Finite Group Databasebeta

← #14739038

Subgroups — #14739038

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#13079777C211yesmaximal, characteristic, complemented
2#13078715C211yesmaximal, characteristic
3#13078624C211yesmaximal, characteristic
4#13068067C212yesmaximal, complemented
5#13068039C212yesmaximal, complemented
6#13068005C212yesmaximal, complemented
7#13067991C212yesmaximal, complemented
8#13067396C211yesmaximal, characteristic, complemented
9#13067324C211yesmaximal, characteristic, complemented
10#13067280C211yesmaximal, characteristic, complemented
11C11×#2972C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13#10623001C2211yescharacteristic
14#10623001C2211yescharacteristic
15C8×D4×C11—22no—
16C8×D4×C11C2212yes—
17C8×D4×C11C2212yes—
18C11×#431C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C2×C11×C22⋊C8—22no—
21#10622831—21no—
22#10622831—21no—
23#10622632C2212yes—
24#10622632C2212yes—
25#10622631—22no—
26C4×#4324—22no—
27#10622621C2212yes—
28#10622620C2212yes—
29#10622584—21no—
30#10622583—21no—
31#10622539C2211yescharacteristic
32#10622538C2211yescharacteristic
33#10622442—22no—
34#10622336—22no—
35#10622295C2211yescharacteristic, complemented
36#10622294C2211yescharacteristic, complemented
37#10622294C2211yescharacteristic, complemented
38#10622293C2211yescharacteristic, complemented
39#10622124C2212yescomplemented
40#10622124C2212yescomplemented
41#10622120C2212yescomplemented
42#10622119C2212yescomplemented
43#10622096C2212yescomplemented
44#10622095C2212yescomplemented
45C22×D4×C11D411yescharacteristic
46C23×C4×C11—21no—
47C22×C8×C11—22no—
48C22×C8×C11—22no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11D412yes—
52C4×D4×C11C2312yes—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C22⋊C4—21no—
55C2×C42×C11C2311yescharacteristic
56C2×#4324—22no—
57C2×#4324—22no—
58#66979—21no—
59#66979—21no—
60#66977—21no—
61#66977—21no—
62#66977—21no—
63#66977—21no—
64#66923—21no—
65#66923—21no—
66#66922C2311yescharacteristic
67#66922C2311yescharacteristic
68#66922C2311yescharacteristic
69#66922C2311yescharacteristic
70C4×Dic22—21no—
71C4×Dic22—21no—
72C4×Dic22—21no—
73C4×Dic22—21no—
74C11×C4⋊C8D412yes—
75C11×C4⋊C8C2312yes—
76C11×C22⋊C8—21no—
77C11×C22⋊C8—22no—
78C11×C22⋊C8—22no—
79C11×C22⋊C8D412yes—
80C4×C8×C11—21no—
81C4×C8×C11C2311yescharacteristic
82C4×C8×C11C2311yescharacteristic
83#66896—22no—
84#66896—22no—
85C22⋊(C11⋊C8)—21no—
86C22⋊(C11⋊C8)—21no—
87#66882—22no—
88#66881—22no—
89#66880—22no—
90#66880—22no—
91#66874—22no—
92#66874—22no—
93#66872—22no—
94#66871—22no—
95C4⋊(C11⋊C8)C2312yes—
96C4⋊(C11⋊C8)C2312yes—
97#66867—21no—
98C4×C11⋊C8—21no—
99#19395—111nomaximal, Sylow
100C24×C11—21no—
101C2×D4×C11—24no—
102C2×D4×C11—21no—
103C2×D4×C11C2×D412yes—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—82no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C2×Dic22—21no—
112C2×Dic22—21no—
113C2×Dic22—21no—
114C2×Dic22—21no—
115C2×C8×C11—22no—
116C2×C8×C11—82no—
117C2×C8×C11—82no—
118C2×C8×C11C2×D412yes—
119C2×C8×C11C2×D412yes—
120C11×C4⋊C4—21no—
121C11×C4⋊C4C2×D412yes—
122C11×C22⋊C4—22no—
123C11×C22⋊C4—22no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11#4111yescharacteristic
127C42×C11C2411yescharacteristic
128C22⋊Dic11—41no—
129C22⋊Dic11—41no—
130#4324—44no—
131#4324—44no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140Dic11⋊C4—41no—
141Dic11⋊C4—41no—
142Dic11⋊C4—41no—
143Dic11⋊C4—41no—
144C4×Dic11—41no—
145C4×Dic11—41no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148#3231—111no—
149#3110—111no—
150#3101—111no—
151#2972D1111yescharacteristic
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
164D4×C11—24no—
165D4×C11—22no—
166D4×C11#13514yes—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—82no—
174C2×C4×C11—81no—
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11C22×D411yescharacteristic
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185Dic22—42no—
186Dic22—42no—
187Dic22—42no—
188Dic22—81no—
189C8×C11—22no—
190C8×C11—22no—
191C8×C11—42no—
192C11⋊C8—42no—
193C11⋊C8—42no—
194#533—111no—
195#533—111no—
196C2×C4×D4C2×D1111yescharacteristic
197#500—111no—
198#498—111no—
199#487—111no—
200#487—111no—
201#485—222no—
202#484—221no—
203#483—221no—
204#479—222no—
205#476—112no—
206#474—112no—
207#461—112no—
208#461—112no—
209#450—221no—
210#450—221no—
211#440—222no—
212C4×SD16—222no—
213C8×D4—22no—
