Finite Group Databasebeta

← #14739035

Subgroups — #14739035

Order 2816.

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#13079775C211yesmaximal, characteristic, complemented
2#13078715C211yesmaximal, characteristic
3#13077640C211yesmaximal, characteristic
4#13068069C212yesmaximal, complemented
5#13068041C212yesmaximal, complemented
6#13068003C212yesmaximal, complemented
7#13067993C212yesmaximal, complemented
8#13067394C211yesmaximal, characteristic, complemented
9#13067326C211yesmaximal, characteristic, complemented
10#13067280C211yesmaximal, characteristic, complemented
11C11×#3101C211yesmaximal, characteristic
12C11×#533C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14#10623001C2211yescharacteristic
15C11×#483—21no—
16C11×#476C2212yes—
17C11×#461C2212yes—
18C11×#450—21no—
19C4×C11×SD16—22no—
20C11×#431C2211yescharacteristic
21#10622831—21no—
22C2×C22⋊(C11⋊C8)—22no—
23#10622706C2211yescharacteristic, complemented
24#10622706C2211yescharacteristic, complemented
25#10622692C2211yescharacteristic, complemented
26#10622691C2211yescharacteristic, complemented
27#10622676—22no—
28#10622632C2212yes—
29#10622631—22no—
30D4×C11⋊C8—22no—
31D4×C11⋊C8C2212yes—
32D4×C11⋊C8C2212yes—
33#10622620C2212yes—
34#10622609—22no—
35#10622583—21no—
36#10622539C2211yescharacteristic
37#10622538C2211yescharacteristic
38#10622538C2211yescharacteristic
39#10622185C2212yescomplemented
40#10622184C2212yescomplemented
41#10622124C2212yescomplemented
42#10622120C2212yescomplemented
43#10622118C2212yescomplemented
44#10622117C2212yescomplemented
45C22×D4×C11D411yescharacteristic
46C23×C4×C11—21no—
47C2×C11×SD16—22no—
48C11×C4⋊Q8C2311yescharacteristic
49C11×C4⋊Q8C2311yescharacteristic
50C11×#125—21no—
51C11×C22⋊Q8—21no—
52C11×C22⋊Q8—21no—
53C4×Q8×C11—21no—
54C4×Q8×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11D412yes—
58C4×D4×C11C2312yes—
59C11×#117—21no—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C22⋊C4—21no—
62C2×C42×C11C2311yescharacteristic
63C2×#4324—22no—
64#66979—21no—
65#66977—21no—
66#66977—21no—
67C22×C11⋊C8—22no—
68C22×C11⋊C8—22no—
69#66923—21no—
70#66922C2311yescharacteristic
71#66922C2311yescharacteristic
72C4×Dic22—21no—
73C4×Dic22—21no—
74C11×#106—22no—
75C11×C4⋊C8C2312yes—
76C11×#103—22no—
77C11×#102—22no—
78C11×C22⋊C8—21no—
79C4×C8×C11—21no—
80#66896—22no—
81C22⋊(C11⋊C8)—21no—
82C22⋊(C11⋊C8)—21no—
83C22⋊(C11⋊C8)—22no—
84C22⋊(C11⋊C8)—22no—
85C22⋊(C11⋊C8)D412yes—
86#66874—22no—
87#66874—22no—
88#66874—22no—
89#66872—22no—
90#66871—22no—
91#66871—22no—
92C4⋊(C11⋊C8)D412yes—
93C4⋊(C11⋊C8)C2312yes—
94C4⋊(C11⋊C8)C2312yes—
95#66867—21no—
96C4×C11⋊C8—21no—
97C4×C11⋊C8C2311yescharacteristic
98C4×C11⋊C8C2311yescharacteristic
99#19395—111nomaximal, Sylow
100C24×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×D4×C11—24no—
104C2×D4×C11—21no—
105C2×D4×C11C2×D412yes—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—82no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C2×Dic22—21no—
114C2×Dic22—21no—
115C11×SD16—44no—
116C2×C8×C11—22no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4C2×D412yes—
125C11×C22⋊C4—22no—
126C11×C22⋊C4—22no—
127C11×C22⋊C4—41no—
128C42×C11—41no—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11#4111yescharacteristic
132C42×C11C2411yescharacteristic
133C22⋊Dic11—41no—
134#4324—44no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139Dic11⋊C4—41no—
140Dic11⋊C4—41no—
141C4×Dic11—41no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—82no—
145C2×C11⋊C8—82no—
146C2×C11⋊C8C2×D412yes—
147C2×C11⋊C8C2×D412yes—
148#3231—111no—
149#3110—111no—
150#3101D1111yescharacteristic
151#2972—111no—
152#1683—112no—
153#1679—112no—
154#1673—112no—
155#1671—112no—
156#1572—111no—
157#1554—111no—
158#1544—111no—
159C23×C11—24no—
160C23×C11—22no—
161C23×C11—81no—
162C23×C11—81no—
163C23×C11#12111yescharacteristic
164Q8×C11—42no—
165Q8×C11—81no—
166D4×C11—24no—
167D4×C11—22no—
168D4×C11#13514yes—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—82no—
178C2×C4×C11—81no—
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C2×Dic11—41no—
186C2×Dic11—41no—
187Dic22—42no—
188Dic22—42no—
189C8×C11—42no—
190C11⋊C8—22no—
191C11⋊C8—22no—
192C11⋊C8—42no—
193C11⋊C8—42no—
194#533—111no—
195#533C2×D1111yescharacteristic
196C2×C4×D4C2×D1111yescharacteristic
197#500—111no—
198#498—111no—
199#487—111no—
200#487—111no—
201#485—222no—
202#484—221no—
203#483—21no—
204#479—222no—
205#476C2×D1112yes—
206#474—112no—
207#461—112no—
208#461C2×D1112yes—
209#450—21no—
210#450—221no—
211#440—222no—
212C4×SD16—22no—
213C8×D4—112no—
