2312yes—
74C13×#107—22no—
75C13×#106—22no—
76C13×C4⋊C8D412yes—
77C13×#103—22no—
78C13×#103—22no—
79C13×C22⋊C8D412yes—
80C4×C8×C13C2311yescharacteristic
81C4×C8×C13C2311yescharacteristic
82#88075—22no—
83#88075—22no—
84C22⋊#1055—21no—
85C22⋊#1055—21no—
86C22⋊#1055—21no—
87#88060—22no—
88#88060—22no—
89#88049—22no—
90#88049—22no—
91#88048—22no—
92#88047—22no—
93C4⋊#1055C2312yes—
94C4⋊#1055C2312yes—
95C4⋊#1055C2312yes—
96#88043—21no—
97C4×#1055—21no—
98C4×#1055—21no—
99#19395—131nomaximal, Sylow
100C23×D13—21no—
101C2×Q8×C13—21no—
102C2×Q8×C13—21no—
103C2×Q8×C13—21no—
104C2×Q8×C13—21no—
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13#4111yescharacteristic
108C22×Dic13—21no—
109C2×D52—21no—
110C2×D52—24no—
111C2×D52C2×D412yes—
112C2×C4×D13—22no—
113C2×C4×D13—22no—
114C2×C4×D13—82no—
115C2×C8×C13C2×D412yes—
116C2×C8×C13C2×D412yes—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—21no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4—21no—
121C13×C4⋊C4—21no—
122C13×C4⋊C4—21no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4—41no—
126C13×C4⋊C4—41no—
127C13×C4⋊C4—41no—
128C13×C4⋊C4—41no—
129C13×C22⋊C4—41no—
130C13×C22⋊C4—41no—
131C42×C13—41no—
132C42×C13—41no—
133C42×C13C2×D411yescharacteristic
134C42×C13C2×D411yescharacteristic
135C42×C13#4111yescharacteristic
136C42×C13C2411yescharacteristic
137#6106—44no—
138#6106—44no—
139#6103—22no—
140#6103—22no—
141C4⋊Dic13—21no—
142C4⋊Dic13C2×D412yes—
143C2×#1055—22no—
144C2×#1055—22no—
145C2×#1055—22no—
146C8×D13—82no—
147C8×D13—82no—
148#3231D1311yescharacteristic, complemented
149#3110—131no—
150#3101—131no—
151#2972—131no—
152#1683—132no—
153#1679—132no—
154#1673—132no—
155#1671—132no—
156#1572—131no—
157#1554—131no—
158#1544—131no—
159C23×C13#12111yescharacteristic
160C22×D13—22no—
161C22×D13—24no—
162C22×D13—81no—
163C22×D13—81no—
164Q8×C13—42no—
165Q8×C13—42no—
166Q8×C13—42no—
167Q8×C13—81no—
168C2×C4×C13—22no—
169C2×C4×C13—22no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13#12111yescharacteristic
176C2×C4×C13#12111yescharacteristic
177C2×C4×C13#12111yescharacteristic
178C2×C4×C13C22×D411yescharacteristic
179C2×C4×C13C22×D411yescharacteristic
180C2×C4×C13C2×#4111yescharacteristic
181C2×Dic13—22no—
182C2×Dic13—81no—
183D52—24no—
184D52—22no—
185D52#13514yes—
186C4×D13—42no—
187C4×D13—42no—
188C4×D13—82no—
189C8×C13—22no—
190C8×C13—22no—
191#1055—42no—
192#1055—42no—
193#1055—42no—
194#533C2×D1311yescharacteristic
195#533C2×D1311yescharacteristic
196C2×C4×D4—131no—
197#500C2×D1311yescharacteristic, complemented
198#498C2×D1311yescharacteristic, complemented
199#487C2×D1311yescharacteristic, complemented
200#487C2×D1311yescharacteristic, complemented
201#485—22no—
202#484—261no—
203#483—261no—
204#479—22no—
205#476—132no—
206#474—132no—
207#461—132no—
208#461—132no—
209#450—261no—
210#450—261no—
211#440—262no—
212C4×SD16—262no—
213C8×D4—132no—
214C8×D4—132no—
215C8×D4—262no—
216#432—131no—
217#431—131no—
218#431—131no—
219#431C2×D1311yescharacteristic
220C2×C22⋊C8—262no—
221#335—132no—
222#334—132no—
223#333—132no—
224#332—132no—
225#332—132no—
226#332—132no—
227C22×C13—21no—
228C22×C13—21no—
229C22×C13—21no—
230C22×C13C2×#12111yescharacteristic
231C2×D13—24no—
232C2×D13—42no—
233C2×D13—42no—
234C2×D13—84no—
235C4×C13—21no—
236C4×C13—21no—
237C4×C13—21no—
238C4×C13—21no—
239C4×C13—81no—
240C4×C13—81no—
241C4×C13—81no—
242C4×C13—81no—
243C4×C13C2×#13512yes—
244C4×C13#57712yes—
245Dic13—42no—
246C22×D4—131no—
247C23×C4—261no—
248C2×SD16—262no—
249C2×SD16—262no—
250C22×C8—262no—
251C22×C8—262no—
252C4⋊Q8C22×D1311yescharacteristic
253C4⋊Q8C22×D1311yescharacteristic
254C4⋊Q8C22×D1311yescharacteristic
255C4⋊Q8C22×D1311yescharacteristic
256#125—21no—
257#125—21no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C22⋊Q8—21no—
