Finite Group Databasebeta

← #14738980

Subgroups — #14738980

Order 2816.

684 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079551C211yesmaximal, characteristic, complemented
2#13078707C211yesmaximal, characteristic, complemented
3#13078616C211yesmaximal, characteristic, complemented
4#13068067C212yesmaximal, complemented
5#13068025C212yesmaximal, complemented
6#13067971C212yesmaximal, complemented
7#13067957C212yesmaximal, complemented
8#13067396C211yesmaximal, characteristic, complemented
9#13067319C211yesmaximal, characteristic, complemented
10#13067276C211yesmaximal, characteristic, complemented
11C11×#2972C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13#10623008C2211yescharacteristic
14#10623008C2211yescharacteristic
15C8×D4×C11—22no—
16C8×D4×C11C2212yes—
17C8×D4×C11C2212yes—
18C11×#431C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C2×C11×C22⋊C8—22no—
21#10622830—21no—
22#10622830—21no—
23#10622628C2212yes—
24#10622628C2212yes—
25#10622627—22no—
26C4×#4323—22no—
27#10622621C2212yes—
28#10622620C2212yes—
29#10622581—21no—
30#10622580—21no—
31#10622539C2211yescharacteristic
32#10622538C2211yescharacteristic
33#10622457—22no—
34#10622347—22no—
35#10622308C2211yescharacteristic, complemented
36#10622307C2211yescharacteristic, complemented
37#10622306C2211yescharacteristic, complemented
38#10622294C2211yescharacteristic, complemented
39#10622123C2212yescomplemented
40#10622123C2212yescomplemented
41#10622120C2212yescomplemented
42#10622119C2212yescomplemented
43#10622096C2212yescomplemented
44#10622095C2212yescomplemented
45C22×D4×C11D411yescharacteristic
46C23×C4×C11—21no—
47C2×#4339—21no—
48C2×#4339—21no—
49C22×C8×C11—22no—
50C22×C8×C11—22no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C4×D4×C11D412yes—
54C4×D4×C11C2312yes—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C22⋊C4—21no—
57C2×C42×C11C2311yescharacteristic
58C2×#4323—22no—
59C2×#4323—22no—
60#66983—21no—
61#66983—21no—
62#66983—21no—
63#66983—21no—
64C2×D88—22no—
65C2×#4314—22no—
66#66928—21no—
67#66928—21no—
68#66927C2311yescharacteristic
69#66927C2311yescharacteristic
70C4×D44—21no—
71C4×D44—21no—
72C4×D44—21no—
73C4×D44—21no—
74#66922C2311yescharacteristic
75#66922C2311yescharacteristic
76C11×C4⋊C8D412yes—
77C11×C4⋊C8C2312yes—
78C11×C22⋊C8—21no—
79C11×C22⋊C8—22no—
80C11×C22⋊C8—22no—
81C11×C22⋊C8D412yes—
82C4×C8×C11—21no—
83C4×C8×C11C2311yescharacteristic
84C4×C8×C11C2311yescharacteristic
85#66896—22no—
86#66896—22no—
87C22⋊(C11⋊C8)—21no—
88C22⋊(C11⋊C8)—21no—
89#66885—22no—
90#66880—22no—
91#66873—22no—
92#66873—22no—
93#66872—22no—
94#66871—22no—
95C4⋊(C11⋊C8)C2312yes—
96C4⋊(C11⋊C8)C2312yes—
97#66867—21no—
98C4×C11⋊C8—21no—
99#19389—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×C22⋊D11—41no—
112C2×C22⋊D11—41no—
113#4339—82no—
114#4339—82no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—21no—
120C2×D44—21no—
121C2×C4×D11—41no—
122C2×C4×D11—41no—
123C2×Dic22—21no—
124C2×Dic22—21no—
125C2×C8×C11—22no—
126C2×C8×C11—82no—
127C2×C8×C11—82no—
128C2×C8×C11C2×D412yes—
129C2×C8×C11C2×D412yes—
130C11×C4⋊C4—21no—
131C11×C4⋊C4C2×D412yes—
132C11×C22⋊C4—22no—
133C11×C22⋊C4—22no—
