Finite Group Databasebeta

← #14737786

Subgroups — #14737786

Order 2816.

766 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079191C211yesmaximal, characteristic, complemented
2#13078080C211yesmaximal, characteristic, complemented
3C2×#10622625C211yesmaximal, characteristic, complemented
4#13068179C212yesmaximal, complemented
5#13068175C212yesmaximal, complemented
6#13068127C212yesmaximal, complemented
7#13068093C212yesmaximal, complemented
8#13067371C211yesmaximal, characteristic, complemented
9#13067294C211yesmaximal, characteristic, complemented
10#13067293C211yesmaximal, characteristic, complemented
11C11×#3036C211yesmaximal, characteristic, complemented
12C2×C11×AGL(1,ℤ/8)—21no—
13C11×#532C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66985—21no—
16C22×#4318—21no—
17#10623008C2211yescharacteristic
18C11×#463—22no—
19C11×#461C2212yes—
20C11×#459C2212yes—
21C11×#423C2211yescharacteristic
22C11×#417—21no—
23C2×C22⋊(C11⋊C8)—21no—
24#10622701C2211yescharacteristic, complemented
25#10622691C2211yescharacteristic, complemented
26#10622686C2211yescharacteristic, complemented
27#10622683C2211yescharacteristic, complemented
28#10622651—21no—
29#10622651—21no—
30#10622632C2212yes—
31#10622629—22no—
32#10622628C2212yes—
33C4×#4323—21no—
34C4×#4323—21no—
35#10622625—21no—
36#10622625—21no—
37#10622625C2212yes—
38#10622625C2212yes—
39#10622579—21no—
40#10622537C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622185C2212yescomplemented
44#10622182C2212yescomplemented
45#10622123C2212yescomplemented
46#10622120C2212yescomplemented
47#10622118C2212yescomplemented
48#10622118C2212yescomplemented
49C2×C11×#41—21no—
50C22×D4×C11D411yescharacteristic
51C23×C4×C11—21no—
52C2×#4339—21no—
53C11×AGL(1,ℤ/8)—44no—
54C2×C11×SD16—22no—
55C2×C11×D8—22no—
56C2×C11×M16—21no—
57C11×C4⋊Q8C2311yescharacteristic
58C11×#127C2311yescharacteristic
59C11×#124—21no—
60C11×#121—21no—
61C11×#121—21no—
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65C4×D4×C11—21no—
66C4×D4×C11D412yes—
67C4×D4×C11C2312yes—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C42×C11C2311yescharacteristic
71C2×#4324—22no—
72#66985—44no—
73C2×#4323—22no—
74C2×#4323—21no—
75C2×#4323—21no—
76#66983—21no—
77#66983—21no—
78C2×#4318—21no—
79C2×#4318—22no—
80C2×#4318—22no—
81C2×#4318—44no—
82C22×C11⋊C8—21no—
83C22×C11⋊C8D411yescharacteristic
84C22×C11⋊C8D411yescharacteristic
85#66928—21no—
86#66927C2311yescharacteristic
87C4×D44—21no—
88C4×D44—21no—
89#66922C2311yescharacteristic
90C11×C4⋊C8—21no—
91C11×C4⋊C8C2312yes—
92C11×#103—22no—
93C11×#102—22no—
94#66896—21no—
95#66896—21no—
96C22⋊(C11⋊C8)—22no—
97C22⋊(C11⋊C8)—22no—
98#66874—22no—
99#66873—22no—
100#66873—21no—
101#66873—21no—
102#66871—21no—
103#66871—21no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2312yes—
108C4×C11⋊C8D411yescharacteristic
109C4×C11⋊C8D411yescharacteristic
110C4×C11⋊C8C2311yescharacteristic
111C4×C11⋊C8C2311yescharacteristic
112#19280—111nomaximal, Sylow
113C24×C11—21no—
114C11×#41—42no—
115C11×#41—42no—
116C2×Q8×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—41no—
124C2×D4×C11C2×D412yes—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11—41no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11#4111yescharacteristic
134C2×C22⋊D11—41no—
135#4339—42no—
136#4339—42no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×C4×D11—41no—
141C2×Dic22—21no—
142C11×SD16—44no—
143C11×D8—44no—
144C11×M16—42no—
145C2×C8×C11—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4C2×D412yes—
150C11×C22⋊C4—22no—
151C11×C22⋊C4—22no—
152C11×C22⋊C4—41no—
153C11×C22⋊C4—41no—
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11#4111yescharacteristic
157C42×C11C2411yescharacteristic
158#4324—44no—
159#4323—44no—
160#4323—42no—