262C4×Q8—21no—
263C4×Q8—21no—
264C4×Q8—21no—
265C4×Q8—21no—
266C4×D4—132no—
267C4×D4—132no—
268C4×D4—261no—
269C4×D4—261no—
270#117—21no—
271#117—21no—
272C2×C4⋊C4—131no—
273C2×C22⋊C4—261no—
274C2×C42C22×D1311yescharacteristic
275#107—22no—
276#107—262no—
277#106—22no—
278#106—262no—
279C4⋊C8—132no—
280C4⋊C8—132no—
281C4⋊C8—132no—
282C4⋊C8C22⋊D1312yes—
283#103—22no—
284#103—22no—
285#103—262no—
286#103—262no—
287#102—262no—
288#102—262no—
289C22⋊C8—261no—
290C22⋊C8—261no—
291C22⋊C8—261no—
292C22⋊C8—262no—
293C22⋊C8—262no—
294C22⋊C8C22⋊D1312yes—
295#97—261no—
296C4×C8—261no—
297C4×C8—261no—
298C4×C8C22×D1311yescharacteristic
299C4×C8C22×D1311yescharacteristic
300C2×C13—41no—
301C2×C13#304211yescharacteristic
302C2×C13#305011yescharacteristic
303C2×C13#306911yescharacteristic
304D13—44no—
305C24—261no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×D4—132no—
311C2×D4—264no—
312C2×D4—261no—
313C22×C4—261no—
314C22×C4—262no—
315C22×C4—262no—
316C22×C4—1042no—
317C22×C4D4×D1311yescharacteristic
318C22×C4#612911yescharacteristic
319C22×C4C2×C22⋊D1311yescharacteristic
320SD16—524no—
321SD16—524no—
322C2×C8—262no—
323C2×C8—262no—
324C2×C8—262no—
325C2×C8—1042no—
326C2×C8—1042no—
327C2×C8C2×C22⋊D1312yes—
328C2×C8C2×C22⋊D1312yes—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—132no—
342C4⋊C4—261no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—262no—
346C22⋊C4—262no—
347C42—41no—
348C42—41no—
349C42D4×D1311yescharacteristic
350C42#612911yescharacteristic
351C42C2×C22⋊D1311yescharacteristic
352C42C23×D1311yescharacteristic
353C13#1939511yescharacteristic, complemented, Sylow
354C23—264no—
355C23—262no—
356C23—1041no—
357C23—1041no—
358C23#8819211yescharacteristic
359Q8—42no—
360Q8—42no—
361Q8—42no—
362Q8—81no—
363D4—134no—
364D4—264no—
365D4—262no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—262no—
374C2×C4—522no—
375C2×C4—522no—
376C2×C4—1042no—
377C2×C4—1041no—
378C2×C4#8819211yescharacteristic
379C2×C4#8819211yescharacteristic
380C2×C4#8819211yescharacteristic
381C2×C4C2×D4×D1311yescharacteristic
382C2×C4C2×#612911yescharacteristic
383C2×C4C22×C22⋊D1311yescharacteristic
384C8—22no—
385C8—22no—
386C8—522no—
387C8—522no—
388C8—522no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—264no—
393C22—522no—
394C22—522no—
395C22—1044no—
396C22C2×#8819211yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—81no—
402C4—81no—
403C4—81no—
404C4—81no—
405C4—522no—
406C4D13×#13512yes—
407C4#1171954212yes—
408C2—41no—
409C2—524no—
410C2#1312434411yescharacteristic
411C2#1312441311yescharacteristic
412C2#1312456911yescharacteristic
subgroupG/H
centerC22C2×#88192
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#3231C2
socleC22×C13C2×#121
prime radicalC22×D52D4
hypercenter#3231D13
hypocenterC13#19395
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3231

Complements

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

NH ≅ G/Ntype
4. #13114284C2semidirect
5. #13114256C2semidirect
6. #13114222C2semidirect
7. #13114208C2semidirect
8. #13113616C2semidirect
9. #13113546C2semidirect
10. #13113501C2semidirect
11. C13×#3231C2semidirect
15. C13×#500C22semidirect
16. C13×#498C22semidirect
17. C13×#487C22semidirect
18. C13×#487C22semidirect
39. #11718139C22semidirect
40. #11718139C22semidirect
41. #11718139C22semidirect
42. #11718138C22semidirect
43. #11718050C22semidirect
44. #11718049C22semidirect
148. #3231D13semidirect
197. #500C2×D13semidirect
198. #498C2×D13semidirect
199. #487C2×D13semidirect
200. #487C2×D13semidirect
353. C13#19395semidirect

Maximal subgroups

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

subgroupindex
#131249312
#131248402
#131238592
#131142842
#131142562
#131142222
#131142082
#131136162
#131135462
#131135012
C13×#32312
#1939513