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137C42×C11C2411yescharacteristic
138#4323—44no—
139#4323—44no—
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150D88—82no—
151#4314—82no—
152#3207—111no—
153#3109—111no—
154#3100—111no—
155#2972D1111yescharacteristic, complemented
156#1683—112no—
157#1677—112no—
158#1667—112no—
159#1665—112no—
160#1572—111no—
161#1553—111no—
162#1543—111no—
163C23×C11—24no—
164C23×C11—22no—
165C23×C11—81no—
166C23×C11—81no—
167C23×C11#12111yescharacteristic
168C22×D11—41no—
169C22×D11—41no—
170D4×C11—24no—
171D4×C11—22no—
172D4×C11#13514yes—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—82no—
180C2×C4×C11—81no—
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C22⋊D11—82no—
188C22⋊D11—82no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191D44—42no—
192D44—42no—
193D44—42no—
194D44—42no—
195D44—81no—
196D44—81no—
197C4×D11—82no—
198C4×D11—82no—
199Dic22—42no—
200Dic22—81no—
201C8×C11—22no—
202C8×C11—22no—
203C8×C11—42no—
204C11⋊C8—42no—
205C11⋊C8—42no—
206#532—111no—
207#532—111no—
208C2×C4×D4C2×D1111yescharacteristic
209#493—111no—
210#492—111no—
211#487—111no—
212#486—111no—
213#481—221no—
214#480—221no—
215#476—112no—
216#474—112no—
217#463—222no—
218#459—112no—
219#459—112no—
220#449—222no—
221#447—221no—
222#447—221no—
223#442—222no—
224C4×D8—222no—
225C8×D4—22no—
226C8×D4C2×D1112yes—
227C8×D4C2×D1112yes—
228#432—111no—
229#431—111no—
230#431C2×D1111yescharacteristic
231#431C2×D1111yescharacteristic
232C2×C22⋊C8—22no—
233#335—112no—
234#334—112no—
235#333—112no—
236#332—112no—
237#331—112no—
238#331—112no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—24no—
242C22×C11—21no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—84no—
246C22×C11C2×#12111yescharacteristic
247C2×D11—81no—
248C2×D11—81no—
249C2×D11—81no—
250C2×D11—81no—
251C2×D11—81no—
252C2×D11—81no—
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—42no—
258C4×C11C2×#13512yes—
259C4×C11#57612yes—
260Dic11—81no—
261Dic11—81no—
262C2×#41—221no—
263C2×#41—221no—
264C22×D4D4411yescharacteristic
265C23×C4—21no—
266C2×SD16—222no—
267C2×D8—222no—
268C2×D8—222no—
269C2×D8—222no—
270C22×C8—22no—
271C22×C8—22no—
272C4⋊Q8—111no—
273C4⋊Q8—111no—
274#127—111no—
275#127—111no—
276#124—221no—
277#124—221no—
278#121—221no—
279#121—221no—
280#121—221no—
281#121—221no—
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—221no—
285C4×D4—221no—
286C4×D4—221no—
287C4×D4—221no—
288C4×D4D4412yes—
289C4×D4C22×D1112yes—
290C2×C4⋊C4D4411yescharacteristic
291C2×C22⋊C4—21no—
292C2×C42C22×D1111yescharacteristic
293#107—222no—
294#106—222no—
295C4⋊C8—112no—
296C4⋊C8—112no—
297C4⋊C8C22⋊D1112yes—
298C4⋊C8C22×D1112yes—
299#103—222no—
300#102—222no—
301#102—222no—
302#102—222no—
303#102—222no—
304#102—222no—
305C22⋊C8—21no—
306C22⋊C8—22no—
307C22⋊C8—22no—
308C22⋊C8—221no—
309C22⋊C8—221no—
310C22⋊C8C22⋊D1112yes—
311#97—221no—
312C4×C8—21no—
313C4×C8—221no—
314C4×C8C22×D1111yescharacteristic
315C4×C8C22×D1111yescharacteristic
316C2×C11—41no—
317C2×C11—44no—
318C2×C11#304111yescharacteristic
319C2×C11#305011yescharacteristic
320C2×C11#306811yescharacteristic
321D11—161no—
322D11—161no—
323C24—21no—