161#4323—42no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4—41no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166#4318—44no—
167#4318—44no—
168#4318—42no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—41no—
173C2×C11⋊C8—42no—
174C2×C11⋊C8C2×D411yescharacteristic
175C2×C11⋊C8C2×D411yescharacteristic
176C2×C11⋊C8C2×D411yescharacteristic
177C2×C11⋊C8C2×D411yescharacteristic
178#3169—111no—
179#3036—111no—
180#3036D1111yescharacteristic, complemented
181C2×#436—111no—
182#1701—112no—
183#1701—112no—
184#1693—112no—
185#1687—112no—
186#1566—111no—
187#1547—111no—
188#1547—111no—
189C23×C11—22no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—41no—
194C23×C11#12111yescharacteristic
195C22×D11—41no—
196Q8×C11—41no—
197Q8×C11—41no—
198D4×C11—22no—
199D4×C11—22no—
200D4×C11—41no—
201D4×C11—41no—
202D4×C11—41no—
203D4×C11—41no—
204D4×C11—42no—
205D4×C11—81no—
206D4×C11—82no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—22no—
210C2×C4×C11—41no—
211C2×C4×C11—44no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—82no—
217C2×C4×C11#12111yescharacteristic
218C2×C4×C11#12111yescharacteristic
219C2×C4×C11#12111yescharacteristic
220C2×C4×C11AGL(1,ℤ/8)12yes—
221C2×C4×C11AGL(1,ℤ/8)12yes—
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C22⋊D11—82no—
226C2×Dic11—41no—
227D44—41no—
228D44—41no—
229D44—41no—
230D44—41no—
231D44—81no—
232C4×D11—82no—
233Dic22—41no—
234Dic22—41no—
235C8×C11—42no—
236C11⋊C8—21no—
237C11⋊C8—21no—
238C11⋊C8—21no—
239C11⋊C8—42no—
240C11⋊C8—42no—
241C11⋊C8AGL(1,ℤ/8)12yescomplemented
242C2×AGL(1,ℤ/8)—21no—
243C2×AGL(1,ℤ/8)—221no—
244C22×M16—221no—
245#532—111no—
246#532C2×D1111yescharacteristic
247C2×C4×D4C2×D1111yescharacteristic
248#500—111no—
249#493—111no—
250#486—111no—
251#486—111no—
252#466—221no—
253#466—221no—
254#463—22no—
255#463—222no—
256#461—112no—
257#461C2×D1112yes—
258#459—112no—
259#459C2×D1112yes—
260C4×D8—221no—
261C4×D8—221no—
262#436—112no—
263#436—112no—
264#436—221no—
265#436—221no—
266#423—111no—
267#423C2×D1111yescharacteristic
268C2×C4⋊C8—111no—
269#417—21no—
270#417—221no—
271C2×C22⋊C8—221no—
272C2×C4×C8—111no—
273#334—112no—
274#334—112no—
275#332—112no—
276#332—112no—
277#331—112no—
278#331—112no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—84no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11#46912yes—
289C22×C11C2×#12111yescharacteristic
290C2×D11—81no—
291C2×D11—81no—
292C2×D11—81no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—42no—
297C4×C11—81no—
298C4×C11#46912yes—
299C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
300C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
301C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
302C4×C11#57511yescharacteristic
303Dic11—81no—
304C2×#41—21no—
305C2×#41—221no—
306C22×D4C22⋊D1111yescharacteristic
307C23×C4—21no—
308AGL(1,ℤ/8)—44no—
309AGL(1,ℤ/8)—444no—
310C2×SD16—22no—
311C2×SD16—222no—
312C2×D8—22no—
313C2×D8—221no—
314C2×D8—221no—
315C2×D8—222no—
316C2×M16—21no—
317C2×M16—222no—
318C2×M16—222no—
319C2×M16—221no—
320C2×M16—444no—
321C22×C8—111no—
322C22×C8—111no—
323C22×C8—221no—
324C4⋊Q8—111no—
325C4⋊Q8C22×D1111yescharacteristic
326#127—111no—
327#127C22×D1111yescharacteristic
328#124—21no—
329#124—221no—
330#121—21no—
331#121—21no—
332#121—221no—
333#121—221no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—221no—
339C4×D4—221no—
340C4×D4C22⋊D1112yes—
341C4×D4C22×D1112yes—
342C2×C4⋊C4C22⋊D1111yescharacteristic
343C2×C22⋊C4—21no—
344C2×C42C22×D1111yescharacteristic
345#107—221no—
346#107—221no—
347C4⋊C8—21no—
348C4⋊C8—112no—
349C4⋊C8—112no—
350C4⋊C8—221no—
351C4⋊C8—221no—
352C4⋊C8C22×D1112yes—
353#103—22no—
354#103—222no—
355#102—22no—
356#102—221no—
357#102—221no—
358#102—221no—
359#102—221no—
360#102—222no—
361C22⋊C8—222no—
362C22⋊C8—222no—
363C4×C8—111no—
364C4×C8—111no—
365C4×C8—111no—
366C4×C8—111no—
367C2×C11—22no—