214C8×D4—112no—
215C8×D4—222no—
216#432—111no—
217#431—111no—
218#431—111no—
219#431C2×D1111yescharacteristic
220C2×C22⋊C8—222no—
221#335—112no—
222#334—112no—
223#333—112no—
224#332—112no—
225#332—112no—
226#332—112no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—24no—
230C22×C11—21no—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11—84no—
234C22×C11C2×#12111yescharacteristic
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—42no—
240C4×C11—81no—
241C4×C11—81no—
242C4×C11C2×#13512yes—
243C4×C11#57712yes—
244Dic11—81no—
245Dic11—81no—
246C22×D4C22⋊D1111yescharacteristic
247C23×C4—21no—
248C2×SD16—22no—
249C2×SD16—222no—
250C22×C8—222no—
251C22×C8—222no—
252C4⋊Q8—111no—
253C4⋊Q8—111no—
254C4⋊Q8C22×D1111yescharacteristic
255C4⋊Q8C22×D1111yescharacteristic
256#125—21no—
257#125—221no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—221no—
261C22⋊Q8—221no—
262C4×Q8—21no—
263C4×Q8—21no—
264C4×Q8—221no—
265C4×Q8—221no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4C22⋊D1112yes—
269C4×D4C22×D1112yes—
270#117—21no—
271#117—221no—
272C2×C4⋊C4C22⋊D1111yescharacteristic
273C2×C22⋊C4—21no—
274C2×C42C22×D1111yescharacteristic
275#107—222no—
276#107—222no—
277#106—22no—
278#106—222no—
279C4⋊C8—112no—
280C4⋊C8—112no—
281C4⋊C8—112no—
282C4⋊C8C22×D1112yes—
283#103—22no—
284#103—222no—
285#103—222no—
286#103—222no—
287#102—22no—
288#102—222no—
289C22⋊C8—21no—
290C22⋊C8—112no—
291C22⋊C8—222no—
292C22⋊C8—222no—
293C22⋊C8—221no—
294C22⋊C8—221no—
295#97—221no—
296C4×C8—21no—
297C4×C8—111no—
298C4×C8—111no—
299C4×C8—221no—
300C2×C11—41no—
301C2×C11—44no—
302C2×C11#304211yescharacteristic
303C2×C11#305011yescharacteristic
304C2×C11#306911yescharacteristic
305C24—21no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—221no—
309C2×Q8—221no—
310C2×D4—24no—
311C2×D4—21no—
312C2×D4C2×C22⋊D1112yes—
313C22×C4—21no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—82no—
317C22×C4D4×D1111yescharacteristic
318C22×C4#434111yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320SD16—44no—
321SD16—444no—
322C2×C8—22no—
323C2×C8—112no—
324C2×C8—112no—
325C2×C8—222no—
326C2×C8—222no—
327C2×C8—882no—
328C2×C8—882no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—221no—
337C4⋊C4—221no—
338C4⋊C4—221no—
339C4⋊C4—221no—
340C4⋊C4—441no—
341C4⋊C4—441no—
342C4⋊C4C2×C22⋊D1112yes—
343C22⋊C4—22no—
344C22⋊C4—22no—
345C22⋊C4—41no—
346C22⋊C4—441no—
347C42—41no—
348C42—441no—
349C42D4×D1111yescharacteristic
350C42#434111yescharacteristic
351C42C2×C22⋊D1111yescharacteristic
352C42C23×D1111yescharacteristic
353C11#1939511yescharacteristic, complemented, Sylow
354C23—24no—
355C23—22no—
356C23—81no—
357C23—81no—
358C23#6699211yescharacteristic
359Q8—42no—
360Q8—81no—
361Q8—442no—
362Q8—442no—
363D4—24no—
364D4—22no—
365D4#6700314yes—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—82no—
375C2×C4—81no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4#6699211yescharacteristic
379C2×C4#6699211yescharacteristic
380C2×C4#6699211yescharacteristic
381C2×C4C2×D4×D1111yescharacteristic
382C2×C4C2×#434111yescharacteristic
383C2×C4C22×C22⋊D1111yescharacteristic
384C8—42no—
385C8—222no—
386C8—222no—
387C8—442no—
388C8—442no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—24no—
393C22—42no—
394C22—42no—
395C22—84no—
396C22C2×#6699211yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—42no—
402C4—81no—
403C4—81no—
404C4—881no—
405C4—881no—
406C4#1062329312yes—
407C4C2×#6700312yes—
408C2—41no—
409C2—44no—
410C2#1307812511yescharacteristic
411C2#1307819411yescharacteristic
412C2#1307835511yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3101C2
socleC22×C11C2×#121
prime radicalC22×D4×C11D4
hypercenter#3101D11
hypocenterC11#19395
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3101

Complements

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

NH ≅ G/Ntype
1. #13079775C2semidirect
4. #13068069C2semidirect
5. #13068041C2semidirect
6. #13068003C2semidirect
7. #13067993C2semidirect
8. #13067394C2semidirect
9. #13067326C2semidirect
10. #13067280C2semidirect
23. #10622706C22semidirect
24. #10622706C22semidirect
25. #10622692C22semidirect
26. #10622691C22semidirect
39. #10622185C22semidirect
40. #10622184C22semidirect
41. #10622124C22semidirect
42. #10622120C22semidirect
43. #10622118C22semidirect
44. #10622117C22semidirect
353. C11#19395semidirect

Maximal subgroups

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

subgroupindex
#130797752
#130787152
#130776402
#130680692
#130680412
#130680032
#130679932
#130673942
#130673262
#130672802
C11×#31012
#1939511