214C8×D4C2×D1112yes—
215C8×D4C2×D1112yes—
216#432—111no—
217#431—111no—
218#431C2×D1111yescharacteristic
219#431C2×D1111yescharacteristic
220C2×C22⋊C8—22no—
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×C11C2×#13512yes—
241C4×C11#57712yes—
242Dic11—81no—
243Dic11—81no—
244Dic11—81no—
245Dic11—81no—
246C22×D4D4411yescharacteristic
247C23×C4—21no—
248C2×SD16—222no—
249C2×SD16—222no—
250C22×C8—22no—
251C22×C8—22no—
252C4⋊Q8—111no—
253C4⋊Q8—111no—
254C4⋊Q8—111no—
255C4⋊Q8—111no—
256#125—221no—
257#125—221no—
258C22⋊Q8—221no—
259C22⋊Q8—221no—
260C22⋊Q8—221no—
261C22⋊Q8—221no—
262C4×Q8—221no—
263C4×Q8—221no—
264C4×Q8—221no—
265C4×Q8—221no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4D4412yes—
269C4×D4C22×D1112yes—
270#117—221no—
271#117—221no—
272C2×C4⋊C4D4411yescharacteristic
273C2×C22⋊C4—21no—
274C2×C42C22×D1111yescharacteristic
275#107—222no—
276#107—222no—
277#106—222no—
278#106—222no—
279C4⋊C8—112no—
280C4⋊C8—112no—
281C4⋊C8C22⋊D1112yes—
282C4⋊C8C22×D1112yes—
283#103—222no—
284#103—222no—
285#103—222no—
286#103—222no—
287#102—222no—
288#102—222no—
289C22⋊C8—21no—
290C22⋊C8—22no—
291C22⋊C8—22no—
292C22⋊C8—221no—
293C22⋊C8—221no—
294C22⋊C8C22⋊D1112yes—
295#97—221no—
296C4×C8—21no—
297C4×C8—221no—
298C4×C8C22×D1111yescharacteristic
299C4×C8C22×D1111yescharacteristic
300C2×C11—41no—
301C2×C11—44no—
302C2×C11#304211yescharacteristic
303C2×C11#305011yescharacteristic
304C2×C11#306911yescharacteristic
305C24—21no—
306C2×Q8—221no—
307C2×Q8—221no—
308C2×Q8—221no—
309C2×Q8—221no—
310C2×D4—24no—
311C2×D4—21no—
312C2×D4C2×D4412yes—
313C22×C4—21no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—82no—
317C22×C4C2×D4411yescharacteristic
318C22×C4#433911yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320SD16—444no—
321SD16—444no—
322C2×C8—22no—
323C2×C8—82no—
324C2×C8—82no—
325C2×C8—222no—
326C2×C8—222no—
327C2×C8C2×C22⋊D1112yes—
328C2×C8C2×C22⋊D1112yes—
329C4⋊C4—21no—
330C4⋊C4—221no—
331C4⋊C4—221no—
332C4⋊C4—221no—
333C4⋊C4—221no—
334C4⋊C4—221no—
335C4⋊C4—221no—
336C4⋊C4—221no—
337C4⋊C4—221no—
338C4⋊C4—441no—
339C4⋊C4—441no—
340C4⋊C4—441no—
341C4⋊C4—441no—
342C4⋊C4C2×D4412yes—
343C22⋊C4—22no—
344C22⋊C4—22no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C42—441no—
348C42—441no—
349C42C2×D4411yescharacteristic
350C42#433911yescharacteristic
351C42C2×C22⋊D1111yescharacteristic
352C42C23×D1111yescharacteristic
353C11#1939511yescharacteristic, complemented, Sylow
354C23—24no—
355C23—22no—
356C23—81no—
357C23—81no—
358C23#6698311yescharacteristic
359Q8—442no—
360Q8—442no—
361Q8—442no—
362Q8—881no—
363D4—24no—
364D4—22no—
365D4#6695714yes—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—82no—
373C2×C4—81no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4#6698311yescharacteristic
379C2×C4#6698311yescharacteristic
380C2×C4#6698311yescharacteristic
381C2×C4C22×D4411yescharacteristic
382C2×C4C2×#433911yescharacteristic
383C2×C4C22×C22⋊D1111yescharacteristic
384C8—22no—
385C8—22no—
386C8—42no—
387C8—442no—
388C8—442no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—24no—
393C22—42no—
394C22—42no—
395C22—84no—
396C22C2×#6698311yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—42no—
402C4—881no—
403C4—881no—
404C4—881no—
405C4—881no—
406C4C2×#6695712yes—
407C4#1062336712yes—
408C2—41no—
409C2—44no—
410C2#1307812811yescharacteristic
411C2#1307819711yescharacteristic
412C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2972C2
socleC22×C11C2×#121
prime radicalC22×D4×C11D4
hypercenter#2972D11
hypocenterC11#19395
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2972

Complements

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

NH ≅ G/Ntype
1. #13079777C2semidirect
4. #13068067C2semidirect
5. #13068039C2semidirect
6. #13068005C2semidirect
7. #13067991C2semidirect
8. #13067396C2semidirect
9. #13067324C2semidirect
10. #13067280C2semidirect
35. #10622295C22semidirect
36. #10622294C22semidirect
37. #10622294C22semidirect
38. #10622293C22semidirect
39. #10622124C22semidirect
40. #10622124C22semidirect
41. #10622120C22semidirect
42. #10622119C22semidirect
43. #10622096C22semidirect
44. #10622095C22semidirect
353. C11#19395semidirect

Maximal subgroups

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

subgroupindex
#130797772
#130787152
#130786242
#130680672
#130680392
#130680052
#130679912
#130673962
#130673242
#130672802
C11×#29722
#1939511