368C2×C11—82no—
369C2×C11—161no—
370C2×C11#303611yescharacteristic
371C2×C11C2×#46911yescharacteristic
372C2×C11#306711yescharacteristic
373D11—161no—
374C24—21no—
375#41—42no—
376#41—42no—
377#41—442no—
378#41—442no—
379C2×Q8—21no—
380C2×Q8—221no—
381C2×D4—22no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—41no—
388C2×D4—221no—
389C2×D4—221no—
390C2×D4—221no—
391C2×D4—441no—
392C2×D4C2×C22⋊D1112yes—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—41no—
399C22×C4—441no—
400C22×C4D4×D1111yescharacteristic
401C22×C4#434111yescharacteristic
402C22×C4C2×C22⋊D1111yescharacteristic
403SD16—44no—
404SD16—444no—
405D8—44no—
406D8—442no—
407D8—442no—
408D8—444no—
409M16—42no—
410M16—444no—
411M16—444no—
412M16—442no—
413C2×C8—22no—
414C2×C8—111no—
415C2×C8—111no—
416C2×C8—111no—
417C2×C8—111no—
418C2×C8—222no—
419C2×C8—222no—
420C2×C8—222no—
421C2×C8—441no—
422C2×C8—442no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—221no—
427C4⋊C4—221no—
428C4⋊C4C2×C22⋊D1112yes—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—41no—
432C22⋊C4—41no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C42D4×D1111yescharacteristic
436C42#434111yescharacteristic
437C42C2×C22⋊D1111yescharacteristic
438C42C23×D1111yescharacteristic
439C11#1928011yescharacteristic, complemented, Sylow
440C23—22no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—41no—
445C23—441no—
446C23#6699211yescharacteristic
447Q8—41no—
448Q8—41no—
449Q8—441no—
450Q8—441no—
451D4—22no—
452D4—22no—
453D4—41no—
454D4—41no—
455D4—41no—
456D4—41no—
457D4—42no—
458D4—81no—
459D4—82no—
460D4—441no—
461D4—441no—
462D4—441no—
463D4—441no—
464D4—881no—
465D4—882no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—41no—
470C2×C4—44no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—82no—
476C2×C4—441no—
477C2×C4—882no—
478C2×C4#6698512yes—
479C2×C4#6699211yescharacteristic
480C2×C4#6699211yescharacteristic
481C2×C4#6699211yescharacteristic
482C2×C4#6700212yes—
483C2×C4C2×D4×D1111yescharacteristic
484C2×C4C2×#434111yescharacteristic
485C2×C4C22×C22⋊D1111yescharacteristic
486C8—42no—
487C8—112no—
488C8—221no—
489C8—221no—
490C8—221no—
491C8—442no—
492C8—442no—
493C22—21no—
494C22—21no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—84no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—881no—
503C22—881no—
504C22—881no—
505C22#1062265212yes—
506C22C2×#6699211yescharacteristic
507C4—21no—
508C4—21no—
509C4—21no—
510C4—42no—
511C4—81no—
512C4—881no—
513C4#1062265212yes—
514C4D11×AGL(1,ℤ/8)11yescharacteristic
515C4#1062330411yescharacteristic
516C4C2×#6698511yescharacteristic
517C4C2×#6700211yescharacteristic
518C2—22no—
519C2—82no—
520C2—161no—
521C2—1761no—
522C2#1307807711yescharacteristic
523C2C2×#1062265211yescharacteristic
524C2#1307833311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3036C2
socleC22×C11C2×#121
hypercenter#3036D11
hypocenterC11#19280
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #13079191C2semidirect
2. #13078080C2semidirect
3. C2×#10622625C2semidirect
4. #13068179C2semidirect
5. #13068175C2semidirect
6. #13068127C2semidirect
7. #13068093C2semidirect
8. #13067371C2semidirect
9. #13067294C2semidirect
10. #13067293C2semidirect
11. C11×#3036C2semidirect
24. #10622701C22semidirect
25. #10622691C22semidirect
26. #10622686C22semidirect
27. #10622683C22semidirect
43. #10622185C22semidirect
44. #10622182C22semidirect
45. #10622123C22semidirect
46. #10622120C22semidirect
47. #10622118C22semidirect
48. #10622118C22semidirect
180. #3036D11semidirect
241. C11⋊C8AGL(1,ℤ/8)semidirect
439. C11#19280semidirect

Maximal subgroups

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

subgroupindex
#130791912
#130780802
C2×#106226252
#130681792
#130681752
#130681272
#130680932
#130673712
#130672942
#130672932
C11×#30362
#1928011