324#41—882no—
325#41—882no—
326C2×Q8—221no—
327C2×Q8—221no—
328C2×D4—24no—
329C2×D4—21no—
330C2×D4—221no—
331C2×D4—221no—
332C2×D4—221no—
333C2×D4—221no—
334C2×D4—221no—
335C2×D4—221no—
336C2×D4—441no—
337C2×D4—441no—
338C2×D4C2×D4412yes—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—82no—
343C22×C4—441no—
344C22×C4—441no—
345C22×C4C2×D4411yescharacteristic
346C22×C4#433911yescharacteristic
347C22×C4C2×C22⋊D1111yescharacteristic
348SD16—882no—
349D8—444no—
350D8—444no—
351D8—882no—
352C2×C8—22no—
353C2×C8—82no—
354C2×C8—82no—
355C2×C8—222no—
356C2×C8—222no—
357C2×C8C2×C22⋊D1112yes—
358C2×C8C2×C22⋊D1112yes—
359C4⋊C4—21no—
360C4⋊C4—221no—
361C4⋊C4—221no—
362C4⋊C4—221no—
363C4⋊C4—221no—
364C4⋊C4C2×D4412yes—
365C22⋊C4—22no—
366C22⋊C4—22no—
367C22⋊C4—441no—
368C22⋊C4—441no—
369C22⋊C4—441no—
370C22⋊C4—441no—
371C42C2×D4411yescharacteristic
372C42#433911yescharacteristic
373C42C2×C22⋊D1111yescharacteristic
374C42C23×D1111yescharacteristic
375C11#1938911yescharacteristic, complemented, Sylow
376C23—24no—
377C23—22no—
378C23—81no—
379C23—81no—
380C23—441no—
381C23—441no—
382C23#6698311yescharacteristic
383Q8—442no—
384Q8—881no—
385D4—24no—
386D4—22no—
387D4—442no—
388D4—442no—
389D4—442no—
390D4—442no—
391D4—881no—
392D4—881no—
393D4—882no—
394D4—882no—
395D4#6695714yes—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—82no—
403C2×C4—81no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—882no—
407C2×C4—882no—
408C2×C4#6698311yescharacteristic
409C2×C4#6698311yescharacteristic
410C2×C4#6698311yescharacteristic
411C2×C4C22×D4411yescharacteristic
412C2×C4C2×#433911yescharacteristic
413C2×C4C22×C22⋊D1111yescharacteristic
414C8—22no—
415C8—22no—
416C8—42no—
417C8—442no—
418C8—442no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—24no—
423C22—42no—
424C22—42no—
425C22—84no—
426C22—881no—
427C22—881no—
428C22—881no—
429C22—881no—
430C22—881no—
431C22—881no—
432C22C2×#6698311yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—42no—
438C4—881no—
439C4—881no—
440C4C2×#6695712yes—
441C4#1062336612yes—
442C2—41no—
443C2—44no—
444C2—1761no—
445C2—1761no—
446C2#1307811911yescharacteristic
447C2#1307819711yescharacteristic
448C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2972C2
socleC22×C11C2×#121
hypercenter#2972D11
hypocenterC11#19389
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. #13079551C2semidirect
2. #13078707C2semidirect
3. #13078616C2semidirect
4. #13068067C2semidirect
5. #13068025C2semidirect
6. #13067971C2semidirect
7. #13067957C2semidirect
8. #13067396C2semidirect
9. #13067319C2semidirect
10. #13067276C2semidirect
11. C11×#2972C2semidirect
35. #10622308C22semidirect
36. #10622307C22semidirect
37. #10622306C22semidirect
38. #10622294C22semidirect
39. #10622123C22semidirect
40. #10622123C22semidirect
41. #10622120C22semidirect
42. #10622119C22semidirect
43. #10622096C22semidirect
44. #10622095C22semidirect
155. #2972D11semidirect
375. C11#19389semidirect

Maximal subgroups

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

subgroupindex
#130795512
#130787072
#130786162
#130680672
#130680252
#130679712
#130679572
#130673962
#130673192
#130672762
C11×#29722
#1938911